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 ∧ arg1P − arg1 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 3 − 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 ∧ − x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0
0	2	3:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ − arg2 ≤ 0 ∧ −2 + arg1P − arg1 ≤ 0 ∧ −2 − arg1 + arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 3 − arg2P ≤ 0 ∧ 1 − arg4P ≤ 0 ∧ −1 + 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 ∧ − x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0
3	3	3:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg4 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ 2 + arg2P − arg2 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ −1 − arg3P + arg3 ≤ 0 ∧ 1 + arg3P − arg3 ≤ 0 ∧ 1 − arg4P + arg4 ≤ 0 ∧ −1 + arg4P − 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 ∧ − x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0
3	4	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 ∧ 1 − arg3 ≤ 0 ∧ 1 − x30 ≤ 0 ∧ − arg4 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ 2 + arg2P − arg2 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ −1 − arg3P + arg3 ≤ 0 ∧ 1 + arg3P − arg3 ≤ 0 ∧ 1 − arg4P + arg4 ≤ 0 ∧ −1 + arg4P − 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 ∧ − x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0
3	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 ∧ 1 − arg3 ≤ 0 ∧ 1 − x37 ≤ 0 ∧ − arg4 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 2 − arg2 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 3 − arg2P ≤ 0 ∧ −1 − arg3P + arg3 ≤ 0 ∧ 1 + arg3P − arg3 ≤ 0 ∧ 1 − arg4P + arg4 ≤ 0 ∧ −1 + arg4P − 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 ∧ − x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0
3	6	3:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg4 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 2 − arg2 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 3 − arg2P ≤ 0 ∧ −1 − arg3P + arg3 ≤ 0 ∧ 1 + arg3P − arg3 ≤ 0 ∧ 1 − arg4P + arg4 ≤ 0 ∧ −1 + arg4P − 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 ∧ − x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0
3	7	3:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg4 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ −2 + arg1P − arg1 ≤ 0 ∧ −2 + arg1P − arg2 ≤ 0 ∧ −2 − arg1 + arg2P ≤ 0 ∧ −2 + arg2P − arg2 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 5 − arg1P ≤ 0 ∧ 5 − arg2P ≤ 0 ∧ −1 − arg3P + arg3 ≤ 0 ∧ 1 + arg3P − arg3 ≤ 0 ∧ 1 − arg4P + arg4 ≤ 0 ∧ −1 + arg4P − 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 ∧ − x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 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 ∧ 1 − arg3 ≤ 0 ∧ 1 − x56 ≤ 0 ∧ − arg4 ≤ 0 ∧ −2 + arg1P − arg1 ≤ 0 ∧ −2 + arg1P − arg2 ≤ 0 ∧ −2 − arg1 + arg2P ≤ 0 ∧ −2 + arg2P − arg2 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 5 − arg1P ≤ 0 ∧ 5 − arg2P ≤ 0 ∧ −1 − arg3P + arg3 ≤ 0 ∧ 1 + arg3P − arg3 ≤ 0 ∧ 1 − arg4P + arg4 ≤ 0 ∧ −1 + arg4P − 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 ∧ − x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0
0	9	4:	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 − arg2 ≤ 0 ∧ 1 − arg1 + arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ arg2 − arg3P ≤ 0 ∧ − arg2 + arg3P ≤ 0 ∧ 1 − arg4P ≤ 0 ∧ −1 + 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 ∧ − x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0
1	10	4:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg2 ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 3 − arg2P ≤ 0 ∧ 2 − arg2 + arg4 ≤ 0 ∧ arg3 − arg4P ≤ 0 ∧ − arg3 + 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 ∧ − x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0
4	11	5:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg3 ≤ 0 ∧ 42 − x75 ≤ 0 ∧ − arg4 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ arg1P − arg2 ≤ 0 ∧ 1 − arg1 + arg2P ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 2 − arg1 + arg5P ≤ 0 ∧ 2 − arg2 + arg5P ≤ 0 ∧ 1 − arg4P + arg4 ≤ 0 ∧ −1 + arg4P − arg4 ≤ 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 ∧ − x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0
4	12	5:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg3 ≤ 0 ∧ − arg4 ≤ 0 ∧ −41 + x83 ≤ 0 ∧ − x83 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ arg1P − arg2 ≤ 0 ∧ 2 − arg1 + arg2P ≤ 0 ∧ 2 + arg2P − arg2 ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ 2 − arg2 ≤ 0 ∧ 2 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 2 − arg1 + arg5P ≤ 0 ∧ 2 − arg2 + arg5P ≤ 0 ∧ 1 − arg4P + arg4 ≤ 0 ∧ −1 + arg4P − arg4 ≤ 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 ∧ − x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0
4	13	4:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg3 ≤ 0 ∧ − arg4 ≤ 0 ∧ −41 + x90 ≤ 0 ∧ − x90 ≤ 0 ∧ 2 + arg1P − arg1 ≤ 0 ∧ 2 + arg1P − arg2 ≤ 0 ∧ 2 − arg1 + arg2P ≤ 0 ∧ 2 + arg2P − arg2 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 1 − arg4P + arg4 ≤ 0 ∧ −1 + arg4P − arg4 ≤ 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 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0
5	14	4:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 + arg1P − arg1 ≤ 0 ∧ arg1P − arg2 ≤ 0 ∧ 2 − arg1 + arg2P ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 2 − arg1 + arg5 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0
6	15	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 ∧ − x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0

Proof

1 Invariant Updates

The following invariants are asserted.

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

The invariants are proved as follows.

IMPACT Invariant Proof

nodes (location) invariant:

0	(0)	TRUE
1	(1)	1 − arg1P ≤ 0 ∧ 3 − arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 3 − arg2 ≤ 0
3	(3)	3 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ − arg2 ≤ 0
4	(4)	− arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − arg1 ≤ 0 ∧ − arg2 ≤ 0
5	(5)	1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg3 ≤ 0
6	(6)	TRUE

initial node: 6
cover edges:
transition edges:

0 0 1

0 2 3

0 9 4

1 10 4

3 3 3

3 4 3

3 5 3

3 6 3

3 7 3

3 8 3

4 11 5

4 12 5

4 13 4

5 14 4

6 15 0

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

3	16	3:	− x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 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	23	4:	− x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 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, 9, 10, 15 using the following ranking functions, which are bounded by −17.

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

4 Location Addition

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

3* 19 3: − x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 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 Location Addition

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

3 17 3_var_snapshot: − x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 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 Location Addition

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

4* 26 4: − x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 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 Location Addition

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

4 24 4_var_snapshot: − x90 + x90 ≤ 0 ∧ x90 − x90 ≤ 0 ∧ − x83 + x83 ≤ 0 ∧ x83 − x83 ≤ 0 ∧ − x75 + x75 ≤ 0 ∧ x75 − x75 ≤ 0 ∧ − x56 + x56 ≤ 0 ∧ x56 − x56 ≤ 0 ∧ − x37 + x37 ≤ 0 ∧ x37 − x37 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 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

8 SCC Decomposition

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

8.1 SCC Subproblem 1/2

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

8.1.1 Transition Removal

We remove transitions 3, 4, 5, 6, 7, 8 using the following ranking functions, which are bounded by 2.

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

8.1.2 Transition Removal

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

3:	0
3_var_snapshot:	−1
3*:	1

8.1.3 Transition Removal

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

3:	0
3_var_snapshot:	−1
3*:	0

8.1.4 Splitting Cut-Point Transitions

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

8.1.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 16.

8.1.4.1.1 Splitting Cut-Point Transitions

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

8.2 SCC Subproblem 2/2

Here we consider the SCC { 4, 5, 4_var_snapshot, 4* }.

8.2.1 Transition Removal

We remove transitions 24, 26, 12, 13, 14 using the following ranking functions, which are bounded by −4.

4:	−2 + 4⋅arg1
5:	4⋅arg2
4_var_snapshot:	−3 + 4⋅arg1
4*:	−1 + 4⋅arg1

8.2.2 Transition Removal

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

4:	0
5:	−1
4_var_snapshot:	0
4*:	0

8.2.3 Splitting Cut-Point Transitions

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

8.2.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 23.

8.2.3.1.1 Splitting Cut-Point Transitions

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

Tool configuration

T2Cert

version: 1.0

0	0 1
0	2 3
0	9 4
1	10 4
3	3 3
3	4 3
3	5 3
3	6 3
3	7 3
3	8 3
4	11 5
4	12 5
4	13 4
5	14 4
6	15 0