# LTS Termination Proof

by T2Cert

## Input

Integer Transition System
• Initial Location: 21
• Transitions: (pre-variables and post-variables)  0 0 1: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 2 1 3: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 4 2 5: 0 ≤ 0 ∧ 0 ≤ 0 ∧ −1 + tmp___1_post ≤ 0 ∧ 1 − tmp___1_post ≤ 0 ∧ tmp___1_0 − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 6 3 5: 0 ≤ 0 ∧ 0 ≤ 0 ∧ −1 + tmp___1_post ≤ 0 ∧ 1 − tmp___1_post ≤ 0 ∧ tmp___1_0 − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 7 4 5: 0 ≤ 0 ∧ 0 ≤ 0 ∧ −1 + tmp___1_post ≤ 0 ∧ 1 − tmp___1_post ≤ 0 ∧ tmp___1_0 − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 8 5 5: 0 ≤ 0 ∧ 0 ≤ 0 ∧ −1 + tmp___1_post ≤ 0 ∧ 1 − tmp___1_post ≤ 0 ∧ tmp___1_0 − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 5 6 9: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 10 7 8: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 10 8 5: 0 ≤ 0 ∧ 0 ≤ 0 ∧ tmp___1_post ≤ 0 ∧ − tmp___1_post ≤ 0 ∧ tmp___1_0 − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 10 9 8: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 11 10 7: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 11 11 7: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 11 12 10: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 12 13 6: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 12 14 6: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 12 15 11: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 13 16 14: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 15 17 4: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 15 18 4: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 15 19 12: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 16 20 17: 0 ≤ 0 ∧ 0 ≤ 0 ∧ nDim_0 − nk_0 ≤ 0 ∧ −1 − nj_0 + nj_post ≤ 0 ∧ 1 + nj_0 − nj_post ≤ 0 ∧ nj_0 − nj_post ≤ 0 ∧ − nj_0 + nj_post ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 16 21 18: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − nDim_0 + nk_0 ≤ 0 ∧ −1 − nk_0 + nk_post ≤ 0 ∧ 1 + nk_0 − nk_post ≤ 0 ∧ nk_0 − nk_post ≤ 0 ∧ − nk_0 + nk_post ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 17 22 19: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 19 23 13: 0 ≤ 0 ∧ 0 ≤ 0 ∧ nDim_0 − nj_0 ≤ 0 ∧ −1 − ni_0 + ni_post ≤ 0 ∧ 1 + ni_0 − ni_post ≤ 0 ∧ ni_0 − ni_post ≤ 0 ∧ − ni_0 + ni_post ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 19 24 18: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − nDim_0 + nj_0 ≤ 0 ∧ nk_post ≤ 0 ∧ − nk_post ≤ 0 ∧ nk_0 − nk_post ≤ 0 ∧ − nk_0 + nk_post ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 14 25 15: nDim_0 − ni_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 14 26 17: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − nDim_0 + ni_0 ≤ 0 ∧ nj_post ≤ 0 ∧ − nj_post ≤ 0 ∧ nj_0 − nj_post ≤ 0 ∧ − nj_0 + nj_post ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 18 27 16: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 3 28 0: 0 ≤ 0 ∧ 0 ≤ 0 ∧ nDim_0 − nj_0 ≤ 0 ∧ −1 − ni_0 + ni_post ≤ 0 ∧ 1 + ni_0 − ni_post ≤ 0 ∧ ni_0 − ni_post ≤ 0 ∧ − ni_0 + ni_post ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 3 29 2: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − nDim_0 + nj_0 ≤ 0 ∧ −1 − nj_0 + nj_post ≤ 0 ∧ 1 + nj_0 − nj_post ≤ 0 ∧ nj_0 − nj_post ≤ 0 ∧ − nj_0 + nj_post ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 1 30 13: 0 ≤ 0 ∧ 0 ≤ 0 ∧ nDim_0 − ni_0 ≤ 0 ∧ ni_post ≤ 0 ∧ − ni_post ≤ 0 ∧ ni_0 − ni_post ≤ 0 ∧ − ni_0 + ni_post ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 1 31 2: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − nDim_0 + ni_0 ≤ 0 ∧ nj_post ≤ 0 ∧ − nj_post ≤ 0 ∧ nj_0 − nj_post ≤ 0 ∧ − nj_0 + nj_post ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 20 32 0: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ ni_post ≤ 0 ∧ − ni_post ≤ 0 ∧ nDim_0 − nDim_post ≤ 0 ∧ − nDim_0 + nDim_post ≤ 0 ∧ ni_0 − ni_post ≤ 0 ∧ − ni_0 + ni_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 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 0 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 21 33 20: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0

## Proof

### 1 Invariant Updates

The following invariants are asserted.

 0: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ −2 + nDim_0 ≤ 0 ∧ 2 − nDim_0 ≤ 0 1: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ −2 + nDim_0 ≤ 0 ∧ 2 − nDim_0 ≤ 0 2: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ −2 + nDim_0 ≤ 0 ∧ 2 − nDim_0 ≤ 0 3: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ −2 + nDim_0 ≤ 0 ∧ 2 − nDim_0 ≤ 0 4: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 5: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 ∧ −1 + tmp___1_post ≤ 0 ∧ −1 + tmp___1_0 ≤ 0 6: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 7: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 8: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 9: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 ∧ −1 + tmp___1_post ≤ 0 ∧ −1 + tmp___1_0 ≤ 0 10: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 11: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 12: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 13: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 14: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 15: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 16: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 17: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 18: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 19: −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 20: TRUE 21: TRUE

The invariants are proved as follows.

### IMPACT Invariant Proof

• nodes (location) invariant:  0 (0) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ −2 + nDim_0 ≤ 0 ∧ 2 − nDim_0 ≤ 0 1 (1) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ −2 + nDim_0 ≤ 0 ∧ 2 − nDim_0 ≤ 0 2 (2) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ −2 + nDim_0 ≤ 0 ∧ 2 − nDim_0 ≤ 0 3 (3) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ −2 + nDim_0 ≤ 0 ∧ 2 − nDim_0 ≤ 0 4 (4) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 5 (5) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 ∧ −1 + tmp___1_post ≤ 0 ∧ −1 + tmp___1_0 ≤ 0 6 (6) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 7 (7) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 8 (8) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 9 (9) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 ∧ −1 + tmp___1_post ≤ 0 ∧ −1 + tmp___1_0 ≤ 0 10 (10) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 11 (11) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 12 (12) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 13 (13) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 14 (14) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 15 (15) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 16 (16) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 17 (17) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 18 (18) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 19 (19) −2 + nDim_post ≤ 0 ∧ 2 − nDim_post ≤ 0 ∧ 2 − nDim_0 ≤ 0 20 (20) TRUE 21 (21) TRUE
• initial node: 21
• cover edges:
• transition edges:  0 0 1 1 30 13 1 31 2 2 1 3 3 28 0 3 29 2 4 2 5 5 6 9 6 3 5 7 4 5 8 5 5 10 7 8 10 8 5 10 9 8 11 10 7 11 11 7 11 12 10 12 13 6 12 14 6 12 15 11 13 16 14 14 25 15 14 26 17 15 17 4 15 18 4 15 19 12 16 20 17 16 21 18 17 22 19 18 27 16 19 23 13 19 24 18 20 32 0 21 33 20

### 2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 0 34 0: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 2 41 2: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 13 48 13: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 17 55 17: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0 18 62 18: − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 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 ∧ − nk_post + nk_post ≤ 0 ∧ nk_post − nk_post ≤ 0 ∧ − nk_0 + nk_0 ≤ 0 ∧ nk_0 − nk_0 ≤ 0 ∧ − nj_post + nj_post ≤ 0 ∧ nj_post − nj_post ≤ 0 ∧ − nj_0 + nj_0 ≤ 0 ∧ nj_0 − nj_0 ≤ 0 ∧ − ni_post + ni_post ≤ 0 ∧ ni_post − ni_post ≤ 0 ∧ − ni_0 + ni_0 ≤ 0 ∧ ni_0 − ni_0 ≤ 0 ∧ − nDim_post + nDim_post ≤ 0 ∧ nDim_post − nDim_post ≤ 0 ∧ − nDim_0 + nDim_0 ≤ 0 ∧ nDim_0 − nDim_0 ≤ 0
and for every transition t, a duplicate t is considered.

### 3 Transition Removal

We remove transitions 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 25, 30, 32, 33 using the following ranking functions, which are bounded by −41.

 21: 0 20: 0 0: 0 1: 0 2: 0 3: 0 13: 0 14: 0 16: 0 17: 0 18: 0 19: 0 15: 0 4: 0 12: 0 6: 0 11: 0 7: 0 10: 0 8: 0 5: 0 9: 0 21: −15 20: −16 0: −17 1: −17 2: −17 3: −17 0_var_snapshot: −17 0*: −17 2_var_snapshot: −17 2*: −17 13: −20 14: −20 16: −20 17: −20 18: −20 19: −20 13_var_snapshot: −20 13*: −20 17_var_snapshot: −20 17*: −20 18_var_snapshot: −20 18*: −20 15: −25 4: −26 12: −27 6: −28 11: −29 7: −30 10: −31 8: −32 5: −33 9: −34

### 4 Location Addition

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

0* 37 0: tmp_post + tmp_post ≤ 0tmp_posttmp_post ≤ 0tmp___1_post + tmp___1_post ≤ 0tmp___1_posttmp___1_post ≤ 0tmp___1_0 + tmp___1_0 ≤ 0tmp___1_0tmp___1_0 ≤ 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 ≤ 0nk_post + nk_post ≤ 0nk_postnk_post ≤ 0nk_0 + nk_0 ≤ 0nk_0nk_0 ≤ 0nj_post + nj_post ≤ 0nj_postnj_post ≤ 0nj_0 + nj_0 ≤ 0nj_0nj_0 ≤ 0ni_post + ni_post ≤ 0ni_postni_post ≤ 0ni_0 + ni_0 ≤ 0ni_0ni_0 ≤ 0nDim_post + nDim_post ≤ 0nDim_postnDim_post ≤ 0nDim_0 + nDim_0 ≤ 0nDim_0nDim_0 ≤ 0

### 5 Location Addition

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

0 35 0_var_snapshot: tmp_post + tmp_post ≤ 0tmp_posttmp_post ≤ 0tmp___1_post + tmp___1_post ≤ 0tmp___1_posttmp___1_post ≤ 0tmp___1_0 + tmp___1_0 ≤ 0tmp___1_0tmp___1_0 ≤ 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 ≤ 0nk_post + nk_post ≤ 0nk_postnk_post ≤ 0nk_0 + nk_0 ≤ 0nk_0nk_0 ≤ 0nj_post + nj_post ≤ 0nj_postnj_post ≤ 0nj_0 + nj_0 ≤ 0nj_0nj_0 ≤ 0ni_post + ni_post ≤ 0ni_postni_post ≤ 0ni_0 + ni_0 ≤ 0ni_0ni_0 ≤ 0nDim_post + nDim_post ≤ 0nDim_postnDim_post ≤ 0nDim_0 + nDim_0 ≤ 0nDim_0nDim_0 ≤ 0

### 6 Location Addition

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

2* 44 2: tmp_post + tmp_post ≤ 0tmp_posttmp_post ≤ 0tmp___1_post + tmp___1_post ≤ 0tmp___1_posttmp___1_post ≤ 0tmp___1_0 + tmp___1_0 ≤ 0tmp___1_0tmp___1_0 ≤ 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 ≤ 0nk_post + nk_post ≤ 0nk_postnk_post ≤ 0nk_0 + nk_0 ≤ 0nk_0nk_0 ≤ 0nj_post + nj_post ≤ 0nj_postnj_post ≤ 0nj_0 + nj_0 ≤ 0nj_0nj_0 ≤ 0ni_post + ni_post ≤ 0ni_postni_post ≤ 0ni_0 + ni_0 ≤ 0ni_0ni_0 ≤ 0nDim_post + nDim_post ≤ 0nDim_postnDim_post ≤ 0nDim_0 + nDim_0 ≤ 0nDim_0nDim_0 ≤ 0

### 7 Location Addition

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

2 42 2_var_snapshot: tmp_post + tmp_post ≤ 0tmp_posttmp_post ≤ 0tmp___1_post + tmp___1_post ≤ 0tmp___1_posttmp___1_post ≤ 0tmp___1_0 + tmp___1_0 ≤ 0tmp___1_0tmp___1_0 ≤ 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 ≤ 0nk_post + nk_post ≤ 0nk_postnk_post ≤ 0nk_0 + nk_0 ≤ 0nk_0nk_0 ≤ 0nj_post + nj_post ≤ 0nj_postnj_post ≤ 0nj_0 + nj_0 ≤ 0nj_0nj_0 ≤ 0ni_post + ni_post ≤ 0ni_postni_post ≤ 0ni_0 + ni_0 ≤ 0ni_0ni_0 ≤ 0nDim_post + nDim_post ≤ 0nDim_postnDim_post ≤ 0nDim_0 + nDim_0 ≤ 0nDim_0nDim_0 ≤ 0

### 8 Location Addition

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

13* 51 13: tmp_post + tmp_post ≤ 0tmp_posttmp_post ≤ 0tmp___1_post + tmp___1_post ≤ 0tmp___1_posttmp___1_post ≤ 0tmp___1_0 + tmp___1_0 ≤ 0tmp___1_0tmp___1_0 ≤ 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 ≤ 0nk_post + nk_post ≤ 0nk_postnk_post ≤ 0nk_0 + nk_0 ≤ 0nk_0nk_0 ≤ 0nj_post + nj_post ≤ 0nj_postnj_post ≤ 0nj_0 + nj_0 ≤ 0nj_0nj_0 ≤ 0ni_post + ni_post ≤ 0ni_postni_post ≤ 0ni_0 + ni_0 ≤ 0ni_0ni_0 ≤ 0nDim_post + nDim_post ≤ 0nDim_postnDim_post ≤ 0nDim_0 + nDim_0 ≤ 0nDim_0nDim_0 ≤ 0

### 9 Location Addition

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

13 49 13_var_snapshot: tmp_post + tmp_post ≤ 0tmp_posttmp_post ≤ 0tmp___1_post + tmp___1_post ≤ 0tmp___1_posttmp___1_post ≤ 0tmp___1_0 + tmp___1_0 ≤ 0tmp___1_0tmp___1_0 ≤ 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 ≤ 0nk_post + nk_post ≤ 0nk_postnk_post ≤ 0nk_0 + nk_0 ≤ 0nk_0nk_0 ≤ 0nj_post + nj_post ≤ 0nj_postnj_post ≤ 0nj_0 + nj_0 ≤ 0nj_0nj_0 ≤ 0ni_post + ni_post ≤ 0ni_postni_post ≤ 0ni_0 + ni_0 ≤ 0ni_0ni_0 ≤ 0nDim_post + nDim_post ≤ 0nDim_postnDim_post ≤ 0nDim_0 + nDim_0 ≤ 0nDim_0nDim_0 ≤ 0

### 10 Location Addition

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

17* 58 17: tmp_post + tmp_post ≤ 0tmp_posttmp_post ≤ 0tmp___1_post + tmp___1_post ≤ 0tmp___1_posttmp___1_post ≤ 0tmp___1_0 + tmp___1_0 ≤ 0tmp___1_0tmp___1_0 ≤ 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 ≤ 0nk_post + nk_post ≤ 0nk_postnk_post ≤ 0nk_0 + nk_0 ≤ 0nk_0nk_0 ≤ 0nj_post + nj_post ≤ 0nj_postnj_post ≤ 0nj_0 + nj_0 ≤ 0nj_0nj_0 ≤ 0ni_post + ni_post ≤ 0ni_postni_post ≤ 0ni_0 + ni_0 ≤ 0ni_0ni_0 ≤ 0nDim_post + nDim_post ≤ 0nDim_postnDim_post ≤ 0nDim_0 + nDim_0 ≤ 0nDim_0nDim_0 ≤ 0

### 11 Location Addition

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

17 56 17_var_snapshot: tmp_post + tmp_post ≤ 0tmp_posttmp_post ≤ 0tmp___1_post + tmp___1_post ≤ 0tmp___1_posttmp___1_post ≤ 0tmp___1_0 + tmp___1_0 ≤ 0tmp___1_0tmp___1_0 ≤ 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 ≤ 0nk_post + nk_post ≤ 0nk_postnk_post ≤ 0nk_0 + nk_0 ≤ 0nk_0nk_0 ≤ 0nj_post + nj_post ≤ 0nj_postnj_post ≤ 0nj_0 + nj_0 ≤ 0nj_0nj_0 ≤ 0ni_post + ni_post ≤ 0ni_postni_post ≤ 0ni_0 + ni_0 ≤ 0ni_0ni_0 ≤ 0nDim_post + nDim_post ≤ 0nDim_postnDim_post ≤ 0nDim_0 + nDim_0 ≤ 0nDim_0nDim_0 ≤ 0

### 12 Location Addition

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

18* 65 18: tmp_post + tmp_post ≤ 0tmp_posttmp_post ≤ 0tmp___1_post + tmp___1_post ≤ 0tmp___1_posttmp___1_post ≤ 0tmp___1_0 + tmp___1_0 ≤ 0tmp___1_0tmp___1_0 ≤ 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 ≤ 0nk_post + nk_post ≤ 0nk_postnk_post ≤ 0nk_0 + nk_0 ≤ 0nk_0nk_0 ≤ 0nj_post + nj_post ≤ 0nj_postnj_post ≤ 0nj_0 + nj_0 ≤ 0nj_0nj_0 ≤ 0ni_post + ni_post ≤ 0ni_postni_post ≤ 0ni_0 + ni_0 ≤ 0ni_0ni_0 ≤ 0nDim_post + nDim_post ≤ 0nDim_postnDim_post ≤ 0nDim_0 + nDim_0 ≤ 0nDim_0nDim_0 ≤ 0

### 13 Location Addition

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

18 63 18_var_snapshot: tmp_post + tmp_post ≤ 0tmp_posttmp_post ≤ 0tmp___1_post + tmp___1_post ≤ 0tmp___1_posttmp___1_post ≤ 0tmp___1_0 + tmp___1_0 ≤ 0tmp___1_0tmp___1_0 ≤ 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 ≤ 0nk_post + nk_post ≤ 0nk_postnk_post ≤ 0nk_0 + nk_0 ≤ 0nk_0nk_0 ≤ 0nj_post + nj_post ≤ 0nj_postnj_post ≤ 0nj_0 + nj_0 ≤ 0nj_0nj_0 ≤ 0ni_post + ni_post ≤ 0ni_postni_post ≤ 0ni_0 + ni_0 ≤ 0ni_0ni_0 ≤ 0nDim_post + nDim_post ≤ 0nDim_postnDim_post ≤ 0nDim_0 + nDim_0 ≤ 0nDim_0nDim_0 ≤ 0

### 14 SCC Decomposition

We consider subproblems for each of the 2 SCC(s) of the program graph.

### 14.1 SCC Subproblem 1/2

Here we consider the SCC { 13, 14, 16, 17, 18, 19, 13_var_snapshot, 13*, 17_var_snapshot, 17*, 18_var_snapshot, 18* }.

### 14.1.1 Transition Removal

We remove transition 26 using the following ranking functions, which are bounded by 17.

 13: 8 + 12⋅nDim_0 − 12⋅ni_0 14: 6 + 12⋅nDim_0 − 12⋅ni_0 16: 12⋅nDim_0 − 12⋅ni_0 17: 12⋅nDim_0 − 12⋅ni_0 18: 12⋅nDim_0 − 12⋅ni_0 19: 12⋅nDim_0 − 12⋅ni_0 13_var_snapshot: 12⋅nDim_0 + 4⋅nDim_post − 12⋅ni_0 13*: 10 + 12⋅nDim_0 − 12⋅ni_0 17_var_snapshot: 12⋅nDim_0 − 12⋅ni_0 17*: 12⋅nDim_0 − 12⋅ni_0 18_var_snapshot: 12⋅nDim_0 − 12⋅ni_0 18*: 12⋅nDim_0 − 12⋅ni_0

### 14.1.2 Transition Removal

We remove transition 24 using the following ranking functions, which are bounded by 5.

 13: −1 − 5⋅nj_0 14: −1 − nDim_post − 5⋅nj_0 16: 5⋅nDim_0 − 5⋅nj_0 17: 3 + 5⋅nDim_0 − 5⋅nj_0 18: 5⋅nDim_0 − 5⋅nj_0 19: 1 + 5⋅nDim_0 − 5⋅nj_0 13_var_snapshot: − nDim_post − 5⋅nj_0 13*: −5⋅nj_0 17_var_snapshot: 2 + 5⋅nDim_0 − 5⋅nj_0 17*: 4 + 5⋅nDim_0 − 5⋅nj_0 18_var_snapshot: 5⋅nDim_0 − 5⋅nj_0 18*: 5⋅nDim_0 − 5⋅nj_0

### 14.1.3 Transition Removal

We remove transition 21 using the following ranking functions, which are bounded by 5.

 13: nDim_0 − 4⋅nk_0 14: −1 + nDim_0 − nDim_post − 4⋅nk_0 16: −2 + 4⋅nDim_0 + 2⋅nDim_post − 4⋅nk_0 17: 4⋅nDim_0 − 4⋅nk_0 18: 4 + 4⋅nDim_0 − 4⋅nk_0 19: 3⋅nDim_0 − nDim_post − 4⋅nk_0 13_var_snapshot: nDim_0 − nDim_post − 4⋅nk_0 13*: 2⋅nDim_0 − 4⋅nk_0 17_var_snapshot: 3⋅nDim_0 − 4⋅nk_0 17*: −4 + 4⋅nDim_0 + 2⋅nDim_post − 4⋅nk_0 18_var_snapshot: 4⋅nDim_0 + 2⋅nDim_post − 4⋅nk_0 18*: 1 + 4⋅nDim_0 + 2⋅nDim_post − 4⋅nk_0

### 14.1.4 Transition Removal

We remove transitions 49, 56, 58, 63, 65, 16, 20, 22, 23, 27 using the following ranking functions, which are bounded by −9.

 13: −6 14: −1 − 4⋅nDim_post 16: −2 + 2⋅nDim_0 + 2⋅nDim_post 17: −2 + 2⋅nDim_post 18: 2⋅nDim_0 + 3⋅nDim_post 19: − nDim_post 13_var_snapshot: −4⋅nDim_post 13*: −2 − nDim_post 17_var_snapshot: 0 17*: 2⋅nDim_post 18_var_snapshot: 2⋅nDim_0 + 2⋅nDim_post 18*: 2⋅nDim_0 + 4⋅nDim_post

### 14.1.5 Transition Removal

We remove transition 51 using the following ranking functions, which are bounded by 0.

 13: 0 14: 0 16: 0 17: 0 18: 0 19: 0 13_var_snapshot: 0 13*: 1 17_var_snapshot: 0 17*: 0 18_var_snapshot: 0 18*: 0

### 14.1.6 Splitting Cut-Point Transitions

We consider 3 subproblems corresponding to sets of cut-point transitions as follows.

### 14.1.6.1 Cut-Point Subproblem 1/3

Here we consider cut-point transition 48.

### 14.1.6.1.1 Splitting Cut-Point Transitions

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

### 14.1.6.2 Cut-Point Subproblem 2/3

Here we consider cut-point transition 55.

### 14.1.6.2.1 Splitting Cut-Point Transitions

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

### 14.1.6.3 Cut-Point Subproblem 3/3

Here we consider cut-point transition 62.

### 14.1.6.3.1 Splitting Cut-Point Transitions

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

### 14.2 SCC Subproblem 2/2

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

### 14.2.1 Transition Removal

We remove transition 31 using the following ranking functions, which are bounded by −8.

 0: nDim_post − 7⋅ni_0 1: 2 − nDim_0 − 7⋅ni_0 2: − nDim_0 − 7⋅ni_0 3: −4 + 2⋅nDim_0 − nDim_post − 7⋅ni_0 0_var_snapshot: −7⋅ni_0 0*: 2⋅nDim_0 − 7⋅ni_0 2_var_snapshot: − nDim_post − 7⋅ni_0 2*: − nDim_0 − 7⋅ni_0

### 14.2.2 Transition Removal

We remove transition 29 using the following ranking functions, which are bounded by −6.

 0: − nDim_post − 7⋅nj_0 1: −2⋅nDim_0 − nDim_post − 7⋅nj_0 2: −2 + 4⋅nDim_0 − 7⋅nj_0 3: nDim_0 − 7⋅nj_0 0_var_snapshot: −2 − nDim_post − 7⋅nj_0 0*: −7⋅nj_0 2_var_snapshot: 4⋅nDim_0 − 2⋅nDim_post − 7⋅nj_0 2*: 4⋅nDim_0 − 7⋅nj_0

### 14.2.3 Transition Removal

We remove transitions 35, 37, 42, 44, 0, 1, 28 using the following ranking functions, which are bounded by −9.

 0: −4 − nDim_post 1: −5⋅nDim_post 2: nDim_0 3: − nDim_post 0_var_snapshot: −3⋅nDim_0 − nDim_post 0*: − nDim_0 − nDim_post 2_var_snapshot: 0 2*: 2⋅nDim_0

### 14.2.4 Splitting Cut-Point Transitions

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

### 14.2.4.1 Cut-Point Subproblem 1/2

Here we consider cut-point transition 34.

### 14.2.4.1.1 Splitting Cut-Point Transitions

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

### 14.2.4.2 Cut-Point Subproblem 2/2

Here we consider cut-point transition 41.

### 14.2.4.2.1 Splitting Cut-Point Transitions

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

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