# LTS Termination Proof

by T2Cert

## Input

Integer Transition System
• Initial Location: 10
• Transitions: (pre-variables and post-variables)  0 0 1: 1 + i34_0 ≤ 0 ∧ − i8_post + i8_post ≤ 0 ∧ i8_post − i8_post ≤ 0 ∧ − i8_0 + i8_0 ≤ 0 ∧ i8_0 − i8_0 ≤ 0 ∧ − i6_post + i6_post ≤ 0 ∧ i6_post − i6_post ≤ 0 ∧ − i6_0 + i6_0 ≤ 0 ∧ i6_0 − i6_0 ≤ 0 ∧ − i34_post + i34_post ≤ 0 ∧ i34_post − i34_post ≤ 0 ∧ − i34_0 + i34_0 ≤ 0 ∧ i34_0 − i34_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0 ∧ − ___const_999_0 + ___const_999_0 ≤ 0 ∧ ___const_999_0 − ___const_999_0 ≤ 0 0 1 2: 0 ≤ 0 ∧ 0 ≤ 0 ∧ − i34_0 ≤ 0 ∧ 1 − i34_0 + i34_post ≤ 0 ∧ −1 + i34_0 − i34_post ≤ 0 ∧ i34_0 − i34_post ≤ 0 ∧ − i34_0 + i34_post ≤ 0 ∧ − i8_post + i8_post ≤ 0 ∧ i8_post − i8_post ≤ 0 ∧ − i8_0 + i8_0 ≤ 0 ∧ i8_0 − i8_0 ≤ 0 ∧ − i6_post + i6_post ≤ 0 ∧ i6_post − i6_post ≤ 0 ∧ − i6_0 + i6_0 ≤ 0 ∧ i6_0 − i6_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0 ∧ − ___const_999_0 + ___const_999_0 ≤ 0 ∧ ___const_999_0 − ___const_999_0 ≤ 0 3 2 1: 1 − i2_0 ≤ 0 ∧ − i8_post + i8_post ≤ 0 ∧ i8_post − i8_post ≤ 0 ∧ − i8_0 + i8_0 ≤ 0 ∧ i8_0 − i8_0 ≤ 0 ∧ − i6_post + i6_post ≤ 0 ∧ i6_post − i6_post ≤ 0 ∧ − i6_0 + i6_0 ≤ 0 ∧ i6_0 − i6_0 ≤ 0 ∧ − i34_post + i34_post ≤ 0 ∧ i34_post − i34_post ≤ 0 ∧ − i34_0 + i34_0 ≤ 0 ∧ i34_0 − i34_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0 ∧ − ___const_999_0 + ___const_999_0 ≤ 0 ∧ ___const_999_0 − ___const_999_0 ≤ 0 3 3 1: 1 + i2_0 ≤ 0 ∧ − i8_post + i8_post ≤ 0 ∧ i8_post − i8_post ≤ 0 ∧ − i8_0 + i8_0 ≤ 0 ∧ i8_0 − i8_0 ≤ 0 ∧ − i6_post + i6_post ≤ 0 ∧ i6_post − i6_post ≤ 0 ∧ − i6_0 + i6_0 ≤ 0 ∧ i6_0 − i6_0 ≤ 0 ∧ − i34_post + i34_post ≤ 0 ∧ i34_post − i34_post ≤ 0 ∧ − i34_0 + i34_0 ≤ 0 ∧ i34_0 − i34_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0 ∧ − ___const_999_0 + ___const_999_0 ≤ 0 ∧ ___const_999_0 − ___const_999_0 ≤ 0 3 4 2: 0 ≤ 0 ∧ 0 ≤ 0 ∧ i2_0 ≤ 0 ∧ − i2_0 ≤ 0 ∧ − ___const_999_0 + i34_post ≤ 0 ∧ ___const_999_0 − i34_post ≤ 0 ∧ i34_0 − i34_post ≤ 0 ∧ − i34_0 + i34_post ≤ 0 ∧ − i8_post + i8_post ≤ 0 ∧ i8_post − i8_post ≤ 0 ∧ − i8_0 + i8_0 ≤ 0 ∧ i8_0 − i8_0 ≤ 0 ∧ − i6_post + i6_post ≤ 0 ∧ i6_post − i6_post ≤ 0 ∧ − i6_0 + i6_0 ≤ 0 ∧ i6_0 − i6_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0 ∧ − ___const_999_0 + ___const_999_0 ≤ 0 ∧ ___const_999_0 − ___const_999_0 ≤ 0 2 5 0: − i8_post + i8_post ≤ 0 ∧ i8_post − i8_post ≤ 0 ∧ − i8_0 + i8_0 ≤ 0 ∧ i8_0 − i8_0 ≤ 0 ∧ − i6_post + i6_post ≤ 0 ∧ i6_post − i6_post ≤ 0 ∧ − i6_0 + i6_0 ≤ 0 ∧ i6_0 − i6_0 ≤ 0 ∧ − i34_post + i34_post ≤ 0 ∧ i34_post − i34_post ≤ 0 ∧ − i34_0 + i34_0 ≤ 0 ∧ i34_0 − i34_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0 ∧ − ___const_999_0 + ___const_999_0 ≤ 0 ∧ ___const_999_0 − ___const_999_0 ≤ 0 4 6 5: − i8_post + i8_post ≤ 0 ∧ i8_post − i8_post ≤ 0 ∧ − i8_0 + i8_0 ≤ 0 ∧ i8_0 − i8_0 ≤ 0 ∧ − i6_post + i6_post ≤ 0 ∧ i6_post − i6_post ≤ 0 ∧ − i6_0 + i6_0 ≤ 0 ∧ i6_0 − i6_0 ≤ 0 ∧ − i34_post + i34_post ≤ 0 ∧ i34_post − i34_post ≤ 0 ∧ − i34_0 + i34_0 ≤ 0 ∧ i34_0 − i34_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0 ∧ − ___const_999_0 + ___const_999_0 ≤ 0 ∧ ___const_999_0 − ___const_999_0 ≤ 0 6 7 7: 1 + i8_0 ≤ 0 ∧ − i8_post + i8_post ≤ 0 ∧ i8_post − i8_post ≤ 0 ∧ − i8_0 + i8_0 ≤ 0 ∧ i8_0 − i8_0 ≤ 0 ∧ − i6_post + i6_post ≤ 0 ∧ i6_post − i6_post ≤ 0 ∧ − i6_0 + i6_0 ≤ 0 ∧ i6_0 − i6_0 ≤ 0 ∧ − i34_post + i34_post ≤ 0 ∧ i34_post − i34_post ≤ 0 ∧ − i34_0 + i34_0 ≤ 0 ∧ i34_0 − i34_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0 ∧ − ___const_999_0 + ___const_999_0 ≤ 0 ∧ ___const_999_0 − ___const_999_0 ≤ 0 6 8 8: 0 ≤ 0 ∧ 0 ≤ 0 ∧ − i8_0 ≤ 0 ∧ 1 − i8_0 + i8_post ≤ 0 ∧ −1 + i8_0 − i8_post ≤ 0 ∧ i8_0 − i8_post ≤ 0 ∧ − i8_0 + i8_post ≤ 0 ∧ − i6_post + i6_post ≤ 0 ∧ i6_post − i6_post ≤ 0 ∧ − i6_0 + i6_0 ≤ 0 ∧ i6_0 − i6_0 ≤ 0 ∧ − i34_post + i34_post ≤ 0 ∧ i34_post − i34_post ≤ 0 ∧ − i34_0 + i34_0 ≤ 0 ∧ i34_0 − i34_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0 ∧ − ___const_999_0 + ___const_999_0 ≤ 0 ∧ ___const_999_0 − ___const_999_0 ≤ 0 8 9 6: − i8_post + i8_post ≤ 0 ∧ i8_post − i8_post ≤ 0 ∧ − i8_0 + i8_0 ≤ 0 ∧ i8_0 − i8_0 ≤ 0 ∧ − i6_post + i6_post ≤ 0 ∧ i6_post − i6_post ≤ 0 ∧ − i6_0 + i6_0 ≤ 0 ∧ i6_0 − i6_0 ≤ 0 ∧ − i34_post + i34_post ≤ 0 ∧ i34_post − i34_post ≤ 0 ∧ − i34_0 + i34_0 ≤ 0 ∧ i34_0 − i34_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0 ∧ − ___const_999_0 + ___const_999_0 ≤ 0 ∧ ___const_999_0 − ___const_999_0 ≤ 0 5 10 8: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + i6_0 ≤ 0 ∧ − ___const_999_0 + i8_post ≤ 0 ∧ ___const_999_0 − i8_post ≤ 0 ∧ i8_0 − i8_post ≤ 0 ∧ − i8_0 + i8_post ≤ 0 ∧ − i6_post + i6_post ≤ 0 ∧ i6_post − i6_post ≤ 0 ∧ − i6_0 + i6_0 ≤ 0 ∧ i6_0 − i6_0 ≤ 0 ∧ − i34_post + i34_post ≤ 0 ∧ i34_post − i34_post ≤ 0 ∧ − i34_0 + i34_0 ≤ 0 ∧ i34_0 − i34_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0 ∧ − ___const_999_0 + ___const_999_0 ≤ 0 ∧ ___const_999_0 − ___const_999_0 ≤ 0 5 11 4: 0 ≤ 0 ∧ 0 ≤ 0 ∧ − i6_0 ≤ 0 ∧ 1 − i6_0 + i6_post ≤ 0 ∧ −1 + i6_0 − i6_post ≤ 0 ∧ i6_0 − i6_post ≤ 0 ∧ − i6_0 + i6_post ≤ 0 ∧ − i8_post + i8_post ≤ 0 ∧ i8_post − i8_post ≤ 0 ∧ − i8_0 + i8_0 ≤ 0 ∧ i8_0 − i8_0 ≤ 0 ∧ − i34_post + i34_post ≤ 0 ∧ i34_post − i34_post ≤ 0 ∧ − i34_0 + i34_0 ≤ 0 ∧ i34_0 − i34_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0 ∧ − ___const_999_0 + ___const_999_0 ≤ 0 ∧ ___const_999_0 − ___const_999_0 ≤ 0 1 12 4: 0 ≤ 0 ∧ 0 ≤ 0 ∧ − ___const_999_0 + i6_post ≤ 0 ∧ ___const_999_0 − i6_post ≤ 0 ∧ i6_0 − i6_post ≤ 0 ∧ − i6_0 + i6_post ≤ 0 ∧ − i8_post + i8_post ≤ 0 ∧ i8_post − i8_post ≤ 0 ∧ − i8_0 + i8_0 ≤ 0 ∧ i8_0 − i8_0 ≤ 0 ∧ − i34_post + i34_post ≤ 0 ∧ i34_post − i34_post ≤ 0 ∧ − i34_0 + i34_0 ≤ 0 ∧ i34_0 − i34_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0 ∧ − ___const_999_0 + ___const_999_0 ≤ 0 ∧ ___const_999_0 − ___const_999_0 ≤ 0 9 13 3: 0 ≤ 0 ∧ 0 ≤ 0 ∧ −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ i2_0 − i2_post ≤ 0 ∧ − i2_0 + i2_post ≤ 0 ∧ − i8_post + i8_post ≤ 0 ∧ i8_post − i8_post ≤ 0 ∧ − i8_0 + i8_0 ≤ 0 ∧ i8_0 − i8_0 ≤ 0 ∧ − i6_post + i6_post ≤ 0 ∧ i6_post − i6_post ≤ 0 ∧ − i6_0 + i6_0 ≤ 0 ∧ i6_0 − i6_0 ≤ 0 ∧ − i34_post + i34_post ≤ 0 ∧ i34_post − i34_post ≤ 0 ∧ − i34_0 + i34_0 ≤ 0 ∧ i34_0 − i34_0 ≤ 0 ∧ − ___const_999_0 + ___const_999_0 ≤ 0 ∧ ___const_999_0 − ___const_999_0 ≤ 0 10 14 9: − i8_post + i8_post ≤ 0 ∧ i8_post − i8_post ≤ 0 ∧ − i8_0 + i8_0 ≤ 0 ∧ i8_0 − i8_0 ≤ 0 ∧ − i6_post + i6_post ≤ 0 ∧ i6_post − i6_post ≤ 0 ∧ − i6_0 + i6_0 ≤ 0 ∧ i6_0 − i6_0 ≤ 0 ∧ − i34_post + i34_post ≤ 0 ∧ i34_post − i34_post ≤ 0 ∧ − i34_0 + i34_0 ≤ 0 ∧ i34_0 − i34_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0 ∧ − ___const_999_0 + ___const_999_0 ≤ 0 ∧ ___const_999_0 − ___const_999_0 ≤ 0

## Proof

The following invariants are asserted.

 0: −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ 1 − i2_0 ≤ 0 ∧ i2_0 ≤ 0 1: −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ −1 + i2_0 ≤ 0 ∧ 1 − i2_0 ≤ 0 2: −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ 1 − i2_0 ≤ 0 ∧ i2_0 ≤ 0 3: −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ −1 + i2_0 ≤ 0 ∧ 1 − i2_0 ≤ 0 4: −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ −1 + i2_0 ≤ 0 ∧ 1 − i2_0 ≤ 0 5: −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ −1 + i2_0 ≤ 0 ∧ 1 − i2_0 ≤ 0 6: −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ −1 + i2_0 ≤ 0 ∧ 1 − i2_0 ≤ 0 ∧ 1 + i6_0 ≤ 0 7: −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ −1 + i2_0 ≤ 0 ∧ 1 − i2_0 ≤ 0 ∧ 1 + i6_0 ≤ 0 ∧ 1 + i8_0 ≤ 0 8: −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ −1 + i2_0 ≤ 0 ∧ 1 − i2_0 ≤ 0 ∧ 1 + i6_0 ≤ 0 9: TRUE 10: TRUE

The invariants are proved as follows.

### IMPACT Invariant Proof

• nodes (location) invariant:  0 (0) −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ 1 − i2_0 ≤ 0 ∧ i2_0 ≤ 0 1 (1) −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ −1 + i2_0 ≤ 0 ∧ 1 − i2_0 ≤ 0 2 (2) −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ 1 − i2_0 ≤ 0 ∧ i2_0 ≤ 0 3 (3) −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ −1 + i2_0 ≤ 0 ∧ 1 − i2_0 ≤ 0 4 (4) −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ −1 + i2_0 ≤ 0 ∧ 1 − i2_0 ≤ 0 5 (5) −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ −1 + i2_0 ≤ 0 ∧ 1 − i2_0 ≤ 0 6 (6) −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ −1 + i2_0 ≤ 0 ∧ 1 − i2_0 ≤ 0 ∧ 1 + i6_0 ≤ 0 7 (7) −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ −1 + i2_0 ≤ 0 ∧ 1 − i2_0 ≤ 0 ∧ 1 + i6_0 ≤ 0 ∧ 1 + i8_0 ≤ 0 8 (8) −1 + i2_post ≤ 0 ∧ 1 − i2_post ≤ 0 ∧ −1 + i2_0 ≤ 0 ∧ 1 − i2_0 ≤ 0 ∧ 1 + i6_0 ≤ 0 9 (9) TRUE 10 (10) TRUE
• initial node: 10
• cover edges:
• transition edges:  0 0 1 0 1 2 1 12 4 2 5 0 3 2 1 3 3 1 3 4 2 4 6 5 5 10 8 5 11 4 6 7 7 6 8 8 8 9 6 9 13 3 10 14 9

### 2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 2 15 2: − i8_post + i8_post ≤ 0 ∧ i8_post − i8_post ≤ 0 ∧ − i8_0 + i8_0 ≤ 0 ∧ i8_0 − i8_0 ≤ 0 ∧ − i6_post + i6_post ≤ 0 ∧ i6_post − i6_post ≤ 0 ∧ − i6_0 + i6_0 ≤ 0 ∧ i6_0 − i6_0 ≤ 0 ∧ − i34_post + i34_post ≤ 0 ∧ i34_post − i34_post ≤ 0 ∧ − i34_0 + i34_0 ≤ 0 ∧ i34_0 − i34_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0 ∧ − ___const_999_0 + ___const_999_0 ≤ 0 ∧ ___const_999_0 − ___const_999_0 ≤ 0 4 22 4: − i8_post + i8_post ≤ 0 ∧ i8_post − i8_post ≤ 0 ∧ − i8_0 + i8_0 ≤ 0 ∧ i8_0 − i8_0 ≤ 0 ∧ − i6_post + i6_post ≤ 0 ∧ i6_post − i6_post ≤ 0 ∧ − i6_0 + i6_0 ≤ 0 ∧ i6_0 − i6_0 ≤ 0 ∧ − i34_post + i34_post ≤ 0 ∧ i34_post − i34_post ≤ 0 ∧ − i34_0 + i34_0 ≤ 0 ∧ i34_0 − i34_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0 ∧ − ___const_999_0 + ___const_999_0 ≤ 0 ∧ ___const_999_0 − ___const_999_0 ≤ 0 8 29 8: − i8_post + i8_post ≤ 0 ∧ i8_post − i8_post ≤ 0 ∧ − i8_0 + i8_0 ≤ 0 ∧ i8_0 − i8_0 ≤ 0 ∧ − i6_post + i6_post ≤ 0 ∧ i6_post − i6_post ≤ 0 ∧ − i6_0 + i6_0 ≤ 0 ∧ i6_0 − i6_0 ≤ 0 ∧ − i34_post + i34_post ≤ 0 ∧ i34_post − i34_post ≤ 0 ∧ − i34_0 + i34_0 ≤ 0 ∧ i34_0 − i34_0 ≤ 0 ∧ − i2_post + i2_post ≤ 0 ∧ i2_post − i2_post ≤ 0 ∧ − i2_0 + i2_0 ≤ 0 ∧ i2_0 − i2_0 ≤ 0 ∧ − ___const_999_0 + ___const_999_0 ≤ 0 ∧ ___const_999_0 − ___const_999_0 ≤ 0
and for every transition t, a duplicate t is considered.

### 3 Transition Removal

We remove transitions 0, 2, 3, 4, 7, 10, 12, 13, 14 using the following ranking functions, which are bounded by −25.

 10: 0 9: 0 3: 0 0: 0 2: 0 1: 0 4: 0 5: 0 6: 0 8: 0 7: 0 10: −9 9: −10 3: −11 0: −12 2: −12 2_var_snapshot: −12 2*: −12 1: −13 4: −14 5: −14 4_var_snapshot: −14 4*: −14 6: −15 8: −15 8_var_snapshot: −15 8*: −15 7: −16
Hints:
 16 lexWeak[ [0, 0, 1, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 23 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 30 lexWeak[ [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, 1, 1, 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, 1, 1, 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] ] 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] ] 9 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 11 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 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] ] 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] ] 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] ] 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] ] 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] ] 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] ] 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] ] 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] ]

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

2* 18 2: i8_post + i8_post ≤ 0i8_posti8_post ≤ 0i8_0 + i8_0 ≤ 0i8_0i8_0 ≤ 0i6_post + i6_post ≤ 0i6_posti6_post ≤ 0i6_0 + i6_0 ≤ 0i6_0i6_0 ≤ 0i34_post + i34_post ≤ 0i34_posti34_post ≤ 0i34_0 + i34_0 ≤ 0i34_0i34_0 ≤ 0i2_post + i2_post ≤ 0i2_posti2_post ≤ 0i2_0 + i2_0 ≤ 0i2_0i2_0 ≤ 0___const_999_0 + ___const_999_0 ≤ 0___const_999_0___const_999_0 ≤ 0

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

2 16 2_var_snapshot: i8_post + i8_post ≤ 0i8_posti8_post ≤ 0i8_0 + i8_0 ≤ 0i8_0i8_0 ≤ 0i6_post + i6_post ≤ 0i6_posti6_post ≤ 0i6_0 + i6_0 ≤ 0i6_0i6_0 ≤ 0i34_post + i34_post ≤ 0i34_posti34_post ≤ 0i34_0 + i34_0 ≤ 0i34_0i34_0 ≤ 0i2_post + i2_post ≤ 0i2_posti2_post ≤ 0i2_0 + i2_0 ≤ 0i2_0i2_0 ≤ 0___const_999_0 + ___const_999_0 ≤ 0___const_999_0___const_999_0 ≤ 0

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

4* 25 4: i8_post + i8_post ≤ 0i8_posti8_post ≤ 0i8_0 + i8_0 ≤ 0i8_0i8_0 ≤ 0i6_post + i6_post ≤ 0i6_posti6_post ≤ 0i6_0 + i6_0 ≤ 0i6_0i6_0 ≤ 0i34_post + i34_post ≤ 0i34_posti34_post ≤ 0i34_0 + i34_0 ≤ 0i34_0i34_0 ≤ 0i2_post + i2_post ≤ 0i2_posti2_post ≤ 0i2_0 + i2_0 ≤ 0i2_0i2_0 ≤ 0___const_999_0 + ___const_999_0 ≤ 0___const_999_0___const_999_0 ≤ 0

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

4 23 4_var_snapshot: i8_post + i8_post ≤ 0i8_posti8_post ≤ 0i8_0 + i8_0 ≤ 0i8_0i8_0 ≤ 0i6_post + i6_post ≤ 0i6_posti6_post ≤ 0i6_0 + i6_0 ≤ 0i6_0i6_0 ≤ 0i34_post + i34_post ≤ 0i34_posti34_post ≤ 0i34_0 + i34_0 ≤ 0i34_0i34_0 ≤ 0i2_post + i2_post ≤ 0i2_posti2_post ≤ 0i2_0 + i2_0 ≤ 0i2_0i2_0 ≤ 0___const_999_0 + ___const_999_0 ≤ 0___const_999_0___const_999_0 ≤ 0

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

8* 32 8: i8_post + i8_post ≤ 0i8_posti8_post ≤ 0i8_0 + i8_0 ≤ 0i8_0i8_0 ≤ 0i6_post + i6_post ≤ 0i6_posti6_post ≤ 0i6_0 + i6_0 ≤ 0i6_0i6_0 ≤ 0i34_post + i34_post ≤ 0i34_posti34_post ≤ 0i34_0 + i34_0 ≤ 0i34_0i34_0 ≤ 0i2_post + i2_post ≤ 0i2_posti2_post ≤ 0i2_0 + i2_0 ≤ 0i2_0i2_0 ≤ 0___const_999_0 + ___const_999_0 ≤ 0___const_999_0___const_999_0 ≤ 0

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

8 30 8_var_snapshot: i8_post + i8_post ≤ 0i8_posti8_post ≤ 0i8_0 + i8_0 ≤ 0i8_0i8_0 ≤ 0i6_post + i6_post ≤ 0i6_posti6_post ≤ 0i6_0 + i6_0 ≤ 0i6_0i6_0 ≤ 0i34_post + i34_post ≤ 0i34_posti34_post ≤ 0i34_0 + i34_0 ≤ 0i34_0i34_0 ≤ 0i2_post + i2_post ≤ 0i2_posti2_post ≤ 0i2_0 + i2_0 ≤ 0i2_0i2_0 ≤ 0___const_999_0 + ___const_999_0 ≤ 0___const_999_0___const_999_0 ≤ 0

### 10 SCC Decomposition

We consider subproblems for each of the 3 SCC(s) of the program graph.

### 10.1 SCC Subproblem 1/3

Here we consider the SCC { 6, 8, 8_var_snapshot, 8* }.

### 10.1.1 Transition Removal

We remove transition 8 using the following ranking functions, which are bounded by −4.

 6: − i2_0 − 2⋅i2_post + 4⋅i8_0 8: −1 + 4⋅i8_0 8_var_snapshot: −2⋅i2_post + 4⋅i8_0 8*: 4⋅i8_0
Hints:
 30 lexWeak[ [0, 2, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0] ] 32 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 8 lexStrict[ [2, 0, 1, 0, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [2, 0, 1, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 9 lexWeak[ [0, 0, 0, 1, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 1, 0, 0] ]

### 10.1.2 Transition Removal

We remove transitions 30, 32, 9 using the following ranking functions, which are bounded by −2.

 6: −2⋅i2_0 8: 0 8_var_snapshot: − i2_0 8*: i2_post
Hints:
 30 lexStrict[ [0, 0, 0, 1, 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] ] 32 lexStrict[ [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] ] 9 lexStrict[ [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 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] ]

### 10.1.3 Splitting Cut-Point Transitions

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

### 10.1.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 29.

### 10.1.3.1.1 Splitting Cut-Point Transitions

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

### 10.2 SCC Subproblem 2/3

Here we consider the SCC { 4, 5, 4_var_snapshot, 4* }.

### 10.2.1 Transition Removal

We remove transition 11 using the following ranking functions, which are bounded by 0.

 4: 3⋅i2_0 + 4⋅i6_0 5: i2_post + 4⋅i6_0 4_var_snapshot: 2⋅i2_post + 4⋅i6_0 4*: 3⋅i2_0 + i2_post + 4⋅i6_0
Hints:
 23 lexWeak[ [2, 0, 0, 3, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0] ] 25 lexWeak[ [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0] ] 6 lexWeak[ [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0] ] 11 lexStrict[ [0, 0, 3, 0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 3, 0, 0, 0] , [0, 1, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

### 10.2.2 Transition Removal

We remove transitions 25, 6 using the following ranking functions, which are bounded by −1.

 4: 0 5: − i2_0 4_var_snapshot: 0 4*: 1
Hints:
 23 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 25 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] ] 6 lexStrict[ [0, 0, 0, 1, 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] ]

### 10.2.3 Transition Removal

We remove transition 23 using the following ranking functions, which are bounded by −1.

 4: 0 5: 0 4_var_snapshot: − i2_0 4*: 0
Hints:
 23 lexStrict[ [0, 0, 0, 1, 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] ]

### 10.2.4 Splitting Cut-Point Transitions

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

### 10.2.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 22.

### 10.2.4.1.1 Splitting Cut-Point Transitions

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

### 10.3 SCC Subproblem 3/3

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

### 10.3.1 Transition Removal

We remove transitions 16, 18, 1, 5 using the following ranking functions, which are bounded by −2.

 0: 1 2: − i2_post 2_var_snapshot: 0 2*: 0
Hints:
 16 lexStrict[ [1, 0, 2, 2, 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] ] 18 lexStrict[ [0, 1, 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] ] 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] ] 5 lexStrict[ [0, 0, 2, 2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

### 10.3.2 Splitting Cut-Point Transitions

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

### 10.3.2.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 15.

### 10.3.2.1.1 Splitting Cut-Point Transitions

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

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