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 ∧ 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 ∧ 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 − 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	2	1:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 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 ≤ 0 ∧ oldX1_post ≤ 0 ∧ − oldX1_post ≤ 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	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 ∧ 1 − oldX1_post ≤ 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	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 ∧ 1 + oldX1_post ≤ 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	5	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 ∧ 1 − oldX0_post ≤ 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	6	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 ∧ 1 + oldX0_post ≤ 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
4	7	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 ≤ 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	8	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
4	9	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 ∧ 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	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 ∧ − 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	11	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
5	12	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
5	13	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
5	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
5	15	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
6	16	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

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, 2, 3, 4, 5, 6, 8, 9, 11, 12, 13, 14, 15, 16 using the following ranking functions, which are bounded by −15.

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

Hints:

18	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] ]
7	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] ]
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] ]
2	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] ]
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, 0, 0] ]
4	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] ]
5	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] ]
6	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] ]
8	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] ]
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] ]

3 Location Addition

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

2* 20 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 18 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, 4, 2_var_snapshot, 2* }.

5.1.1 Transition Removal

We remove transition 7 using the following ranking functions, which are bounded by 4.

0:	−4 + 4⋅x0_0 + 2⋅x1_0
2:	1 + 4⋅x0_0 + 2⋅x1_0
4:	−1 + 4⋅x0_0 + 2⋅x1_0
2_var_snapshot:	4⋅x0_0 + 2⋅x1_0
2*:	2 + 4⋅x0_0 + 2⋅x1_0

Hints:

18	lexWeak[ [0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
20	lexWeak[ [0, 0, 2, 0, 0, 0, 4, 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, 4, 0, 2, 0, 4, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
7	lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 2, 0, 4, 2, 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, 4, 0, 2, 0, 4, 0, 2, 0, 0, 0, 0, 0, 4, 0, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

5.1.2 Transition Removal

We remove transitions 18, 20, 1, 10 using the following ranking functions, which are bounded by −3.

0:	1
2:	−1
4:	−3
2_var_snapshot:	−2
2*:	0

Hints:

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] ]
20	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] ]
1	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] ]
10	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] ]

5.1.3 Splitting Cut-Point Transitions

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

5.1.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 17.

5.1.3.1.1 Splitting Cut-Point Transitions

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

Tool configuration

T2Cert

version: 1.0