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 ∧ arg1P − arg1 ≤ 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 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0
0	3	4:	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 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0
0	5	6:	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 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0
6	6	7:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − x25 ≤ 0 ∧ − arg2P ≤ 0 ∧ −3 + arg1P − arg1 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 4 − arg1P ≤ 0 ∧ 1 − arg4P + x25 ≤ 0 ∧ −1 + arg4P − x25 ≤ 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 ∧ − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0
4	7	7:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − x30 ≤ 0 ∧ − arg2P ≤ 0 ∧ −1 + arg1P − arg1 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 2 − arg1P ≤ 0 ∧ 1 − arg4P + x30 ≤ 0 ∧ −1 + arg4P − x30 ≤ 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 ∧ − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0
7	8	7:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 2 + arg1P − arg1 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 2 − arg1 ≤ 0 ∧ − arg1P ≤ 0 ∧ −1 − arg2P + arg2 ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 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
7	9	7:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ 1 − x45 ≤ 0 ∧ −2 + arg1P − arg1 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 4 − arg1P ≤ 0 ∧ −1 − arg2P + arg2 ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0
7	10	7:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ 1 − x52 ≤ 0 ∧ −2 + arg1P − arg1 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 4 − arg1P ≤ 0 ∧ −1 − arg2P + arg2 ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0
7	11	7:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ 1 − x59 ≤ 0 ∧ −3 + arg1P − arg1 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 6 − arg1P ≤ 0 ∧ −1 − arg2P + arg2 ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0
7	12	7:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ 1 − x66 ≤ 0 ∧ −3 + arg1P − arg1 ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 6 − arg1P ≤ 0 ∧ −1 − arg2P + arg2 ≤ 0 ∧ 1 + arg2P − arg2 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0
0	13	8:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg1 + arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ 1 − arg1P ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg3P ≤ 0 ∧ arg3P ≤ 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 ∧ − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0
7	14	8:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ − arg3 ≤ 0 ∧ 2 − arg1 + arg2P ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 1 − arg2P ≤ 0 ∧ − arg3P + arg4 ≤ 0 ∧ arg3P − 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 ∧ − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0
7	15	8:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg2 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ 1 − arg3P ≤ 0 ∧ − arg3 ≤ 0 ∧ 2 − arg1 + arg2P ≤ 0 ∧ 3 − arg1 ≤ 0 ∧ 1 − 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 ∧ − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0
1	16	9:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ arg1P − arg2 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg1P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0
9	17	9:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg3 ≤ 0 ∧ −42 + x93 ≤ 0 ∧ − x93 ≤ 0 ∧ 1 + arg1P − arg1 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg1P ≤ 0 ∧ 1 − arg3P + arg3 ≤ 0 ∧ −1 + arg3P − arg3 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0
9	18	9:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg2 ≤ 0 ∧ 43 − x98 ≤ 0 ∧ − arg3 ≤ 0 ∧ 1 + arg1P − arg1 ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg1P ≤ 0 ∧ 1 − arg3P + arg3 ≤ 0 ∧ −1 + arg3P − arg3 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0
10	19	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 ∧ − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 0

Proof

1 Invariant Updates

The following invariants are asserted.

0:	TRUE
1:	1 − arg1P ≤ 0 ∧ − arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg2 ≤ 0
4:	1 − arg1P ≤ 0 ∧ 1 − arg1 ≤ 0
6:	1 − arg1P ≤ 0 ∧ 1 − arg1 ≤ 0
7:	TRUE
8:	1 − arg2P ≤ 0 ∧ 1 − arg2 ≤ 0
9:	− arg1P ≤ 0 ∧ − arg1 ≤ 0
10:	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
4	(4)	1 − arg1P ≤ 0 ∧ 1 − arg1 ≤ 0
6	(6)	1 − arg1P ≤ 0 ∧ 1 − arg1 ≤ 0
7	(7)	TRUE
8	(8)	1 − arg2P ≤ 0 ∧ 1 − arg2 ≤ 0
9	(9)	− arg1P ≤ 0 ∧ − arg1 ≤ 0
10	(10)	TRUE

initial node: 10
cover edges:
transition edges:

0 0 1

0 3 4

0 5 6

0 13 8

1 16 9

4 7 7

6 6 7

7 8 7

7 9 7

7 10 7

7 11 7

7 12 7

7 14 8

7 15 8

9 17 9

9 18 9

10 19 0

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

7	20	7:	− x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 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	27	9:	− x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 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, 3, 5, 6, 7, 13, 14, 15, 16, 19 using the following ranking functions, which are bounded by −23.

10:	0
0:	0
1:	0
9:	0
4:	0
6:	0
7:	0
8:	0
10:	−9
0:	−10
1:	−11
9:	−12
9_var_snapshot:	−12
9*:	−12
4:	−15
6:	−16
7:	−17
7_var_snapshot:	−17
7*:	−17
8:	−21

4 Location Addition

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

7* 23 7: − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 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.

7 21 7_var_snapshot: − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 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.

9* 30 9: − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 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.

9 28 9_var_snapshot: − x98 + x98 ≤ 0 ∧ x98 − x98 ≤ 0 ∧ − x93 + x93 ≤ 0 ∧ x93 − x93 ≤ 0 ∧ − x66 + x66 ≤ 0 ∧ x66 − x66 ≤ 0 ∧ − x59 + x59 ≤ 0 ∧ x59 − x59 ≤ 0 ∧ − x52 + x52 ≤ 0 ∧ x52 − x52 ≤ 0 ∧ − x45 + x45 ≤ 0 ∧ x45 − x45 ≤ 0 ∧ − x30 + x30 ≤ 0 ∧ x30 − x30 ≤ 0 ∧ − x25 + x25 ≤ 0 ∧ x25 − x25 ≤ 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 { 9, 9_var_snapshot, 9* }.

8.1.1 Transition Removal

We remove transitions 28, 30, 17, 18 using the following ranking functions, which are bounded by −1.

9:	1 + 3⋅arg1
9_var_snapshot:	3⋅arg1
9*:	2 + 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 27.

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 { 7, 7_var_snapshot, 7* }.

8.2.1 Transition Removal

We remove transitions 8, 9, 10, 11, 12 using the following ranking functions, which are bounded by 2.

7:	1 + 3⋅arg2
7_var_snapshot:	3⋅arg2
7*:	2 + 3⋅arg2

8.2.2 Transition Removal

We remove transition 21 using the following ranking functions, which are bounded by −1.

7:	0
7_var_snapshot:	−1
7*:	1

8.2.3 Transition Removal

We remove transition 23 using the following ranking functions, which are bounded by 0.

7:	0
7_var_snapshot:	0
7*:	1

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 20.

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	3 4
0	5 6
0	13 8
1	16 9
4	7 7
6	6 7
7	8 7
7	9 7
7	10 7
7	11 7
7	12 7
7	14 8
7	15 8
9	17 9
9	18 9
10	19 0