LTS Termination Proof

by T2Cert

Input

Integer Transition System

Initial Location: 4

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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ 10 − arg2 ≤ 0 ∧ 10 − arg2P ≤ 0 ∧ 5 − arg2 + arg6 ≤ 0 ∧ 3 − arg2 + arg7 ≤ 0 ∧ − arg3P ≤ 0 ∧ arg3P ≤ 0 ∧ − arg4P ≤ 0 ∧ arg4P ≤ 0 ∧ arg3 − arg5P ≤ 0 ∧ − arg3 + arg5P ≤ 0 ∧ − arg7P ≤ 0 ∧ arg7P ≤ 0 ∧ − arg8P ≤ 0 ∧ arg8P ≤ 0 ∧ − arg9P ≤ 0 ∧ arg9P ≤ 0 ∧ − arg13P + arg3 ≤ 0 ∧ arg13P − arg3 ≤ 0 ∧ − arg14P + arg4 ≤ 0 ∧ arg14P − arg4 ≤ 0 ∧ − arg15P + arg4 ≤ 0 ∧ arg15P − arg4 ≤ 0 ∧ − arg17P + arg5 ≤ 0 ∧ arg17P − arg5 ≤ 0 ∧ − arg18P + arg6 ≤ 0 ∧ arg18P − arg6 ≤ 0 ∧ − arg19P + arg7 ≤ 0 ∧ arg19P − arg7 ≤ 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 ∧ − arg11P + arg11 ≤ 0 ∧ arg11P − arg11 ≤ 0 ∧ − arg12P + arg12 ≤ 0 ∧ arg12P − arg12 ≤ 0 ∧ − arg13P + arg13 ≤ 0 ∧ arg13P − arg13 ≤ 0 ∧ − arg14P + arg14 ≤ 0 ∧ arg14P − arg14 ≤ 0 ∧ − arg15P + arg15 ≤ 0 ∧ arg15P − arg15 ≤ 0 ∧ − arg16P + arg16 ≤ 0 ∧ arg16P − arg16 ≤ 0 ∧ − arg17P + arg17 ≤ 0 ∧ arg17P − arg17 ≤ 0 ∧ − arg18P + arg18 ≤ 0 ∧ arg18P − arg18 ≤ 0 ∧ − arg19P + arg19 ≤ 0 ∧ arg19P − arg19 ≤ 0 ∧ − arg20P + arg20 ≤ 0 ∧ arg20P − arg20 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0
2	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 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 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 ∧ −7 − arg1 + arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 8 − arg2P ≤ 0 ∧ 1 − arg5P ≤ 0 ∧ −1 + arg5P ≤ 0 ∧ − arg6P ≤ 0 ∧ arg6P ≤ 0 ∧ − arg7P ≤ 0 ∧ arg7P ≤ 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 ∧ − arg11P + arg11 ≤ 0 ∧ arg11P − arg11 ≤ 0 ∧ − arg12P + arg12 ≤ 0 ∧ arg12P − arg12 ≤ 0 ∧ − arg13P + arg13 ≤ 0 ∧ arg13P − arg13 ≤ 0 ∧ − arg14P + arg14 ≤ 0 ∧ arg14P − arg14 ≤ 0 ∧ − arg15P + arg15 ≤ 0 ∧ arg15P − arg15 ≤ 0 ∧ − arg16P + arg16 ≤ 0 ∧ arg16P − arg16 ≤ 0 ∧ − arg17P + arg17 ≤ 0 ∧ arg17P − arg17 ≤ 0 ∧ − arg18P + arg18 ≤ 0 ∧ arg18P − arg18 ≤ 0 ∧ − arg19P + arg19 ≤ 0 ∧ arg19P − arg19 ≤ 0 ∧ − arg20P + arg20 ≤ 0 ∧ arg20P − arg20 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 12 − arg2 ≤ 0 ∧ 12 − arg1P ≤ 0 ∧ 5 + arg18 − arg2 ≤ 0 ∧ 3 + arg19 − arg2 ≤ 0 ∧ arg1 − arg2P ≤ 0 ∧ − arg1 + arg2P ≤ 0 ∧ − arg3P + arg4 ≤ 0 ∧ arg3P − arg4 ≤ 0 ∧ − arg4P + arg5 ≤ 0 ∧ arg4P − arg5 ≤ 0 ∧ arg11 − arg5P ≤ 0 ∧ − arg11 + arg5P ≤ 0 ∧ arg10 − arg6P ≤ 0 ∧ − arg10 + arg6P ≤ 0 ∧ arg3 − arg7P ≤ 0 ∧ − arg3 + arg7P ≤ 0 ∧ arg6 − arg8P ≤ 0 ∧ − arg6 + arg8P ≤ 0 ∧ arg7 − arg9P ≤ 0 ∧ − arg7 + arg9P ≤ 0 ∧ − arg10P + arg8 ≤ 0 ∧ arg10P − arg8 ≤ 0 ∧ − arg11P + arg9 ≤ 0 ∧ arg11P − arg9 ≤ 0 ∧ − arg16P + arg17 ≤ 0 ∧ arg16P − arg17 ≤ 0 ∧ − arg17P + arg18 ≤ 0 ∧ arg17P − arg18 ≤ 0 ∧ arg19 − arg20P ≤ 0 ∧ − arg19 + arg20P ≤ 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 ∧ − arg11P + arg11 ≤ 0 ∧ arg11P − arg11 ≤ 0 ∧ − arg16P + arg16 ≤ 0 ∧ arg16P − arg16 ≤ 0 ∧ − arg17P + arg17 ≤ 0 ∧ arg17P − arg17 ≤ 0 ∧ − arg18P + arg18 ≤ 0 ∧ arg18P − arg18 ≤ 0 ∧ − arg19P + arg19 ≤ 0 ∧ arg19P − arg19 ≤ 0 ∧ − arg20P + arg20 ≤ 0 ∧ arg20P − arg20 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0 ∧ − arg15P + arg15P ≤ 0 ∧ arg15P − arg15P ≤ 0 ∧ − arg15 + arg15 ≤ 0 ∧ arg15 − arg15 ≤ 0 ∧ − arg14P + arg14P ≤ 0 ∧ arg14P − arg14P ≤ 0 ∧ − arg14 + arg14 ≤ 0 ∧ arg14 − arg14 ≤ 0 ∧ − arg13P + arg13P ≤ 0 ∧ arg13P − arg13P ≤ 0 ∧ − arg13 + arg13 ≤ 0 ∧ arg13 − arg13 ≤ 0 ∧ − arg12P + arg12P ≤ 0 ∧ arg12P − arg12P ≤ 0 ∧ − arg12 + arg12 ≤ 0 ∧ arg12 − arg12 ≤ 0
3	3	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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 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 ≤ 0 ∧ − x41 ≤ 0 ∧ 1 − arg16 ≤ 0 ∧ 1 + arg16 − x41 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 1 − arg7 ≤ 0 ∧ 1 − arg6 ≤ 0 ∧ 1 − arg5 ≤ 0 ∧ 1 − arg15 ≤ 0 ∧ − x76 ≤ 0 ∧ 1 − arg9 ≤ 0 ∧ 1 − arg12 ≤ 0 ∧ 1 − arg10 ≤ 0 ∧ 1 − arg14 ≤ 0 ∧ 1 − arg13 ≤ 0 ∧ 1 − arg11 ≤ 0 ∧ 1 − arg8 ≤ 0 ∧ − arg20 ≤ 0 ∧ − arg17 ≤ 0 ∧ 12 − arg1 ≤ 0 ∧ 12 − arg1P ≤ 0 ∧ 5 + arg17 − arg1 ≤ 0 ∧ 11 + arg18 − arg1 ≤ 0 ∧ 3 − arg1 + arg20 ≤ 0 ∧ 9 + arg19 − arg1 ≤ 0 ∧ −1 − arg2P + arg2 ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ 1 − arg16P + arg16 ≤ 0 ∧ −1 + arg16P − arg16 ≤ 0 ∧ 1 − arg17P + arg17 ≤ 0 ∧ −1 + arg17P − arg17 ≤ 0 ∧ 1 − arg20P + arg20 ≤ 0 ∧ −1 + arg20P − arg20 ≤ 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 ∧ − arg8P + arg8 ≤ 0 ∧ arg8P − arg8 ≤ 0 ∧ − arg9P + arg9 ≤ 0 ∧ arg9P − arg9 ≤ 0 ∧ − arg10P + arg10 ≤ 0 ∧ arg10P − arg10 ≤ 0 ∧ − arg11P + arg11 ≤ 0 ∧ arg11P − arg11 ≤ 0 ∧ − arg12P + arg12 ≤ 0 ∧ arg12P − arg12 ≤ 0 ∧ − arg13P + arg13 ≤ 0 ∧ arg13P − arg13 ≤ 0 ∧ − arg14P + arg14 ≤ 0 ∧ arg14P − arg14 ≤ 0 ∧ − arg15P + arg15 ≤ 0 ∧ arg15P − arg15 ≤ 0 ∧ − arg16P + arg16 ≤ 0 ∧ arg16P − arg16 ≤ 0 ∧ − arg17P + arg17 ≤ 0 ∧ arg17P − arg17 ≤ 0 ∧ − arg18P + arg18 ≤ 0 ∧ arg18P − arg18 ≤ 0 ∧ − arg19P + arg19 ≤ 0 ∧ arg19P − arg19 ≤ 0 ∧ − arg20P + arg20 ≤ 0 ∧ arg20P − arg20 ≤ 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	4	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 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 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 ∧ − arg11P + arg11 ≤ 0 ∧ arg11P − arg11 ≤ 0 ∧ − arg12P + arg12 ≤ 0 ∧ arg12P − arg12 ≤ 0 ∧ − arg13P + arg13 ≤ 0 ∧ arg13P − arg13 ≤ 0 ∧ − arg14P + arg14 ≤ 0 ∧ arg14P − arg14 ≤ 0 ∧ − arg15P + arg15 ≤ 0 ∧ arg15P − arg15 ≤ 0 ∧ − arg16P + arg16 ≤ 0 ∧ arg16P − arg16 ≤ 0 ∧ − arg17P + arg17 ≤ 0 ∧ arg17P − arg17 ≤ 0 ∧ − arg18P + arg18 ≤ 0 ∧ arg18P − arg18 ≤ 0 ∧ − arg19P + arg19 ≤ 0 ∧ arg19P − arg19 ≤ 0 ∧ − arg20P + arg20 ≤ 0 ∧ arg20P − arg20 ≤ 0 ∧ − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 0

Proof

1 Invariant Updates

The following invariants are asserted.

0:	− arg1P ≤ 0 ∧ 8 − arg2P ≤ 0 ∧ −1 + arg5P ≤ 0 ∧ 1 − arg5P ≤ 0 ∧ arg6P ≤ 0 ∧ − arg6P ≤ 0 ∧ arg7P ≤ 0 ∧ − arg7P ≤ 0 ∧ − arg1 ≤ 0 ∧ 8 − arg2 ≤ 0 ∧ −1 + arg5 ≤ 0 ∧ 1 − arg5 ≤ 0 ∧ arg6 ≤ 0 ∧ − arg6 ≤ 0 ∧ arg7 ≤ 0 ∧ − arg7 ≤ 0
1:	− arg1P ≤ 0 ∧ 10 − arg2P ≤ 0 ∧ arg3P ≤ 0 ∧ − arg3P ≤ 0 ∧ arg4P ≤ 0 ∧ − arg4P ≤ 0 ∧ arg7P ≤ 0 ∧ − arg7P ≤ 0 ∧ arg8P ≤ 0 ∧ − arg8P ≤ 0 ∧ arg9P ≤ 0 ∧ − arg9P ≤ 0 ∧ −1 + arg17P ≤ 0 ∧ arg18P ≤ 0 ∧ arg19P ≤ 0 ∧ − arg1 ≤ 0 ∧ 10 − arg2 ≤ 0 ∧ arg3 ≤ 0 ∧ − arg3 ≤ 0 ∧ arg4 ≤ 0 ∧ − arg4 ≤ 0 ∧ arg7 ≤ 0 ∧ − arg7 ≤ 0 ∧ arg8 ≤ 0 ∧ − arg8 ≤ 0 ∧ arg9 ≤ 0 ∧ − arg9 ≤ 0 ∧ −1 + arg17 ≤ 0 ∧ arg18 ≤ 0 ∧ arg19 ≤ 0
2:	TRUE
3:	12 − arg1P ≤ 0 ∧ arg3P ≤ 0 ∧ 12 − arg1 ≤ 0 ∧ arg3 ≤ 0
4:	TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

nodes (location) invariant:

0	(0)	− arg1P ≤ 0 ∧ 8 − arg2P ≤ 0 ∧ −1 + arg5P ≤ 0 ∧ 1 − arg5P ≤ 0 ∧ arg6P ≤ 0 ∧ − arg6P ≤ 0 ∧ arg7P ≤ 0 ∧ − arg7P ≤ 0 ∧ − arg1 ≤ 0 ∧ 8 − arg2 ≤ 0 ∧ −1 + arg5 ≤ 0 ∧ 1 − arg5 ≤ 0 ∧ arg6 ≤ 0 ∧ − arg6 ≤ 0 ∧ arg7 ≤ 0 ∧ − arg7 ≤ 0
1	(1)	− arg1P ≤ 0 ∧ 10 − arg2P ≤ 0 ∧ arg3P ≤ 0 ∧ − arg3P ≤ 0 ∧ arg4P ≤ 0 ∧ − arg4P ≤ 0 ∧ arg7P ≤ 0 ∧ − arg7P ≤ 0 ∧ arg8P ≤ 0 ∧ − arg8P ≤ 0 ∧ arg9P ≤ 0 ∧ − arg9P ≤ 0 ∧ −1 + arg17P ≤ 0 ∧ arg18P ≤ 0 ∧ arg19P ≤ 0 ∧ − arg1 ≤ 0 ∧ 10 − arg2 ≤ 0 ∧ arg3 ≤ 0 ∧ − arg3 ≤ 0 ∧ arg4 ≤ 0 ∧ − arg4 ≤ 0 ∧ arg7 ≤ 0 ∧ − arg7 ≤ 0 ∧ arg8 ≤ 0 ∧ − arg8 ≤ 0 ∧ arg9 ≤ 0 ∧ − arg9 ≤ 0 ∧ −1 + arg17 ≤ 0 ∧ arg18 ≤ 0 ∧ arg19 ≤ 0
2	(2)	TRUE
3	(3)	12 − arg1P ≤ 0 ∧ arg3P ≤ 0 ∧ 12 − arg1 ≤ 0 ∧ arg3 ≤ 0
4	(4)	TRUE

initial node: 4
cover edges:
transition edges:

0 0 1

1 2 3

2 1 0

3 3 3

4 4 2

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

− x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 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 ∧ − arg20P + arg20P ≤ 0 ∧ arg20P − arg20P ≤ 0 ∧ − arg20 + arg20 ≤ 0 ∧ arg20 − arg20 ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg19P + arg19P ≤ 0 ∧ arg19P − arg19P ≤ 0 ∧ − arg19 + arg19 ≤ 0 ∧ arg19 − arg19 ≤ 0 ∧ − arg18P + arg18P ≤ 0 ∧ arg18P − arg18P ≤ 0 ∧ − arg18 + arg18 ≤ 0 ∧ arg18 − arg18 ≤ 0 ∧ − arg17P + arg17P ≤ 0 ∧ arg17P − arg17P ≤ 0 ∧ − arg17 + arg17 ≤ 0 ∧ arg17 − arg17 ≤ 0 ∧ − arg16P + arg16P ≤ 0 ∧ arg16P − arg16P ≤ 0 ∧ − arg16 + arg16 ≤ 0 ∧ arg16 − arg16 ≤ 0 ∧ − arg15P + arg15P ≤ 0 ∧ arg15P − arg15P ≤ 0 ∧ − arg15 + arg15 ≤ 0 ∧ arg15 − arg15 ≤ 0 ∧ − arg14P + arg14P ≤ 0 ∧ arg14P − arg14P ≤ 0 ∧ − arg14 + arg14 ≤ 0 ∧ arg14 − arg14 ≤ 0 ∧ − arg13P + arg13P ≤ 0 ∧ arg13P − arg13P ≤ 0 ∧ − arg13 + arg13 ≤ 0 ∧ arg13 − arg13 ≤ 0 ∧ − arg12P + arg12P ≤ 0 ∧ arg12P − arg12P ≤ 0 ∧ − arg12 + arg12 ≤ 0 ∧ arg12 − arg12 ≤ 0 ∧ − arg11P + arg11P ≤ 0 ∧ arg11P − arg11P ≤ 0 ∧ − arg11 + arg11 ≤ 0 ∧ arg11 − arg11 ≤ 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, 2, 4 using the following ranking functions, which are bounded by −15.

4:	0
2:	0
0:	0
1:	0
3:	0
4:	−6
2:	−7
0:	−8
1:	−9
3:	−10
3_var_snapshot:	−10
3*:	−10

4 Location Addition

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

3* 8 3: − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 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 ∧ − arg20P + arg20P ≤ 0 ∧ arg20P − arg20P ≤ 0 ∧ − arg20 + arg20 ≤ 0 ∧ arg20 − arg20 ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg19P + arg19P ≤ 0 ∧ arg19P − arg19P ≤ 0 ∧ − arg19 + arg19 ≤ 0 ∧ arg19 − arg19 ≤ 0 ∧ − arg18P + arg18P ≤ 0 ∧ arg18P − arg18P ≤ 0 ∧ − arg18 + arg18 ≤ 0 ∧ arg18 − arg18 ≤ 0 ∧ − arg17P + arg17P ≤ 0 ∧ arg17P − arg17P ≤ 0 ∧ − arg17 + arg17 ≤ 0 ∧ arg17 − arg17 ≤ 0 ∧ − arg16P + arg16P ≤ 0 ∧ arg16P − arg16P ≤ 0 ∧ − arg16 + arg16 ≤ 0 ∧ arg16 − arg16 ≤ 0 ∧ − arg15P + arg15P ≤ 0 ∧ arg15P − arg15P ≤ 0 ∧ − arg15 + arg15 ≤ 0 ∧ arg15 − arg15 ≤ 0 ∧ − arg14P + arg14P ≤ 0 ∧ arg14P − arg14P ≤ 0 ∧ − arg14 + arg14 ≤ 0 ∧ arg14 − arg14 ≤ 0 ∧ − arg13P + arg13P ≤ 0 ∧ arg13P − arg13P ≤ 0 ∧ − arg13 + arg13 ≤ 0 ∧ arg13 − arg13 ≤ 0 ∧ − arg12P + arg12P ≤ 0 ∧ arg12P − arg12P ≤ 0 ∧ − arg12 + arg12 ≤ 0 ∧ arg12 − arg12 ≤ 0 ∧ − arg11P + arg11P ≤ 0 ∧ arg11P − arg11P ≤ 0 ∧ − arg11 + arg11 ≤ 0 ∧ arg11 − arg11 ≤ 0 ∧ − arg10P + arg10P ≤ 0 ∧ arg10P − arg10P ≤ 0 ∧ − arg10 + arg10 ≤ 0 ∧ arg10 − arg10 ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0

5 Location Addition

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

3 6 3_var_snapshot: − x76 + x76 ≤ 0 ∧ x76 − x76 ≤ 0 ∧ − x41 + x41 ≤ 0 ∧ x41 − x41 ≤ 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 ∧ − arg20P + arg20P ≤ 0 ∧ arg20P − arg20P ≤ 0 ∧ − arg20 + arg20 ≤ 0 ∧ arg20 − arg20 ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg19P + arg19P ≤ 0 ∧ arg19P − arg19P ≤ 0 ∧ − arg19 + arg19 ≤ 0 ∧ arg19 − arg19 ≤ 0 ∧ − arg18P + arg18P ≤ 0 ∧ arg18P − arg18P ≤ 0 ∧ − arg18 + arg18 ≤ 0 ∧ arg18 − arg18 ≤ 0 ∧ − arg17P + arg17P ≤ 0 ∧ arg17P − arg17P ≤ 0 ∧ − arg17 + arg17 ≤ 0 ∧ arg17 − arg17 ≤ 0 ∧ − arg16P + arg16P ≤ 0 ∧ arg16P − arg16P ≤ 0 ∧ − arg16 + arg16 ≤ 0 ∧ arg16 − arg16 ≤ 0 ∧ − arg15P + arg15P ≤ 0 ∧ arg15P − arg15P ≤ 0 ∧ − arg15 + arg15 ≤ 0 ∧ arg15 − arg15 ≤ 0 ∧ − arg14P + arg14P ≤ 0 ∧ arg14P − arg14P ≤ 0 ∧ − arg14 + arg14 ≤ 0 ∧ arg14 − arg14 ≤ 0 ∧ − arg13P + arg13P ≤ 0 ∧ arg13P − arg13P ≤ 0 ∧ − arg13 + arg13 ≤ 0 ∧ arg13 − arg13 ≤ 0 ∧ − arg12P + arg12P ≤ 0 ∧ arg12P − arg12P ≤ 0 ∧ − arg12 + arg12 ≤ 0 ∧ arg12 − arg12 ≤ 0 ∧ − arg11P + arg11P ≤ 0 ∧ arg11P − arg11P ≤ 0 ∧ − arg11 + arg11 ≤ 0 ∧ arg11 − arg11 ≤ 0 ∧ − arg10P + arg10P ≤ 0 ∧ arg10P − arg10P ≤ 0 ∧ − arg10 + arg10 ≤ 0 ∧ arg10 − arg10 ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0

6 SCC Decomposition

We consider subproblems for each of the 1 SCC(s) of the program graph.

6.1 SCC Subproblem 1/1

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

6.1.1 Transition Removal

We remove transitions 6, 3 using the following ranking functions, which are bounded by −1.

3:	1
3_var_snapshot:	0
3*:	2

6.1.2 Transition Removal

We remove transition 8 using the following ranking functions, which are bounded by 11.

3:	0
3_var_snapshot:	0
3*:	arg1P

6.1.3 Splitting Cut-Point Transitions

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

6.1.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 5.

6.1.3.1.1 Splitting Cut-Point Transitions

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

Tool configuration

T2Cert

version: 1.0