LTS Termination Proof

by T2Cert

Input

Integer Transition System

Initial Location: 8

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 ∧ oldX0_post − x0_0 ≤ 0 ∧ − oldX0_post + x0_0 ≤ 0 ∧ oldX1_post − x1_0 ≤ 0 ∧ − oldX1_post + x1_0 ≤ 0 ∧ − oldX2_post + x0_post ≤ 0 ∧ oldX2_post − x0_post ≤ 0 ∧ − oldX3_post + x1_post ≤ 0 ∧ oldX3_post − x1_post ≤ 0 ∧ oldX0_0 − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_post ≤ 0 ∧ oldX1_0 − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_post ≤ 0 ∧ oldX2_0 − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_post ≤ 0 ∧ oldX3_0 − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_post ≤ 0 ∧ x0_0 − x0_post ≤ 0 ∧ − x0_0 + x0_post ≤ 0 ∧ x1_0 − x1_post ≤ 0 ∧ − x1_0 + x1_post ≤ 0
0	1	2:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ oldX0_post − x0_0 ≤ 0 ∧ − oldX0_post + x0_0 ≤ 0 ∧ oldX1_post − x1_0 ≤ 0 ∧ − oldX1_post + x1_0 ≤ 0 ∧ 1 − oldX0_post + x0_post ≤ 0 ∧ −1 + oldX0_post − x0_post ≤ 0 ∧ − oldX2_post + x1_post ≤ 0 ∧ oldX2_post − x1_post ≤ 0 ∧ oldX0_0 − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_post ≤ 0 ∧ oldX1_0 − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_post ≤ 0 ∧ oldX2_0 − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_post ≤ 0 ∧ x0_0 − x0_post ≤ 0 ∧ − x0_0 + x0_post ≤ 0 ∧ x1_0 − x1_post ≤ 0 ∧ − x1_0 + x1_post ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0
0	2	2:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ oldX0_post − x0_0 ≤ 0 ∧ − oldX0_post + x0_0 ≤ 0 ∧ oldX1_post − x1_0 ≤ 0 ∧ − oldX1_post + x1_0 ≤ 0 ∧ − oldX0_post + x0_post ≤ 0 ∧ oldX0_post − x0_post ≤ 0 ∧ 1 − oldX1_post + x1_post ≤ 0 ∧ −1 + oldX1_post − x1_post ≤ 0 ∧ oldX0_0 − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_post ≤ 0 ∧ oldX1_0 − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_post ≤ 0 ∧ x0_0 − x0_post ≤ 0 ∧ − x0_0 + x0_post ≤ 0 ∧ x1_0 − x1_post ≤ 0 ∧ − x1_0 + x1_post ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0 ∧ − oldX2_post + oldX2_post ≤ 0 ∧ oldX2_post − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_0 ≤ 0 ∧ oldX2_0 − oldX2_0 ≤ 0
3	3	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 ∧ oldX0_post − x0_0 ≤ 0 ∧ − oldX0_post + x0_0 ≤ 0 ∧ oldX1_post − x1_0 ≤ 0 ∧ − oldX1_post + x1_0 ≤ 0 ∧ − oldX2_post + x0_post ≤ 0 ∧ oldX2_post − x0_post ≤ 0 ∧ − oldX3_post + x1_post ≤ 0 ∧ oldX3_post − x1_post ≤ 0 ∧ oldX0_0 − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_post ≤ 0 ∧ oldX1_0 − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_post ≤ 0 ∧ oldX2_0 − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_post ≤ 0 ∧ oldX3_0 − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_post ≤ 0 ∧ x0_0 − x0_post ≤ 0 ∧ − x0_0 + x0_post ≤ 0 ∧ x1_0 − x1_post ≤ 0 ∧ − x1_0 + x1_post ≤ 0
3	4	2:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ oldX0_post − x0_0 ≤ 0 ∧ − oldX0_post + x0_0 ≤ 0 ∧ oldX1_post − x1_0 ≤ 0 ∧ − oldX1_post + x1_0 ≤ 0 ∧ 1 − oldX0_post + x0_post ≤ 0 ∧ −1 + oldX0_post − x0_post ≤ 0 ∧ −1 + x1_post ≤ 0 ∧ 1 − x1_post ≤ 0 ∧ oldX0_0 − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_post ≤ 0 ∧ oldX1_0 − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_post ≤ 0 ∧ x0_0 − x0_post ≤ 0 ∧ − x0_0 + x0_post ≤ 0 ∧ x1_0 − x1_post ≤ 0 ∧ − x1_0 + x1_post ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0 ∧ − oldX2_post + oldX2_post ≤ 0 ∧ oldX2_post − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_0 ≤ 0 ∧ oldX2_0 − oldX2_0 ≤ 0
4	5	0:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ oldX0_post − x0_0 ≤ 0 ∧ − oldX0_post + x0_0 ≤ 0 ∧ oldX1_post − x1_0 ≤ 0 ∧ − oldX1_post + x1_0 ≤ 0 ∧ 1 − oldX1_post ≤ 0 ∧ − oldX0_post + x0_post ≤ 0 ∧ oldX0_post − x0_post ≤ 0 ∧ − oldX1_post + x1_post ≤ 0 ∧ oldX1_post − x1_post ≤ 0 ∧ oldX0_0 − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_post ≤ 0 ∧ oldX1_0 − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_post ≤ 0 ∧ x0_0 − x0_post ≤ 0 ∧ − x0_0 + x0_post ≤ 0 ∧ x1_0 − x1_post ≤ 0 ∧ − x1_0 + x1_post ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0 ∧ − oldX2_post + oldX2_post ≤ 0 ∧ oldX2_post − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_0 ≤ 0 ∧ oldX2_0 − oldX2_0 ≤ 0
4	6	3:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ oldX0_post − x0_0 ≤ 0 ∧ − oldX0_post + x0_0 ≤ 0 ∧ oldX1_post − x1_0 ≤ 0 ∧ − oldX1_post + x1_0 ≤ 0 ∧ oldX1_post ≤ 0 ∧ − oldX0_post + x0_post ≤ 0 ∧ oldX0_post − x0_post ≤ 0 ∧ − oldX1_post + x1_post ≤ 0 ∧ oldX1_post − x1_post ≤ 0 ∧ oldX0_0 − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_post ≤ 0 ∧ oldX1_0 − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_post ≤ 0 ∧ x0_0 − x0_post ≤ 0 ∧ − x0_0 + x0_post ≤ 0 ∧ x1_0 − x1_post ≤ 0 ∧ − x1_0 + x1_post ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0 ∧ − oldX2_post + oldX2_post ≤ 0 ∧ oldX2_post − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_0 ≤ 0 ∧ oldX2_0 − oldX2_0 ≤ 0
5	7	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 ∧ oldX0_post − x0_0 ≤ 0 ∧ − oldX0_post + x0_0 ≤ 0 ∧ oldX1_post − x1_0 ≤ 0 ∧ − oldX1_post + x1_0 ≤ 0 ∧ − oldX2_post + x0_post ≤ 0 ∧ oldX2_post − x0_post ≤ 0 ∧ − oldX3_post + x1_post ≤ 0 ∧ oldX3_post − x1_post ≤ 0 ∧ oldX0_0 − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_post ≤ 0 ∧ oldX1_0 − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_post ≤ 0 ∧ oldX2_0 − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_post ≤ 0 ∧ oldX3_0 − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_post ≤ 0 ∧ x0_0 − x0_post ≤ 0 ∧ − x0_0 + x0_post ≤ 0 ∧ x1_0 − x1_post ≤ 0 ∧ − x1_0 + x1_post ≤ 0
6	8	4:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ oldX0_post − x0_0 ≤ 0 ∧ − oldX0_post + x0_0 ≤ 0 ∧ oldX1_post − x1_0 ≤ 0 ∧ − oldX1_post + x1_0 ≤ 0 ∧ 1 − oldX0_post ≤ 0 ∧ − oldX0_post + x0_post ≤ 0 ∧ oldX0_post − x0_post ≤ 0 ∧ − oldX1_post + x1_post ≤ 0 ∧ oldX1_post − x1_post ≤ 0 ∧ oldX0_0 − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_post ≤ 0 ∧ oldX1_0 − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_post ≤ 0 ∧ x0_0 − x0_post ≤ 0 ∧ − x0_0 + x0_post ≤ 0 ∧ x1_0 − x1_post ≤ 0 ∧ − x1_0 + x1_post ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0 ∧ − oldX2_post + oldX2_post ≤ 0 ∧ oldX2_post − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_0 ≤ 0 ∧ oldX2_0 − oldX2_0 ≤ 0
6	9	5:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ oldX0_post − x0_0 ≤ 0 ∧ − oldX0_post + x0_0 ≤ 0 ∧ oldX1_post − x1_0 ≤ 0 ∧ − oldX1_post + x1_0 ≤ 0 ∧ oldX0_post ≤ 0 ∧ − oldX0_post + x0_post ≤ 0 ∧ oldX0_post − x0_post ≤ 0 ∧ − oldX1_post + x1_post ≤ 0 ∧ oldX1_post − x1_post ≤ 0 ∧ oldX0_0 − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_post ≤ 0 ∧ oldX1_0 − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_post ≤ 0 ∧ x0_0 − x0_post ≤ 0 ∧ − x0_0 + x0_post ≤ 0 ∧ x1_0 − x1_post ≤ 0 ∧ − x1_0 + x1_post ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0 ∧ − oldX2_post + oldX2_post ≤ 0 ∧ oldX2_post − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_0 ≤ 0 ∧ oldX2_0 − oldX2_0 ≤ 0
2	10	6:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ oldX0_post − x0_0 ≤ 0 ∧ − oldX0_post + x0_0 ≤ 0 ∧ oldX1_post − x1_0 ≤ 0 ∧ − oldX1_post + x1_0 ≤ 0 ∧ − oldX0_post + x0_post ≤ 0 ∧ oldX0_post − x0_post ≤ 0 ∧ − oldX1_post + x1_post ≤ 0 ∧ oldX1_post − x1_post ≤ 0 ∧ oldX0_0 − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_post ≤ 0 ∧ oldX1_0 − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_post ≤ 0 ∧ x0_0 − x0_post ≤ 0 ∧ − x0_0 + x0_post ≤ 0 ∧ x1_0 − x1_post ≤ 0 ∧ − x1_0 + x1_post ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0 ∧ − oldX2_post + oldX2_post ≤ 0 ∧ oldX2_post − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_0 ≤ 0 ∧ oldX2_0 − oldX2_0 ≤ 0
7	11	0:	− x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − x0_post + x0_post ≤ 0 ∧ x0_post − x0_post ≤ 0 ∧ − x0_0 + x0_0 ≤ 0 ∧ x0_0 − x0_0 ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0 ∧ − oldX2_post + oldX2_post ≤ 0 ∧ oldX2_post − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_0 ≤ 0 ∧ oldX2_0 − oldX2_0 ≤ 0 ∧ − oldX1_post + oldX1_post ≤ 0 ∧ oldX1_post − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_0 ≤ 0 ∧ oldX1_0 − oldX1_0 ≤ 0 ∧ − oldX0_post + oldX0_post ≤ 0 ∧ oldX0_post − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_0 ≤ 0 ∧ oldX0_0 − oldX0_0 ≤ 0
7	12	3:	− x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − x0_post + x0_post ≤ 0 ∧ x0_post − x0_post ≤ 0 ∧ − x0_0 + x0_0 ≤ 0 ∧ x0_0 − x0_0 ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0 ∧ − oldX2_post + oldX2_post ≤ 0 ∧ oldX2_post − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_0 ≤ 0 ∧ oldX2_0 − oldX2_0 ≤ 0 ∧ − oldX1_post + oldX1_post ≤ 0 ∧ oldX1_post − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_0 ≤ 0 ∧ oldX1_0 − oldX1_0 ≤ 0 ∧ − oldX0_post + oldX0_post ≤ 0 ∧ oldX0_post − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_0 ≤ 0 ∧ oldX0_0 − oldX0_0 ≤ 0
7	13	1:	− x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − x0_post + x0_post ≤ 0 ∧ x0_post − x0_post ≤ 0 ∧ − x0_0 + x0_0 ≤ 0 ∧ x0_0 − x0_0 ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0 ∧ − oldX2_post + oldX2_post ≤ 0 ∧ oldX2_post − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_0 ≤ 0 ∧ oldX2_0 − oldX2_0 ≤ 0 ∧ − oldX1_post + oldX1_post ≤ 0 ∧ oldX1_post − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_0 ≤ 0 ∧ oldX1_0 − oldX1_0 ≤ 0 ∧ − oldX0_post + oldX0_post ≤ 0 ∧ oldX0_post − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_0 ≤ 0 ∧ oldX0_0 − oldX0_0 ≤ 0
7	14	4:	− x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − x0_post + x0_post ≤ 0 ∧ x0_post − x0_post ≤ 0 ∧ − x0_0 + x0_0 ≤ 0 ∧ x0_0 − x0_0 ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0 ∧ − oldX2_post + oldX2_post ≤ 0 ∧ oldX2_post − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_0 ≤ 0 ∧ oldX2_0 − oldX2_0 ≤ 0 ∧ − oldX1_post + oldX1_post ≤ 0 ∧ oldX1_post − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_0 ≤ 0 ∧ oldX1_0 − oldX1_0 ≤ 0 ∧ − oldX0_post + oldX0_post ≤ 0 ∧ oldX0_post − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_0 ≤ 0 ∧ oldX0_0 − oldX0_0 ≤ 0
7	15	5:	− x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − x0_post + x0_post ≤ 0 ∧ x0_post − x0_post ≤ 0 ∧ − x0_0 + x0_0 ≤ 0 ∧ x0_0 − x0_0 ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0 ∧ − oldX2_post + oldX2_post ≤ 0 ∧ oldX2_post − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_0 ≤ 0 ∧ oldX2_0 − oldX2_0 ≤ 0 ∧ − oldX1_post + oldX1_post ≤ 0 ∧ oldX1_post − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_0 ≤ 0 ∧ oldX1_0 − oldX1_0 ≤ 0 ∧ − oldX0_post + oldX0_post ≤ 0 ∧ oldX0_post − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_0 ≤ 0 ∧ oldX0_0 − oldX0_0 ≤ 0
7	16	6:	− x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − x0_post + x0_post ≤ 0 ∧ x0_post − x0_post ≤ 0 ∧ − x0_0 + x0_0 ≤ 0 ∧ x0_0 − x0_0 ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0 ∧ − oldX2_post + oldX2_post ≤ 0 ∧ oldX2_post − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_0 ≤ 0 ∧ oldX2_0 − oldX2_0 ≤ 0 ∧ − oldX1_post + oldX1_post ≤ 0 ∧ oldX1_post − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_0 ≤ 0 ∧ oldX1_0 − oldX1_0 ≤ 0 ∧ − oldX0_post + oldX0_post ≤ 0 ∧ oldX0_post − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_0 ≤ 0 ∧ oldX0_0 − oldX0_0 ≤ 0
7	17	2:	− x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − x0_post + x0_post ≤ 0 ∧ x0_post − x0_post ≤ 0 ∧ − x0_0 + x0_0 ≤ 0 ∧ x0_0 − x0_0 ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0 ∧ − oldX2_post + oldX2_post ≤ 0 ∧ oldX2_post − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_0 ≤ 0 ∧ oldX2_0 − oldX2_0 ≤ 0 ∧ − oldX1_post + oldX1_post ≤ 0 ∧ oldX1_post − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_0 ≤ 0 ∧ oldX1_0 − oldX1_0 ≤ 0 ∧ − oldX0_post + oldX0_post ≤ 0 ∧ oldX0_post − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_0 ≤ 0 ∧ oldX0_0 − oldX0_0 ≤ 0
8	18	7:	− x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − x0_post + x0_post ≤ 0 ∧ x0_post − x0_post ≤ 0 ∧ − x0_0 + x0_0 ≤ 0 ∧ x0_0 − x0_0 ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0 ∧ − oldX2_post + oldX2_post ≤ 0 ∧ oldX2_post − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_0 ≤ 0 ∧ oldX2_0 − oldX2_0 ≤ 0 ∧ − oldX1_post + oldX1_post ≤ 0 ∧ oldX1_post − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_0 ≤ 0 ∧ oldX1_0 − oldX1_0 ≤ 0 ∧ − oldX0_post + oldX0_post ≤ 0 ∧ oldX0_post − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_0 ≤ 0 ∧ oldX0_0 − oldX0_0 ≤ 0

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

− x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − x0_post + x0_post ≤ 0 ∧ x0_post − x0_post ≤ 0 ∧ − x0_0 + x0_0 ≤ 0 ∧ x0_0 − x0_0 ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0 ∧ − oldX2_post + oldX2_post ≤ 0 ∧ oldX2_post − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_0 ≤ 0 ∧ oldX2_0 − oldX2_0 ≤ 0 ∧ − oldX1_post + oldX1_post ≤ 0 ∧ oldX1_post − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_0 ≤ 0 ∧ oldX1_0 − oldX1_0 ≤ 0 ∧ − oldX0_post + oldX0_post ≤ 0 ∧ oldX0_post − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_0 ≤ 0 ∧ oldX0_0 − oldX0_0 ≤ 0

and for every transition t, a duplicate t is considered.

2 Transition Removal

We remove transitions 0, 3, 7, 9, 11, 12, 13, 14, 15, 16, 17, 18 using the following ranking functions, which are bounded by −15.

8:	0
7:	0
0:	0
2:	0
3:	0
4:	0
6:	0
5:	0
1:	0
8:	−6
7:	−7
0:	−8
2:	−8
3:	−8
4:	−8
6:	−8
2_var_snapshot:	−8
2*:	−8
5:	−9
1:	−10

Hints:

20	lexWeak[ [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	lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 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	lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
4	lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
5	lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
6	lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
8	lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
10	lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
0	lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
3	lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
7	lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
9	lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
11	lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [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	lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
13	lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
14	lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
15	lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
16	lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
17	lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
18	lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

3 Location Addition

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

2* 22 2: − x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − x0_post + x0_post ≤ 0 ∧ x0_post − x0_post ≤ 0 ∧ − x0_0 + x0_0 ≤ 0 ∧ x0_0 − x0_0 ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0 ∧ − oldX2_post + oldX2_post ≤ 0 ∧ oldX2_post − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_0 ≤ 0 ∧ oldX2_0 − oldX2_0 ≤ 0 ∧ − oldX1_post + oldX1_post ≤ 0 ∧ oldX1_post − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_0 ≤ 0 ∧ oldX1_0 − oldX1_0 ≤ 0 ∧ − oldX0_post + oldX0_post ≤ 0 ∧ oldX0_post − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_0 ≤ 0 ∧ oldX0_0 − oldX0_0 ≤ 0

4 Location Addition

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

2 20 2_var_snapshot: − x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − x0_post + x0_post ≤ 0 ∧ x0_post − x0_post ≤ 0 ∧ − x0_0 + x0_0 ≤ 0 ∧ x0_0 − x0_0 ≤ 0 ∧ − oldX3_post + oldX3_post ≤ 0 ∧ oldX3_post − oldX3_post ≤ 0 ∧ − oldX3_0 + oldX3_0 ≤ 0 ∧ oldX3_0 − oldX3_0 ≤ 0 ∧ − oldX2_post + oldX2_post ≤ 0 ∧ oldX2_post − oldX2_post ≤ 0 ∧ − oldX2_0 + oldX2_0 ≤ 0 ∧ oldX2_0 − oldX2_0 ≤ 0 ∧ − oldX1_post + oldX1_post ≤ 0 ∧ oldX1_post − oldX1_post ≤ 0 ∧ − oldX1_0 + oldX1_0 ≤ 0 ∧ oldX1_0 − oldX1_0 ≤ 0 ∧ − oldX0_post + oldX0_post ≤ 0 ∧ oldX0_post − oldX0_post ≤ 0 ∧ − oldX0_0 + oldX0_0 ≤ 0 ∧ oldX0_0 − oldX0_0 ≤ 0

5 SCC Decomposition

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

5.1 SCC Subproblem 1/1

Here we consider the SCC { 0, 2, 3, 4, 6, 2_var_snapshot, 2* }.

5.1.1 Splitting Cut-Point Transitions

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

5.1.1.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 19.

5.1.1.1.1 Fresh Variable Addition

The new variable __snapshot_2_x1_post is introduced. The transition formulas are extended as follows:

20:	__snapshot_2_x1_post ≤ x1_post ∧ x1_post ≤ __snapshot_2_x1_post
22:	__snapshot_2_x1_post ≤ __snapshot_2_x1_post ∧ __snapshot_2_x1_post ≤ __snapshot_2_x1_post
1:	__snapshot_2_x1_post ≤ __snapshot_2_x1_post ∧ __snapshot_2_x1_post ≤ __snapshot_2_x1_post
2:	__snapshot_2_x1_post ≤ __snapshot_2_x1_post ∧ __snapshot_2_x1_post ≤ __snapshot_2_x1_post
4:	__snapshot_2_x1_post ≤ __snapshot_2_x1_post ∧ __snapshot_2_x1_post ≤ __snapshot_2_x1_post
5:	__snapshot_2_x1_post ≤ __snapshot_2_x1_post ∧ __snapshot_2_x1_post ≤ __snapshot_2_x1_post
6:	__snapshot_2_x1_post ≤ __snapshot_2_x1_post ∧ __snapshot_2_x1_post ≤ __snapshot_2_x1_post
8:	__snapshot_2_x1_post ≤ __snapshot_2_x1_post ∧ __snapshot_2_x1_post ≤ __snapshot_2_x1_post
10:	__snapshot_2_x1_post ≤ __snapshot_2_x1_post ∧ __snapshot_2_x1_post ≤ __snapshot_2_x1_post

5.1.1.1.2 Fresh Variable Addition

The new variable __snapshot_2_x1_0 is introduced. The transition formulas are extended as follows:

20:	__snapshot_2_x1_0 ≤ x1_0 ∧ x1_0 ≤ __snapshot_2_x1_0
22:	__snapshot_2_x1_0 ≤ __snapshot_2_x1_0 ∧ __snapshot_2_x1_0 ≤ __snapshot_2_x1_0
1:	__snapshot_2_x1_0 ≤ __snapshot_2_x1_0 ∧ __snapshot_2_x1_0 ≤ __snapshot_2_x1_0
2:	__snapshot_2_x1_0 ≤ __snapshot_2_x1_0 ∧ __snapshot_2_x1_0 ≤ __snapshot_2_x1_0
4:	__snapshot_2_x1_0 ≤ __snapshot_2_x1_0 ∧ __snapshot_2_x1_0 ≤ __snapshot_2_x1_0
5:	__snapshot_2_x1_0 ≤ __snapshot_2_x1_0 ∧ __snapshot_2_x1_0 ≤ __snapshot_2_x1_0
6:	__snapshot_2_x1_0 ≤ __snapshot_2_x1_0 ∧ __snapshot_2_x1_0 ≤ __snapshot_2_x1_0
8:	__snapshot_2_x1_0 ≤ __snapshot_2_x1_0 ∧ __snapshot_2_x1_0 ≤ __snapshot_2_x1_0
10:	__snapshot_2_x1_0 ≤ __snapshot_2_x1_0 ∧ __snapshot_2_x1_0 ≤ __snapshot_2_x1_0

5.1.1.1.3 Fresh Variable Addition

The new variable __snapshot_2_x0_post is introduced. The transition formulas are extended as follows:

20:	__snapshot_2_x0_post ≤ x0_post ∧ x0_post ≤ __snapshot_2_x0_post
22:	__snapshot_2_x0_post ≤ __snapshot_2_x0_post ∧ __snapshot_2_x0_post ≤ __snapshot_2_x0_post
1:	__snapshot_2_x0_post ≤ __snapshot_2_x0_post ∧ __snapshot_2_x0_post ≤ __snapshot_2_x0_post
2:	__snapshot_2_x0_post ≤ __snapshot_2_x0_post ∧ __snapshot_2_x0_post ≤ __snapshot_2_x0_post
4:	__snapshot_2_x0_post ≤ __snapshot_2_x0_post ∧ __snapshot_2_x0_post ≤ __snapshot_2_x0_post
5:	__snapshot_2_x0_post ≤ __snapshot_2_x0_post ∧ __snapshot_2_x0_post ≤ __snapshot_2_x0_post
6:	__snapshot_2_x0_post ≤ __snapshot_2_x0_post ∧ __snapshot_2_x0_post ≤ __snapshot_2_x0_post
8:	__snapshot_2_x0_post ≤ __snapshot_2_x0_post ∧ __snapshot_2_x0_post ≤ __snapshot_2_x0_post
10:	__snapshot_2_x0_post ≤ __snapshot_2_x0_post ∧ __snapshot_2_x0_post ≤ __snapshot_2_x0_post

5.1.1.1.4 Fresh Variable Addition

The new variable __snapshot_2_x0_0 is introduced. The transition formulas are extended as follows:

20:	__snapshot_2_x0_0 ≤ x0_0 ∧ x0_0 ≤ __snapshot_2_x0_0
22:	__snapshot_2_x0_0 ≤ __snapshot_2_x0_0 ∧ __snapshot_2_x0_0 ≤ __snapshot_2_x0_0
1:	__snapshot_2_x0_0 ≤ __snapshot_2_x0_0 ∧ __snapshot_2_x0_0 ≤ __snapshot_2_x0_0
2:	__snapshot_2_x0_0 ≤ __snapshot_2_x0_0 ∧ __snapshot_2_x0_0 ≤ __snapshot_2_x0_0
4:	__snapshot_2_x0_0 ≤ __snapshot_2_x0_0 ∧ __snapshot_2_x0_0 ≤ __snapshot_2_x0_0
5:	__snapshot_2_x0_0 ≤ __snapshot_2_x0_0 ∧ __snapshot_2_x0_0 ≤ __snapshot_2_x0_0
6:	__snapshot_2_x0_0 ≤ __snapshot_2_x0_0 ∧ __snapshot_2_x0_0 ≤ __snapshot_2_x0_0
8:	__snapshot_2_x0_0 ≤ __snapshot_2_x0_0 ∧ __snapshot_2_x0_0 ≤ __snapshot_2_x0_0
10:	__snapshot_2_x0_0 ≤ __snapshot_2_x0_0 ∧ __snapshot_2_x0_0 ≤ __snapshot_2_x0_0

5.1.1.1.5 Fresh Variable Addition

The new variable __snapshot_2_oldX3_post is introduced. The transition formulas are extended as follows:

20:	__snapshot_2_oldX3_post ≤ oldX3_post ∧ oldX3_post ≤ __snapshot_2_oldX3_post
22:	__snapshot_2_oldX3_post ≤ __snapshot_2_oldX3_post ∧ __snapshot_2_oldX3_post ≤ __snapshot_2_oldX3_post
1:	__snapshot_2_oldX3_post ≤ __snapshot_2_oldX3_post ∧ __snapshot_2_oldX3_post ≤ __snapshot_2_oldX3_post
2:	__snapshot_2_oldX3_post ≤ __snapshot_2_oldX3_post ∧ __snapshot_2_oldX3_post ≤ __snapshot_2_oldX3_post
4:	__snapshot_2_oldX3_post ≤ __snapshot_2_oldX3_post ∧ __snapshot_2_oldX3_post ≤ __snapshot_2_oldX3_post
5:	__snapshot_2_oldX3_post ≤ __snapshot_2_oldX3_post ∧ __snapshot_2_oldX3_post ≤ __snapshot_2_oldX3_post
6:	__snapshot_2_oldX3_post ≤ __snapshot_2_oldX3_post ∧ __snapshot_2_oldX3_post ≤ __snapshot_2_oldX3_post
8:	__snapshot_2_oldX3_post ≤ __snapshot_2_oldX3_post ∧ __snapshot_2_oldX3_post ≤ __snapshot_2_oldX3_post
10:	__snapshot_2_oldX3_post ≤ __snapshot_2_oldX3_post ∧ __snapshot_2_oldX3_post ≤ __snapshot_2_oldX3_post

5.1.1.1.6 Fresh Variable Addition

The new variable __snapshot_2_oldX3_0 is introduced. The transition formulas are extended as follows:

20:	__snapshot_2_oldX3_0 ≤ oldX3_0 ∧ oldX3_0 ≤ __snapshot_2_oldX3_0
22:	__snapshot_2_oldX3_0 ≤ __snapshot_2_oldX3_0 ∧ __snapshot_2_oldX3_0 ≤ __snapshot_2_oldX3_0
1:	__snapshot_2_oldX3_0 ≤ __snapshot_2_oldX3_0 ∧ __snapshot_2_oldX3_0 ≤ __snapshot_2_oldX3_0
2:	__snapshot_2_oldX3_0 ≤ __snapshot_2_oldX3_0 ∧ __snapshot_2_oldX3_0 ≤ __snapshot_2_oldX3_0
4:	__snapshot_2_oldX3_0 ≤ __snapshot_2_oldX3_0 ∧ __snapshot_2_oldX3_0 ≤ __snapshot_2_oldX3_0
5:	__snapshot_2_oldX3_0 ≤ __snapshot_2_oldX3_0 ∧ __snapshot_2_oldX3_0 ≤ __snapshot_2_oldX3_0
6:	__snapshot_2_oldX3_0 ≤ __snapshot_2_oldX3_0 ∧ __snapshot_2_oldX3_0 ≤ __snapshot_2_oldX3_0
8:	__snapshot_2_oldX3_0 ≤ __snapshot_2_oldX3_0 ∧ __snapshot_2_oldX3_0 ≤ __snapshot_2_oldX3_0
10:	__snapshot_2_oldX3_0 ≤ __snapshot_2_oldX3_0 ∧ __snapshot_2_oldX3_0 ≤ __snapshot_2_oldX3_0

5.1.1.1.7 Fresh Variable Addition

The new variable __snapshot_2_oldX2_post is introduced. The transition formulas are extended as follows:

20:	__snapshot_2_oldX2_post ≤ oldX2_post ∧ oldX2_post ≤ __snapshot_2_oldX2_post
22:	__snapshot_2_oldX2_post ≤ __snapshot_2_oldX2_post ∧ __snapshot_2_oldX2_post ≤ __snapshot_2_oldX2_post
1:	__snapshot_2_oldX2_post ≤ __snapshot_2_oldX2_post ∧ __snapshot_2_oldX2_post ≤ __snapshot_2_oldX2_post
2:	__snapshot_2_oldX2_post ≤ __snapshot_2_oldX2_post ∧ __snapshot_2_oldX2_post ≤ __snapshot_2_oldX2_post
4:	__snapshot_2_oldX2_post ≤ __snapshot_2_oldX2_post ∧ __snapshot_2_oldX2_post ≤ __snapshot_2_oldX2_post
5:	__snapshot_2_oldX2_post ≤ __snapshot_2_oldX2_post ∧ __snapshot_2_oldX2_post ≤ __snapshot_2_oldX2_post
6:	__snapshot_2_oldX2_post ≤ __snapshot_2_oldX2_post ∧ __snapshot_2_oldX2_post ≤ __snapshot_2_oldX2_post
8:	__snapshot_2_oldX2_post ≤ __snapshot_2_oldX2_post ∧ __snapshot_2_oldX2_post ≤ __snapshot_2_oldX2_post
10:	__snapshot_2_oldX2_post ≤ __snapshot_2_oldX2_post ∧ __snapshot_2_oldX2_post ≤ __snapshot_2_oldX2_post

5.1.1.1.8 Fresh Variable Addition

The new variable __snapshot_2_oldX2_0 is introduced. The transition formulas are extended as follows:

20:	__snapshot_2_oldX2_0 ≤ oldX2_0 ∧ oldX2_0 ≤ __snapshot_2_oldX2_0
22:	__snapshot_2_oldX2_0 ≤ __snapshot_2_oldX2_0 ∧ __snapshot_2_oldX2_0 ≤ __snapshot_2_oldX2_0
1:	__snapshot_2_oldX2_0 ≤ __snapshot_2_oldX2_0 ∧ __snapshot_2_oldX2_0 ≤ __snapshot_2_oldX2_0
2:	__snapshot_2_oldX2_0 ≤ __snapshot_2_oldX2_0 ∧ __snapshot_2_oldX2_0 ≤ __snapshot_2_oldX2_0
4:	__snapshot_2_oldX2_0 ≤ __snapshot_2_oldX2_0 ∧ __snapshot_2_oldX2_0 ≤ __snapshot_2_oldX2_0
5:	__snapshot_2_oldX2_0 ≤ __snapshot_2_oldX2_0 ∧ __snapshot_2_oldX2_0 ≤ __snapshot_2_oldX2_0
6:	__snapshot_2_oldX2_0 ≤ __snapshot_2_oldX2_0 ∧ __snapshot_2_oldX2_0 ≤ __snapshot_2_oldX2_0
8:	__snapshot_2_oldX2_0 ≤ __snapshot_2_oldX2_0 ∧ __snapshot_2_oldX2_0 ≤ __snapshot_2_oldX2_0
10:	__snapshot_2_oldX2_0 ≤ __snapshot_2_oldX2_0 ∧ __snapshot_2_oldX2_0 ≤ __snapshot_2_oldX2_0

5.1.1.1.9 Fresh Variable Addition

The new variable __snapshot_2_oldX1_post is introduced. The transition formulas are extended as follows:

20:	__snapshot_2_oldX1_post ≤ oldX1_post ∧ oldX1_post ≤ __snapshot_2_oldX1_post
22:	__snapshot_2_oldX1_post ≤ __snapshot_2_oldX1_post ∧ __snapshot_2_oldX1_post ≤ __snapshot_2_oldX1_post
1:	__snapshot_2_oldX1_post ≤ __snapshot_2_oldX1_post ∧ __snapshot_2_oldX1_post ≤ __snapshot_2_oldX1_post
2:	__snapshot_2_oldX1_post ≤ __snapshot_2_oldX1_post ∧ __snapshot_2_oldX1_post ≤ __snapshot_2_oldX1_post
4:	__snapshot_2_oldX1_post ≤ __snapshot_2_oldX1_post ∧ __snapshot_2_oldX1_post ≤ __snapshot_2_oldX1_post
5:	__snapshot_2_oldX1_post ≤ __snapshot_2_oldX1_post ∧ __snapshot_2_oldX1_post ≤ __snapshot_2_oldX1_post
6:	__snapshot_2_oldX1_post ≤ __snapshot_2_oldX1_post ∧ __snapshot_2_oldX1_post ≤ __snapshot_2_oldX1_post
8:	__snapshot_2_oldX1_post ≤ __snapshot_2_oldX1_post ∧ __snapshot_2_oldX1_post ≤ __snapshot_2_oldX1_post
10:	__snapshot_2_oldX1_post ≤ __snapshot_2_oldX1_post ∧ __snapshot_2_oldX1_post ≤ __snapshot_2_oldX1_post

5.1.1.1.10 Fresh Variable Addition

The new variable __snapshot_2_oldX1_0 is introduced. The transition formulas are extended as follows:

20:	__snapshot_2_oldX1_0 ≤ oldX1_0 ∧ oldX1_0 ≤ __snapshot_2_oldX1_0
22:	__snapshot_2_oldX1_0 ≤ __snapshot_2_oldX1_0 ∧ __snapshot_2_oldX1_0 ≤ __snapshot_2_oldX1_0
1:	__snapshot_2_oldX1_0 ≤ __snapshot_2_oldX1_0 ∧ __snapshot_2_oldX1_0 ≤ __snapshot_2_oldX1_0
2:	__snapshot_2_oldX1_0 ≤ __snapshot_2_oldX1_0 ∧ __snapshot_2_oldX1_0 ≤ __snapshot_2_oldX1_0
4:	__snapshot_2_oldX1_0 ≤ __snapshot_2_oldX1_0 ∧ __snapshot_2_oldX1_0 ≤ __snapshot_2_oldX1_0
5:	__snapshot_2_oldX1_0 ≤ __snapshot_2_oldX1_0 ∧ __snapshot_2_oldX1_0 ≤ __snapshot_2_oldX1_0
6:	__snapshot_2_oldX1_0 ≤ __snapshot_2_oldX1_0 ∧ __snapshot_2_oldX1_0 ≤ __snapshot_2_oldX1_0
8:	__snapshot_2_oldX1_0 ≤ __snapshot_2_oldX1_0 ∧ __snapshot_2_oldX1_0 ≤ __snapshot_2_oldX1_0
10:	__snapshot_2_oldX1_0 ≤ __snapshot_2_oldX1_0 ∧ __snapshot_2_oldX1_0 ≤ __snapshot_2_oldX1_0

5.1.1.1.11 Fresh Variable Addition

The new variable __snapshot_2_oldX0_post is introduced. The transition formulas are extended as follows:

20:	__snapshot_2_oldX0_post ≤ oldX0_post ∧ oldX0_post ≤ __snapshot_2_oldX0_post
22:	__snapshot_2_oldX0_post ≤ __snapshot_2_oldX0_post ∧ __snapshot_2_oldX0_post ≤ __snapshot_2_oldX0_post
1:	__snapshot_2_oldX0_post ≤ __snapshot_2_oldX0_post ∧ __snapshot_2_oldX0_post ≤ __snapshot_2_oldX0_post
2:	__snapshot_2_oldX0_post ≤ __snapshot_2_oldX0_post ∧ __snapshot_2_oldX0_post ≤ __snapshot_2_oldX0_post
4:	__snapshot_2_oldX0_post ≤ __snapshot_2_oldX0_post ∧ __snapshot_2_oldX0_post ≤ __snapshot_2_oldX0_post
5:	__snapshot_2_oldX0_post ≤ __snapshot_2_oldX0_post ∧ __snapshot_2_oldX0_post ≤ __snapshot_2_oldX0_post
6:	__snapshot_2_oldX0_post ≤ __snapshot_2_oldX0_post ∧ __snapshot_2_oldX0_post ≤ __snapshot_2_oldX0_post
8:	__snapshot_2_oldX0_post ≤ __snapshot_2_oldX0_post ∧ __snapshot_2_oldX0_post ≤ __snapshot_2_oldX0_post
10:	__snapshot_2_oldX0_post ≤ __snapshot_2_oldX0_post ∧ __snapshot_2_oldX0_post ≤ __snapshot_2_oldX0_post

5.1.1.1.12 Fresh Variable Addition

The new variable __snapshot_2_oldX0_0 is introduced. The transition formulas are extended as follows:

20:	__snapshot_2_oldX0_0 ≤ oldX0_0 ∧ oldX0_0 ≤ __snapshot_2_oldX0_0
22:	__snapshot_2_oldX0_0 ≤ __snapshot_2_oldX0_0 ∧ __snapshot_2_oldX0_0 ≤ __snapshot_2_oldX0_0
1:	__snapshot_2_oldX0_0 ≤ __snapshot_2_oldX0_0 ∧ __snapshot_2_oldX0_0 ≤ __snapshot_2_oldX0_0
2:	__snapshot_2_oldX0_0 ≤ __snapshot_2_oldX0_0 ∧ __snapshot_2_oldX0_0 ≤ __snapshot_2_oldX0_0
4:	__snapshot_2_oldX0_0 ≤ __snapshot_2_oldX0_0 ∧ __snapshot_2_oldX0_0 ≤ __snapshot_2_oldX0_0
5:	__snapshot_2_oldX0_0 ≤ __snapshot_2_oldX0_0 ∧ __snapshot_2_oldX0_0 ≤ __snapshot_2_oldX0_0
6:	__snapshot_2_oldX0_0 ≤ __snapshot_2_oldX0_0 ∧ __snapshot_2_oldX0_0 ≤ __snapshot_2_oldX0_0
8:	__snapshot_2_oldX0_0 ≤ __snapshot_2_oldX0_0 ∧ __snapshot_2_oldX0_0 ≤ __snapshot_2_oldX0_0
10:	__snapshot_2_oldX0_0 ≤ __snapshot_2_oldX0_0 ∧ __snapshot_2_oldX0_0 ≤ __snapshot_2_oldX0_0

5.1.1.1.13 Invariant Updates

The following invariants are asserted.

0:	TRUE
1:	TRUE
2:	TRUE
3:	TRUE
4:	TRUE
5:	TRUE
6:	TRUE
7:	TRUE
8:	TRUE
0:	− __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ − __snapshot_2_x1_0 + x1_0 ≤ 0 ∧ 1 − __snapshot_2_x0_0 ≤ 0 ∧ 1 − __snapshot_2_x1_0 ≤ 0
2:	TRUE ∨ 1 − __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ 1 − __snapshot_2_x0_0 ≤ 0 ∨ − __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ 1 − __snapshot_2_x1_0 + x1_0 ≤ 0 ∧ 1 − __snapshot_2_x0_0 ≤ 0 ∧ 1 − __snapshot_2_x1_0 ≤ 0
3:	− __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ 1 − __snapshot_2_x0_0 ≤ 0
4:	− __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ − __snapshot_2_x1_0 + x1_0 ≤ 0 ∧ 1 − __snapshot_2_x0_0 ≤ 0
6:	− __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ − __snapshot_2_x1_0 + x1_0 ≤ 0
2_var_snapshot:	− __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ − __snapshot_2_x1_0 + x1_0 ≤ 0
2*:	1 − __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ 1 − __snapshot_2_x0_0 ≤ 0 ∨ − __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ 1 − __snapshot_2_x1_0 + x1_0 ≤ 0 ∧ 1 − __snapshot_2_x0_0 ≤ 0 ∧ 1 − __snapshot_2_x1_0 ≤ 0

The invariants are proved as follows.

IMPACT Invariant Proof

nodes (location) invariant:

0	(8)	TRUE
1	(7)	TRUE
2	(0)	TRUE
3	(3)	TRUE
4	(1)	TRUE
5	(4)	TRUE
6	(5)	TRUE
7	(6)	TRUE
8	(2)	TRUE
9	(6)	TRUE
10	(2)	TRUE
11	(2_var_snapshot)	− __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ − __snapshot_2_x1_0 + x1_0 ≤ 0
16	(1)	TRUE
17	(2)	TRUE
18	(2)	TRUE
19	(1)	TRUE
20	(2)	TRUE
21	(0)	TRUE
22	(3)	TRUE
23	(4)	TRUE
24	(5)	TRUE
25	(6)	− __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ − __snapshot_2_x1_0 + x1_0 ≤ 0
26	(4)	− __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ − __snapshot_2_x1_0 + x1_0 ≤ 0 ∧ 1 − __snapshot_2_x0_0 ≤ 0
27	(0)	− __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ − __snapshot_2_x1_0 + x1_0 ≤ 0 ∧ 1 − __snapshot_2_x0_0 ≤ 0 ∧ 1 − __snapshot_2_x1_0 ≤ 0
28	(3)	− __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ 1 − __snapshot_2_x0_0 ≤ 0
29	(2*)	1 − __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ 1 − __snapshot_2_x0_0 ≤ 0
30	(2)	1 − __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ 1 − __snapshot_2_x0_0 ≤ 0
31	(2_var_snapshot)	− __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ − __snapshot_2_x1_0 + x1_0 ≤ 0
36	(1)	TRUE
37	(2*)	1 − __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ 1 − __snapshot_2_x0_0 ≤ 0
38	(2*)	− __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ 1 − __snapshot_2_x1_0 + x1_0 ≤ 0 ∧ 1 − __snapshot_2_x0_0 ≤ 0 ∧ 1 − __snapshot_2_x1_0 ≤ 0
43	(2)	− __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ 1 − __snapshot_2_x1_0 + x1_0 ≤ 0 ∧ 1 − __snapshot_2_x0_0 ≤ 0 ∧ 1 − __snapshot_2_x1_0 ≤ 0
44	(2_var_snapshot)	− __snapshot_2_x0_0 + x0_0 ≤ 0 ∧ − __snapshot_2_x1_0 + x1_0 ≤ 0

initial node: 0

cover edges:

→ 36

Hint: auto

→ 24

Hint: auto

→ 7

Hint: auto

→ 36

Hint: auto

→ 8

Hint: auto

→ 8

Hint: auto

→ 36

Hint: auto

→ 8

Hint: auto

→ 2

Hint: auto

→ 3

Hint: auto

→ 5

Hint: auto

→ 11

Hint: distribute conclusion

	[1, 0]
	[0, 1]

→ 29

Hint: distribute conclusion

	[1, 0]
	[0, 1]

→ 11

Hint: distribute conclusion

	[1, 0]
	[0, 1]

transition edges:

18 1

Hint: auto

11 2

Hint: auto

12 3

Hint: auto

13 4

Hint: auto

14 5

Hint: auto

15 6

Hint: auto

16 7

Hint: auto

17 8

Hint: auto

0 16

Hint: auto

1 17

Hint: auto

2 18

Hint: auto

3 19

Hint: auto

4 20

Hint: auto

5 21

Hint: auto

6 22

Hint: auto

8 23

Hint: auto

9 24

Hint: auto

10 9

Hint: auto

19 10

Hint: auto

20 11

Hint: distribute conclusion

	[0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
	[0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

10 25

Hint: distribute conclusion

	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
	[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

7 36

Hint: auto

8 26

Hint: distribute conclusion

	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
	[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

5 27

Hint: distribute conclusion

	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
	[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
	[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

6 28

Hint: distribute conclusion

	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
	[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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

1 37

Hint: distribute conclusion

	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
	[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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

2 38

Hint: distribute conclusion

	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
	[0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
	[0, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

4 29

Hint: distribute conclusion

	[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

22 30

Hint: distribute conclusion

	[1, 0, 0, 0, 0, 0, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

20 31

Hint: distribute conclusion

	[0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
	[0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

22 43

Hint: distribute conclusion

	[1, 0, 0, 0, 0, 0, 0, 0, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
	[0, 1, 0, 0, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
	[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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
	[0, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

20 44

Hint: distribute conclusion

	[0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]
	[0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]

5.1.1.1.14 Transition Removal

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

0:	[__snapshot_2_x0_0, __snapshot_2_x1_0]
2:	[x0_0, x1_0]
3:	[__snapshot_2_x0_0, __snapshot_2_x1_0]
4:	[__snapshot_2_x0_0, __snapshot_2_x1_0]
6:	[__snapshot_2_x0_0, __snapshot_2_x1_0]
2_var_snapshot:	[__snapshot_2_x0_0, __snapshot_2_x1_0]
2*:	[__snapshot_2_x0_0, __snapshot_2_x1_0]

Hints:

distribute assertion

	lexWeak[ [0, 0, 0, 0, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
	lexWeak[ [0, 0, 0, 0, 0, 0, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
	lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 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, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

distribute assertion

lexStrict[ [1, 0, 0, 0, 0, 0, 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, 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] ]

lexStrict[ [1, 0, 0, 0, 0, 0, 0, 0, 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, 1, 0, 0, 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, 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] ]

lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

5.1.1.1.15 Transition Removal

We remove transition 20 using the following ranking functions, which are bounded by −9.

2:	−1
2_var_snapshot:	−2
6:	−3
4:	−4
0:	−5
3:	−6
2*:	−7

Hints:

distribute assertion

	lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
	lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
	lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

5.1.1.1.16 Splitting Cut-Point Transitions

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

Tool configuration

T2Cert

version: 1.0