LTS Termination Proof

by T2Cert

Input

Integer Transition System

Initial Location: 7

Transitions: (pre-variables and post-variables)

0	0	1:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ − arg2 ≤ 0 ∧ arg2 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 0
0	1	1:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ −1 + arg1P − arg1 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 2 − arg1P ≤ 0 ∧ − arg2 ≤ 0 ∧ arg2 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 0
0	2	2:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − x6 ≤ 0 ∧ 3 − arg1P ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ −1 + arg2 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 0
0	3	2:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ −1 + arg1P − arg1 ≤ 0 ∧ − x64 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 2 − arg1P ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ −1 + arg2 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 0
0	4	3:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 − arg2 ≤ 0 ∧ − x15 ≤ 0 ∧ − x14 ≤ 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 ∧ − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0
0	5	3:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 − arg2 ≤ 0 ∧ − x21 ≤ 0 ∧ − x20 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ −1 − arg1 + arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 2 − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 0
0	6	4:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ arg2 ≤ 0 ∧ 10 − arg1P ≤ 0 ∧ −10 + arg1P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 0
0	7	4:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − x69 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ −1 + arg2 ≤ 0 ∧ 10 − arg1P ≤ 0 ∧ −10 + arg1P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 0
0	8	4:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 − arg2 ≤ 0 ∧ − x28 ≤ 0 ∧ − x27 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 0
4	9	4:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ 0 ≤ 0 ∧ −1 − arg1P + arg1 ≤ 0 ∧ 1 + arg1P − arg1 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 0
4	10	5:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 5 − arg1P ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ −1 + arg1 − arg2P ≤ 0 ∧ 1 − arg1 + arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 0
4	11	5:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 4 − arg1P ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ −1 + arg1 − arg2P ≤ 0 ∧ 1 − arg1 + arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 0
5	12	4:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ − arg1P + arg2 ≤ 0 ∧ arg1P − arg2 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 0
1	13	6:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ 1 − arg1 + arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 0
2	14	6:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ 1 − arg1 + arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 0
3	15	6:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg2 ≤ 0 ∧ 2 − x46 ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 0
6	16	6:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 + arg1P − arg1 ≤ 0 ∧ arg1P − arg2 ≤ 0 ∧ 3 − arg1 + arg2P ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 0
6	17	6:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 + arg1P − arg1 ≤ 0 ∧ 3 − arg1 + arg2P ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 0
7	18	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 ∧ − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 0

Proof

1 Invariant Updates

The following invariants are asserted.

0:	TRUE
1:	1 − arg1P ≤ 0 ∧ 1 − arg1 ≤ 0
2:	1 − arg1P ≤ 0 ∧ 1 − arg1 ≤ 0
3:	1 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0
4:	TRUE
5:	1 − arg1P ≤ 0 ∧ 1 − arg1 ≤ 0
6:	1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0
7:	TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

nodes (location) invariant:

0	(0)	TRUE
1	(1)	1 − arg1P ≤ 0 ∧ 1 − arg1 ≤ 0
2	(2)	1 − arg1P ≤ 0 ∧ 1 − arg1 ≤ 0
3	(3)	1 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0
4	(4)	TRUE
5	(5)	1 − arg1P ≤ 0 ∧ 1 − arg1 ≤ 0
6	(6)	1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0
7	(7)	TRUE

initial node: 7
cover edges:
transition edges:

0 0 1

0 1 1

0 2 2

0 3 2

0 4 3

0 5 3

0 6 4

0 7 4

0 8 4

1 13 6

2 14 6

3 15 6

4 9 4

4 10 5

4 11 5

5 12 4

6 16 6

6 17 6

7 18 0

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

4	19	4:	− x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 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	26	6:	− x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 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, 1, 2, 3, 4, 5, 6, 7, 8, 13, 14, 15, 18 using the following ranking functions, which are bounded by −21.

7:	0
0:	0
1:	0
2:	0
3:	0
6:	0
4:	0
5:	0
7:	−8
0:	−9
1:	−10
2:	−11
3:	−12
6:	−13
6_var_snapshot:	−13
6*:	−13
4:	−16
5:	−16
4_var_snapshot:	−16
4*:	−16

4 Location Addition

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

4* 22 4: − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 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.

4 20 4_var_snapshot: − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 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.

6* 29 6: − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 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.

6 27 6_var_snapshot: − x69 + x69 ≤ 0 ∧ x69 − x69 ≤ 0 ∧ − x64 + x64 ≤ 0 ∧ x64 − x64 ≤ 0 ∧ − x6 + x6 ≤ 0 ∧ x6 − x6 ≤ 0 ∧ − x46 + x46 ≤ 0 ∧ x46 − x46 ≤ 0 ∧ − x28 + x28 ≤ 0 ∧ x28 − x28 ≤ 0 ∧ − x27 + x27 ≤ 0 ∧ x27 − x27 ≤ 0 ∧ − x21 + x21 ≤ 0 ∧ x21 − x21 ≤ 0 ∧ − x20 + x20 ≤ 0 ∧ x20 − x20 ≤ 0 ∧ − x15 + x15 ≤ 0 ∧ x15 − x15 ≤ 0 ∧ − x14 + x14 ≤ 0 ∧ x14 − x14 ≤ 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 { 6, 6_var_snapshot, 6* }.

8.1.1 Transition Removal

We remove transitions 27, 29, 16, 17 using the following ranking functions, which are bounded by 2.

6:	2 + 3⋅arg1
6_var_snapshot:	3⋅arg1
6*:	4 + 3⋅arg1

8.1.2 Splitting Cut-Point Transitions

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

8.1.2.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 26.

8.1.2.1.1 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 9, 10, 11, 12 using the following ranking functions, which are bounded by 6.

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

8.2.2 Transition Removal

We remove transition 20 using the following ranking functions, which are bounded by −1.

4:	0
5:	0
4_var_snapshot:	−1
4*:	1

8.2.3 Transition Removal

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

4:	−1
5:	0
4_var_snapshot:	0
4*:	0

8.2.4 Splitting Cut-Point Transitions

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

8.2.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 19.

8.2.4.1.1 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	1 1
0	2 2
0	3 2
0	4 3
0	5 3
0	6 4
0	7 4
0	8 4
1	13 6
2	14 6
3	15 6
4	9 4
4	10 5
4	11 5
5	12 4
6	16 6
6	17 6
7	18 0