LTS Termination Proof

by T2Cert

Input

• Initial Location: 13
• Transitions: (pre-variables and post-variables)

  0	0	1:		5 − i2_0 ≤ 0 ∧ − x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  0	1	2:		0 ≤ 0 ∧ 0 ≤ 0 ∧ −4 + i2_0 ≤ 0 ∧ j3_post ≤ 0 ∧ − j3_post ≤ 0 ∧ j3_0 − j3_post ≤ 0 ∧ − j3_0 + j3_post ≤ 0 ∧ − x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  3	2	0:		− x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  2	3	4:		− x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  1	4	5:		− x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  6	5	7:		− x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  8	6	9:		0 ≤ 0 ∧ 0 ≤ 0 ∧ −1 − l5_0 + l5_post ≤ 0 ∧ 1 + l5_0 − l5_post ≤ 0 ∧ l5_0 − l5_post ≤ 0 ∧ − l5_0 + l5_post ≤ 0 ∧ − x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  9	7	10:		− x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  11	8	8:		− x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  11	9	1:		− x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  11	10	8:		− x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  10	11	6:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 5 − l5_0 ≤ 0 ∧ −1 − k4_0 + k4_post ≤ 0 ∧ 1 + k4_0 − k4_post ≤ 0 ∧ k4_0 − k4_post ≤ 0 ∧ − k4_0 + k4_post ≤ 0 ∧ − x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  10	12	11:		−4 + l5_0 ≤ 0 ∧ − x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  7	13	2:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 5 − k4_0 ≤ 0 ∧ −1 − j3_0 + j3_post ≤ 0 ∧ 1 + j3_0 − j3_post ≤ 0 ∧ j3_0 − j3_post ≤ 0 ∧ − j3_0 + j3_post ≤ 0 ∧ − x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  7	14	9:		0 ≤ 0 ∧ 0 ≤ 0 ∧ −4 + k4_0 ≤ 0 ∧ l5_post ≤ 0 ∧ − l5_post ≤ 0 ∧ l5_0 − l5_post ≤ 0 ∧ − l5_0 + l5_post ≤ 0 ∧ − x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  4	15	3:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 5 − j3_0 ≤ 0 ∧ −1 − i2_0 + i2_post ≤ 0 ∧ 1 + i2_0 − i2_post ≤ 0 ∧ i2_0 − i2_post ≤ 0 ∧ − i2_0 + i2_post ≤ 0 ∧ − x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0
  4	16	6:		0 ≤ 0 ∧ 0 ≤ 0 ∧ −4 + j3_0 ≤ 0 ∧ k4_post ≤ 0 ∧ − k4_post ≤ 0 ∧ k4_0 − k4_post ≤ 0 ∧ − k4_0 + k4_post ≤ 0 ∧ − x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0
  12	17	3:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ −400 + x1_post ≤ 0 ∧ 400 − x1_post ≤ 0 ∧ i2_post ≤ 0 ∧ − i2_post ≤ 0 ∧ i2_0 − i2_post ≤ 0 ∧ − i2_0 + i2_post ≤ 0 ∧ x1_0 − x1_post ≤ 0 ∧ − x1_0 + x1_post ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0
  13	18	12:		− x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0

Proof

1 Invariant Updates

The following invariants are asserted.

The invariants are proved as follows.

IMPACT Invariant Proof

• nodes (location) invariant:

  0		(0)		−400 + x1_post ≤ 0 ∧ 400 − x1_post ≤ 0 ∧ −400 + x1_0 ≤ 0 ∧ 400 − x1_0 ≤ 0
  1		(1)		−400 + x1_post ≤ 0 ∧ 400 − x1_post ≤ 0 ∧ −400 + x1_0 ≤ 0 ∧ 400 − x1_0 ≤ 0
  2		(2)		−400 + x1_post ≤ 0 ∧ 400 − x1_post ≤ 0 ∧ −400 + x1_0 ≤ 0 ∧ 400 − x1_0 ≤ 0
  3		(3)		−400 + x1_post ≤ 0 ∧ 400 − x1_post ≤ 0 ∧ −400 + x1_0 ≤ 0 ∧ 400 − x1_0 ≤ 0
  4		(4)		−400 + x1_post ≤ 0 ∧ 400 − x1_post ≤ 0 ∧ −400 + x1_0 ≤ 0 ∧ 400 − x1_0 ≤ 0
  5		(5)		−400 + x1_post ≤ 0 ∧ 400 − x1_post ≤ 0 ∧ −400 + x1_0 ≤ 0 ∧ 400 − x1_0 ≤ 0
  6		(6)		−400 + x1_post ≤ 0 ∧ 400 − x1_post ≤ 0 ∧ −400 + x1_0 ≤ 0 ∧ 400 − x1_0 ≤ 0
  7		(7)		−400 + x1_post ≤ 0 ∧ 400 − x1_post ≤ 0 ∧ −400 + x1_0 ≤ 0 ∧ 400 − x1_0 ≤ 0
  8		(8)		−400 + x1_post ≤ 0 ∧ 400 − x1_post ≤ 0 ∧ −400 + x1_0 ≤ 0 ∧ 400 − x1_0 ≤ 0
  9		(9)		−400 + x1_post ≤ 0 ∧ 400 − x1_post ≤ 0 ∧ −400 + x1_0 ≤ 0 ∧ 400 − x1_0 ≤ 0
  10		(10)		−400 + x1_post ≤ 0 ∧ 400 − x1_post ≤ 0 ∧ −400 + x1_0 ≤ 0 ∧ 400 − x1_0 ≤ 0
  11		(11)		−400 + x1_post ≤ 0 ∧ 400 − x1_post ≤ 0 ∧ −400 + x1_0 ≤ 0 ∧ 400 − x1_0 ≤ 0
  12		(12)		TRUE
  13		(13)		TRUE

• initial node: 13
• cover edges:
• transition edges:

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

2 Switch to Cooperation Termination Proof

3 Transition Removal

We remove transitions 0, 4, 9, 17, 18 using the following ranking functions, which are bounded by −21.

4 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 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0

5 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 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0

6 Location Addition

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

3* 29 3: − x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0

7 Location Addition

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

3 27 3_var_snapshot: − x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0

8 Location Addition

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

6* 36 6: − x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0

9 Location Addition

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

6 34 6_var_snapshot: − x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0

10 Location Addition

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

9* 43 9: − x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0

11 Location Addition

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

9 41 9_var_snapshot: − x1_post + x1_post ≤ 0 ∧ x1_post − x1_post ≤ 0 ∧ − x1_0 + x1_0 ≤ 0 ∧ x1_0 − x1_0 ≤ 0 ∧ − l5_post + l5_post ≤ 0 ∧ l5_post − l5_post ≤ 0 ∧ − l5_0 + l5_0 ≤ 0 ∧ l5_0 − l5_0 ≤ 0 ∧ − k4_post + k4_post ≤ 0 ∧ k4_post − k4_post ≤ 0 ∧ − k4_0 + k4_0 ≤ 0 ∧ k4_0 − k4_0 ≤ 0 ∧ − j3_post + j3_post ≤ 0 ∧ j3_post − j3_post ≤ 0 ∧ − j3_0 + j3_0 ≤ 0 ∧ j3_0 − j3_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0

12 SCC Decomposition

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

12.1 SCC Subproblem 1/1

Here we consider the SCC { 2, 4, 6, 7, 8, 9, 10, 11, 0, 3, 2_var_snapshot, 2*, 3_var_snapshot, 3*, 6_var_snapshot, 6*, 9_var_snapshot, 9* }.

12.1.1 Transition Removal

We remove transition 1 using the following ranking functions, which are bounded by −6005.

12.1.2 Transition Removal

We remove transition 16 using the following ranking functions, which are bounded by −5605.

12.1.3 Transition Removal

We remove transition 14 using the following ranking functions, which are bounded by −23.

12.1.4 Transition Removal

We remove transitions 20, 22, 27, 29, 34, 36, 2, 3, 5, 11, 13, 15 using the following ranking functions, which are bounded by −3201.

12.1.5 Transition Removal

We remove transition 12 using the following ranking functions, which are bounded by −4409.

12.1.6 Transition Removal

We remove transitions 41, 43, 6, 7, 8, 10 using the following ranking functions, which are bounded by −1601.

12.1.7 Splitting Cut-Point Transitions

We consider 4 subproblems corresponding to sets of cut-point transitions as follows.

12.1.7.1 Cut-Point Subproblem 1/4

12.1.7.1.1 Splitting Cut-Point Transitions

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

12.1.7.2 Cut-Point Subproblem 2/4

12.1.7.2.1 Splitting Cut-Point Transitions

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

12.1.7.3 Cut-Point Subproblem 3/4

12.1.7.3.1 Splitting Cut-Point Transitions

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

12.1.7.4 Cut-Point Subproblem 4/4

12.1.7.4.1 Splitting Cut-Point Transitions

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

Tool configuration

T2Cert

• version: 1.0