# LTS Termination Proof

by T2Cert

## Input

Integer Transition System
• Initial Location: 6
• Transitions: (pre-variables and post-variables)  0 0 1: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − res5_0 + res5_post − tmp7_0 ≤ 0 ∧ res5_0 − res5_post + tmp7_0 ≤ 0 ∧ −1 − nI6_0 + nI6_post ≤ 0 ∧ 1 + nI6_0 − nI6_post ≤ 0 ∧ nI6_0 − nI6_post ≤ 0 ∧ − nI6_0 + nI6_post ≤ 0 ∧ res5_0 − res5_post ≤ 0 ∧ − res5_0 + res5_post ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − tmp7_post + tmp7_post ≤ 0 ∧ tmp7_post − tmp7_post ≤ 0 ∧ − tmp7_0 + tmp7_0 ≤ 0 ∧ tmp7_0 − tmp7_0 ≤ 0 ∧ − ret_nBC211_post + ret_nBC211_post ≤ 0 ∧ ret_nBC211_post − ret_nBC211_post ≤ 0 ∧ − ret_nBC211_0 + ret_nBC211_0 ≤ 0 ∧ ret_nBC211_0 − ret_nBC211_0 ≤ 0 ∧ − ret_nBC18_post + ret_nBC18_post ≤ 0 ∧ ret_nBC18_post − ret_nBC18_post ≤ 0 ∧ − ret_nBC18_0 + ret_nBC18_0 ≤ 0 ∧ ret_nBC18_0 − ret_nBC18_0 ≤ 0 ∧ − res10_post + res10_post ≤ 0 ∧ res10_post − res10_post ≤ 0 ∧ − res10_4 + res10_4 ≤ 0 ∧ res10_4 − res10_4 ≤ 0 ∧ − res10_3 + res10_3 ≤ 0 ∧ res10_3 − res10_3 ≤ 0 ∧ − res10_2 + res10_2 ≤ 0 ∧ res10_2 − res10_2 ≤ 0 ∧ − res10_1 + res10_1 ≤ 0 ∧ res10_1 − res10_1 ≤ 0 ∧ − res10_0 + res10_0 ≤ 0 ∧ res10_0 − res10_0 ≤ 0 ∧ − nX_0 + nX_0 ≤ 0 ∧ nX_0 − nX_0 ≤ 0 ∧ − nX9_post + nX9_post ≤ 0 ∧ nX9_post − nX9_post ≤ 0 ∧ − nX9_0 + nX9_0 ≤ 0 ∧ nX9_0 − nX9_0 ≤ 0 ∧ − nX4_post + nX4_post ≤ 0 ∧ nX4_post − nX4_post ≤ 0 ∧ − nX4_0 + nX4_0 ≤ 0 ∧ nX4_0 − nX4_0 ≤ 0 2 1 0: 0 ≤ 0 ∧ 0 ≤ 0 ∧ tmp7_post ≤ 0 ∧ − tmp7_post ≤ 0 ∧ tmp7_0 − tmp7_post ≤ 0 ∧ − tmp7_0 + tmp7_post ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_nBC211_post + ret_nBC211_post ≤ 0 ∧ ret_nBC211_post − ret_nBC211_post ≤ 0 ∧ − ret_nBC211_0 + ret_nBC211_0 ≤ 0 ∧ ret_nBC211_0 − ret_nBC211_0 ≤ 0 ∧ − ret_nBC18_post + ret_nBC18_post ≤ 0 ∧ ret_nBC18_post − ret_nBC18_post ≤ 0 ∧ − ret_nBC18_0 + ret_nBC18_0 ≤ 0 ∧ ret_nBC18_0 − ret_nBC18_0 ≤ 0 ∧ − res5_post + res5_post ≤ 0 ∧ res5_post − res5_post ≤ 0 ∧ − res5_0 + res5_0 ≤ 0 ∧ res5_0 − res5_0 ≤ 0 ∧ − res10_post + res10_post ≤ 0 ∧ res10_post − res10_post ≤ 0 ∧ − res10_4 + res10_4 ≤ 0 ∧ res10_4 − res10_4 ≤ 0 ∧ − res10_3 + res10_3 ≤ 0 ∧ res10_3 − res10_3 ≤ 0 ∧ − res10_2 + res10_2 ≤ 0 ∧ res10_2 − res10_2 ≤ 0 ∧ − res10_1 + res10_1 ≤ 0 ∧ res10_1 − res10_1 ≤ 0 ∧ − res10_0 + res10_0 ≤ 0 ∧ res10_0 − res10_0 ≤ 0 ∧ − nX_0 + nX_0 ≤ 0 ∧ nX_0 − nX_0 ≤ 0 ∧ − nX9_post + nX9_post ≤ 0 ∧ nX9_post − nX9_post ≤ 0 ∧ − nX9_0 + nX9_0 ≤ 0 ∧ nX9_0 − nX9_0 ≤ 0 ∧ − nX4_post + nX4_post ≤ 0 ∧ nX4_post − nX4_post ≤ 0 ∧ − nX4_0 + nX4_0 ≤ 0 ∧ nX4_0 − nX4_0 ≤ 0 ∧ − nI6_post + nI6_post ≤ 0 ∧ nI6_post − nI6_post ≤ 0 ∧ − nI6_0 + nI6_0 ≤ 0 ∧ nI6_0 − nI6_0 ≤ 0 2 2 0: 0 ≤ 0 ∧ 0 ≤ 0 ∧ −1 + tmp7_post ≤ 0 ∧ 1 − tmp7_post ≤ 0 ∧ tmp7_0 − tmp7_post ≤ 0 ∧ − tmp7_0 + tmp7_post ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − ret_nBC211_post + ret_nBC211_post ≤ 0 ∧ ret_nBC211_post − ret_nBC211_post ≤ 0 ∧ − ret_nBC211_0 + ret_nBC211_0 ≤ 0 ∧ ret_nBC211_0 − ret_nBC211_0 ≤ 0 ∧ − ret_nBC18_post + ret_nBC18_post ≤ 0 ∧ ret_nBC18_post − ret_nBC18_post ≤ 0 ∧ − ret_nBC18_0 + ret_nBC18_0 ≤ 0 ∧ ret_nBC18_0 − ret_nBC18_0 ≤ 0 ∧ − res5_post + res5_post ≤ 0 ∧ res5_post − res5_post ≤ 0 ∧ − res5_0 + res5_0 ≤ 0 ∧ res5_0 − res5_0 ≤ 0 ∧ − res10_post + res10_post ≤ 0 ∧ res10_post − res10_post ≤ 0 ∧ − res10_4 + res10_4 ≤ 0 ∧ res10_4 − res10_4 ≤ 0 ∧ − res10_3 + res10_3 ≤ 0 ∧ res10_3 − res10_3 ≤ 0 ∧ − res10_2 + res10_2 ≤ 0 ∧ res10_2 − res10_2 ≤ 0 ∧ − res10_1 + res10_1 ≤ 0 ∧ res10_1 − res10_1 ≤ 0 ∧ − res10_0 + res10_0 ≤ 0 ∧ res10_0 − res10_0 ≤ 0 ∧ − nX_0 + nX_0 ≤ 0 ∧ nX_0 − nX_0 ≤ 0 ∧ − nX9_post + nX9_post ≤ 0 ∧ nX9_post − nX9_post ≤ 0 ∧ − nX9_0 + nX9_0 ≤ 0 ∧ nX9_0 − nX9_0 ≤ 0 ∧ − nX4_post + nX4_post ≤ 0 ∧ nX4_post − nX4_post ≤ 0 ∧ − nX4_0 + nX4_0 ≤ 0 ∧ nX4_0 − nX4_0 ≤ 0 ∧ − nI6_post + nI6_post ≤ 0 ∧ nI6_post − nI6_post ≤ 0 ∧ − nI6_0 + nI6_0 ≤ 0 ∧ nI6_0 − nI6_0 ≤ 0 3 3 4: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 16 − nI6_0 ≤ 0 ∧ − res5_0 + ret_nBC18_post ≤ 0 ∧ res5_0 − ret_nBC18_post ≤ 0 ∧ − ret_nBC18_post + tmp_post ≤ 0 ∧ ret_nBC18_post − tmp_post ≤ 0 ∧ nX9_post − nX_0 ≤ 0 ∧ − nX9_post + nX_0 ≤ 0 ∧ − nX9_post + res10_1 ≤ 0 ∧ nX9_post − res10_1 ≤ 0 ∧ − res10_post + ret_nBC211_post ≤ 0 ∧ res10_post − ret_nBC211_post ≤ 0 ∧ − ret_nBC211_post + tmp___0_post ≤ 0 ∧ ret_nBC211_post − tmp___0_post ≤ 0 ∧ nX9_0 − nX9_post ≤ 0 ∧ − nX9_0 + nX9_post ≤ 0 ∧ res10_0 − res10_post ≤ 0 ∧ − res10_0 + res10_post ≤ 0 ∧ ret_nBC18_0 − ret_nBC18_post ≤ 0 ∧ − ret_nBC18_0 + ret_nBC18_post ≤ 0 ∧ ret_nBC211_0 − ret_nBC211_post ≤ 0 ∧ − ret_nBC211_0 + ret_nBC211_post ≤ 0 ∧ tmp_0 − tmp_post ≤ 0 ∧ − tmp_0 + tmp_post ≤ 0 ∧ tmp___0_0 − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_post ≤ 0 ∧ − tmp7_post + tmp7_post ≤ 0 ∧ tmp7_post − tmp7_post ≤ 0 ∧ − tmp7_0 + tmp7_0 ≤ 0 ∧ tmp7_0 − tmp7_0 ≤ 0 ∧ − res5_post + res5_post ≤ 0 ∧ res5_post − res5_post ≤ 0 ∧ − res5_0 + res5_0 ≤ 0 ∧ res5_0 − res5_0 ≤ 0 ∧ − nX_0 + nX_0 ≤ 0 ∧ nX_0 − nX_0 ≤ 0 ∧ − nX4_post + nX4_post ≤ 0 ∧ nX4_post − nX4_post ≤ 0 ∧ − nX4_0 + nX4_0 ≤ 0 ∧ nX4_0 − nX4_0 ≤ 0 ∧ − nI6_post + nI6_post ≤ 0 ∧ nI6_post − nI6_post ≤ 0 ∧ − nI6_0 + nI6_0 ≤ 0 ∧ nI6_0 − nI6_0 ≤ 0 3 4 2: −15 + nI6_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − tmp7_post + tmp7_post ≤ 0 ∧ tmp7_post − tmp7_post ≤ 0 ∧ − tmp7_0 + tmp7_0 ≤ 0 ∧ tmp7_0 − tmp7_0 ≤ 0 ∧ − ret_nBC211_post + ret_nBC211_post ≤ 0 ∧ ret_nBC211_post − ret_nBC211_post ≤ 0 ∧ − ret_nBC211_0 + ret_nBC211_0 ≤ 0 ∧ ret_nBC211_0 − ret_nBC211_0 ≤ 0 ∧ − ret_nBC18_post + ret_nBC18_post ≤ 0 ∧ ret_nBC18_post − ret_nBC18_post ≤ 0 ∧ − ret_nBC18_0 + ret_nBC18_0 ≤ 0 ∧ ret_nBC18_0 − ret_nBC18_0 ≤ 0 ∧ − res5_post + res5_post ≤ 0 ∧ res5_post − res5_post ≤ 0 ∧ − res5_0 + res5_0 ≤ 0 ∧ res5_0 − res5_0 ≤ 0 ∧ − res10_post + res10_post ≤ 0 ∧ res10_post − res10_post ≤ 0 ∧ − res10_4 + res10_4 ≤ 0 ∧ res10_4 − res10_4 ≤ 0 ∧ − res10_3 + res10_3 ≤ 0 ∧ res10_3 − res10_3 ≤ 0 ∧ − res10_2 + res10_2 ≤ 0 ∧ res10_2 − res10_2 ≤ 0 ∧ − res10_1 + res10_1 ≤ 0 ∧ res10_1 − res10_1 ≤ 0 ∧ − res10_0 + res10_0 ≤ 0 ∧ res10_0 − res10_0 ≤ 0 ∧ − nX_0 + nX_0 ≤ 0 ∧ nX_0 − nX_0 ≤ 0 ∧ − nX9_post + nX9_post ≤ 0 ∧ nX9_post − nX9_post ≤ 0 ∧ − nX9_0 + nX9_0 ≤ 0 ∧ nX9_0 − nX9_0 ≤ 0 ∧ − nX4_post + nX4_post ≤ 0 ∧ nX4_post − nX4_post ≤ 0 ∧ − nX4_0 + nX4_0 ≤ 0 ∧ nX4_0 − nX4_0 ≤ 0 ∧ − nI6_post + nI6_post ≤ 0 ∧ nI6_post − nI6_post ≤ 0 ∧ − nI6_0 + nI6_0 ≤ 0 ∧ nI6_0 − nI6_0 ≤ 0 1 5 3: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − tmp7_post + tmp7_post ≤ 0 ∧ tmp7_post − tmp7_post ≤ 0 ∧ − tmp7_0 + tmp7_0 ≤ 0 ∧ tmp7_0 − tmp7_0 ≤ 0 ∧ − ret_nBC211_post + ret_nBC211_post ≤ 0 ∧ ret_nBC211_post − ret_nBC211_post ≤ 0 ∧ − ret_nBC211_0 + ret_nBC211_0 ≤ 0 ∧ ret_nBC211_0 − ret_nBC211_0 ≤ 0 ∧ − ret_nBC18_post + ret_nBC18_post ≤ 0 ∧ ret_nBC18_post − ret_nBC18_post ≤ 0 ∧ − ret_nBC18_0 + ret_nBC18_0 ≤ 0 ∧ ret_nBC18_0 − ret_nBC18_0 ≤ 0 ∧ − res5_post + res5_post ≤ 0 ∧ res5_post − res5_post ≤ 0 ∧ − res5_0 + res5_0 ≤ 0 ∧ res5_0 − res5_0 ≤ 0 ∧ − res10_post + res10_post ≤ 0 ∧ res10_post − res10_post ≤ 0 ∧ − res10_4 + res10_4 ≤ 0 ∧ res10_4 − res10_4 ≤ 0 ∧ − res10_3 + res10_3 ≤ 0 ∧ res10_3 − res10_3 ≤ 0 ∧ − res10_2 + res10_2 ≤ 0 ∧ res10_2 − res10_2 ≤ 0 ∧ − res10_1 + res10_1 ≤ 0 ∧ res10_1 − res10_1 ≤ 0 ∧ − res10_0 + res10_0 ≤ 0 ∧ res10_0 − res10_0 ≤ 0 ∧ − nX_0 + nX_0 ≤ 0 ∧ nX_0 − nX_0 ≤ 0 ∧ − nX9_post + nX9_post ≤ 0 ∧ nX9_post − nX9_post ≤ 0 ∧ − nX9_0 + nX9_0 ≤ 0 ∧ nX9_0 − nX9_0 ≤ 0 ∧ − nX4_post + nX4_post ≤ 0 ∧ nX4_post − nX4_post ≤ 0 ∧ − nX4_0 + nX4_0 ≤ 0 ∧ nX4_0 − nX4_0 ≤ 0 ∧ − nI6_post + nI6_post ≤ 0 ∧ nI6_post − nI6_post ≤ 0 ∧ − nI6_0 + nI6_0 ≤ 0 ∧ nI6_0 − nI6_0 ≤ 0 5 6 1: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ nX4_post − nX_0 ≤ 0 ∧ − nX4_post + nX_0 ≤ 0 ∧ res5_post ≤ 0 ∧ − res5_post ≤ 0 ∧ nI6_post ≤ 0 ∧ − nI6_post ≤ 0 ∧ nI6_0 − nI6_post ≤ 0 ∧ − nI6_0 + nI6_post ≤ 0 ∧ nX4_0 − nX4_post ≤ 0 ∧ − nX4_0 + nX4_post ≤ 0 ∧ res5_0 − res5_post ≤ 0 ∧ − res5_0 + res5_post ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − tmp7_post + tmp7_post ≤ 0 ∧ tmp7_post − tmp7_post ≤ 0 ∧ − tmp7_0 + tmp7_0 ≤ 0 ∧ tmp7_0 − tmp7_0 ≤ 0 ∧ − ret_nBC211_post + ret_nBC211_post ≤ 0 ∧ ret_nBC211_post − ret_nBC211_post ≤ 0 ∧ − ret_nBC211_0 + ret_nBC211_0 ≤ 0 ∧ ret_nBC211_0 − ret_nBC211_0 ≤ 0 ∧ − ret_nBC18_post + ret_nBC18_post ≤ 0 ∧ ret_nBC18_post − ret_nBC18_post ≤ 0 ∧ − ret_nBC18_0 + ret_nBC18_0 ≤ 0 ∧ ret_nBC18_0 − ret_nBC18_0 ≤ 0 ∧ − res10_post + res10_post ≤ 0 ∧ res10_post − res10_post ≤ 0 ∧ − res10_4 + res10_4 ≤ 0 ∧ res10_4 − res10_4 ≤ 0 ∧ − res10_3 + res10_3 ≤ 0 ∧ res10_3 − res10_3 ≤ 0 ∧ − res10_2 + res10_2 ≤ 0 ∧ res10_2 − res10_2 ≤ 0 ∧ − res10_1 + res10_1 ≤ 0 ∧ res10_1 − res10_1 ≤ 0 ∧ − res10_0 + res10_0 ≤ 0 ∧ res10_0 − res10_0 ≤ 0 ∧ − nX_0 + nX_0 ≤ 0 ∧ nX_0 − nX_0 ≤ 0 ∧ − nX9_post + nX9_post ≤ 0 ∧ nX9_post − nX9_post ≤ 0 ∧ − nX9_0 + nX9_0 ≤ 0 ∧ nX9_0 − nX9_0 ≤ 0 6 7 5: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − tmp7_post + tmp7_post ≤ 0 ∧ tmp7_post − tmp7_post ≤ 0 ∧ − tmp7_0 + tmp7_0 ≤ 0 ∧ tmp7_0 − tmp7_0 ≤ 0 ∧ − ret_nBC211_post + ret_nBC211_post ≤ 0 ∧ ret_nBC211_post − ret_nBC211_post ≤ 0 ∧ − ret_nBC211_0 + ret_nBC211_0 ≤ 0 ∧ ret_nBC211_0 − ret_nBC211_0 ≤ 0 ∧ − ret_nBC18_post + ret_nBC18_post ≤ 0 ∧ ret_nBC18_post − ret_nBC18_post ≤ 0 ∧ − ret_nBC18_0 + ret_nBC18_0 ≤ 0 ∧ ret_nBC18_0 − ret_nBC18_0 ≤ 0 ∧ − res5_post + res5_post ≤ 0 ∧ res5_post − res5_post ≤ 0 ∧ − res5_0 + res5_0 ≤ 0 ∧ res5_0 − res5_0 ≤ 0 ∧ − res10_post + res10_post ≤ 0 ∧ res10_post − res10_post ≤ 0 ∧ − res10_4 + res10_4 ≤ 0 ∧ res10_4 − res10_4 ≤ 0 ∧ − res10_3 + res10_3 ≤ 0 ∧ res10_3 − res10_3 ≤ 0 ∧ − res10_2 + res10_2 ≤ 0 ∧ res10_2 − res10_2 ≤ 0 ∧ − res10_1 + res10_1 ≤ 0 ∧ res10_1 − res10_1 ≤ 0 ∧ − res10_0 + res10_0 ≤ 0 ∧ res10_0 − res10_0 ≤ 0 ∧ − nX_0 + nX_0 ≤ 0 ∧ nX_0 − nX_0 ≤ 0 ∧ − nX9_post + nX9_post ≤ 0 ∧ nX9_post − nX9_post ≤ 0 ∧ − nX9_0 + nX9_0 ≤ 0 ∧ nX9_0 − nX9_0 ≤ 0 ∧ − nX4_post + nX4_post ≤ 0 ∧ nX4_post − nX4_post ≤ 0 ∧ − nX4_0 + nX4_0 ≤ 0 ∧ nX4_0 − nX4_0 ≤ 0 ∧ − nI6_post + nI6_post ≤ 0 ∧ nI6_post − nI6_post ≤ 0 ∧ − nI6_0 + nI6_0 ≤ 0 ∧ nI6_0 − nI6_0 ≤ 0

## Proof

### 1 Invariant Updates

The following invariants are asserted.

 0: − tmp7_post ≤ 0 ∧ − tmp7_0 ≤ 0 1: TRUE 2: TRUE 3: TRUE 4: 16 − nI6_0 ≤ 0 5: TRUE 6: TRUE

The invariants are proved as follows.

### IMPACT Invariant Proof

• nodes (location) invariant:  0 (0) − tmp7_post ≤ 0 ∧ − tmp7_0 ≤ 0 1 (1) TRUE 2 (2) TRUE 3 (3) TRUE 4 (4) 16 − nI6_0 ≤ 0 5 (5) TRUE 6 (6) TRUE
• initial node: 6
• cover edges:
• transition edges:  0 0 1 1 5 3 2 1 0 2 2 0 3 3 4 3 4 2 5 6 1 6 7 5

### 2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 1 8 1: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − tmp7_post + tmp7_post ≤ 0 ∧ tmp7_post − tmp7_post ≤ 0 ∧ − tmp7_0 + tmp7_0 ≤ 0 ∧ tmp7_0 − tmp7_0 ≤ 0 ∧ − ret_nBC211_post + ret_nBC211_post ≤ 0 ∧ ret_nBC211_post − ret_nBC211_post ≤ 0 ∧ − ret_nBC211_0 + ret_nBC211_0 ≤ 0 ∧ ret_nBC211_0 − ret_nBC211_0 ≤ 0 ∧ − ret_nBC18_post + ret_nBC18_post ≤ 0 ∧ ret_nBC18_post − ret_nBC18_post ≤ 0 ∧ − ret_nBC18_0 + ret_nBC18_0 ≤ 0 ∧ ret_nBC18_0 − ret_nBC18_0 ≤ 0 ∧ − res5_post + res5_post ≤ 0 ∧ res5_post − res5_post ≤ 0 ∧ − res5_0 + res5_0 ≤ 0 ∧ res5_0 − res5_0 ≤ 0 ∧ − res10_post + res10_post ≤ 0 ∧ res10_post − res10_post ≤ 0 ∧ − res10_4 + res10_4 ≤ 0 ∧ res10_4 − res10_4 ≤ 0 ∧ − res10_3 + res10_3 ≤ 0 ∧ res10_3 − res10_3 ≤ 0 ∧ − res10_2 + res10_2 ≤ 0 ∧ res10_2 − res10_2 ≤ 0 ∧ − res10_1 + res10_1 ≤ 0 ∧ res10_1 − res10_1 ≤ 0 ∧ − res10_0 + res10_0 ≤ 0 ∧ res10_0 − res10_0 ≤ 0 ∧ − nX_0 + nX_0 ≤ 0 ∧ nX_0 − nX_0 ≤ 0 ∧ − nX9_post + nX9_post ≤ 0 ∧ nX9_post − nX9_post ≤ 0 ∧ − nX9_0 + nX9_0 ≤ 0 ∧ nX9_0 − nX9_0 ≤ 0 ∧ − nX4_post + nX4_post ≤ 0 ∧ nX4_post − nX4_post ≤ 0 ∧ − nX4_0 + nX4_0 ≤ 0 ∧ nX4_0 − nX4_0 ≤ 0 ∧ − nI6_post + nI6_post ≤ 0 ∧ nI6_post − nI6_post ≤ 0 ∧ − nI6_0 + nI6_0 ≤ 0 ∧ nI6_0 − nI6_0 ≤ 0
and for every transition t, a duplicate t is considered.

### 3 Transition Removal

We remove transitions 3, 6, 7 using the following ranking functions, which are bounded by −13.

 6: 0 5: 0 0: 0 1: 0 2: 0 3: 0 4: 0 6: −5 5: −6 0: −7 1: −7 2: −7 3: −7 1_var_snapshot: −7 1*: −7 4: −8

### 4 Location Addition

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

1* 11 1: tmp_post + tmp_post ≤ 0tmp_posttmp_post ≤ 0tmp___0_post + tmp___0_post ≤ 0tmp___0_posttmp___0_post ≤ 0tmp___0_0 + tmp___0_0 ≤ 0tmp___0_0tmp___0_0 ≤ 0tmp_0 + tmp_0 ≤ 0tmp_0tmp_0 ≤ 0tmp7_post + tmp7_post ≤ 0tmp7_posttmp7_post ≤ 0tmp7_0 + tmp7_0 ≤ 0tmp7_0tmp7_0 ≤ 0ret_nBC211_post + ret_nBC211_post ≤ 0ret_nBC211_postret_nBC211_post ≤ 0ret_nBC211_0 + ret_nBC211_0 ≤ 0ret_nBC211_0ret_nBC211_0 ≤ 0ret_nBC18_post + ret_nBC18_post ≤ 0ret_nBC18_postret_nBC18_post ≤ 0ret_nBC18_0 + ret_nBC18_0 ≤ 0ret_nBC18_0ret_nBC18_0 ≤ 0res5_post + res5_post ≤ 0res5_postres5_post ≤ 0res5_0 + res5_0 ≤ 0res5_0res5_0 ≤ 0res10_post + res10_post ≤ 0res10_postres10_post ≤ 0res10_4 + res10_4 ≤ 0res10_4res10_4 ≤ 0res10_3 + res10_3 ≤ 0res10_3res10_3 ≤ 0res10_2 + res10_2 ≤ 0res10_2res10_2 ≤ 0res10_1 + res10_1 ≤ 0res10_1res10_1 ≤ 0res10_0 + res10_0 ≤ 0res10_0res10_0 ≤ 0nX_0 + nX_0 ≤ 0nX_0nX_0 ≤ 0nX9_post + nX9_post ≤ 0nX9_postnX9_post ≤ 0nX9_0 + nX9_0 ≤ 0nX9_0nX9_0 ≤ 0nX4_post + nX4_post ≤ 0nX4_postnX4_post ≤ 0nX4_0 + nX4_0 ≤ 0nX4_0nX4_0 ≤ 0nI6_post + nI6_post ≤ 0nI6_postnI6_post ≤ 0nI6_0 + nI6_0 ≤ 0nI6_0nI6_0 ≤ 0

### 5 Location Addition

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

1 9 1_var_snapshot: tmp_post + tmp_post ≤ 0tmp_posttmp_post ≤ 0tmp___0_post + tmp___0_post ≤ 0tmp___0_posttmp___0_post ≤ 0tmp___0_0 + tmp___0_0 ≤ 0tmp___0_0tmp___0_0 ≤ 0tmp_0 + tmp_0 ≤ 0tmp_0tmp_0 ≤ 0tmp7_post + tmp7_post ≤ 0tmp7_posttmp7_post ≤ 0tmp7_0 + tmp7_0 ≤ 0tmp7_0tmp7_0 ≤ 0ret_nBC211_post + ret_nBC211_post ≤ 0ret_nBC211_postret_nBC211_post ≤ 0ret_nBC211_0 + ret_nBC211_0 ≤ 0ret_nBC211_0ret_nBC211_0 ≤ 0ret_nBC18_post + ret_nBC18_post ≤ 0ret_nBC18_postret_nBC18_post ≤ 0ret_nBC18_0 + ret_nBC18_0 ≤ 0ret_nBC18_0ret_nBC18_0 ≤ 0res5_post + res5_post ≤ 0res5_postres5_post ≤ 0res5_0 + res5_0 ≤ 0res5_0res5_0 ≤ 0res10_post + res10_post ≤ 0res10_postres10_post ≤ 0res10_4 + res10_4 ≤ 0res10_4res10_4 ≤ 0res10_3 + res10_3 ≤ 0res10_3res10_3 ≤ 0res10_2 + res10_2 ≤ 0res10_2res10_2 ≤ 0res10_1 + res10_1 ≤ 0res10_1res10_1 ≤ 0res10_0 + res10_0 ≤ 0res10_0res10_0 ≤ 0nX_0 + nX_0 ≤ 0nX_0nX_0 ≤ 0nX9_post + nX9_post ≤ 0nX9_postnX9_post ≤ 0nX9_0 + nX9_0 ≤ 0nX9_0nX9_0 ≤ 0nX4_post + nX4_post ≤ 0nX4_postnX4_post ≤ 0nX4_0 + nX4_0 ≤ 0nX4_0nX4_0 ≤ 0nI6_post + nI6_post ≤ 0nI6_postnI6_post ≤ 0nI6_0 + nI6_0 ≤ 0nI6_0nI6_0 ≤ 0

### 6 SCC Decomposition

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

### 6.1 SCC Subproblem 1/1

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

### 6.1.1 Transition Removal

We remove transition 4 using the following ranking functions, which are bounded by −92.

 0: −3 − 6⋅nI6_0 1: 1 − 6⋅nI6_0 2: −2 − 6⋅nI6_0 3: −1 − 6⋅nI6_0 1_var_snapshot: −6⋅nI6_0 1*: 2 − 6⋅nI6_0

### 6.1.2 Transition Removal

We remove transitions 9, 11, 0, 1, 2, 5 using the following ranking functions, which are bounded by −5.

 0: −1 1: −3 2: 0 3: −5 1_var_snapshot: −4 1*: −2

### 6.1.3 Splitting Cut-Point Transitions

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

### 6.1.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 8.

### 6.1.3.1.1 Splitting Cut-Point Transitions

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

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