# 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 ∧ 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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 0 2 1 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 + 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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 0 4 2 5: 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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 0 3 3 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 + ___const_11_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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 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 ∧ − ___const_11_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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 0 1 5 4: 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 + ___const_9_0 − oldX0_post ≤ 0 ∧ − oldX0_post + x0_post ≤ 0 ∧ 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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 0 1 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 ∧ − ___const_9_0 + oldX0_post ≤ 0 ∧ − oldX0_post + x0_post ≤ 0 ∧ oldX0_post − x0_post ≤ 0 ∧ −3 + x1_post ≤ 0 ∧ 3 − 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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 0 6 7 1: 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 ∧ x0_post ≤ 0 ∧ − 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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 0 7 8 6: 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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 0 7 9 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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 0 7 10 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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 0 7 11 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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 0 7 12 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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 0 7 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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 0 7 14 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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 0 7 15 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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 0 8 16 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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 0

## Proof

### 1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 1 17 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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 0 3 24 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 ∧ − ___const_9_0 + ___const_9_0 ≤ 0 ∧ ___const_9_0 − ___const_9_0 ≤ 0 ∧ − ___const_11_0 + ___const_11_0 ≤ 0 ∧ ___const_11_0 − ___const_11_0 ≤ 0
and for every transition t, a duplicate t is considered.

### 2 Transition Removal

We remove transitions 2, 5, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16 using the following ranking functions, which are bounded by −19.

 8: 0 7: 0 6: 0 0: 0 1: 0 2: 0 3: 0 4: 0 5: 0 8: −7 7: −8 6: −9 0: −10 1: −10 2: −10 3: −10 1_var_snapshot: −10 1*: −10 3_var_snapshot: −10 3*: −10 4: −16 5: −17
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, 0, 0, 0, 0] ] 25 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 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] ] 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, 0, 0, 0, 0] ] 3 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] ] 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, 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, 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] ] 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, 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, 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, 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] ] 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] ] 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, 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, 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, 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, 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, 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, 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.

1* 20 1: x1_post + x1_post ≤ 0x1_postx1_post ≤ 0x1_0 + x1_0 ≤ 0x1_0x1_0 ≤ 0x0_post + x0_post ≤ 0x0_postx0_post ≤ 0x0_0 + x0_0 ≤ 0x0_0x0_0 ≤ 0oldX3_post + oldX3_post ≤ 0oldX3_postoldX3_post ≤ 0oldX3_0 + oldX3_0 ≤ 0oldX3_0oldX3_0 ≤ 0oldX2_post + oldX2_post ≤ 0oldX2_postoldX2_post ≤ 0oldX2_0 + oldX2_0 ≤ 0oldX2_0oldX2_0 ≤ 0oldX1_post + oldX1_post ≤ 0oldX1_postoldX1_post ≤ 0oldX1_0 + oldX1_0 ≤ 0oldX1_0oldX1_0 ≤ 0oldX0_post + oldX0_post ≤ 0oldX0_postoldX0_post ≤ 0oldX0_0 + oldX0_0 ≤ 0oldX0_0oldX0_0 ≤ 0___const_9_0 + ___const_9_0 ≤ 0___const_9_0___const_9_0 ≤ 0___const_11_0 + ___const_11_0 ≤ 0___const_11_0___const_11_0 ≤ 0

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

1 18 1_var_snapshot: x1_post + x1_post ≤ 0x1_postx1_post ≤ 0x1_0 + x1_0 ≤ 0x1_0x1_0 ≤ 0x0_post + x0_post ≤ 0x0_postx0_post ≤ 0x0_0 + x0_0 ≤ 0x0_0x0_0 ≤ 0oldX3_post + oldX3_post ≤ 0oldX3_postoldX3_post ≤ 0oldX3_0 + oldX3_0 ≤ 0oldX3_0oldX3_0 ≤ 0oldX2_post + oldX2_post ≤ 0oldX2_postoldX2_post ≤ 0oldX2_0 + oldX2_0 ≤ 0oldX2_0oldX2_0 ≤ 0oldX1_post + oldX1_post ≤ 0oldX1_postoldX1_post ≤ 0oldX1_0 + oldX1_0 ≤ 0oldX1_0oldX1_0 ≤ 0oldX0_post + oldX0_post ≤ 0oldX0_postoldX0_post ≤ 0oldX0_0 + oldX0_0 ≤ 0oldX0_0oldX0_0 ≤ 0___const_9_0 + ___const_9_0 ≤ 0___const_9_0___const_9_0 ≤ 0___const_11_0 + ___const_11_0 ≤ 0___const_11_0___const_11_0 ≤ 0

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

3* 27 3: x1_post + x1_post ≤ 0x1_postx1_post ≤ 0x1_0 + x1_0 ≤ 0x1_0x1_0 ≤ 0x0_post + x0_post ≤ 0x0_postx0_post ≤ 0x0_0 + x0_0 ≤ 0x0_0x0_0 ≤ 0oldX3_post + oldX3_post ≤ 0oldX3_postoldX3_post ≤ 0oldX3_0 + oldX3_0 ≤ 0oldX3_0oldX3_0 ≤ 0oldX2_post + oldX2_post ≤ 0oldX2_postoldX2_post ≤ 0oldX2_0 + oldX2_0 ≤ 0oldX2_0oldX2_0 ≤ 0oldX1_post + oldX1_post ≤ 0oldX1_postoldX1_post ≤ 0oldX1_0 + oldX1_0 ≤ 0oldX1_0oldX1_0 ≤ 0oldX0_post + oldX0_post ≤ 0oldX0_postoldX0_post ≤ 0oldX0_0 + oldX0_0 ≤ 0oldX0_0oldX0_0 ≤ 0___const_9_0 + ___const_9_0 ≤ 0___const_9_0___const_9_0 ≤ 0___const_11_0 + ___const_11_0 ≤ 0___const_11_0___const_11_0 ≤ 0

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

3 25 3_var_snapshot: x1_post + x1_post ≤ 0x1_postx1_post ≤ 0x1_0 + x1_0 ≤ 0x1_0x1_0 ≤ 0x0_post + x0_post ≤ 0x0_postx0_post ≤ 0x0_0 + x0_0 ≤ 0x0_0x0_0 ≤ 0oldX3_post + oldX3_post ≤ 0oldX3_postoldX3_post ≤ 0oldX3_0 + oldX3_0 ≤ 0oldX3_0oldX3_0 ≤ 0oldX2_post + oldX2_post ≤ 0oldX2_postoldX2_post ≤ 0oldX2_0 + oldX2_0 ≤ 0oldX2_0oldX2_0 ≤ 0oldX1_post + oldX1_post ≤ 0oldX1_postoldX1_post ≤ 0oldX1_0 + oldX1_0 ≤ 0oldX1_0oldX1_0 ≤ 0oldX0_post + oldX0_post ≤ 0oldX0_postoldX0_post ≤ 0oldX0_0 + oldX0_0 ≤ 0oldX0_0oldX0_0 ≤ 0___const_9_0 + ___const_9_0 ≤ 0___const_9_0___const_9_0 ≤ 0___const_11_0 + ___const_11_0 ≤ 0___const_11_0___const_11_0 ≤ 0

### 7 SCC Decomposition

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

### 7.1 SCC Subproblem 1/1

Here we consider the SCC { 0, 1, 2, 3, 1_var_snapshot, 1*, 3_var_snapshot, 3* }.

### 7.1.1 Transition Removal

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

 0: −2 + 4⋅___const_9_0 − 4⋅x0_0 1: 1 + 4⋅___const_9_0 − 4⋅x0_0 2: −1 + 4⋅___const_9_0 − 4⋅x0_0 3: −1 + 4⋅___const_9_0 − 4⋅x0_0 1_var_snapshot: 4⋅___const_9_0 − 4⋅x0_0 1*: 2 + 4⋅___const_9_0 − 4⋅x0_0 3_var_snapshot: −1 + 4⋅___const_9_0 − 4⋅x0_0 3*: −1 + 4⋅___const_9_0 − 4⋅x0_0
Hints:
 18 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0] ] 20 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0] ] 25 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0] ] 27 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0] ] 0 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0] ] 1 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0] ] 3 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0] ] 4 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0] ] 6 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

### 7.1.2 Transition Removal

We remove transition 4 using the following ranking functions, which are bounded by −1.

 0: −1 + 4⋅___const_11_0 − 4⋅x1_0 1: −2 + 4⋅___const_11_0 − 4⋅oldX1_post 2: −1 + 4⋅___const_11_0 − 4⋅x1_0 3: 1 + 4⋅___const_11_0 − 4⋅x1_0 1_var_snapshot: −2 + 4⋅___const_11_0 − 4⋅oldX1_post 1*: −1 + 4⋅___const_11_0 − 4⋅oldX1_post 3_var_snapshot: 4⋅___const_11_0 − 4⋅x1_0 3*: 2 + 4⋅___const_11_0 − 4⋅x1_0
Hints:
 18 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0] ] 20 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0] ] 25 lexWeak[ [0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0] ] 27 lexWeak[ [0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0] ] 0 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0] ] 1 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0] ] 3 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0] ] 4 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

### 7.1.3 Transition Removal

We remove transitions 18, 20, 25, 27, 0, 1, 3 using the following ranking functions, which are bounded by −4.

 0: −1 1: −3 2: 3 3: 1 1_var_snapshot: −4 1*: −2 3_var_snapshot: 0 3*: 2
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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 27 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 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] ] 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, 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, 0, 0, 0, 0, 0, 0, 0, 0] ]

### 7.1.4 Splitting Cut-Point Transitions

We consider 2 subproblems corresponding to sets of cut-point transitions as follows.

### 7.1.4.1 Cut-Point Subproblem 1/2

Here we consider cut-point transition 17.

### 7.1.4.1.1 Splitting Cut-Point Transitions

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

### 7.1.4.2 Cut-Point Subproblem 2/2

Here we consider cut-point transition 24.

### 7.1.4.2.1 Splitting Cut-Point Transitions

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

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