Proof: Proof: A Program that Computes Fibonacci Numbers

In this example, we present a program that computes Fibonacci numbers.

The Fibonacci numbers are a sequence where every number is the sum of the two previous numbers. Here are the first 6:

0, 1, 1, 2, 3, 5

Then we show that

Let's prove the following theorem:

if the following are true:
  • the PC at time 0 = 0
  • instruction #0 is addi dst=1 src=0 imm=0
  • instruction #1 is addi dst=2 src=0 imm=1
  • instruction #2 is addi dst=4 src=0 imm=0
  • instruction #3 is addi dst=5 src=0 imm=4
  • instruction #4 is add dst=3 src1=1 src2=2
  • instruction #5 is addi dst=1 src=2 imm=0
  • instruction #6 is addi dst=2 src=3 imm=0
  • instruction #7 is addi dst=4 src=4 imm=1
  • instruction #8 is beq left=4 right=5 imm=1
  • instruction #9 is jump imm=4

then value of cell 3 at time 25 = 5

After the following program is executed, cell #3 will contain the 6th Fibonacci number (5).

We need at least 2 numbers before we can calculate sums, so we start with 0 and 1. But notice that 5 is the sum of the two previous numbers 2 and 3.

Instructions
Memory Cells
Program Counter Time
0 0
LW Computer Simulator

Memory cell #1 contains the nth Fibonacci number (initially the 1st Fibonacci number 0).

Cell #2 contains the n + 1th Fibonacci number (initially the 2nd Fibonacci number 1).

Memory cell #4 contains the current count or index.

Cell #5 contains 4. In each iteration, the computer will increment #4 and finish when it reaches the value in cell #5.

The computer computes the next Fibonacci number by adding values in cells #1 and #2 and storing it in cell #3. Then, to prepare for the next iteration, the values are "moved down" 1: cell #2 is copied to cell #1 and cell #3 is copied to cell #2.

Then the counter increments by 1, and the computer jumps back to instruction #4, and the next iteration begins.

At the end of the program, cell #3 contains the 6th Fibonacci number.

Proof:

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Given
1 the PC at time 0 = 0
2 instruction #0 is addi dst=1 src=0 imm=0
3 instruction #1 is addi dst=2 src=0 imm=1
4 instruction #2 is addi dst=4 src=0 imm=0
5 instruction #3 is addi dst=5 src=0 imm=4
6 instruction #4 is add dst=3 src1=1 src2=2
7 instruction #5 is addi dst=1 src=2 imm=0
8 instruction #6 is addi dst=2 src=3 imm=0
9 instruction #7 is addi dst=4 src=4 imm=1
10 instruction #8 is beq left=4 right=5 imm=1
11 instruction #9 is jump imm=4
Proof Table
# Claim Reason
1 value of cell 1 at time 1 = 0 if instruction #0 is addi dst=1 src=0 imm=0 and the PC at time 0 = 0, then value of cell 1 at time 1 = 0
2 the PC at time 1 = 1 if instruction #0 is addi dst=1 src=0 imm=0 and the PC at time 0 = 0, then the PC at time 1 = 1
3 value of cell 2 at time 2 = 1 if instruction #1 is addi dst=2 src=0 imm=1 and the PC at time 1 = 1, then value of cell 2 at time 2 = 1
4 the PC at time 2 = 2 if instruction #1 is addi dst=2 src=0 imm=1 and the PC at time 1 = 1, then the PC at time 2 = 2
5 value of cell 1 at time 2 = 0 if instruction #1 is addi dst=2 src=0 imm=1 and the PC at time 1 = 1 and value of cell 1 at time 1 = 0, then value of cell 1 at time 2 = 0
6 value of cell 4 at time 3 = 0 if instruction #2 is addi dst=4 src=0 imm=0 and the PC at time 2 = 2, then value of cell 4 at time 3 = 0
7 the PC at time 3 = 3 if instruction #2 is addi dst=4 src=0 imm=0 and the PC at time 2 = 2, then the PC at time 3 = 3
8 value of cell 1 at time 3 = 0 if instruction #2 is addi dst=4 src=0 imm=0 and the PC at time 2 = 2 and value of cell 1 at time 2 = 0, then value of cell 1 at time 3 = 0
9 value of cell 2 at time 3 = 1 if instruction #2 is addi dst=4 src=0 imm=0 and the PC at time 2 = 2 and value of cell 2 at time 2 = 1, then value of cell 2 at time 3 = 1
10 value of cell 5 at time 4 = 4 if instruction #3 is addi dst=5 src=0 imm=4 and the PC at time 3 = 3, then value of cell 5 at time 4 = 4
11 the PC at time 4 = 4 if instruction #3 is addi dst=5 src=0 imm=4 and the PC at time 3 = 3, then the PC at time 4 = 4
12 value of cell 1 at time 4 = 0 if instruction #3 is addi dst=5 src=0 imm=4 and the PC at time 3 = 3 and value of cell 1 at time 3 = 0, then value of cell 1 at time 4 = 0
13 value of cell 2 at time 4 = 1 if instruction #3 is addi dst=5 src=0 imm=4 and the PC at time 3 = 3 and value of cell 2 at time 3 = 1, then value of cell 2 at time 4 = 1
14 value of cell 4 at time 4 = 0 if instruction #3 is addi dst=5 src=0 imm=4 and the PC at time 3 = 3 and value of cell 4 at time 3 = 0, then value of cell 4 at time 4 = 0
15 value of cell 3 at time 5 = (value of cell 1 at time 4) + (value of cell 2 at time 4) if the PC at time 4 = 4 and instruction #4 is add dst=3 src1=1 src2=2, then value of cell 3 at time 5 = (value of cell 1 at time 4) + (value of cell 2 at time 4)
16 value of cell 3 at time 5 = 1 if value of cell 3 at time 5 = (value of cell 1 at time 4) + (value of cell 2 at time 4) and value of cell 1 at time 4 = 0 and value of cell 2 at time 4 = 1, then value of cell 3 at time 5 = 1
17 the PC at time 5 = 5 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 4 = 4, then the PC at time 5 = 5
18 value of cell 1 at time 5 = 0 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 4 = 4 and value of cell 1 at time 4 = 0, then value of cell 1 at time 5 = 0
19 value of cell 2 at time 5 = 1 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 4 = 4 and value of cell 2 at time 4 = 1, then value of cell 2 at time 5 = 1
20 value of cell 4 at time 5 = 0 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 4 = 4 and value of cell 4 at time 4 = 0, then value of cell 4 at time 5 = 0
21 value of cell 5 at time 5 = 4 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 4 = 4 and value of cell 5 at time 4 = 4, then value of cell 5 at time 5 = 4
22 value of cell 1 at time 6 = 1 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 5 = 5 and value of cell 2 at time 5 = 1, then value of cell 1 at time 6 = 1
23 the PC at time 6 = 6 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 5 = 5, then the PC at time 6 = 6
24 value of cell 2 at time 6 = 1 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 5 = 5 and value of cell 2 at time 5 = 1, then value of cell 2 at time 6 = 1
25 value of cell 4 at time 6 = 0 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 5 = 5 and value of cell 4 at time 5 = 0, then value of cell 4 at time 6 = 0
26 value of cell 5 at time 6 = 4 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 5 = 5 and value of cell 5 at time 5 = 4, then value of cell 5 at time 6 = 4
27 value of cell 3 at time 6 = 1 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 5 = 5 and value of cell 3 at time 5 = 1, then value of cell 3 at time 6 = 1
28 value of cell 2 at time 7 = 1 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 6 = 6 and value of cell 3 at time 6 = 1, then value of cell 2 at time 7 = 1
29 the PC at time 7 = 7 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 6 = 6, then the PC at time 7 = 7
30 value of cell 1 at time 7 = 1 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 6 = 6 and value of cell 1 at time 6 = 1, then value of cell 1 at time 7 = 1
31 value of cell 4 at time 7 = 0 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 6 = 6 and value of cell 4 at time 6 = 0, then value of cell 4 at time 7 = 0
32 value of cell 5 at time 7 = 4 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 6 = 6 and value of cell 5 at time 6 = 4, then value of cell 5 at time 7 = 4
33 value of cell 3 at time 7 = 1 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 6 = 6 and value of cell 3 at time 6 = 1, then value of cell 3 at time 7 = 1
34 value of cell 4 at time 8 = 1 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 7 = 7 and value of cell 4 at time 7 = 0, then value of cell 4 at time 8 = 1
35 the PC at time 8 = 8 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 7 = 7, then the PC at time 8 = 8
36 value of cell 1 at time 8 = 1 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 7 = 7 and value of cell 1 at time 7 = 1, then value of cell 1 at time 8 = 1
37 value of cell 2 at time 8 = 1 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 7 = 7 and value of cell 2 at time 7 = 1, then value of cell 2 at time 8 = 1
38 value of cell 5 at time 8 = 4 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 7 = 7 and value of cell 5 at time 7 = 4, then value of cell 5 at time 8 = 4
39 value of cell 3 at time 8 = 1 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 7 = 7 and value of cell 3 at time 7 = 1, then value of cell 3 at time 8 = 1
40 the PC at time 9 = 9 if instruction #8 is beq left=4 right=5 imm=1 and the PC at time 8 = 8 and value of cell 4 at time 8 = 1 and value of cell 5 at time 8 = 4, then the PC at time 9 = 9
41 value of cell 1 at time 9 = 1 if instruction #8 is beq left=4 right=5 imm=1 and the PC at time 8 = 8 and value of cell 1 at time 8 = 1, then value of cell 1 at time 9 = 1
42 value of cell 2 at time 9 = 1 if instruction #8 is beq left=4 right=5 imm=1 and the PC at time 8 = 8 and value of cell 2 at time 8 = 1, then value of cell 2 at time 9 = 1
43 value of cell 4 at time 9 = 1 if instruction #8 is beq left=4 right=5 imm=1 and the PC at time 8 = 8 and value of cell 4 at time 8 = 1, then value of cell 4 at time 9 = 1
44 value of cell 5 at time 9 = 4 if instruction #8 is beq left=4 right=5 imm=1 and the PC at time 8 = 8 and value of cell 5 at time 8 = 4, then value of cell 5 at time 9 = 4
45 value of cell 3 at time 9 = 1 if instruction #8 is beq left=4 right=5 imm=1 and the PC at time 8 = 8 and value of cell 3 at time 8 = 1, then value of cell 3 at time 9 = 1
46 the PC at time 10 = 4 if instruction #9 is jump imm=4 and the PC at time 9 = 9, then the PC at time 10 = 4
47 value of cell 1 at time 10 = 1 if instruction #9 is jump imm=4 and the PC at time 9 = 9 and value of cell 1 at time 9 = 1, then value of cell 1 at time 10 = 1
48 value of cell 2 at time 10 = 1 if instruction #9 is jump imm=4 and the PC at time 9 = 9 and value of cell 2 at time 9 = 1, then value of cell 2 at time 10 = 1
49 value of cell 4 at time 10 = 1 if instruction #9 is jump imm=4 and the PC at time 9 = 9 and value of cell 4 at time 9 = 1, then value of cell 4 at time 10 = 1
50 value of cell 5 at time 10 = 4 if instruction #9 is jump imm=4 and the PC at time 9 = 9 and value of cell 5 at time 9 = 4, then value of cell 5 at time 10 = 4
51 value of cell 3 at time 10 = 1 if instruction #9 is jump imm=4 and the PC at time 9 = 9 and value of cell 3 at time 9 = 1, then value of cell 3 at time 10 = 1
52 value of cell 3 at time 11 = (value of cell 1 at time 10) + (value of cell 2 at time 10) if the PC at time 10 = 4 and instruction #4 is add dst=3 src1=1 src2=2, then value of cell 3 at time 11 = (value of cell 1 at time 10) + (value of cell 2 at time 10)
53 value of cell 3 at time 11 = 2 if value of cell 3 at time 11 = (value of cell 1 at time 10) + (value of cell 2 at time 10) and value of cell 1 at time 10 = 1 and value of cell 2 at time 10 = 1, then value of cell 3 at time 11 = 2
54 the PC at time 11 = 5 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 10 = 4, then the PC at time 11 = 5
55 value of cell 1 at time 11 = 1 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 10 = 4 and value of cell 1 at time 10 = 1, then value of cell 1 at time 11 = 1
56 value of cell 2 at time 11 = 1 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 10 = 4 and value of cell 2 at time 10 = 1, then value of cell 2 at time 11 = 1
57 value of cell 4 at time 11 = 1 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 10 = 4 and value of cell 4 at time 10 = 1, then value of cell 4 at time 11 = 1
58 value of cell 5 at time 11 = 4 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 10 = 4 and value of cell 5 at time 10 = 4, then value of cell 5 at time 11 = 4
59 value of cell 1 at time 12 = 1 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 11 = 5 and value of cell 2 at time 11 = 1, then value of cell 1 at time 12 = 1
60 the PC at time 12 = 6 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 11 = 5, then the PC at time 12 = 6
61 value of cell 2 at time 12 = 1 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 11 = 5 and value of cell 2 at time 11 = 1, then value of cell 2 at time 12 = 1
62 value of cell 4 at time 12 = 1 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 11 = 5 and value of cell 4 at time 11 = 1, then value of cell 4 at time 12 = 1
63 value of cell 5 at time 12 = 4 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 11 = 5 and value of cell 5 at time 11 = 4, then value of cell 5 at time 12 = 4
64 value of cell 3 at time 12 = 2 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 11 = 5 and value of cell 3 at time 11 = 2, then value of cell 3 at time 12 = 2
65 value of cell 2 at time 13 = 2 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 12 = 6 and value of cell 3 at time 12 = 2, then value of cell 2 at time 13 = 2
66 the PC at time 13 = 7 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 12 = 6, then the PC at time 13 = 7
67 value of cell 1 at time 13 = 1 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 12 = 6 and value of cell 1 at time 12 = 1, then value of cell 1 at time 13 = 1
68 value of cell 4 at time 13 = 1 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 12 = 6 and value of cell 4 at time 12 = 1, then value of cell 4 at time 13 = 1
69 value of cell 5 at time 13 = 4 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 12 = 6 and value of cell 5 at time 12 = 4, then value of cell 5 at time 13 = 4
70 value of cell 3 at time 13 = 2 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 12 = 6 and value of cell 3 at time 12 = 2, then value of cell 3 at time 13 = 2
71 value of cell 4 at time 14 = 2 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 13 = 7 and value of cell 4 at time 13 = 1, then value of cell 4 at time 14 = 2
72 the PC at time 14 = 8 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 13 = 7, then the PC at time 14 = 8
73 value of cell 1 at time 14 = 1 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 13 = 7 and value of cell 1 at time 13 = 1, then value of cell 1 at time 14 = 1
74 value of cell 2 at time 14 = 2 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 13 = 7 and value of cell 2 at time 13 = 2, then value of cell 2 at time 14 = 2
75 value of cell 5 at time 14 = 4 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 13 = 7 and value of cell 5 at time 13 = 4, then value of cell 5 at time 14 = 4
76 value of cell 3 at time 14 = 2 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 13 = 7 and value of cell 3 at time 13 = 2, then value of cell 3 at time 14 = 2
77 the PC at time 15 = 9 if instruction #8 is beq left=4 right=5 imm=1 and the PC at time 14 = 8 and value of cell 4 at time 14 = 2 and value of cell 5 at time 14 = 4, then the PC at time 15 = 9
78 value of cell 1 at time 15 = 1 if instruction #8 is beq left=4 right=5 imm=1 and the PC at time 14 = 8 and value of cell 1 at time 14 = 1, then value of cell 1 at time 15 = 1
79 value of cell 2 at time 15 = 2 if instruction #8 is beq left=4 right=5 imm=1 and the PC at time 14 = 8 and value of cell 2 at time 14 = 2, then value of cell 2 at time 15 = 2
80 value of cell 4 at time 15 = 2 if instruction #8 is beq left=4 right=5 imm=1 and the PC at time 14 = 8 and value of cell 4 at time 14 = 2, then value of cell 4 at time 15 = 2
81 value of cell 5 at time 15 = 4 if instruction #8 is beq left=4 right=5 imm=1 and the PC at time 14 = 8 and value of cell 5 at time 14 = 4, then value of cell 5 at time 15 = 4
82 value of cell 3 at time 15 = 2 if instruction #8 is beq left=4 right=5 imm=1 and the PC at time 14 = 8 and value of cell 3 at time 14 = 2, then value of cell 3 at time 15 = 2
83 the PC at time 16 = 4 if instruction #9 is jump imm=4 and the PC at time 15 = 9, then the PC at time 16 = 4
84 value of cell 1 at time 16 = 1 if instruction #9 is jump imm=4 and the PC at time 15 = 9 and value of cell 1 at time 15 = 1, then value of cell 1 at time 16 = 1
85 value of cell 2 at time 16 = 2 if instruction #9 is jump imm=4 and the PC at time 15 = 9 and value of cell 2 at time 15 = 2, then value of cell 2 at time 16 = 2
86 value of cell 4 at time 16 = 2 if instruction #9 is jump imm=4 and the PC at time 15 = 9 and value of cell 4 at time 15 = 2, then value of cell 4 at time 16 = 2
87 value of cell 5 at time 16 = 4 if instruction #9 is jump imm=4 and the PC at time 15 = 9 and value of cell 5 at time 15 = 4, then value of cell 5 at time 16 = 4
88 value of cell 3 at time 16 = 2 if instruction #9 is jump imm=4 and the PC at time 15 = 9 and value of cell 3 at time 15 = 2, then value of cell 3 at time 16 = 2
89 value of cell 3 at time 17 = (value of cell 1 at time 16) + (value of cell 2 at time 16) if the PC at time 16 = 4 and instruction #4 is add dst=3 src1=1 src2=2, then value of cell 3 at time 17 = (value of cell 1 at time 16) + (value of cell 2 at time 16)
90 value of cell 3 at time 17 = 3 if value of cell 3 at time 17 = (value of cell 1 at time 16) + (value of cell 2 at time 16) and value of cell 1 at time 16 = 1 and value of cell 2 at time 16 = 2, then value of cell 3 at time 17 = 3
91 the PC at time 17 = 5 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 16 = 4, then the PC at time 17 = 5
92 value of cell 1 at time 17 = 1 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 16 = 4 and value of cell 1 at time 16 = 1, then value of cell 1 at time 17 = 1
93 value of cell 2 at time 17 = 2 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 16 = 4 and value of cell 2 at time 16 = 2, then value of cell 2 at time 17 = 2
94 value of cell 4 at time 17 = 2 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 16 = 4 and value of cell 4 at time 16 = 2, then value of cell 4 at time 17 = 2
95 value of cell 5 at time 17 = 4 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 16 = 4 and value of cell 5 at time 16 = 4, then value of cell 5 at time 17 = 4
96 value of cell 1 at time 18 = 2 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 17 = 5 and value of cell 2 at time 17 = 2, then value of cell 1 at time 18 = 2
97 the PC at time 18 = 6 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 17 = 5, then the PC at time 18 = 6
98 value of cell 2 at time 18 = 2 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 17 = 5 and value of cell 2 at time 17 = 2, then value of cell 2 at time 18 = 2
99 value of cell 4 at time 18 = 2 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 17 = 5 and value of cell 4 at time 17 = 2, then value of cell 4 at time 18 = 2
100 value of cell 5 at time 18 = 4 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 17 = 5 and value of cell 5 at time 17 = 4, then value of cell 5 at time 18 = 4
101 value of cell 3 at time 18 = 3 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 17 = 5 and value of cell 3 at time 17 = 3, then value of cell 3 at time 18 = 3
102 value of cell 2 at time 19 = 3 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 18 = 6 and value of cell 3 at time 18 = 3, then value of cell 2 at time 19 = 3
103 the PC at time 19 = 7 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 18 = 6, then the PC at time 19 = 7
104 value of cell 1 at time 19 = 2 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 18 = 6 and value of cell 1 at time 18 = 2, then value of cell 1 at time 19 = 2
105 value of cell 4 at time 19 = 2 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 18 = 6 and value of cell 4 at time 18 = 2, then value of cell 4 at time 19 = 2
106 value of cell 5 at time 19 = 4 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 18 = 6 and value of cell 5 at time 18 = 4, then value of cell 5 at time 19 = 4
107 value of cell 3 at time 19 = 3 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 18 = 6 and value of cell 3 at time 18 = 3, then value of cell 3 at time 19 = 3
108 value of cell 4 at time 20 = 3 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 19 = 7 and value of cell 4 at time 19 = 2, then value of cell 4 at time 20 = 3
109 the PC at time 20 = 8 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 19 = 7, then the PC at time 20 = 8
110 value of cell 1 at time 20 = 2 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 19 = 7 and value of cell 1 at time 19 = 2, then value of cell 1 at time 20 = 2
111 value of cell 2 at time 20 = 3 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 19 = 7 and value of cell 2 at time 19 = 3, then value of cell 2 at time 20 = 3
112 value of cell 5 at time 20 = 4 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 19 = 7 and value of cell 5 at time 19 = 4, then value of cell 5 at time 20 = 4
113 value of cell 3 at time 20 = 3 if instruction #7 is addi dst=4 src=4 imm=1 and the PC at time 19 = 7 and value of cell 3 at time 19 = 3, then value of cell 3 at time 20 = 3
114 the PC at time 21 = 9 if instruction #8 is beq left=4 right=5 imm=1 and the PC at time 20 = 8 and value of cell 4 at time 20 = 3 and value of cell 5 at time 20 = 4, then the PC at time 21 = 9
115 value of cell 1 at time 21 = 2 if instruction #8 is beq left=4 right=5 imm=1 and the PC at time 20 = 8 and value of cell 1 at time 20 = 2, then value of cell 1 at time 21 = 2
116 value of cell 2 at time 21 = 3 if instruction #8 is beq left=4 right=5 imm=1 and the PC at time 20 = 8 and value of cell 2 at time 20 = 3, then value of cell 2 at time 21 = 3
117 value of cell 4 at time 21 = 3 if instruction #8 is beq left=4 right=5 imm=1 and the PC at time 20 = 8 and value of cell 4 at time 20 = 3, then value of cell 4 at time 21 = 3
118 value of cell 5 at time 21 = 4 if instruction #8 is beq left=4 right=5 imm=1 and the PC at time 20 = 8 and value of cell 5 at time 20 = 4, then value of cell 5 at time 21 = 4
119 value of cell 3 at time 21 = 3 if instruction #8 is beq left=4 right=5 imm=1 and the PC at time 20 = 8 and value of cell 3 at time 20 = 3, then value of cell 3 at time 21 = 3
120 the PC at time 22 = 4 if instruction #9 is jump imm=4 and the PC at time 21 = 9, then the PC at time 22 = 4
121 value of cell 1 at time 22 = 2 if instruction #9 is jump imm=4 and the PC at time 21 = 9 and value of cell 1 at time 21 = 2, then value of cell 1 at time 22 = 2
122 value of cell 2 at time 22 = 3 if instruction #9 is jump imm=4 and the PC at time 21 = 9 and value of cell 2 at time 21 = 3, then value of cell 2 at time 22 = 3
123 value of cell 4 at time 22 = 3 if instruction #9 is jump imm=4 and the PC at time 21 = 9 and value of cell 4 at time 21 = 3, then value of cell 4 at time 22 = 3
124 value of cell 5 at time 22 = 4 if instruction #9 is jump imm=4 and the PC at time 21 = 9 and value of cell 5 at time 21 = 4, then value of cell 5 at time 22 = 4
125 value of cell 3 at time 22 = 3 if instruction #9 is jump imm=4 and the PC at time 21 = 9 and value of cell 3 at time 21 = 3, then value of cell 3 at time 22 = 3
126 value of cell 3 at time 23 = (value of cell 1 at time 22) + (value of cell 2 at time 22) if the PC at time 22 = 4 and instruction #4 is add dst=3 src1=1 src2=2, then value of cell 3 at time 23 = (value of cell 1 at time 22) + (value of cell 2 at time 22)
127 value of cell 3 at time 23 = 5 if value of cell 3 at time 23 = (value of cell 1 at time 22) + (value of cell 2 at time 22) and value of cell 1 at time 22 = 2 and value of cell 2 at time 22 = 3, then value of cell 3 at time 23 = 5
128 the PC at time 23 = 5 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 22 = 4, then the PC at time 23 = 5
129 value of cell 1 at time 23 = 2 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 22 = 4 and value of cell 1 at time 22 = 2, then value of cell 1 at time 23 = 2
130 value of cell 2 at time 23 = 3 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 22 = 4 and value of cell 2 at time 22 = 3, then value of cell 2 at time 23 = 3
131 value of cell 4 at time 23 = 3 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 22 = 4 and value of cell 4 at time 22 = 3, then value of cell 4 at time 23 = 3
132 value of cell 5 at time 23 = 4 if instruction #4 is add dst=3 src1=1 src2=2 and the PC at time 22 = 4 and value of cell 5 at time 22 = 4, then value of cell 5 at time 23 = 4
133 value of cell 1 at time 24 = 3 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 23 = 5 and value of cell 2 at time 23 = 3, then value of cell 1 at time 24 = 3
134 the PC at time 24 = 6 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 23 = 5, then the PC at time 24 = 6
135 value of cell 2 at time 24 = 3 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 23 = 5 and value of cell 2 at time 23 = 3, then value of cell 2 at time 24 = 3
136 value of cell 4 at time 24 = 3 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 23 = 5 and value of cell 4 at time 23 = 3, then value of cell 4 at time 24 = 3
137 value of cell 5 at time 24 = 4 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 23 = 5 and value of cell 5 at time 23 = 4, then value of cell 5 at time 24 = 4
138 value of cell 3 at time 24 = 5 if instruction #5 is addi dst=1 src=2 imm=0 and the PC at time 23 = 5 and value of cell 3 at time 23 = 5, then value of cell 3 at time 24 = 5
139 value of cell 2 at time 25 = 5 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 24 = 6 and value of cell 3 at time 24 = 5, then value of cell 2 at time 25 = 5
140 the PC at time 25 = 7 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 24 = 6, then the PC at time 25 = 7
141 value of cell 1 at time 25 = 3 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 24 = 6 and value of cell 1 at time 24 = 3, then value of cell 1 at time 25 = 3
142 value of cell 4 at time 25 = 3 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 24 = 6 and value of cell 4 at time 24 = 3, then value of cell 4 at time 25 = 3
143 value of cell 5 at time 25 = 4 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 24 = 6 and value of cell 5 at time 24 = 4, then value of cell 5 at time 25 = 4
144 value of cell 3 at time 25 = 5 if instruction #6 is addi dst=2 src=3 imm=0 and the PC at time 24 = 6 and value of cell 3 at time 24 = 5, then value of cell 3 at time 25 = 5

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