# LTS Termination Proof

by T2Cert

## Input

Integer Transition System
• Initial Location: 6
• Transitions: (pre-variables and post-variables)  0 0 1: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg1P ≤ 0 ∧ 2 − arg2 ≤ 0 ∧ − x5 ≤ 0 ∧ −1 − arg1 + arg2P ≤ 0 ∧ −1 − arg1 + arg3P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 2 − arg2P ≤ 0 ∧ 2 − arg3P ≤ 0 ∧ −2 − arg4P + x5 ≤ 0 ∧ 2 + arg4P − x5 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 1 1 2: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 − arg2 ≤ 0 ∧ arg4 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ −1 + arg1 − arg2P ≤ 0 ∧ 1 − arg1 + arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 1 2 1: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ −2 + arg3P − arg3 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 3 − arg3P ≤ 0 ∧ −1 − arg4P + arg4 ≤ 0 ∧ 1 + arg4P − arg4 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0 2 3 2: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ −1 − arg2P + arg2 ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 1 4 2: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ arg4 ≤ 0 ∧ −3 + arg1P − arg2 ≤ 0 ∧ −3 + arg1P − arg3 ≤ 0 ∧ 2 − arg2 ≤ 0 ∧ 2 − arg3 ≤ 0 ∧ 5 − arg1P ≤ 0 ∧ −2 + arg1 − arg2P ≤ 0 ∧ 2 − arg1 + arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 1 5 3: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ −1 + arg1 ≤ 0 ∧ arg4 ≤ 0 ∧ arg1P − arg2 ≤ 0 ∧ arg1P − arg3 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ arg2P − arg3 ≤ 0 ∧ 2 − arg2 ≤ 0 ∧ 2 − arg3 ≤ 0 ∧ 2 − arg1P ≤ 0 ∧ 2 − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 2 6 3: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ −1 + arg1P − arg1 ≤ 0 ∧ arg2 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 2 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 2 7 3: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + arg1P − arg1 ≤ 0 ∧ arg2 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 2 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 2 8 4: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + arg1P − arg1 ≤ 0 ∧ arg2 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 2 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 3 9 5: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + arg1P − arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg1 + arg3P ≤ 0 ∧ 1 − arg2 + arg4P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ − arg4P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 5 10 3: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg1 + arg2P ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ arg2P − arg4 ≤ 0 ∧ − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ − arg4 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 5 11 3: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ −3 + arg1P − arg1 ≤ 0 ∧ −2 + arg1P − arg2 ≤ 0 ∧ −2 + arg1P − arg3 ≤ 0 ∧ −3 + arg1P − arg4 ≤ 0 ∧ − arg1 + arg2P ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ 1 + arg2P − arg3 ≤ 0 ∧ arg2P − arg4 ≤ 0 ∧ − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ − arg4 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 4 12 4: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ 1 + arg4P − arg4 ≤ 0 ∧ −2 + arg1P − arg1 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 4 13 5: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − x79 ≤ 0 ∧ − x78 ≤ 0 ∧ 1 − x78 + x79 ≤ 0 ∧ −2 − arg1 + arg3P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 3 − arg3P ≤ 0 ∧ − arg4P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 4 14 3: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − x86 ≤ 0 ∧ 1 − x86 + x87 ≤ 0 ∧ −2 + arg1P − arg1 ≤ 0 ∧ arg1P − arg2 ≤ 0 ∧ − arg1 + arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 6 15 0: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0

## Proof

The following invariants are asserted.

 0: TRUE 1: − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 2 − arg3P ≤ 0 ∧ − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ 2 − arg3 ≤ 0 ∧ − x5 ≤ 0 2: 1 − arg1P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − x5 ≤ 0 3: 2 − arg1P ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ − x5 ≤ 0 4: 2 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − x5 ≤ 0 5: − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ − arg4P ≤ 0 ∧ − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ − arg4 ≤ 0 ∧ − x5 ≤ 0 6: TRUE

The invariants are proved as follows.

### IMPACT Invariant Proof

• nodes (location) invariant:  0 (0) TRUE 1 (1) − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 2 − arg3P ≤ 0 ∧ − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ 2 − arg3 ≤ 0 ∧ − x5 ≤ 0 2 (2) 1 − arg1P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − x5 ≤ 0 3 (3) 2 − arg1P ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ − x5 ≤ 0 4 (4) 2 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − x5 ≤ 0 5 (5) − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ − arg4P ≤ 0 ∧ − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ − arg4 ≤ 0 ∧ − x5 ≤ 0 6 (6) TRUE
• initial node: 6
• cover edges:
• transition edges:  0 0 1 1 1 2 1 2 1 1 4 2 1 5 3 2 3 2 2 6 3 2 7 3 2 8 4 3 9 5 4 12 4 4 13 5 4 14 3 5 10 3 5 11 3 6 15 0

### 2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 1 16 1: − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0 2 23 2: − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0 3 30 3: − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0 4 37 4: − x87 + x87 ≤ 0 ∧ x87 − x87 ≤ 0 ∧ − x86 + x86 ≤ 0 ∧ x86 − x86 ≤ 0 ∧ − x79 + x79 ≤ 0 ∧ x79 − x79 ≤ 0 ∧ − x78 + x78 ≤ 0 ∧ x78 − x78 ≤ 0 ∧ − x5 + x5 ≤ 0 ∧ x5 − x5 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0
and for every transition t, a duplicate t is considered.

### 3 Transition Removal

We remove transitions 0, 1, 4, 5, 6, 7, 8, 13, 14, 15 using the following ranking functions, which are bounded by −23.

 6: 0 0: 0 1: 0 2: 0 4: 0 3: 0 5: 0 6: −7 0: −8 1: −9 1_var_snapshot: −9 1*: −9 2: −12 2_var_snapshot: −12 2*: −12 4: −15 4_var_snapshot: −15 4*: −15 3: −18 5: −18 3_var_snapshot: −18 3*: −18

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

1* 19 1: x87 + x87 ≤ 0x87x87 ≤ 0x86 + x86 ≤ 0x86x86 ≤ 0x79 + x79 ≤ 0x79x79 ≤ 0x78 + x78 ≤ 0x78x78 ≤ 0x5 + x5 ≤ 0x5x5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

1 17 1_var_snapshot: x87 + x87 ≤ 0x87x87 ≤ 0x86 + x86 ≤ 0x86x86 ≤ 0x79 + x79 ≤ 0x79x79 ≤ 0x78 + x78 ≤ 0x78x78 ≤ 0x5 + x5 ≤ 0x5x5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

2* 26 2: x87 + x87 ≤ 0x87x87 ≤ 0x86 + x86 ≤ 0x86x86 ≤ 0x79 + x79 ≤ 0x79x79 ≤ 0x78 + x78 ≤ 0x78x78 ≤ 0x5 + x5 ≤ 0x5x5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

2 24 2_var_snapshot: x87 + x87 ≤ 0x87x87 ≤ 0x86 + x86 ≤ 0x86x86 ≤ 0x79 + x79 ≤ 0x79x79 ≤ 0x78 + x78 ≤ 0x78x78 ≤ 0x5 + x5 ≤ 0x5x5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

3* 33 3: x87 + x87 ≤ 0x87x87 ≤ 0x86 + x86 ≤ 0x86x86 ≤ 0x79 + x79 ≤ 0x79x79 ≤ 0x78 + x78 ≤ 0x78x78 ≤ 0x5 + x5 ≤ 0x5x5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

3 31 3_var_snapshot: x87 + x87 ≤ 0x87x87 ≤ 0x86 + x86 ≤ 0x86x86 ≤ 0x79 + x79 ≤ 0x79x79 ≤ 0x78 + x78 ≤ 0x78x78 ≤ 0x5 + x5 ≤ 0x5x5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

4* 40 4: x87 + x87 ≤ 0x87x87 ≤ 0x86 + x86 ≤ 0x86x86 ≤ 0x79 + x79 ≤ 0x79x79 ≤ 0x78 + x78 ≤ 0x78x78 ≤ 0x5 + x5 ≤ 0x5x5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

The following skip-transition is inserted and corresponding redirections w.r.t. the old location are performed.

4 38 4_var_snapshot: x87 + x87 ≤ 0x87x87 ≤ 0x86 + x86 ≤ 0x86x86 ≤ 0x79 + x79 ≤ 0x79x79 ≤ 0x78 + x78 ≤ 0x78x78 ≤ 0x5 + x5 ≤ 0x5x5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

### 12 SCC Decomposition

We consider subproblems for each of the 4 SCC(s) of the program graph.

### 12.1 SCC Subproblem 1/4

Here we consider the SCC { 4, 4_var_snapshot, 4* }.

### 12.1.1 Transition Removal

We remove transition 12 using the following ranking functions, which are bounded by 2.

 4: 1 + 3⋅arg4 4_var_snapshot: 3⋅arg4 4*: 2 + 3⋅arg4

### 12.1.2 Transition Removal

We remove transitions 38, 40 using the following ranking functions, which are bounded by −1.

 4: 0 4_var_snapshot: − arg1 4*: arg1P

### 12.1.3 Splitting Cut-Point Transitions

We consider 1 subproblems corresponding to sets of cut-point transitions as follows.

### 12.1.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 37.

### 12.1.3.1.1 Splitting Cut-Point Transitions

There remain no cut-point transition to consider. Hence the cooperation termination is trivial.

### 12.2 SCC Subproblem 2/4

Here we consider the SCC { 2, 2_var_snapshot, 2* }.

### 12.2.1 Transition Removal

We remove transition 3 using the following ranking functions, which are bounded by 2.

 2: 1 + 3⋅arg2 2_var_snapshot: 3⋅arg2 2*: 2 + 3⋅arg2

### 12.2.2 Transition Removal

We remove transitions 24, 26 using the following ranking functions, which are bounded by −2.

 2: −1 2_var_snapshot: −2 2*: 0

### 12.2.3 Splitting Cut-Point Transitions

We consider 1 subproblems corresponding to sets of cut-point transitions as follows.

### 12.2.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 23.

### 12.2.3.1.1 Splitting Cut-Point Transitions

There remain no cut-point transition to consider. Hence the cooperation termination is trivial.

### 12.3 SCC Subproblem 3/4

Here we consider the SCC { 3, 5, 3_var_snapshot, 3* }.

### 12.3.1 Transition Removal

We remove transitions 9, 10, 11 using the following ranking functions, which are bounded by −1.

 3: −2 + 4⋅arg2 5: 4⋅arg1 3_var_snapshot: −3 + 4⋅arg2 3*: −1 + 4⋅arg2

### 12.3.2 Transition Removal

We remove transitions 31, 33 using the following ranking functions, which are bounded by −1.

 3: 0 5: 0 3_var_snapshot: −1 3*: arg1P

### 12.3.3 Splitting Cut-Point Transitions

We consider 1 subproblems corresponding to sets of cut-point transitions as follows.

### 12.3.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 30.

### 12.3.3.1.1 Splitting Cut-Point Transitions

There remain no cut-point transition to consider. Hence the cooperation termination is trivial.

### 12.4 SCC Subproblem 4/4

Here we consider the SCC { 1, 1_var_snapshot, 1* }.

### 12.4.1 Transition Removal

We remove transition 2 using the following ranking functions, which are bounded by 2.

 1: 1 + 3⋅arg4 1_var_snapshot: 3⋅arg4 1*: 2 + 3⋅arg4

### 12.4.2 Transition Removal

We remove transitions 17, 19 using the following ranking functions, which are bounded by −1.

 1: 0 1_var_snapshot: − arg3 1*: 1

### 12.4.3 Splitting Cut-Point Transitions

We consider 1 subproblems corresponding to sets of cut-point transitions as follows.

### 12.4.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 16.

### 12.4.3.1.1 Splitting Cut-Point Transitions

There remain no cut-point transition to consider. Hence the cooperation termination is trivial.

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