# 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 ∧ − 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 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x16 + x16 ≤ 0 ∧ x16 − x16 ≤ 0 1 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg2 ≤ 0 ∧ 2 − x16 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 2 − arg2 + arg3 ≤ 0 ∧ 2 − arg2 + arg5 ≤ 0 ∧ 2 − arg2 + arg4 ≤ 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 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 0 3 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 ∧ − 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 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x16 + x16 ≤ 0 ∧ x16 − x16 ≤ 0 4 4 4: 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 ∧ − x37 ≤ 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 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x16 + x16 ≤ 0 ∧ x16 − x16 ≤ 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 4 5 4: 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 ∧ − x46 ≤ 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 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x16 + x16 ≤ 0 ∧ x16 − x16 ≤ 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 4 6 4: 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 ∧ − x55 ≤ 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 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x16 + x16 ≤ 0 ∧ x16 − x16 ≤ 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 4 7 4: 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 ∧ − x64 ≤ 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 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x16 + x16 ≤ 0 ∧ x16 − x16 ≤ 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 8 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 ∧ 3 + arg1P − arg1 ≤ 0 ∧ 3 + arg1P − arg2 ≤ 0 ∧ 3 − arg1 + arg2P ≤ 0 ∧ 3 + arg2P − arg2 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ − 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x16 + x16 ≤ 0 ∧ x16 − x16 ≤ 0 3 9 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 ∧ 2 + arg1P − arg1 ≤ 0 ∧ 2 + arg1P − arg2 ≤ 0 ∧ 2 − arg1 + arg2P ≤ 0 ∧ 2 + arg2P − arg2 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ − 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x16 + x16 ≤ 0 ∧ x16 − x16 ≤ 0 4 10 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 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x16 + x16 ≤ 0 ∧ x16 − x16 ≤ 0 5 11 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 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x16 + x16 ≤ 0 ∧ x16 − x16 ≤ 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 12 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 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x16 + x16 ≤ 0 ∧ x16 − x16 ≤ 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 13 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 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x16 + x16 ≤ 0 ∧ x16 − x16 ≤ 0

## Proof

The following invariants are asserted.

 0: TRUE 1: 1 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − x7 ≤ 0 3: − x7 ≤ 0 ∧ 2 − x16 ≤ 0 4: 2 − arg1P ≤ 0 ∧ − arg3P ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ − arg3 ≤ 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 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − x7 ≤ 0 3 (3) − x7 ≤ 0 ∧ 2 − x16 ≤ 0 4 (4) 2 − arg1P ≤ 0 ∧ − arg3P ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ − arg3 ≤ 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 3 4 1 2 3 3 8 3 3 9 3 4 4 4 4 5 4 4 6 4 4 7 4 4 10 5 5 11 5 5 12 5 6 13 0

### 2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 3 14 3: − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x16 + x16 ≤ 0 ∧ x16 − x16 ≤ 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 21 4: − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x16 + x16 ≤ 0 ∧ x16 − x16 ≤ 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 28 5: − x7 + x7 ≤ 0 ∧ x7 − x7 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x55 + x55 ≤ 0 ∧ x55 − x55 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x16 + x16 ≤ 0 ∧ x16 − x16 ≤ 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, 3, 10, 13 using the following ranking functions, which are bounded by −21.

 6: 0 0: 0 1: 0 3: 0 4: 0 5: 0 6: −7 0: −8 1: −9 3: −10 3_var_snapshot: −10 3*: −10 4: −13 4_var_snapshot: −13 4*: −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* 17 3: x7 + x7 ≤ 0x7x7 ≤ 0x64 + x64 ≤ 0x64x64 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x46 + x46 ≤ 0x46x46 ≤ 0x37 + x37 ≤ 0x37x37 ≤ 0x16 + x16 ≤ 0x16x16 ≤ 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 15 3_var_snapshot: x7 + x7 ≤ 0x7x7 ≤ 0x64 + x64 ≤ 0x64x64 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x46 + x46 ≤ 0x46x46 ≤ 0x37 + x37 ≤ 0x37x37 ≤ 0x16 + x16 ≤ 0x16x16 ≤ 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* 24 4: x7 + x7 ≤ 0x7x7 ≤ 0x64 + x64 ≤ 0x64x64 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x46 + x46 ≤ 0x46x46 ≤ 0x37 + x37 ≤ 0x37x37 ≤ 0x16 + x16 ≤ 0x16x16 ≤ 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 22 4_var_snapshot: x7 + x7 ≤ 0x7x7 ≤ 0x64 + x64 ≤ 0x64x64 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x46 + x46 ≤ 0x46x46 ≤ 0x37 + x37 ≤ 0x37x37 ≤ 0x16 + x16 ≤ 0x16x16 ≤ 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* 31 5: x7 + x7 ≤ 0x7x7 ≤ 0x64 + x64 ≤ 0x64x64 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x46 + x46 ≤ 0x46x46 ≤ 0x37 + x37 ≤ 0x37x37 ≤ 0x16 + x16 ≤ 0x16x16 ≤ 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 29 5_var_snapshot: x7 + x7 ≤ 0x7x7 ≤ 0x64 + x64 ≤ 0x64x64 ≤ 0x55 + x55 ≤ 0x55x55 ≤ 0x46 + x46 ≤ 0x46x46 ≤ 0x37 + x37 ≤ 0x37x37 ≤ 0x16 + x16 ≤ 0x16x16 ≤ 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 { 3, 3_var_snapshot, 3* }.

### 10.1.1 Transition Removal

We remove transitions 8, 9 using the following ranking functions, which are bounded by 5.

 3: arg1 + arg2 3_var_snapshot: arg1 + arg2 3*: 2 + arg1 + arg2

### 10.1.2 Transition Removal

We remove transition 15 using the following ranking functions, which are bounded by −1.

 3: 0 3_var_snapshot: −1 3*: 1

### 10.1.3 Transition Removal

We remove transition 17 using the following ranking functions, which are bounded by 1.

 3: 0 3_var_snapshot: 0 3*: x16

### 10.1.4 Splitting Cut-Point Transitions

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

### 10.1.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 14.

### 10.1.4.1.1 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 29, 31, 12 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 11 using the following ranking functions, which are bounded by 2.

 5: 0 5_var_snapshot: arg1 5*: 0

### 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 28.

### 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 { 4, 4_var_snapshot, 4* }.

### 10.3.1 Transition Removal

We remove transitions 4, 5, 6, 7 using the following ranking functions, which are bounded by 2.

 4: 1 − 2⋅arg2 + 2⋅arg3 + arg4 − arg5 4_var_snapshot: −2⋅arg2 + 2⋅arg3 + arg4 − arg5 4*: 2 − 2⋅arg2 + 2⋅arg3 + arg4 − arg5

### 10.3.2 Transition Removal

We remove transitions 22, 24 using the following ranking functions, which are bounded by −1.

 4: 0 4_var_snapshot: −1 4*: arg1P

### 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 21.

### 10.3.3.1.1 Splitting Cut-Point Transitions

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

T2Cert

• version: 1.0