# 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ 1 − arg1 + arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ −1 + arg3P ≤ 0 ∧ arg2 − arg4P ≤ 0 ∧ − arg2 + 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 1 1 2: 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 ∧ arg1P − arg1 ≤ 0 ∧ 1 − arg3 + arg4 ≤ 0 ∧ −1 + arg1P − arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 1 − arg3P ≤ 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 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg3 − arg4 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ − arg3 + arg4 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ −1 + arg1P − arg2 ≤ 0 ∧ −106 + arg2P − arg2 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 106 − arg2P ≤ 0 ∧ −1 − arg4P + arg4 ≤ 0 ∧ 1 + arg4P − arg4 ≤ 0 ∧ arg4 − arg5P ≤ 0 ∧ − arg4 + arg5P ≤ 0 ∧ 40 − arg6P ≤ 0 ∧ −40 + arg6P ≤ 0 ∧ 97 − arg7P ≤ 0 ∧ −97 + arg7P ≤ 0 ∧ 43 − arg8P ≤ 0 ∧ −43 + arg8P ≤ 0 ∧ 98 − arg9P ≤ 0 ∧ −98 + arg9P ≤ 0 ∧ 41 − arg10P ≤ 0 ∧ −41 + arg10P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 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 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 2 3 2: 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 ∧ arg1P − arg1 ≤ 0 ∧ 1 + arg3 − arg4 ≤ 0 ∧ −1 + arg1P − arg2 ≤ 0 ∧ −42 + arg2P − arg2 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 42 − arg2P ≤ 0 ∧ 1 − arg3P + arg3 ≤ 0 ∧ −1 + arg3P − arg3 ≤ 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 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 3 4 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ 1 − arg3 + arg4 ≤ 0 ∧ 105 + arg1P − arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 106 − arg2 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 106 − arg2P ≤ 0 ∧ 40 − arg6 ≤ 0 ∧ −40 + arg6 ≤ 0 ∧ 97 − arg7 ≤ 0 ∧ −97 + arg7 ≤ 0 ∧ 43 − arg8 ≤ 0 ∧ −43 + arg8 ≤ 0 ∧ 98 − arg9 ≤ 0 ∧ −98 + arg9 ≤ 0 ∧ 41 − arg10 ≤ 0 ∧ −41 + arg10 ≤ 0 ∧ 1 − arg3P + arg3 ≤ 0 ∧ −1 + arg3P − arg3 ≤ 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 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 1 5 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 ∧ arg3 − arg4 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ 1 + arg3 − arg4 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ −1 + arg1P − arg2 ≤ 0 ∧ −106 + arg2P − arg2 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 106 − arg2P ≤ 0 ∧ −1 − arg4P + arg4 ≤ 0 ∧ 1 + arg4P − arg4 ≤ 0 ∧ arg4 − arg5P ≤ 0 ∧ − arg4 + arg5P ≤ 0 ∧ 40 − arg6P ≤ 0 ∧ −40 + arg6P ≤ 0 ∧ 97 − arg7P ≤ 0 ∧ −97 + arg7P ≤ 0 ∧ 43 − arg8P ≤ 0 ∧ −43 + arg8P ≤ 0 ∧ 98 − arg9P ≤ 0 ∧ −98 + arg9P ≤ 0 ∧ 41 − arg10P ≤ 0 ∧ −41 + arg10P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 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 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 3 6 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ arg3 − arg4 ≤ 0 ∧ 105 + arg1P − arg2 ≤ 0 ∧ −2 + arg2P − arg2 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 106 − arg2 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 108 − arg2P ≤ 0 ∧ 40 − arg6 ≤ 0 ∧ −40 + arg6 ≤ 0 ∧ 97 − arg7 ≤ 0 ∧ −97 + arg7 ≤ 0 ∧ 43 − arg8 ≤ 0 ∧ −43 + arg8 ≤ 0 ∧ 98 − arg9 ≤ 0 ∧ −98 + arg9 ≤ 0 ∧ 41 − arg10 ≤ 0 ∧ −41 + arg10 ≤ 0 ∧ 1 − arg3P + arg3 ≤ 0 ∧ −1 + arg3P − arg3 ≤ 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 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 2 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg2 ≤ 0 ∧ − arg3 + arg4 ≤ 0 ∧ 1 − arg1 + arg2P ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ 1 − arg1 + arg3P ≤ 0 ∧ − arg2 + arg3P ≤ 0 ∧ − arg2 + arg4P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 + arg1P − arg1 ≤ 0 ∧ 2 + arg1P − arg4 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ 2 − arg1 + arg4P ≤ 0 ∧ 2 + arg4P − arg4 ≤ 0 ∧ 42 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ 42 − arg4 ≤ 0 ∧ − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 4 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg3 ≤ 0 ∧ − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ − arg4 ≤ 0 ∧ − 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 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 4 10 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 + arg1P − arg1 ≤ 0 ∧ 2 + arg1P − arg4 ≤ 0 ∧ −44 + arg2P − arg2 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ 2 − arg1 + arg4P ≤ 0 ∧ 2 + arg4P − arg4 ≤ 0 ∧ 44 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ 44 − arg4 ≤ 0 ∧ − arg1P ≤ 0 ∧ 44 − arg2P ≤ 0 ∧ − 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 4 11 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 + arg1P − arg1 ≤ 0 ∧ 2 + arg1P − arg4 ≤ 0 ∧ −45 + arg2P − arg2 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ 2 − arg1 + arg4P ≤ 0 ∧ 2 + arg4P − arg4 ≤ 0 ∧ 45 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ 45 − arg4 ≤ 0 ∧ − arg1P ≤ 0 ∧ 45 − arg2P ≤ 0 ∧ − 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 4 12 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 + arg1P − arg1 ≤ 0 ∧ 2 + arg1P − arg4 ≤ 0 ∧ −47 + arg2P − arg2 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ 2 − arg1 + arg4P ≤ 0 ∧ 2 + arg4P − arg4 ≤ 0 ∧ 47 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ 47 − arg4 ≤ 0 ∧ − arg1P ≤ 0 ∧ 47 − arg2P ≤ 0 ∧ − 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 4 13 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 + arg1P − arg1 ≤ 0 ∧ 2 + arg1P − arg4 ≤ 0 ∧ −49 + arg2P − arg2 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ 2 − arg1 + arg4P ≤ 0 ∧ 2 + arg4P − arg4 ≤ 0 ∧ 49 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ 49 − arg4 ≤ 0 ∧ − arg1P ≤ 0 ∧ 49 − arg2P ≤ 0 ∧ − 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 4 14 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + arg1P − arg1 ≤ 0 ∧ 48 − x103 ≤ 0 ∧ 1 + arg1P − arg4 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ 1 − arg1 + arg4P ≤ 0 ∧ 1 + arg4P − arg4 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ − arg1P ≤ 0 ∧ − 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 4 15 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + arg1P − arg1 ≤ 0 ∧ −39 + x112 ≤ 0 ∧ 1 + arg1P − arg4 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ 1 − arg1 + arg4P ≤ 0 ∧ 1 + arg4P − arg4 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ − arg1P ≤ 0 ∧ − 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 4 16 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 + arg1P − arg1 ≤ 0 ∧ 2 + arg1P − arg4 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ −46 + arg3P − arg3 ≤ 0 ∧ 2 − arg1 + arg4P ≤ 0 ∧ 2 + arg4P − arg4 ≤ 0 ∧ 46 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ 46 − arg4 ≤ 0 ∧ − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 46 − 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 4 17 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 + arg1P − arg1 ≤ 0 ∧ 2 + arg1P − arg4 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ −48 + arg3P − arg3 ≤ 0 ∧ 2 − arg1 + arg4P ≤ 0 ∧ 2 + arg4P − arg4 ≤ 0 ∧ 48 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ 48 − arg4 ≤ 0 ∧ − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 48 − 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 4 18 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 + arg1P − arg1 ≤ 0 ∧ 2 + arg1P − arg4 ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ 2 − arg1 + arg4P ≤ 0 ∧ 2 + arg4P − arg4 ≤ 0 ∧ 43 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ 43 − arg4 ≤ 0 ∧ − arg1P ≤ 0 ∧ − 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 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg6P + arg6 ≤ 0 ∧ arg6P − arg6 ≤ 0 ∧ − arg7P + arg7 ≤ 0 ∧ arg7P − arg7 ≤ 0 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 5 19 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + arg1P − arg1 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − 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 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 6 20 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 ≤ 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 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0

## Proof

### 1 Invariant Updates

The following invariants are asserted.

 0: TRUE 1: 1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0 2: 1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0 3: 1 − arg1P ≤ 0 ∧ 106 − arg2P ≤ 0 ∧ −40 + arg6P ≤ 0 ∧ 40 − arg6P ≤ 0 ∧ −97 + arg7P ≤ 0 ∧ 97 − arg7P ≤ 0 ∧ −43 + arg8P ≤ 0 ∧ 43 − arg8P ≤ 0 ∧ −98 + arg9P ≤ 0 ∧ 98 − arg9P ≤ 0 ∧ −41 + arg10P ≤ 0 ∧ 41 − arg10P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 106 − arg2 ≤ 0 ∧ −40 + arg6 ≤ 0 ∧ 40 − arg6 ≤ 0 ∧ −97 + arg7 ≤ 0 ∧ 97 − arg7 ≤ 0 ∧ −43 + arg8 ≤ 0 ∧ 43 − arg8 ≤ 0 ∧ −98 + arg9 ≤ 0 ∧ 98 − arg9 ≤ 0 ∧ −41 + arg10 ≤ 0 ∧ 41 − arg10 ≤ 0 4: − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − arg3P ≤ 0 ∧ − arg4P ≤ 0 ∧ − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ − arg4 ≤ 0 5: − arg1P ≤ 0 ∧ − arg1 ≤ 0 6: TRUE

The invariants are proved as follows.

### IMPACT Invariant Proof

• nodes (location) invariant:  0 (0) TRUE 1 (1) 1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0 2 (2) 1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0 3 (3) 1 − arg1P ≤ 0 ∧ 106 − arg2P ≤ 0 ∧ −40 + arg6P ≤ 0 ∧ 40 − arg6P ≤ 0 ∧ −97 + arg7P ≤ 0 ∧ 97 − arg7P ≤ 0 ∧ −43 + arg8P ≤ 0 ∧ 43 − arg8P ≤ 0 ∧ −98 + arg9P ≤ 0 ∧ 98 − arg9P ≤ 0 ∧ −41 + arg10P ≤ 0 ∧ 41 − arg10P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 106 − arg2 ≤ 0 ∧ −40 + arg6 ≤ 0 ∧ 40 − arg6 ≤ 0 ∧ −97 + arg7 ≤ 0 ∧ 97 − arg7 ≤ 0 ∧ −43 + arg8 ≤ 0 ∧ 43 − arg8 ≤ 0 ∧ −98 + arg9 ≤ 0 ∧ 98 − arg9 ≤ 0 ∧ −41 + arg10 ≤ 0 ∧ 41 − arg10 ≤ 0 4 (4) − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − arg3P ≤ 0 ∧ − arg4P ≤ 0 ∧ − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ − arg4 ≤ 0 5 (5) − arg1P ≤ 0 ∧ − arg1 ≤ 0 6 (6) TRUE
• initial node: 6
• cover edges:
• transition edges:  0 0 1 1 1 2 1 2 3 1 5 3 2 3 2 2 7 4 3 4 1 3 6 1 4 8 4 4 9 5 4 10 4 4 11 4 4 12 4 4 13 4 4 14 4 4 15 4 4 16 4 4 17 4 4 18 4 5 19 5 6 20 0

### 2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 1 21 1: − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 ∧ − arg9P + arg9P ≤ 0 ∧ arg9P − arg9P ≤ 0 ∧ − arg9 + arg9 ≤ 0 ∧ arg9 − arg9 ≤ 0 ∧ − arg8P + arg8P ≤ 0 ∧ arg8P − arg8P ≤ 0 ∧ − arg8 + arg8 ≤ 0 ∧ arg8 − arg8 ≤ 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 ∧ − arg10P + arg10P ≤ 0 ∧ arg10P − arg10P ≤ 0 ∧ − arg10 + arg10 ≤ 0 ∧ arg10 − arg10 ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0 2 28 2: − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 ∧ − arg9P + arg9P ≤ 0 ∧ arg9P − arg9P ≤ 0 ∧ − arg9 + arg9 ≤ 0 ∧ arg9 − arg9 ≤ 0 ∧ − arg8P + arg8P ≤ 0 ∧ arg8P − arg8P ≤ 0 ∧ − arg8 + arg8 ≤ 0 ∧ arg8 − arg8 ≤ 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 ∧ − arg10P + arg10P ≤ 0 ∧ arg10P − arg10P ≤ 0 ∧ − arg10 + arg10 ≤ 0 ∧ arg10 − arg10 ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0 4 35 4: − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 ∧ − arg9P + arg9P ≤ 0 ∧ arg9P − arg9P ≤ 0 ∧ − arg9 + arg9 ≤ 0 ∧ arg9 − arg9 ≤ 0 ∧ − arg8P + arg8P ≤ 0 ∧ arg8P − arg8P ≤ 0 ∧ − arg8 + arg8 ≤ 0 ∧ arg8 − arg8 ≤ 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 ∧ − arg10P + arg10P ≤ 0 ∧ arg10P − arg10P ≤ 0 ∧ − arg10 + arg10 ≤ 0 ∧ arg10 − arg10 ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0 5 42 5: − x112 + x112 ≤ 0 ∧ x112 − x112 ≤ 0 ∧ − x103 + x103 ≤ 0 ∧ x103 − x103 ≤ 0 ∧ − arg9P + arg9P ≤ 0 ∧ arg9P − arg9P ≤ 0 ∧ − arg9 + arg9 ≤ 0 ∧ arg9 − arg9 ≤ 0 ∧ − arg8P + arg8P ≤ 0 ∧ arg8P − arg8P ≤ 0 ∧ − arg8 + arg8 ≤ 0 ∧ arg8 − arg8 ≤ 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 ∧ − arg10P + arg10P ≤ 0 ∧ arg10P − arg10P ≤ 0 ∧ − arg10 + arg10 ≤ 0 ∧ arg10 − arg10 ≤ 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, 7, 9, 20 using the following ranking functions, which are bounded by −23.

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

### 4 Location Addition

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

1* 24 1: x112 + x112 ≤ 0x112x112 ≤ 0x103 + x103 ≤ 0x103x103 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

### 5 Location Addition

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

1 22 1_var_snapshot: x112 + x112 ≤ 0x112x112 ≤ 0x103 + x103 ≤ 0x103x103 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

### 6 Location Addition

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

2* 31 2: x112 + x112 ≤ 0x112x112 ≤ 0x103 + x103 ≤ 0x103x103 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

### 7 Location Addition

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

2 29 2_var_snapshot: x112 + x112 ≤ 0x112x112 ≤ 0x103 + x103 ≤ 0x103x103 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

### 8 Location Addition

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

4* 38 4: x112 + x112 ≤ 0x112x112 ≤ 0x103 + x103 ≤ 0x103x103 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

### 9 Location Addition

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

4 36 4_var_snapshot: x112 + x112 ≤ 0x112x112 ≤ 0x103 + x103 ≤ 0x103x103 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

### 10 Location Addition

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

5* 45 5: x112 + x112 ≤ 0x112x112 ≤ 0x103 + x103 ≤ 0x103x103 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

### 11 Location Addition

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

5 43 5_var_snapshot: x112 + x112 ≤ 0x112x112 ≤ 0x103 + x103 ≤ 0x103x103 ≤ 0arg9P + arg9P ≤ 0arg9Parg9P ≤ 0arg9 + arg9 ≤ 0arg9arg9 ≤ 0arg8P + arg8P ≤ 0arg8Parg8P ≤ 0arg8 + arg8 ≤ 0arg8arg8 ≤ 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 ≤ 0arg10P + arg10P ≤ 0arg10Parg10P ≤ 0arg10 + arg10 ≤ 0arg10arg10 ≤ 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 { 5, 5_var_snapshot, 5* }.

### 12.1.1 Transition Removal

We remove transitions 43, 45, 19 using the following ranking functions, which are bounded by −1.

 5: 1 + 3⋅arg1 5_var_snapshot: 3⋅arg1 5*: 2 + 3⋅arg1

### 12.1.2 Splitting Cut-Point Transitions

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

### 12.1.2.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 42.

### 12.1.2.1.1 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 { 4, 4_var_snapshot, 4* }.

### 12.2.1 Transition Removal

We remove transitions 36, 38, 8, 10, 11, 12, 13, 14, 16, 17, 18 using the following ranking functions, which are bounded by −1.

 4: 49 + 3⋅arg2 + 147⋅arg4 4_var_snapshot: 3⋅arg2 + 147⋅arg4 4*: 98 + 3⋅arg2 + 147⋅arg4

### 12.2.2 Transition Removal

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

 4: 0 4_var_snapshot: arg1 4*: 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 35.

### 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 { 2, 2_var_snapshot, 2* }.

### 12.3.1 Transition Removal

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

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

### 12.3.2 Transition Removal

We remove transition 31 using the following ranking functions, which are bounded by −2.

 2: −1 2_var_snapshot: −2⋅arg1 2*: 0

### 12.3.3 Transition Removal

We remove transition 29 using the following ranking functions, which are bounded by 0.

 2: arg1 2_var_snapshot: 0 2*: 0

### 12.3.4 Splitting Cut-Point Transitions

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

### 12.3.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 28.

### 12.3.4.1.1 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, 3, 1_var_snapshot, 1* }.

### 12.4.1 Transition Removal

We remove transitions 2, 5 using the following ranking functions, which are bounded by −1.

 1: 1 − 4⋅arg3 + 4⋅arg4 3: −4⋅arg3 + 4⋅arg5 − arg7 − 96⋅arg7P + 96⋅arg9P 1_var_snapshot: −4⋅arg3 + 4⋅arg4 1*: 2 − 4⋅arg3 + 4⋅arg4

### 12.4.2 Transition Removal

We remove transitions 22, 24, 4 using the following ranking functions, which are bounded by −1.

 1: 0 3: arg1 + arg2 1_var_snapshot: −1 1*: arg1P

### 12.4.3 Transition Removal

We remove transition 6 using the following ranking functions, which are bounded by 105.

 1: 0 3: arg2P 1_var_snapshot: 0 1*: 0

### 12.4.4 Splitting Cut-Point Transitions

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

### 12.4.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 21.

### 12.4.4.1.1 Splitting Cut-Point Transitions

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

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