# 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 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 5 5 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 6 6 7: 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 8 7 9: 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 8 8 6: 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 10 9 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 10 10 7: 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 11 11 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 13 12 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 13 11: 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 15 14 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 15 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 16 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 12 17 9: 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 12 18 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 9 19 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 7 20 8: − 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 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 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 11: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ −14 + edgecount_post ≤ 0 ∧ 14 − 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: −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 1: −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 2: −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 3: −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 4: −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 5: −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 6: −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 7: −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 8: −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 9: −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 10: −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 11: −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 12: −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 13: −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 14: −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 15: −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − 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) −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 1 (1) −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 2 (2) −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 3 (3) −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 4 (4) −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 5 (5) −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 6 (6) −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 7 (7) −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 8 (8) −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 9 (9) −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 10 (10) −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 11 (11) −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 12 (12) −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 13 (13) −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 14 (14) −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − edgecount_0 ≤ 0 ∧ −5 + nodecount_0 ≤ 0 ∧ 5 − nodecount_0 ≤ 0 ∧ − source_0 ≤ 0 15 (15) −14 + edgecount_post ≤ 0 ∧ 14 − edgecount_post ≤ 0 ∧ −5 + nodecount_post ≤ 0 ∧ 5 − nodecount_post ≤ 0 ∧ source_post ≤ 0 ∧ − source_post ≤ 0 ∧ −14 + edgecount_0 ≤ 0 ∧ 14 − 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 5 5 4 2 5 5 3 6 6 7 7 20 8 8 7 9 8 8 6 9 19 10 10 9 4 10 10 7 11 11 12 12 17 9 12 18 15 13 12 14 14 13 11 15 14 13 15 15 13 15 16 14 16 23 11 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 7 39 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 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 11 53 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
and for every transition t, a duplicate t is considered.

### 3 Transition Removal

We remove transitions 0, 3, 4, 9, 17, 23, 24 using the following ranking functions, which are bounded by −27.

 17: 0 16: 0 11: 0 12: 0 13: 0 14: 0 15: 0 6: 0 7: 0 8: 0 9: 0 10: 0 3: 0 4: 0 5: 0 0: 0 2: 0 1: 0 17: −8 16: −9 11: −10 12: −10 13: −10 14: −10 15: −10 11_var_snapshot: −10 11*: −10 6: −11 7: −11 8: −11 9: −11 10: −11 7_var_snapshot: −11 7*: −11 9_var_snapshot: −11 9*: −11 3: −14 4: −14 5: −14 4_var_snapshot: −14 4*: −14 0: −15 2: −15 2_var_snapshot: −15 2*: −15 1: −16

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.

7* 42 7: 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.

7 40 7_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.

11* 56 11: 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.

11 54 11_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: −11 + edgecount_post − 6⋅i_0 + 6⋅nodecount_0 − nodecount_post 2*: −6⋅i_0 + 6⋅nodecount_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 + nodecount_post

### 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, 5, 4_var_snapshot, 4* }.

### 14.2.1 Transition Removal

We remove transition 5 using the following ranking functions, which are bounded by −1329.

 3: −6⋅edgecount_0 − edgecount_post − 100⋅i_0 4: −100⋅i_0 5: −6⋅edgecount_0 − edgecount_post − 100⋅i_0 + 14⋅nodecount_post 4_var_snapshot: −6⋅edgecount_0 − 100⋅i_0 + 14⋅nodecount_post 4*: 85 − 6⋅edgecount_0 − 100⋅i_0

### 14.2.2 Transition Removal

We remove transitions 35, 2, 21 using the following ranking functions, which are bounded by −85.

 3: edgecount_post 4: −14⋅nodecount_post 5: −6⋅edgecount_post − nodecount_post 4_var_snapshot: −6⋅edgecount_post 4*: 0

### 14.2.3 Transition Removal

We remove transition 33 using the following ranking functions, which are bounded by 4.

 3: 0 4: nodecount_0 5: 0 4_var_snapshot: 0 4*: 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 { 6, 7, 8, 9, 10, 7_var_snapshot, 7*, 9_var_snapshot, 9* }.

### 14.3.1 Transition Removal

We remove transition 10 using the following ranking functions, which are bounded by 294.

 6: −225⋅i_0 + 225⋅nodecount_0 7: −225⋅i_0 + 225⋅nodecount_0 8: −225⋅i_0 + 225⋅nodecount_0 9: −225⋅i_0 + 225⋅nodecount_0 + 42⋅nodecount_post 10: 5⋅edgecount_0 − 225⋅i_0 + 225⋅nodecount_0 7_var_snapshot: −225⋅i_0 + 225⋅nodecount_0 7*: −225⋅i_0 + 225⋅nodecount_0 9_var_snapshot: 140 − 225⋅i_0 + 225⋅nodecount_0 9*: 16⋅edgecount_post − 225⋅i_0 + 225⋅nodecount_0

### 14.3.2 Transition Removal

We remove transition 8 using the following ranking functions, which are bounded by −113.

 6: −1 − 9⋅j_0 + nodecount_0 7: −8 + edgecount_0 − 9⋅j_0 + nodecount_0 8: −9⋅j_0 + nodecount_0 9: −9⋅j_0 − 14⋅nodecount_post 10: −5⋅edgecount_0 − 9⋅j_0 − nodecount_0 7_var_snapshot: −8 + edgecount_0 − 9⋅j_0 + nodecount_0 7*: 7 − 9⋅j_0 + nodecount_0 9_var_snapshot: −9⋅j_0 − nodecount_0 − 14⋅nodecount_post 9*: −9⋅j_0 + nodecount_0 − 14⋅nodecount_post

### 14.3.3 Transition Removal

We remove transitions 40, 42, 47, 49, 6, 7, 19, 20 using the following ranking functions, which are bounded by −6.

 6: 6⋅edgecount_0 + 16⋅nodecount_0 + nodecount_post 7: 6⋅edgecount_0 + 16⋅nodecount_0 − 14⋅nodecount_post 8: −5⋅edgecount_0 + 16⋅nodecount_0 9: 0 10: −2⋅nodecount_post 7_var_snapshot: 16⋅nodecount_0 7*: 6⋅edgecount_0 + 16⋅nodecount_0 9_var_snapshot: − nodecount_post 9*: −75 + 16⋅nodecount_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 39.

### 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 46.

### 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 { 11, 12, 13, 14, 15, 11_var_snapshot, 11* }.

### 14.4.1 Transition Removal

We remove transitions 15, 16, 18 using the following ranking functions, which are bounded by 78.

 11: −15⋅i_0 + 29⋅nodecount_0 + 15⋅source_0 12: −1 + 10⋅edgecount_post − 15⋅i_0 + 15⋅source_0 13: −8 − 15⋅i_0 + 29⋅nodecount_0 + 15⋅source_0 14: −9 − 15⋅i_0 + 29⋅nodecount_0 + 15⋅source_0 15: 12 + 9⋅edgecount_post − 15⋅i_0 + 15⋅source_0 11_var_snapshot: 5⋅edgecount_0 + 5⋅edgecount_post − 15⋅i_0 + 15⋅source_0 11*: 5 − 15⋅i_0 + 29⋅nodecount_0 + 15⋅source_0

### 14.4.2 Transition Removal

We remove transitions 54, 56, 11, 12, 13 using the following ranking functions, which are bounded by −20.

 11: − edgecount_post 12: − edgecount_post − 2⋅nodecount_post 13: 2⋅nodecount_post 14: − edgecount_post + 2⋅nodecount_post 15: 3⋅nodecount_post 11_var_snapshot: − edgecount_post − nodecount_post 11*: −5 − edgecount_post + 2⋅nodecount_post

### 14.4.3 Transition Removal

We remove transition 14 using the following ranking functions, which are bounded by 0.

 11: 0 12: 0 13: 0 14: 0 15: 1 11_var_snapshot: 0 11*: 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 53.

### 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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