# 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − x7 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg3P ≤ 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x48 + x48 ≤ 0 ∧ x48 − x48 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 0 2 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 ∧ − arg6P ≤ 0 ∧ 2 − arg2 ≤ 0 ∧ − arg3P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 2 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ arg2P ≤ 0 ∧ arg2 − arg4P ≤ 0 ∧ − arg2 + arg4P ≤ 0 ∧ 2 − arg5P ≤ 0 ∧ −2 + arg5P ≤ 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x48 + x48 ≤ 0 ∧ x48 − x48 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 3 3 3: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg5 ≤ 0 ∧ 1 + arg2 − arg3 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 2 − arg4 ≤ 0 ∧ − x30 ≤ 0 ∧ 1 − arg4 + arg5 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 4 − arg1P ≤ 0 ∧ 2 − arg1 + arg6 ≤ 0 ∧ 1 − arg2P + arg2 ≤ 0 ∧ −1 + arg2P − arg2 ≤ 0 ∧ 1 − arg5P + arg5 ≤ 0 ∧ −1 + arg5P − arg5 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x48 + x48 ≤ 0 ∧ x48 − x48 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 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 3 4 3: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg5 ≤ 0 ∧ 1 + arg2 − arg3 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 2 − arg4 ≤ 0 ∧ − x39 ≤ 0 ∧ 1 − arg4 + arg5 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 4 − arg1P ≤ 0 ∧ 2 − arg1 + arg6 ≤ 0 ∧ 1 − arg2P + arg2 ≤ 0 ∧ −1 + arg2P − arg2 ≤ 0 ∧ 1 − arg5P + arg5 ≤ 0 ∧ −1 + arg5P − arg5 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x48 + x48 ≤ 0 ∧ x48 − x48 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 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 3 5 3: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg5 ≤ 0 ∧ 1 + arg2 − arg3 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 2 − arg4 ≤ 0 ∧ − x48 ≤ 0 ∧ 1 − arg4 + arg5 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 2 − arg1 + arg6 ≤ 0 ∧ 1 − arg2P + arg2 ≤ 0 ∧ −1 + arg2P − arg2 ≤ 0 ∧ 1 − arg5P + arg5 ≤ 0 ∧ −1 + arg5P − arg5 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 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 3 6 3: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg5 ≤ 0 ∧ 1 + arg2 − arg3 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 2 − arg4 ≤ 0 ∧ − x57 ≤ 0 ∧ 1 − arg4 + arg5 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 2 − arg1 + arg6 ≤ 0 ∧ 1 − arg2P + arg2 ≤ 0 ∧ −1 + arg2P − arg2 ≤ 0 ∧ 1 − arg5P + arg5 ≤ 0 ∧ −1 + arg5P − arg5 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x48 + x48 ≤ 0 ∧ x48 − x48 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 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 1 7 4: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg2 ≤ 0 ∧ 2 − x58 ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ arg2P − arg3 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 2 − arg2 + arg4 ≤ 0 ∧ 2 − arg2 + arg5 ≤ 0 ∧ − arg3P + arg5 ≤ 0 ∧ arg3P − arg5 ≤ 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x48 + x48 ≤ 0 ∧ x48 − x48 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 4 8 4: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ −2 + arg1P − arg1 ≤ 0 ∧ 3 − arg1 + arg2P ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 4 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 2 − arg1 + arg3 ≤ 0 ∧ − arg3P ≤ 0 ∧ arg3P ≤ 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x48 + x48 ≤ 0 ∧ x48 − x48 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 3 9 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 ∧ − arg5 ≤ 0 ∧ 1 + arg2 − arg3 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 2 − arg4 ≤ 0 ∧ − arg2P ≤ 0 ∧ 1 − arg4 + arg5 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 2 − arg1 + arg6 ≤ 0 ∧ − arg3P + arg4 ≤ 0 ∧ arg3P − arg4 ≤ 0 ∧ − arg4P + arg6 ≤ 0 ∧ arg4P − arg6 ≤ 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x48 + x48 ≤ 0 ∧ x48 − x48 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 5 10 5: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 − arg3 ≤ 0 ∧ 1 − arg2 + arg4 ≤ 0 ∧ 2 + arg1P − arg1 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 2 − arg1 + arg4 ≤ 0 ∧ 4 − arg1 + arg4P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x48 + x48 ≤ 0 ∧ x48 − x48 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 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 5 11 5: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 − arg3 ≤ 0 ∧ arg2 − arg4 ≤ 0 ∧ 2 + arg1P − arg1 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 2 − arg1 + arg4 ≤ 0 ∧ 4 − arg1 + arg4P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x48 + x48 ≤ 0 ∧ x48 − x48 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 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 6 12 0: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x48 + x48 ≤ 0 ∧ x48 − x48 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0

## Proof

The following invariants are asserted.

 0: TRUE 1: 1 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg3P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ − x7 ≤ 0 3: 2 − arg1P ≤ 0 ∧ − arg3P ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ − arg3 ≤ 0 4: 1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − x7 ≤ 0 ∧ 2 − x58 ≤ 0 5: 1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0 6: TRUE

The invariants are proved as follows.

### IMPACT Invariant Proof

• nodes (location) invariant:  0 (0) TRUE 1 (1) 1 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg3P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ − x7 ≤ 0 3 (3) 2 − arg1P ≤ 0 ∧ − arg3P ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ − arg3 ≤ 0 4 (4) 1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − x7 ≤ 0 ∧ 2 − x58 ≤ 0 5 (5) 1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0 6 (6) TRUE
• initial node: 6
• cover edges:
• transition edges:  0 0 1 0 2 3 1 7 4 3 3 3 3 4 3 3 5 3 3 6 3 3 9 5 4 8 4 5 10 5 5 11 5 6 12 0

### 2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 3 13 3: − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x48 + x48 ≤ 0 ∧ x48 − x48 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − arg6P + arg6P ≤ 0 ∧ arg6P − arg6P ≤ 0 ∧ − arg6 + arg6 ≤ 0 ∧ arg6 − arg6 ≤ 0 ∧ − arg5P + arg5P ≤ 0 ∧ arg5P − arg5P ≤ 0 ∧ − arg5 + arg5 ≤ 0 ∧ arg5 − arg5 ≤ 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 20 4: − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x48 + x48 ≤ 0 ∧ x48 − x48 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − arg6P + arg6P ≤ 0 ∧ arg6P − arg6P ≤ 0 ∧ − arg6 + arg6 ≤ 0 ∧ arg6 − arg6 ≤ 0 ∧ − arg5P + arg5P ≤ 0 ∧ arg5P − arg5P ≤ 0 ∧ − arg5 + arg5 ≤ 0 ∧ arg5 − arg5 ≤ 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 5 27 5: − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x58 + x58 ≤ 0 ∧ x58 − x58 ≤ 0 ∧ − x57 + x57 ≤ 0 ∧ x57 − x57 ≤ 0 ∧ − x48 + x48 ≤ 0 ∧ x48 − x48 ≤ 0 ∧ − x39 + x39 ≤ 0 ∧ x39 − x39 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − arg6P + arg6P ≤ 0 ∧ arg6P − arg6P ≤ 0 ∧ − arg6 + arg6 ≤ 0 ∧ arg6 − arg6 ≤ 0 ∧ − arg5P + arg5P ≤ 0 ∧ arg5P − arg5P ≤ 0 ∧ − arg5 + arg5 ≤ 0 ∧ arg5 − arg5 ≤ 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, 2, 7, 9, 12 using the following ranking functions, which are bounded by −21.

 6: 0 0: 0 1: 0 4: 0 3: 0 5: 0 6: −7 0: −8 1: −9 4: −10 4_var_snapshot: −10 4*: −10 3: −13 3_var_snapshot: −13 3*: −13 5: −16 5_var_snapshot: −16 5*: −16

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

3* 16 3: x7 + x7 ≤ 0x7x7 ≤ 0x58 + x58 ≤ 0x58x58 ≤ 0x57 + x57 ≤ 0x57x57 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x39 + x39 ≤ 0x39x39 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 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 14 3_var_snapshot: x7 + x7 ≤ 0x7x7 ≤ 0x58 + x58 ≤ 0x58x58 ≤ 0x57 + x57 ≤ 0x57x57 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x39 + x39 ≤ 0x39x39 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 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* 23 4: x7 + x7 ≤ 0x7x7 ≤ 0x58 + x58 ≤ 0x58x58 ≤ 0x57 + x57 ≤ 0x57x57 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x39 + x39 ≤ 0x39x39 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 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 21 4_var_snapshot: x7 + x7 ≤ 0x7x7 ≤ 0x58 + x58 ≤ 0x58x58 ≤ 0x57 + x57 ≤ 0x57x57 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x39 + x39 ≤ 0x39x39 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 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.

5* 30 5: x7 + x7 ≤ 0x7x7 ≤ 0x58 + x58 ≤ 0x58x58 ≤ 0x57 + x57 ≤ 0x57x57 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x39 + x39 ≤ 0x39x39 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 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.

5 28 5_var_snapshot: x7 + x7 ≤ 0x7x7 ≤ 0x58 + x58 ≤ 0x58x58 ≤ 0x57 + x57 ≤ 0x57x57 ≤ 0x48 + x48 ≤ 0x48x48 ≤ 0x39 + x39 ≤ 0x39x39 ≤ 0x30 + x30 ≤ 0x30x30 ≤ 0arg6P + arg6P ≤ 0arg6Parg6P ≤ 0arg6 + arg6 ≤ 0arg6arg6 ≤ 0arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 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

### 10 SCC Decomposition

We consider subproblems for each of the 3 SCC(s) of the program graph.

### 10.1 SCC Subproblem 1/3

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

### 10.1.1 Transition Removal

We remove transitions 21, 23 using the following ranking functions, which are bounded by −1.

 4: 3⋅arg2 4_var_snapshot: −1 + 3⋅arg2 4*: 1 + 3⋅arg2

### 10.1.2 Transition Removal

We remove transition 8 using the following ranking functions, which are bounded by −1.

 4: 0 4_var_snapshot: arg2 4*: 0

### 10.1.3 Splitting Cut-Point Transitions

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

### 10.1.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 20.

### 10.1.3.1.1 Splitting Cut-Point Transitions

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

### 10.2 SCC Subproblem 2/3

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

### 10.2.1 Transition Removal

We remove transitions 28, 30, 11 using the following ranking functions, which are bounded by 2.

 5: 2 + 3⋅arg1 5_var_snapshot: 3⋅arg1 5*: 4 + 3⋅arg1

### 10.2.2 Transition Removal

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

 5: 0 5_var_snapshot: 0 5*: −1

### 10.2.3 Splitting Cut-Point Transitions

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

### 10.2.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 27.

### 10.2.3.1.1 Splitting Cut-Point Transitions

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

### 10.3 SCC Subproblem 3/3

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

### 10.3.1 Transition Removal

We remove transitions 3, 4, 5, 6 using the following ranking functions, which are bounded by 2.

 3: 1 − 2⋅arg2 + 2⋅arg3 + arg4 − arg5 3_var_snapshot: −2⋅arg2 + 2⋅arg3 + arg4 − arg5 3*: 2 − 2⋅arg2 + 2⋅arg3 + arg4 − arg5

### 10.3.2 Transition Removal

We remove transitions 14, 16 using the following ranking functions, which are bounded by −1.

 3: 0 3_var_snapshot: −1 3*: 1

### 10.3.3 Splitting Cut-Point Transitions

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

### 10.3.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 13.

### 10.3.3.1.1 Splitting Cut-Point Transitions

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

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