# LTS Termination Proof

by T2Cert

## Input

Integer Transition System
• Initial Location: 10
• 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 ∧ − x6 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 4 − arg1P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 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 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − x18 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − x19 ≤ 0 ∧ 1 − arg2 + x19 ≤ 0 ∧ − x20 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg1P ≤ 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 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 1 4 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg2 + x26 ≤ 0 ∧ 1 − x26 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − x34 ≤ 0 ∧ 2 − arg4P ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ 3 − arg1 + arg2P ≤ 0 ∧ 3 − arg1 + arg3P ≤ 0 ∧ 4 − arg1 ≤ 0 ∧ 4 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ 5 − arg1 + arg4 ≤ 0 ∧ 5 − arg1 + arg3 ≤ 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 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 1 5 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg2 + x36 ≤ 0 ∧ 1 − x36 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − x44 ≤ 0 ∧ 2 − arg4P ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ 4 − arg1 ≤ 0 ∧ 4 − arg1P ≤ 0 ∧ 4 − arg2P ≤ 0 ∧ 4 − arg3P ≤ 0 ∧ 5 − arg1 + arg4 ≤ 0 ∧ 5 − arg1 + arg3 ≤ 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 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 0 6 6: 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 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ −1 + arg3P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 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 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 0 7 6: 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − x52 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − x50 ≤ 0 ∧ 1 − arg2 + x50 ≤ 0 ∧ − arg1P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg3P + x50 ≤ 0 ∧ −1 + arg3P − x50 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 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 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 1 8 6: 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 ∧ 1 − arg2 + x54 ≤ 0 ∧ 1 − x54 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − arg1P ≤ 0 ∧ 4 − arg1 ≤ 0 ∧ 5 − arg1 + arg4 ≤ 0 ∧ 5 − arg1 + arg3 ≤ 0 ∧ 1 − arg3P + x54 ≤ 0 ∧ −1 + arg3P − x54 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 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 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 6 9 7: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg2 ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 1 − arg2 + arg3 ≤ 0 ∧ − arg3P ≤ 0 ∧ − arg2P ≤ 0 ∧ arg2P ≤ 0 ∧ arg2 − arg4P ≤ 0 ∧ − arg2 + arg4P ≤ 0 ∧ 1 + arg3 − arg5P ≤ 0 ∧ −1 − arg3 + arg5P ≤ 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 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0 7 10 6: 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 ∧ 1 + arg2 − arg3 ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 2 − arg5 ≤ 0 ∧ 0 ≤ 0 ∧ −1 − arg1P + arg1 ≤ 0 ∧ 1 + arg1P − arg1 ≤ 0 ∧ − arg2P + arg4 ≤ 0 ∧ arg2P − arg4 ≤ 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 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 7 11 7: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + arg2 − arg3 ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 2 − arg5 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg2P + arg2 ≤ 0 ∧ −1 + arg2P − arg2 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 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 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0 5 12 8: 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 − arg1 ≤ 0 ∧ 2 − arg4 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ arg2P − arg3 ≤ 0 ∧ 1 − arg1 + arg6P ≤ 0 ∧ 1 − arg2 + arg7P ≤ 0 ∧ 1 − arg3 + arg7P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg6P ≤ 0 ∧ − arg7P ≤ 0 ∧ − arg3P ≤ 0 ∧ arg3P ≤ 0 ∧ arg4 − arg5P ≤ 0 ∧ − arg4 + 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 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 5 13 8: 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 − arg1 ≤ 0 ∧ 2 − arg4 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ arg2P − arg3 ≤ 0 ∧ 1 − arg1 + arg6P ≤ 0 ∧ 1 − arg2 + arg7P ≤ 0 ∧ 1 − arg3 + arg7P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg6P ≤ 0 ∧ − arg7P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ −1 + arg3P ≤ 0 ∧ arg4 − arg5P ≤ 0 ∧ − arg4 + 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 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 8 14 9: 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 ∧ 1 + arg1P − arg2 ≤ 0 ∧ arg1P − arg7 ≤ 0 ∧ 1 − arg1 + arg2P ≤ 0 ∧ arg2P − arg6 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − arg6 ≤ 0 ∧ − arg7 ≤ 0 ∧ − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ −1 + arg3 ≤ 0 ∧ − arg3P + arg4 ≤ 0 ∧ arg3P − arg4 ≤ 0 ∧ − arg4P + arg5 ≤ 0 ∧ arg4P − 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 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 9 15 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 ∧ 2 + arg1P − arg2 ≤ 0 ∧ 2 − arg4 ≤ 0 ∧ 2 − arg1 + arg2P ≤ 0 ∧ 3 + arg2P − arg2 ≤ 0 ∧ 2 − arg1 + arg3P ≤ 0 ∧ 3 − arg2 + arg3P ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − arg3P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 9 16 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 ∧ 2 + arg1P − arg2 ≤ 0 ∧ 2 − arg4 ≤ 0 ∧ 2 − arg1 + arg2P ≤ 0 ∧ 2 − arg1 + arg3P ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 9 17 9: 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 − arg4 ≤ 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 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 9 18 9: 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 − arg4 ≤ 0 ∧ 2 + arg2P − arg2 ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ − arg1P ≤ 0 ∧ − arg2P ≤ 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 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 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 10 19 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 ≤ 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 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0

## Proof

The following invariants are asserted.

 0: TRUE 1: 4 − arg1P ≤ 0 ∧ 4 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − x6 ≤ 0 3: 1 − arg1P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − x18 ≤ 0 ∧ 1 − x19 ≤ 0 ∧ − x20 ≤ 0 5: − arg1P ≤ 0 ∧ − arg1 ≤ 0 ∧ 2 − arg4 ≤ 0 ∧ − x6 ≤ 0 6: TRUE 7: − arg3P ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ − arg3 ≤ 0 8: 1 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg3P ≤ 0 ∧ − arg6P ≤ 0 ∧ − arg7P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ − arg6 ≤ 0 ∧ − arg7 ≤ 0 ∧ − x6 ≤ 0 9: − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − x6 ≤ 0 10: TRUE

The invariants are proved as follows.

### IMPACT Invariant Proof

• nodes (location) invariant:  0 (0) TRUE 1 (1) 4 − arg1P ≤ 0 ∧ 4 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − x6 ≤ 0 3 (3) 1 − arg1P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − x18 ≤ 0 ∧ 1 − x19 ≤ 0 ∧ − x20 ≤ 0 5 (5) − arg1P ≤ 0 ∧ − arg1 ≤ 0 ∧ 2 − arg4 ≤ 0 ∧ − x6 ≤ 0 6 (6) TRUE 7 (7) − arg3P ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ − arg3 ≤ 0 8 (8) 1 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg3P ≤ 0 ∧ − arg6P ≤ 0 ∧ − arg7P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ − arg6 ≤ 0 ∧ − arg7 ≤ 0 ∧ − x6 ≤ 0 9 (9) − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − x6 ≤ 0 10 (10) TRUE
• initial node: 10
• cover edges:
• transition edges:  0 0 1 0 2 3 0 6 6 0 7 6 1 4 5 1 5 5 1 8 6 5 12 8 5 13 8 6 9 7 7 10 6 7 11 7 8 14 9 9 15 5 9 16 5 9 17 9 9 18 9 10 19 0

### 2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 5 20 5: − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg7P + arg7P ≤ 0 ∧ arg7P − arg7P ≤ 0 ∧ − arg7 + arg7 ≤ 0 ∧ arg7 − arg7 ≤ 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 6 27 6: − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg7P + arg7P ≤ 0 ∧ arg7P − arg7P ≤ 0 ∧ − arg7 + arg7 ≤ 0 ∧ arg7 − arg7 ≤ 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 7 34 7: − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg7P + arg7P ≤ 0 ∧ arg7P − arg7P ≤ 0 ∧ − arg7 + arg7 ≤ 0 ∧ arg7 − arg7 ≤ 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 9 41 9: − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x54 + x54 ≤ 0 ∧ x54 − x54 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x50 + x50 ≤ 0 ∧ x50 − x50 ≤ 0 ∧ − x44 + x44 ≤ 0 ∧ x44 − x44 ≤ 0 ∧ − x36 + x36 ≤ 0 ∧ x36 − x36 ≤ 0 ∧ − x34 + x34 ≤ 0 ∧ x34 − x34 ≤ 0 ∧ − x26 + x26 ≤ 0 ∧ x26 − x26 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x19 + x19 ≤ 0 ∧ x19 − x19 ≤ 0 ∧ − x18 + x18 ≤ 0 ∧ x18 − x18 ≤ 0 ∧ − arg7P + arg7P ≤ 0 ∧ arg7P − arg7P ≤ 0 ∧ − arg7 + arg7 ≤ 0 ∧ arg7 − arg7 ≤ 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, 4, 5, 6, 7, 8, 19 using the following ranking functions, which are bounded by −23.

 10: 0 0: 0 1: 0 5: 0 8: 0 9: 0 3: 0 6: 0 7: 0 10: −7 0: −8 1: −9 5: −10 8: −10 9: −10 5_var_snapshot: −10 5*: −10 9_var_snapshot: −10 9*: −10 3: −15 6: −16 7: −16 6_var_snapshot: −16 6*: −16 7_var_snapshot: −16 7*: −16

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

5* 23 5: x6 + x6 ≤ 0x6x6 ≤ 0x54 + x54 ≤ 0x54x54 ≤ 0x52 + x52 ≤ 0x52x52 ≤ 0x50 + x50 ≤ 0x50x50 ≤ 0x44 + x44 ≤ 0x44x44 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x34 + x34 ≤ 0x34x34 ≤ 0x26 + x26 ≤ 0x26x26 ≤ 0x20 + x20 ≤ 0x20x20 ≤ 0x19 + x19 ≤ 0x19x19 ≤ 0x18 + x18 ≤ 0x18x18 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 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 21 5_var_snapshot: x6 + x6 ≤ 0x6x6 ≤ 0x54 + x54 ≤ 0x54x54 ≤ 0x52 + x52 ≤ 0x52x52 ≤ 0x50 + x50 ≤ 0x50x50 ≤ 0x44 + x44 ≤ 0x44x44 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x34 + x34 ≤ 0x34x34 ≤ 0x26 + x26 ≤ 0x26x26 ≤ 0x20 + x20 ≤ 0x20x20 ≤ 0x19 + x19 ≤ 0x19x19 ≤ 0x18 + x18 ≤ 0x18x18 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 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.

6* 30 6: x6 + x6 ≤ 0x6x6 ≤ 0x54 + x54 ≤ 0x54x54 ≤ 0x52 + x52 ≤ 0x52x52 ≤ 0x50 + x50 ≤ 0x50x50 ≤ 0x44 + x44 ≤ 0x44x44 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x34 + x34 ≤ 0x34x34 ≤ 0x26 + x26 ≤ 0x26x26 ≤ 0x20 + x20 ≤ 0x20x20 ≤ 0x19 + x19 ≤ 0x19x19 ≤ 0x18 + x18 ≤ 0x18x18 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 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.

6 28 6_var_snapshot: x6 + x6 ≤ 0x6x6 ≤ 0x54 + x54 ≤ 0x54x54 ≤ 0x52 + x52 ≤ 0x52x52 ≤ 0x50 + x50 ≤ 0x50x50 ≤ 0x44 + x44 ≤ 0x44x44 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x34 + x34 ≤ 0x34x34 ≤ 0x26 + x26 ≤ 0x26x26 ≤ 0x20 + x20 ≤ 0x20x20 ≤ 0x19 + x19 ≤ 0x19x19 ≤ 0x18 + x18 ≤ 0x18x18 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 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.

7* 37 7: x6 + x6 ≤ 0x6x6 ≤ 0x54 + x54 ≤ 0x54x54 ≤ 0x52 + x52 ≤ 0x52x52 ≤ 0x50 + x50 ≤ 0x50x50 ≤ 0x44 + x44 ≤ 0x44x44 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x34 + x34 ≤ 0x34x34 ≤ 0x26 + x26 ≤ 0x26x26 ≤ 0x20 + x20 ≤ 0x20x20 ≤ 0x19 + x19 ≤ 0x19x19 ≤ 0x18 + x18 ≤ 0x18x18 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 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.

7 35 7_var_snapshot: x6 + x6 ≤ 0x6x6 ≤ 0x54 + x54 ≤ 0x54x54 ≤ 0x52 + x52 ≤ 0x52x52 ≤ 0x50 + x50 ≤ 0x50x50 ≤ 0x44 + x44 ≤ 0x44x44 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x34 + x34 ≤ 0x34x34 ≤ 0x26 + x26 ≤ 0x26x26 ≤ 0x20 + x20 ≤ 0x20x20 ≤ 0x19 + x19 ≤ 0x19x19 ≤ 0x18 + x18 ≤ 0x18x18 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 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.

9* 44 9: x6 + x6 ≤ 0x6x6 ≤ 0x54 + x54 ≤ 0x54x54 ≤ 0x52 + x52 ≤ 0x52x52 ≤ 0x50 + x50 ≤ 0x50x50 ≤ 0x44 + x44 ≤ 0x44x44 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x34 + x34 ≤ 0x34x34 ≤ 0x26 + x26 ≤ 0x26x26 ≤ 0x20 + x20 ≤ 0x20x20 ≤ 0x19 + x19 ≤ 0x19x19 ≤ 0x18 + x18 ≤ 0x18x18 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 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.

9 42 9_var_snapshot: x6 + x6 ≤ 0x6x6 ≤ 0x54 + x54 ≤ 0x54x54 ≤ 0x52 + x52 ≤ 0x52x52 ≤ 0x50 + x50 ≤ 0x50x50 ≤ 0x44 + x44 ≤ 0x44x44 ≤ 0x36 + x36 ≤ 0x36x36 ≤ 0x34 + x34 ≤ 0x34x34 ≤ 0x26 + x26 ≤ 0x26x26 ≤ 0x20 + x20 ≤ 0x20x20 ≤ 0x19 + x19 ≤ 0x19x19 ≤ 0x18 + x18 ≤ 0x18x18 ≤ 0arg7P + arg7P ≤ 0arg7Parg7P ≤ 0arg7 + arg7 ≤ 0arg7arg7 ≤ 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

### 12 SCC Decomposition

We consider subproblems for each of the 2 SCC(s) of the program graph.

### 12.1 SCC Subproblem 1/2

Here we consider the SCC { 5, 8, 9, 5_var_snapshot, 5*, 9_var_snapshot, 9* }.

### 12.1.1 Transition Removal

We remove transitions 21, 23, 42, 44, 12, 13, 14, 15, 16, 17, 18 using the following ranking functions, which are bounded by −1.

 5: 8 + 7⋅arg1 8: 9⋅arg3 + 7⋅arg6 9: 3 + 7⋅arg2 5_var_snapshot: 5 + 7⋅arg1 5*: 11 + 7⋅arg1 9_var_snapshot: 7⋅arg2 9*: 6 + 7⋅arg2

### 12.1.2 Splitting Cut-Point Transitions

We consider 2 subproblems corresponding to sets of cut-point transitions as follows.

### 12.1.2.1 Cut-Point Subproblem 1/2

Here we consider cut-point transition 20.

### 12.1.2.1.1 Splitting Cut-Point Transitions

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

### 12.1.2.2 Cut-Point Subproblem 2/2

Here we consider cut-point transition 41.

### 12.1.2.2.1 Splitting Cut-Point Transitions

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

### 12.2 SCC Subproblem 2/2

Here we consider the SCC { 6, 7, 6_var_snapshot, 6*, 7_var_snapshot, 7* }.

### 12.2.1 Transition Removal

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

 6: 2 + 5⋅arg1 7: 5⋅arg1 6_var_snapshot: 1 + 5⋅arg1 6*: 4 + 5⋅arg1 7_var_snapshot: 5⋅arg1 7*: 5⋅arg1

### 12.2.2 Transition Removal

We remove transitions 30, 11 using the following ranking functions, which are bounded by −1.

 6: 0 7: 1 − 3⋅arg2 + 3⋅arg3 6_var_snapshot: −1 6*: 1 7_var_snapshot: −3⋅arg2 + 3⋅arg3 7*: 2 − 3⋅arg2 + 3⋅arg3

### 12.2.3 Transition Removal

We remove transitions 28, 35, 37 using the following ranking functions, which are bounded by −1.

 6: 0 7: 0 6_var_snapshot: −1 6*: 0 7_var_snapshot: −1 7*: arg1

### 12.2.4 Splitting Cut-Point Transitions

We consider 2 subproblems corresponding to sets of cut-point transitions as follows.

### 12.2.4.1 Cut-Point Subproblem 1/2

Here we consider cut-point transition 27.

### 12.2.4.1.1 Splitting Cut-Point Transitions

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

### 12.2.4.2 Cut-Point Subproblem 2/2

Here we consider cut-point transition 34.

### 12.2.4.2.1 Splitting Cut-Point Transitions

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

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