# LTS Termination Proof

by T2Cert

## Input

Integer Transition System
• Initial Location: 17
• Transitions: (pre-variables and post-variables)  0 0 1: − i_0 + nodecount_0 ≤ 0 ∧ − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 0 1 2: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + i_0 − nodecount_0 ≤ 0 ∧ −1 − i_0 + i_post ≤ 0 ∧ 1 + i_0 − i_post ≤ 0 ∧ i_0 − i_post ≤ 0 ∧ − i_0 + i_post ≤ 0 ∧ − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 3 2 4: 0 ≤ 0 ∧ 0 ≤ 0 ∧ −1 − i_0 + i_post ≤ 0 ∧ 1 + i_0 − i_post ≤ 0 ∧ i_0 − i_post ≤ 0 ∧ − i_0 + i_post ≤ 0 ∧ − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 3 3 1: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 5 4 6: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 7 5 2: 0 ≤ 0 ∧ 0 ≤ 0 ∧ edgecount_0 − i_0 ≤ 0 ∧ i_post ≤ 0 ∧ − i_post ≤ 0 ∧ i_0 − i_post ≤ 0 ∧ − i_0 + i_post ≤ 0 ∧ − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 7 6 3: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − edgecount_0 + i_0 ≤ 0 ∧ x_0 − x_post ≤ 0 ∧ − x_0 + x_post ≤ 0 ∧ y_0 − y_post ≤ 0 ∧ − y_0 + y_post ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 8 7 9: 0 ≤ 0 ∧ 0 ≤ 0 ∧ −1 − j_0 + j_post ≤ 0 ∧ 1 + j_0 − j_post ≤ 0 ∧ j_0 − j_post ≤ 0 ∧ − j_0 + j_post ≤ 0 ∧ − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 10 8 11: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 12 9 10: 0 ≤ 0 ∧ 0 ≤ 0 ∧ edgecount_0 − j_0 ≤ 0 ∧ −1 − i_0 + i_post ≤ 0 ∧ 1 + i_0 − i_post ≤ 0 ∧ i_0 − i_post ≤ 0 ∧ − i_0 + i_post ≤ 0 ∧ − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 12 10 8: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − edgecount_0 + j_0 ≤ 0 ∧ x_0 − x_post ≤ 0 ∧ − x_0 + x_post ≤ 0 ∧ y_0 − y_post ≤ 0 ∧ − y_0 + y_post ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 11 11 4: 0 ≤ 0 ∧ 0 ≤ 0 ∧ − i_0 + nodecount_0 ≤ 0 ∧ i_post ≤ 0 ∧ − i_post ≤ 0 ∧ i_0 − i_post ≤ 0 ∧ − i_0 + i_post ≤ 0 ∧ − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 11 12 9: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + i_0 − nodecount_0 ≤ 0 ∧ j_post ≤ 0 ∧ − j_post ≤ 0 ∧ j_0 − j_post ≤ 0 ∧ − j_0 + j_post ≤ 0 ∧ − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 13 13 14: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 14 14 5: 0 ≤ 0 ∧ 0 ≤ 0 ∧ −1 − i_0 + i_post ≤ 0 ∧ 1 + i_0 − i_post ≤ 0 ∧ i_0 − i_post ≤ 0 ∧ − i_0 + i_post ≤ 0 ∧ − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 9 15 12: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 15 16 13: 1 − i_0 + source_0 ≤ 0 ∧ − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 15 17 13: 1 + i_0 − source_0 ≤ 0 ∧ − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 15 18 14: i_0 − source_0 ≤ 0 ∧ − i_0 + source_0 ≤ 0 ∧ − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 6 19 10: 0 ≤ 0 ∧ 0 ≤ 0 ∧ − i_0 + nodecount_0 ≤ 0 ∧ i_post ≤ 0 ∧ − i_post ≤ 0 ∧ i_0 − i_post ≤ 0 ∧ − i_0 + i_post ≤ 0 ∧ − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 6 20 15: 1 + i_0 − nodecount_0 ≤ 0 ∧ − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 4 21 7: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 2 22 0: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 16 23 5: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ i_post ≤ 0 ∧ − i_post ≤ 0 ∧ edgecount_0 − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_post ≤ 0 ∧ i_0 − i_post ≤ 0 ∧ − i_0 + i_post ≤ 0 ∧ nodecount_0 − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_post ≤ 0 ∧ source_0 − source_post ≤ 0 ∧ − source_0 + source_post ≤ 0 ∧ − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 17 24 16: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0

## Proof

The following invariants are asserted.

 0: −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 1: −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 2: −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 3: −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 4: −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 5: −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 6: −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 7: −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 8: −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 9: −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 10: −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 11: −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 12: −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 13: −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 14: −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 15: −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 16: TRUE 17: TRUE

The invariants are proved as follows.

### IMPACT Invariant Proof

• nodes (location) invariant:  0 (0) −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 1 (1) −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 2 (2) −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 3 (3) −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 4 (4) −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 5 (5) −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 6 (6) −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 7 (7) −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 8 (8) −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 9 (9) −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 10 (10) −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 11 (11) −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 12 (12) −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 13 (13) −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 14 (14) −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 15 (15) −9 + edgecount_post ≤ 0 ∧ 9 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −9 + edgecount_0 ≤ 0 ∧ 9 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 16 (16) TRUE 17 (17) TRUE
• initial node: 17
• cover edges:
• transition edges:  0 0 1 0 1 2 2 22 0 3 2 4 3 3 1 4 21 7 5 4 6 6 19 10 6 20 15 7 5 2 7 6 3 8 7 9 9 15 12 10 8 11 11 11 4 11 12 9 12 9 10 12 10 8 13 13 14 14 14 5 15 16 13 15 17 13 15 18 14 16 23 5 17 24 16

### 2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 2 25 2: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 4 32 4: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 5 39 5: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 9 46 9: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0 10 53 10: − y_post + y_post ≤ 0 ∧ y_post − y_post ≤ 0 ∧ − y_0 + y_0 ≤ 0 ∧ y_0 − y_0 ≤ 0 ∧ − x_post + x_post ≤ 0 ∧ x_post − x_post ≤ 0 ∧ − x_0 + x_0 ≤ 0 ∧ x_0 − x_0 ≤ 0 ∧ − source_post + source_post ≤ 0 ∧ source_post − source_post ≤ 0 ∧ − source_0 + source_0 ≤ 0 ∧ source_0 − source_0 ≤ 0 ∧ − nodecount_post + nodecount_post ≤ 0 ∧ nodecount_post − nodecount_post ≤ 0 ∧ − nodecount_0 + nodecount_0 ≤ 0 ∧ nodecount_0 − nodecount_0 ≤ 0 ∧ − j_post + j_post ≤ 0 ∧ j_post − j_post ≤ 0 ∧ − j_0 + j_0 ≤ 0 ∧ j_0 − j_0 ≤ 0 ∧ − i_post + i_post ≤ 0 ∧ i_post − i_post ≤ 0 ∧ − i_0 + i_0 ≤ 0 ∧ i_0 − i_0 ≤ 0 ∧ − edgecount_post + edgecount_post ≤ 0 ∧ edgecount_post − edgecount_post ≤ 0 ∧ − edgecount_0 + edgecount_0 ≤ 0 ∧ edgecount_0 − edgecount_0 ≤ 0
and for every transition t, a duplicate t is considered.

### 3 Transition Removal

We remove transitions 0, 3, 5, 11, 19, 23, 24 using the following ranking functions, which are bounded by −27.

 17: 0 16: 0 5: 0 6: 0 13: 0 14: 0 15: 0 8: 0 9: 0 10: 0 11: 0 12: 0 3: 0 4: 0 7: 0 0: 0 2: 0 1: 0 17: −8 16: −9 5: −10 6: −10 13: −10 14: −10 15: −10 5_var_snapshot: −10 5*: −10 8: −11 9: −11 12: −11 10: −11 11: −11 9_var_snapshot: −11 9*: −11 10_var_snapshot: −11 10*: −11 3: −14 4: −14 7: −14 4_var_snapshot: −14 4*: −14 0: −15 2: −15 2_var_snapshot: −15 2*: −15 1: −16
Hints:
 26 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] ] 33 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] ] 40 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] ] 47 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] ] 54 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] ] 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, 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, 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, 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, 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, 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, 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, 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, 0, 0, 0, 0, 0, 0] ] 12 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] ] 13 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] ] 14 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] ] 15 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] ] 16 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] ] 17 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] ] 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 21 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] ] 22 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 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] ] 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, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 19 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] ] 23 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] ] 24 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.

2* 28 2: y_post + y_post ≤ 0y_posty_post ≤ 0y_0 + y_0 ≤ 0y_0y_0 ≤ 0x_post + x_post ≤ 0x_postx_post ≤ 0x_0 + x_0 ≤ 0x_0x_0 ≤ 0source_post + source_post ≤ 0source_postsource_post ≤ 0source_0 + source_0 ≤ 0source_0source_0 ≤ 0nodecount_post + nodecount_post ≤ 0nodecount_postnodecount_post ≤ 0nodecount_0 + nodecount_0 ≤ 0nodecount_0nodecount_0 ≤ 0j_post + j_post ≤ 0j_postj_post ≤ 0j_0 + j_0 ≤ 0j_0j_0 ≤ 0i_post + i_post ≤ 0i_posti_post ≤ 0i_0 + i_0 ≤ 0i_0i_0 ≤ 0edgecount_post + edgecount_post ≤ 0edgecount_postedgecount_post ≤ 0edgecount_0 + edgecount_0 ≤ 0edgecount_0edgecount_0 ≤ 0

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

2 26 2_var_snapshot: y_post + y_post ≤ 0y_posty_post ≤ 0y_0 + y_0 ≤ 0y_0y_0 ≤ 0x_post + x_post ≤ 0x_postx_post ≤ 0x_0 + x_0 ≤ 0x_0x_0 ≤ 0source_post + source_post ≤ 0source_postsource_post ≤ 0source_0 + source_0 ≤ 0source_0source_0 ≤ 0nodecount_post + nodecount_post ≤ 0nodecount_postnodecount_post ≤ 0nodecount_0 + nodecount_0 ≤ 0nodecount_0nodecount_0 ≤ 0j_post + j_post ≤ 0j_postj_post ≤ 0j_0 + j_0 ≤ 0j_0j_0 ≤ 0i_post + i_post ≤ 0i_posti_post ≤ 0i_0 + i_0 ≤ 0i_0i_0 ≤ 0edgecount_post + edgecount_post ≤ 0edgecount_postedgecount_post ≤ 0edgecount_0 + edgecount_0 ≤ 0edgecount_0edgecount_0 ≤ 0

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

4* 35 4: y_post + y_post ≤ 0y_posty_post ≤ 0y_0 + y_0 ≤ 0y_0y_0 ≤ 0x_post + x_post ≤ 0x_postx_post ≤ 0x_0 + x_0 ≤ 0x_0x_0 ≤ 0source_post + source_post ≤ 0source_postsource_post ≤ 0source_0 + source_0 ≤ 0source_0source_0 ≤ 0nodecount_post + nodecount_post ≤ 0nodecount_postnodecount_post ≤ 0nodecount_0 + nodecount_0 ≤ 0nodecount_0nodecount_0 ≤ 0j_post + j_post ≤ 0j_postj_post ≤ 0j_0 + j_0 ≤ 0j_0j_0 ≤ 0i_post + i_post ≤ 0i_posti_post ≤ 0i_0 + i_0 ≤ 0i_0i_0 ≤ 0edgecount_post + edgecount_post ≤ 0edgecount_postedgecount_post ≤ 0edgecount_0 + edgecount_0 ≤ 0edgecount_0edgecount_0 ≤ 0

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

4 33 4_var_snapshot: y_post + y_post ≤ 0y_posty_post ≤ 0y_0 + y_0 ≤ 0y_0y_0 ≤ 0x_post + x_post ≤ 0x_postx_post ≤ 0x_0 + x_0 ≤ 0x_0x_0 ≤ 0source_post + source_post ≤ 0source_postsource_post ≤ 0source_0 + source_0 ≤ 0source_0source_0 ≤ 0nodecount_post + nodecount_post ≤ 0nodecount_postnodecount_post ≤ 0nodecount_0 + nodecount_0 ≤ 0nodecount_0nodecount_0 ≤ 0j_post + j_post ≤ 0j_postj_post ≤ 0j_0 + j_0 ≤ 0j_0j_0 ≤ 0i_post + i_post ≤ 0i_posti_post ≤ 0i_0 + i_0 ≤ 0i_0i_0 ≤ 0edgecount_post + edgecount_post ≤ 0edgecount_postedgecount_post ≤ 0edgecount_0 + edgecount_0 ≤ 0edgecount_0edgecount_0 ≤ 0

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

5* 42 5: y_post + y_post ≤ 0y_posty_post ≤ 0y_0 + y_0 ≤ 0y_0y_0 ≤ 0x_post + x_post ≤ 0x_postx_post ≤ 0x_0 + x_0 ≤ 0x_0x_0 ≤ 0source_post + source_post ≤ 0source_postsource_post ≤ 0source_0 + source_0 ≤ 0source_0source_0 ≤ 0nodecount_post + nodecount_post ≤ 0nodecount_postnodecount_post ≤ 0nodecount_0 + nodecount_0 ≤ 0nodecount_0nodecount_0 ≤ 0j_post + j_post ≤ 0j_postj_post ≤ 0j_0 + j_0 ≤ 0j_0j_0 ≤ 0i_post + i_post ≤ 0i_posti_post ≤ 0i_0 + i_0 ≤ 0i_0i_0 ≤ 0edgecount_post + edgecount_post ≤ 0edgecount_postedgecount_post ≤ 0edgecount_0 + edgecount_0 ≤ 0edgecount_0edgecount_0 ≤ 0

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

5 40 5_var_snapshot: y_post + y_post ≤ 0y_posty_post ≤ 0y_0 + y_0 ≤ 0y_0y_0 ≤ 0x_post + x_post ≤ 0x_postx_post ≤ 0x_0 + x_0 ≤ 0x_0x_0 ≤ 0source_post + source_post ≤ 0source_postsource_post ≤ 0source_0 + source_0 ≤ 0source_0source_0 ≤ 0nodecount_post + nodecount_post ≤ 0nodecount_postnodecount_post ≤ 0nodecount_0 + nodecount_0 ≤ 0nodecount_0nodecount_0 ≤ 0j_post + j_post ≤ 0j_postj_post ≤ 0j_0 + j_0 ≤ 0j_0j_0 ≤ 0i_post + i_post ≤ 0i_posti_post ≤ 0i_0 + i_0 ≤ 0i_0i_0 ≤ 0edgecount_post + edgecount_post ≤ 0edgecount_postedgecount_post ≤ 0edgecount_0 + edgecount_0 ≤ 0edgecount_0edgecount_0 ≤ 0

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

9* 49 9: y_post + y_post ≤ 0y_posty_post ≤ 0y_0 + y_0 ≤ 0y_0y_0 ≤ 0x_post + x_post ≤ 0x_postx_post ≤ 0x_0 + x_0 ≤ 0x_0x_0 ≤ 0source_post + source_post ≤ 0source_postsource_post ≤ 0source_0 + source_0 ≤ 0source_0source_0 ≤ 0nodecount_post + nodecount_post ≤ 0nodecount_postnodecount_post ≤ 0nodecount_0 + nodecount_0 ≤ 0nodecount_0nodecount_0 ≤ 0j_post + j_post ≤ 0j_postj_post ≤ 0j_0 + j_0 ≤ 0j_0j_0 ≤ 0i_post + i_post ≤ 0i_posti_post ≤ 0i_0 + i_0 ≤ 0i_0i_0 ≤ 0edgecount_post + edgecount_post ≤ 0edgecount_postedgecount_post ≤ 0edgecount_0 + edgecount_0 ≤ 0edgecount_0edgecount_0 ≤ 0

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

9 47 9_var_snapshot: y_post + y_post ≤ 0y_posty_post ≤ 0y_0 + y_0 ≤ 0y_0y_0 ≤ 0x_post + x_post ≤ 0x_postx_post ≤ 0x_0 + x_0 ≤ 0x_0x_0 ≤ 0source_post + source_post ≤ 0source_postsource_post ≤ 0source_0 + source_0 ≤ 0source_0source_0 ≤ 0nodecount_post + nodecount_post ≤ 0nodecount_postnodecount_post ≤ 0nodecount_0 + nodecount_0 ≤ 0nodecount_0nodecount_0 ≤ 0j_post + j_post ≤ 0j_postj_post ≤ 0j_0 + j_0 ≤ 0j_0j_0 ≤ 0i_post + i_post ≤ 0i_posti_post ≤ 0i_0 + i_0 ≤ 0i_0i_0 ≤ 0edgecount_post + edgecount_post ≤ 0edgecount_postedgecount_post ≤ 0edgecount_0 + edgecount_0 ≤ 0edgecount_0edgecount_0 ≤ 0

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

10* 56 10: y_post + y_post ≤ 0y_posty_post ≤ 0y_0 + y_0 ≤ 0y_0y_0 ≤ 0x_post + x_post ≤ 0x_postx_post ≤ 0x_0 + x_0 ≤ 0x_0x_0 ≤ 0source_post + source_post ≤ 0source_postsource_post ≤ 0source_0 + source_0 ≤ 0source_0source_0 ≤ 0nodecount_post + nodecount_post ≤ 0nodecount_postnodecount_post ≤ 0nodecount_0 + nodecount_0 ≤ 0nodecount_0nodecount_0 ≤ 0j_post + j_post ≤ 0j_postj_post ≤ 0j_0 + j_0 ≤ 0j_0j_0 ≤ 0i_post + i_post ≤ 0i_posti_post ≤ 0i_0 + i_0 ≤ 0i_0i_0 ≤ 0edgecount_post + edgecount_post ≤ 0edgecount_postedgecount_post ≤ 0edgecount_0 + edgecount_0 ≤ 0edgecount_0edgecount_0 ≤ 0

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

10 54 10_var_snapshot: y_post + y_post ≤ 0y_posty_post ≤ 0y_0 + y_0 ≤ 0y_0y_0 ≤ 0x_post + x_post ≤ 0x_postx_post ≤ 0x_0 + x_0 ≤ 0x_0x_0 ≤ 0source_post + source_post ≤ 0source_postsource_post ≤ 0source_0 + source_0 ≤ 0source_0source_0 ≤ 0nodecount_post + nodecount_post ≤ 0nodecount_postnodecount_post ≤ 0nodecount_0 + nodecount_0 ≤ 0nodecount_0nodecount_0 ≤ 0j_post + j_post ≤ 0j_postj_post ≤ 0j_0 + j_0 ≤ 0j_0j_0 ≤ 0i_post + i_post ≤ 0i_posti_post ≤ 0i_0 + i_0 ≤ 0i_0i_0 ≤ 0edgecount_post + edgecount_post ≤ 0edgecount_postedgecount_post ≤ 0edgecount_0 + edgecount_0 ≤ 0edgecount_0edgecount_0 ≤ 0

### 14 SCC Decomposition

We consider subproblems for each of the 4 SCC(s) of the program graph.

### 14.1 SCC Subproblem 1/4

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

### 14.1.1 Transition Removal

We remove transition 1 using the following ranking functions, which are bounded by 0.

 0: −6⋅i_0 + 6⋅nodecount_0 − nodecount_post 2: −1 − 6⋅i_0 + 6⋅nodecount_0 2_var_snapshot: −6 + edgecount_post − 6⋅i_0 + 6⋅nodecount_0 − nodecount_post 2*: −6⋅i_0 + 6⋅nodecount_0
Hints:
 26 lexWeak[ [1, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 0, 0, 0, 0, 0, 0, 0, 0, 6, 1, 0, 0, 0] ] 28 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0] ] 1 lexStrict[ [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0] ] 22 lexWeak[ [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 6, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0] ]

### 14.1.2 Transition Removal

We remove transitions 26, 28, 22 using the following ranking functions, which are bounded by −1.

 0: − nodecount_0 2: edgecount_0 2_var_snapshot: 0 2*: edgecount_0 + edgecount_post
Hints:
 26 lexStrict[ [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, 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] ] 28 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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] ] 22 lexStrict[ [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

### 14.1.3 Splitting Cut-Point Transitions

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

### 14.1.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 25.

### 14.1.3.1.1 Splitting Cut-Point Transitions

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

### 14.2 SCC Subproblem 2/4

Here we consider the SCC { 3, 4, 7, 4_var_snapshot, 4* }.

### 14.2.1 Transition Removal

We remove transition 6 using the following ranking functions, which are bounded by −539.

 3: −6⋅edgecount_0 − edgecount_post − 65⋅i_0 4: −65⋅i_0 7: −6⋅edgecount_0 − edgecount_post − 65⋅i_0 + 9⋅nodecount_post 4_var_snapshot: −6⋅edgecount_0 − 65⋅i_0 + 9⋅nodecount_post 4*: 55 − 6⋅edgecount_0 − 65⋅i_0
Hints:
 33 lexWeak[ [0, 0, 9, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65, 0, 0, 0, 6] ] 35 lexWeak[ [0, 0, 0, 0, 0, 0, 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, 0, 0, 65, 0, 0, 0, 0] ] 2 lexWeak[ [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65, 0, 65, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6] ] 6 lexStrict[ [0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65, 0, 1, 0, 6] , [1, 0, 0, 9, 0, 0, 71, 0, 0, 0, 0, 0, 0, 0, 65, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 21 lexWeak[ [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 65, 0, 1, 0, 6] ]

### 14.2.2 Transition Removal

We remove transitions 35, 2, 21 using the following ranking functions, which are bounded by −55.

 3: edgecount_post 4: −9⋅nodecount_post 7: −6⋅edgecount_post − nodecount_0 4_var_snapshot: −6⋅edgecount_post 4*: 0
Hints:
 33 lexWeak[ [0, 6, 9, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0] ] 35 lexStrict[ [0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 21 lexStrict[ [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0] , [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

### 14.2.3 Transition Removal

We remove transition 33 using the following ranking functions, which are bounded by −1.

 3: 0 4: 0 7: 0 4_var_snapshot: −1 4*: 0
Hints:
 33 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] ]

### 14.2.4 Splitting Cut-Point Transitions

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

### 14.2.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 32.

### 14.2.4.1.1 Splitting Cut-Point Transitions

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

### 14.3 SCC Subproblem 3/4

Here we consider the SCC { 8, 9, 12, 10, 11, 9_var_snapshot, 9*, 10_var_snapshot, 10* }.

### 14.3.1 Transition Removal

We remove transition 12 using the following ranking functions, which are bounded by 84.

 8: edgecount_0 + edgecount_post − 13⋅i_0 + 13⋅nodecount_0 + 9⋅nodecount_post 9: 7⋅edgecount_0 − 13⋅i_0 + 13⋅nodecount_0 12: edgecount_0 + edgecount_post − 13⋅i_0 + 13⋅nodecount_0 + 9⋅nodecount_post 10: 65 + edgecount_0 − 13⋅i_0 + 13⋅nodecount_0 11: edgecount_0 + 7⋅edgecount_post − 13⋅i_0 + 13⋅nodecount_0 9_var_snapshot: edgecount_0 + edgecount_post − 13⋅i_0 + 13⋅nodecount_0 + 9⋅nodecount_post 9*: −9 + edgecount_0 + 7⋅edgecount_post − 13⋅i_0 + 13⋅nodecount_0 10_var_snapshot: 64 + edgecount_0 − 13⋅i_0 + 13⋅nodecount_0 10*: 57 + edgecount_0 + edgecount_post − 13⋅i_0 + 13⋅nodecount_0
Hints:
 47 lexWeak[ [1, 0, 9, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 13, 1, 0, 1, 0] ] 49 lexWeak[ [0, 7, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 7, 0] ] 54 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, 13, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 1, 0] ] 56 lexWeak[ [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 1, 0] ] 7 lexWeak[ [6, 0, 0, 9, 0, 0, 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, 0, 0, 0, 0, 13, 7, 0, 1, 0] ] 8 lexWeak[ [7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 13, 7, 0, 1, 0] ] 9 lexWeak[ [0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13, 0, 0, 0, 0, 0, 1, 0, 1, 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, 9, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 13, 1, 0, 1, 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, 13, 0, 0, 0, 0, 13, 7, 0, 1, 0] , [0, 7, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 13, 0, 0, 0, 0, 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 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 13, 1, 0, 1, 0] ]

### 14.3.2 Transition Removal

We remove transition 10 using the following ranking functions, which are bounded by −867.

 8: −51 − 5⋅edgecount_0 − 5⋅edgecount_post − 97⋅j_0 + 10⋅nodecount_post 9: −97⋅j_0 12: −5⋅edgecount_0 − 5⋅edgecount_post − 97⋅j_0 10: −50 − 97⋅j_0 − 10⋅nodecount_post 11: − edgecount_0 − 97⋅j_0 − 21⋅nodecount_post 9_var_snapshot: −5⋅edgecount_post − 97⋅j_0 9*: −5⋅edgecount_post − 97⋅j_0 + 10⋅nodecount_post 10_var_snapshot: −97⋅j_0 − 21⋅nodecount_post 10*: −5⋅edgecount_0 − 97⋅j_0 − 10⋅nodecount_post
Hints:
 47 lexWeak[ [0, 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, 0, 0, 0, 97, 0, 0, 0, 0, 0, 5, 0, 0] ] 49 lexWeak[ [5, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 0, 0, 0] ] 54 lexWeak[ [0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 0, 0, 0] ] 56 lexWeak[ [0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 0, 0, 0] ] 7 lexWeak[ [0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 97, 0, 97, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0] ] 8 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 21, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 0, 0, 1] ] 9 lexWeak[ [5, 0, 0, 10, 0, 0, 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, 0, 0, 0, 0, 0, 97, 0, 0, 0, 5] ] 10 lexStrict[ [0, 0, 10, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 5, 0, 5] , [5, 0, 0, 0, 0, 0, 102, 0, 0, 0, 0, 0, 0, 0, 97, 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 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 97, 0, 0, 0, 0, 0, 5, 0, 5] ]

### 14.3.3 Transition Removal

We remove transitions 47, 49, 54, 56, 7, 8, 9, 15 using the following ranking functions, which are bounded by −6.

 8: 1 + 12⋅nodecount_0 + nodecount_post 9: 12⋅nodecount_0 12: −5⋅edgecount_post + 11⋅nodecount_post 10: 0 11: − edgecount_post − nodecount_post 9_var_snapshot: 11⋅nodecount_post 9*: 12⋅nodecount_0 + nodecount_post 10_var_snapshot: − nodecount_post 10*: −50 + 11⋅nodecount_post
Hints:
 47 lexStrict[ [0, 0, 11, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 49 lexStrict[ [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 1, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 54 lexStrict[ [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 56 lexStrict[ [0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 1, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 1, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 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, 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, 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] ] 9 lexStrict[ [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, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [5, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 5, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 5, 0, 0] , [0, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

### 14.3.4 Splitting Cut-Point Transitions

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

### 14.3.4.1 Cut-Point Subproblem 1/2

Here we consider cut-point transition 46.

### 14.3.4.1.1 Splitting Cut-Point Transitions

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

### 14.3.4.2 Cut-Point Subproblem 2/2

Here we consider cut-point transition 53.

### 14.3.4.2.1 Splitting Cut-Point Transitions

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

### 14.4 SCC Subproblem 4/4

Here we consider the SCC { 5, 6, 13, 14, 15, 5_var_snapshot, 5* }.

### 14.4.1 Transition Removal

We remove transitions 17, 18, 20 using the following ranking functions, which are bounded by −226.

 5: −90⋅i_0 + 37⋅nodecount_0 + 90⋅source_0 6: −5 + 5⋅edgecount_0 + 5⋅edgecount_post − 90⋅i_0 + nodecount_0 + 9⋅nodecount_post + 90⋅source_0 13: 5⋅edgecount_0 + 8⋅edgecount_post − 90⋅i_0 + nodecount_0 + 90⋅source_0 14: 12⋅edgecount_0 − 90⋅i_0 + nodecount_0 + 90⋅source_0 15: 5⋅edgecount_0 − 90⋅i_0 + nodecount_0 + 16⋅nodecount_post + 90⋅source_0 5_var_snapshot: 5⋅edgecount_0 + 5⋅edgecount_post − 90⋅i_0 + nodecount_0 + 9⋅nodecount_post + 90⋅source_0 5*: 12⋅edgecount_0 − 11⋅edgecount_post − 90⋅i_0 + 37⋅nodecount_0 + 90⋅source_0
Hints:
 40 lexWeak[ [5, 0, 9, 0, 0, 0, 5, 0, 0, 36, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 9, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 90, 5, 0, 5, 0] ] 42 lexWeak[ [11, 0, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 0, 0, 90, 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, 90, 0, 9, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 90, 5, 0, 5, 0] ] 13 lexWeak[ [0, 8, 0, 0, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 12, 0] ] 14 lexWeak[ [0, 11, 0, 0, 0, 0, 0, 0, 36, 0, 0, 0, 0, 0, 90, 0, 90, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 37, 0, 0, 0, 0, 0, 0, 11, 12, 0] ] 16 lexWeak[ [8, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 90, 8, 0, 5, 0] ] 17 lexStrict[ [8, 0, 0, 16, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 90, 8, 0, 5, 0] , [0, 0, 0, 16, 0, 0, 0, 5, 0, 1, 0, 90, 0, 0, 0, 0, 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, 16, 0, 0, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 12, 0] , [0, 0, 0, 16, 0, 0, 0, 5, 0, 1, 0, 90, 0, 0, 0, 0, 0, 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, 5, 7, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 16, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 90, 0, 0, 5, 0] , [0, 5, 0, 9, 0, 0, 0, 5, 89, 0, 90, 90, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

### 14.4.2 Transition Removal

We remove transitions 40, 42, 4, 13, 14 using the following ranking functions, which are bounded by −15.

 5: − edgecount_post 6: − edgecount_0 − edgecount_post − nodecount_0 13: 6⋅edgecount_0 14: 6⋅edgecount_0 − 9⋅nodecount_post 15: 7⋅edgecount_0 5_var_snapshot: − edgecount_post − nodecount_0 5*: 6⋅edgecount_0 − edgecount_post − 9⋅nodecount_post
Hints:
 40 lexStrict[ [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 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] ] 42 lexStrict[ [0, 0, 9, 0, 0, 0, 0, 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, 0, 0, 0, 0, 1, 0, 0] , [1, 0, 9, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0] ] 4 lexStrict[ [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, 1, 0, 1] , [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] ] 13 lexStrict[ [0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0] , [0, 0, 0, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0] ] 14 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, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 0, 1, 6, 0] , [0, 0, 9, 0, 0, 0, 0, 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, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 16 lexWeak[ [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, 6, 0] ]

### 14.4.3 Transition Removal

We remove transition 16 using the following ranking functions, which are bounded by 4.

 5: 0 6: 0 13: 0 14: 0 15: nodecount_0 5_var_snapshot: 0 5*: 0
Hints:
 16 lexStrict[ [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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

### 14.4.4 Splitting Cut-Point Transitions

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

### 14.4.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 39.

### 14.4.4.1.1 Splitting Cut-Point Transitions

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

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