LTS Termination Proof

by T2Cert

Input

Integer Transition System

Proof

1 Invariant Updates

The following invariants are asserted.

0: −3 + nN_post ≤ 0 ∧ 3 − nN_post ≤ 0 ∧ −3 + np9_post ≤ 0 ∧ −3 + nN_0 ≤ 0 ∧ 3 − nN_0 ≤ 0 ∧ −3 + np9_0 ≤ 0
1: −3 + nN_post ≤ 0 ∧ 3 − nN_post ≤ 0 ∧ −3 + np9_post ≤ 0 ∧ −3 + nN_0 ≤ 0 ∧ 3 − nN_0 ≤ 0 ∧ −3 + np9_0 ≤ 0
2: −3 + nN_post ≤ 0 ∧ 3 − nN_post ≤ 0 ∧ −3 + np9_post ≤ 0 ∧ −3 + nN_0 ≤ 0 ∧ 3 − nN_0 ≤ 0 ∧ −3 + np14_post ≤ 0 ∧ −3 + np19_post ≤ 0 ∧ −3 + np19_0 ≤ 0
3: −3 + nN_post ≤ 0 ∧ 3 − nN_post ≤ 0 ∧ −3 + np9_post ≤ 0 ∧ −3 + nN_0 ≤ 0 ∧ 3 − nN_0 ≤ 0 ∧ −3 + np14_post ≤ 0 ∧ −3 + np19_post ≤ 0
4: −3 + nN_post ≤ 0 ∧ 3 − nN_post ≤ 0 ∧ −3 + np9_post ≤ 0 ∧ −3 + nN_0 ≤ 0 ∧ 3 − nN_0 ≤ 0 ∧ −3 + np14_post ≤ 0 ∧ −3 + np19_post ≤ 0 ∧ −3 + np19_0 ≤ 0
5: −3 + nN_post ≤ 0 ∧ 3 − nN_post ≤ 0 ∧ −3 + np9_post ≤ 0 ∧ −3 + nN_0 ≤ 0 ∧ 3 − nN_0 ≤ 0 ∧ −3 + np14_post ≤ 0 ∧ −3 + np14_0 ≤ 0
6: −3 + nN_post ≤ 0 ∧ 3 − nN_post ≤ 0 ∧ −3 + np9_post ≤ 0 ∧ −3 + nN_0 ≤ 0 ∧ 3 − nN_0 ≤ 0 ∧ −3 + np14_post ≤ 0 ∧ −3 + np14_0 ≤ 0
7: TRUE
8: TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
0 11 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 ∧ − ret_nPow22_post + ret_nPow22_post ≤ 0 ∧ ret_nPow22_post − ret_nPow22_post ≤ 0 ∧ − ret_nPow22_0 + ret_nPow22_0 ≤ 0 ∧ ret_nPow22_0 − ret_nPow22_0 ≤ 0 ∧ − ret_nPow17_post + ret_nPow17_post ≤ 0 ∧ ret_nPow17_post − ret_nPow17_post ≤ 0 ∧ − ret_nPow17_0 + ret_nPow17_0 ≤ 0 ∧ ret_nPow17_0 − ret_nPow17_0 ≤ 0 ∧ − ret_nPow12_post + ret_nPow12_post ≤ 0 ∧ ret_nPow12_post − ret_nPow12_post ≤ 0 ∧ − ret_nPow12_0 + ret_nPow12_0 ≤ 0 ∧ ret_nPow12_0 − ret_nPow12_0 ≤ 0 ∧ − nx8_post + nx8_post ≤ 0 ∧ nx8_post − nx8_post ≤ 0 ∧ − nx8_0 + nx8_0 ≤ 0 ∧ nx8_0 − nx8_0 ≤ 0 ∧ − nx18_post + nx18_post ≤ 0 ∧ nx18_post − nx18_post ≤ 0 ∧ − nx18_0 + nx18_0 ≤ 0 ∧ nx18_0 − nx18_0 ≤ 0 ∧ − nx13_post + nx13_post ≤ 0 ∧ nx13_post − nx13_post ≤ 0 ∧ − nx13_0 + nx13_0 ≤ 0 ∧ nx13_0 − nx13_0 ≤ 0 ∧ − np9_post + np9_post ≤ 0 ∧ np9_post − np9_post ≤ 0 ∧ − np9_0 + np9_0 ≤ 0 ∧ np9_0 − np9_0 ≤ 0 ∧ − np19_post + np19_post ≤ 0 ∧ np19_post − np19_post ≤ 0 ∧ − np19_0 + np19_0 ≤ 0 ∧ np19_0 − np19_0 ≤ 0 ∧ − np14_post + np14_post ≤ 0 ∧ np14_post − np14_post ≤ 0 ∧ − np14_0 + np14_0 ≤ 0 ∧ np14_0 − np14_0 ≤ 0 ∧ − ni21_post + ni21_post ≤ 0 ∧ ni21_post − ni21_post ≤ 0 ∧ − ni21_0 + ni21_0 ≤ 0 ∧ ni21_0 − ni21_0 ≤ 0 ∧ − ni16_post + ni16_post ≤ 0 ∧ ni16_post − ni16_post ≤ 0 ∧ − ni16_0 + ni16_0 ≤ 0 ∧ ni16_0 − ni16_0 ≤ 0 ∧ − ni11_post + ni11_post ≤ 0 ∧ ni11_post − ni11_post ≤ 0 ∧ − ni11_0 + ni11_0 ≤ 0 ∧ ni11_0 − ni11_0 ≤ 0 ∧ − nc_0 + nc_0 ≤ 0 ∧ nc_0 − nc_0 ≤ 0 ∧ − nb_0 + nb_0 ≤ 0 ∧ nb_0 − nb_0 ≤ 0 ∧ − na_0 + na_0 ≤ 0 ∧ na_0 − na_0 ≤ 0 ∧ − nPow___020_post + nPow___020_post ≤ 0 ∧ nPow___020_post − nPow___020_post ≤ 0 ∧ − nPow___020_0 + nPow___020_0 ≤ 0 ∧ nPow___020_0 − nPow___020_0 ≤ 0 ∧ − nPow___015_post + nPow___015_post ≤ 0 ∧ nPow___015_post − nPow___015_post ≤ 0 ∧ − nPow___015_0 + nPow___015_0 ≤ 0 ∧ nPow___015_0 − nPow___015_0 ≤ 0 ∧ − nPow___010_post + nPow___010_post ≤ 0 ∧ nPow___010_post − nPow___010_post ≤ 0 ∧ − nPow___010_0 + nPow___010_0 ≤ 0 ∧ nPow___010_0 − nPow___010_0 ≤ 0 ∧ − nN_post + nN_post ≤ 0 ∧ nN_post − nN_post ≤ 0 ∧ − nN_0 + nN_0 ≤ 0 ∧ nN_0 − nN_0 ≤ 0
4 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 ∧ − ret_nPow22_post + ret_nPow22_post ≤ 0 ∧ ret_nPow22_post − ret_nPow22_post ≤ 0 ∧ − ret_nPow22_0 + ret_nPow22_0 ≤ 0 ∧ ret_nPow22_0 − ret_nPow22_0 ≤ 0 ∧ − ret_nPow17_post + ret_nPow17_post ≤ 0 ∧ ret_nPow17_post − ret_nPow17_post ≤ 0 ∧ − ret_nPow17_0 + ret_nPow17_0 ≤ 0 ∧ ret_nPow17_0 − ret_nPow17_0 ≤ 0 ∧ − ret_nPow12_post + ret_nPow12_post ≤ 0 ∧ ret_nPow12_post − ret_nPow12_post ≤ 0 ∧ − ret_nPow12_0 + ret_nPow12_0 ≤ 0 ∧ ret_nPow12_0 − ret_nPow12_0 ≤ 0 ∧ − nx8_post + nx8_post ≤ 0 ∧ nx8_post − nx8_post ≤ 0 ∧ − nx8_0 + nx8_0 ≤ 0 ∧ nx8_0 − nx8_0 ≤ 0 ∧ − nx18_post + nx18_post ≤ 0 ∧ nx18_post − nx18_post ≤ 0 ∧ − nx18_0 + nx18_0 ≤ 0 ∧ nx18_0 − nx18_0 ≤ 0 ∧ − nx13_post + nx13_post ≤ 0 ∧ nx13_post − nx13_post ≤ 0 ∧ − nx13_0 + nx13_0 ≤ 0 ∧ nx13_0 − nx13_0 ≤ 0 ∧ − np9_post + np9_post ≤ 0 ∧ np9_post − np9_post ≤ 0 ∧ − np9_0 + np9_0 ≤ 0 ∧ np9_0 − np9_0 ≤ 0 ∧ − np19_post + np19_post ≤ 0 ∧ np19_post − np19_post ≤ 0 ∧ − np19_0 + np19_0 ≤ 0 ∧ np19_0 − np19_0 ≤ 0 ∧ − np14_post + np14_post ≤ 0 ∧ np14_post − np14_post ≤ 0 ∧ − np14_0 + np14_0 ≤ 0 ∧ np14_0 − np14_0 ≤ 0 ∧ − ni21_post + ni21_post ≤ 0 ∧ ni21_post − ni21_post ≤ 0 ∧ − ni21_0 + ni21_0 ≤ 0 ∧ ni21_0 − ni21_0 ≤ 0 ∧ − ni16_post + ni16_post ≤ 0 ∧ ni16_post − ni16_post ≤ 0 ∧ − ni16_0 + ni16_0 ≤ 0 ∧ ni16_0 − ni16_0 ≤ 0 ∧ − ni11_post + ni11_post ≤ 0 ∧ ni11_post − ni11_post ≤ 0 ∧ − ni11_0 + ni11_0 ≤ 0 ∧ ni11_0 − ni11_0 ≤ 0 ∧ − nc_0 + nc_0 ≤ 0 ∧ nc_0 − nc_0 ≤ 0 ∧ − nb_0 + nb_0 ≤ 0 ∧ nb_0 − nb_0 ≤ 0 ∧ − na_0 + na_0 ≤ 0 ∧ na_0 − na_0 ≤ 0 ∧ − nPow___020_post + nPow___020_post ≤ 0 ∧ nPow___020_post − nPow___020_post ≤ 0 ∧ − nPow___020_0 + nPow___020_0 ≤ 0 ∧ nPow___020_0 − nPow___020_0 ≤ 0 ∧ − nPow___015_post + nPow___015_post ≤ 0 ∧ nPow___015_post − nPow___015_post ≤ 0 ∧ − nPow___015_0 + nPow___015_0 ≤ 0 ∧ nPow___015_0 − nPow___015_0 ≤ 0 ∧ − nPow___010_post + nPow___010_post ≤ 0 ∧ nPow___010_post − nPow___010_post ≤ 0 ∧ − nPow___010_0 + nPow___010_0 ≤ 0 ∧ nPow___010_0 − nPow___010_0 ≤ 0 ∧ − nN_post + nN_post ≤ 0 ∧ nN_post − nN_post ≤ 0 ∧ − nN_0 + nN_0 ≤ 0 ∧ nN_0 − nN_0 ≤ 0
5 25 5: − 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 ∧ − ret_nPow22_post + ret_nPow22_post ≤ 0 ∧ ret_nPow22_post − ret_nPow22_post ≤ 0 ∧ − ret_nPow22_0 + ret_nPow22_0 ≤ 0 ∧ ret_nPow22_0 − ret_nPow22_0 ≤ 0 ∧ − ret_nPow17_post + ret_nPow17_post ≤ 0 ∧ ret_nPow17_post − ret_nPow17_post ≤ 0 ∧ − ret_nPow17_0 + ret_nPow17_0 ≤ 0 ∧ ret_nPow17_0 − ret_nPow17_0 ≤ 0 ∧ − ret_nPow12_post + ret_nPow12_post ≤ 0 ∧ ret_nPow12_post − ret_nPow12_post ≤ 0 ∧ − ret_nPow12_0 + ret_nPow12_0 ≤ 0 ∧ ret_nPow12_0 − ret_nPow12_0 ≤ 0 ∧ − nx8_post + nx8_post ≤ 0 ∧ nx8_post − nx8_post ≤ 0 ∧ − nx8_0 + nx8_0 ≤ 0 ∧ nx8_0 − nx8_0 ≤ 0 ∧ − nx18_post + nx18_post ≤ 0 ∧ nx18_post − nx18_post ≤ 0 ∧ − nx18_0 + nx18_0 ≤ 0 ∧ nx18_0 − nx18_0 ≤ 0 ∧ − nx13_post + nx13_post ≤ 0 ∧ nx13_post − nx13_post ≤ 0 ∧ − nx13_0 + nx13_0 ≤ 0 ∧ nx13_0 − nx13_0 ≤ 0 ∧ − np9_post + np9_post ≤ 0 ∧ np9_post − np9_post ≤ 0 ∧ − np9_0 + np9_0 ≤ 0 ∧ np9_0 − np9_0 ≤ 0 ∧ − np19_post + np19_post ≤ 0 ∧ np19_post − np19_post ≤ 0 ∧ − np19_0 + np19_0 ≤ 0 ∧ np19_0 − np19_0 ≤ 0 ∧ − np14_post + np14_post ≤ 0 ∧ np14_post − np14_post ≤ 0 ∧ − np14_0 + np14_0 ≤ 0 ∧ np14_0 − np14_0 ≤ 0 ∧ − ni21_post + ni21_post ≤ 0 ∧ ni21_post − ni21_post ≤ 0 ∧ − ni21_0 + ni21_0 ≤ 0 ∧ ni21_0 − ni21_0 ≤ 0 ∧ − ni16_post + ni16_post ≤ 0 ∧ ni16_post − ni16_post ≤ 0 ∧ − ni16_0 + ni16_0 ≤ 0 ∧ ni16_0 − ni16_0 ≤ 0 ∧ − ni11_post + ni11_post ≤ 0 ∧ ni11_post − ni11_post ≤ 0 ∧ − ni11_0 + ni11_0 ≤ 0 ∧ ni11_0 − ni11_0 ≤ 0 ∧ − nc_0 + nc_0 ≤ 0 ∧ nc_0 − nc_0 ≤ 0 ∧ − nb_0 + nb_0 ≤ 0 ∧ nb_0 − nb_0 ≤ 0 ∧ − na_0 + na_0 ≤ 0 ∧ na_0 − na_0 ≤ 0 ∧ − nPow___020_post + nPow___020_post ≤ 0 ∧ nPow___020_post − nPow___020_post ≤ 0 ∧ − nPow___020_0 + nPow___020_0 ≤ 0 ∧ nPow___020_0 − nPow___020_0 ≤ 0 ∧ − nPow___015_post + nPow___015_post ≤ 0 ∧ nPow___015_post − nPow___015_post ≤ 0 ∧ − nPow___015_0 + nPow___015_0 ≤ 0 ∧ nPow___015_0 − nPow___015_0 ≤ 0 ∧ − nPow___010_post + nPow___010_post ≤ 0 ∧ nPow___010_post − nPow___010_post ≤ 0 ∧ − nPow___010_0 + nPow___010_0 ≤ 0 ∧ nPow___010_0 − nPow___010_0 ≤ 0 ∧ − nN_post + nN_post ≤ 0 ∧ nN_post − nN_post ≤ 0 ∧ − nN_0 + nN_0 ≤ 0 ∧ nN_0 − nN_0 ≤ 0
and for every transition t, a duplicate t is considered.

3 Transition Removal

We remove transitions 1, 4, 7, 9, 10 using the following ranking functions, which are bounded by −21.

8: 0
7: 0
0: 0
1: 0
5: 0
6: 0
2: 0
4: 0
3: 0
8: −7
7: −8
0: −9
1: −9
0_var_snapshot: −9
0*: −9
5: −10
6: −10
5_var_snapshot: −10
5*: −10
2: −11
4: −11
4_var_snapshot: −11
4*: −11
3: −12

4 Location Addition

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

0* 14 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 ∧ − ret_nPow22_post + ret_nPow22_post ≤ 0 ∧ ret_nPow22_post − ret_nPow22_post ≤ 0 ∧ − ret_nPow22_0 + ret_nPow22_0 ≤ 0 ∧ ret_nPow22_0 − ret_nPow22_0 ≤ 0 ∧ − ret_nPow17_post + ret_nPow17_post ≤ 0 ∧ ret_nPow17_post − ret_nPow17_post ≤ 0 ∧ − ret_nPow17_0 + ret_nPow17_0 ≤ 0 ∧ ret_nPow17_0 − ret_nPow17_0 ≤ 0 ∧ − ret_nPow12_post + ret_nPow12_post ≤ 0 ∧ ret_nPow12_post − ret_nPow12_post ≤ 0 ∧ − ret_nPow12_0 + ret_nPow12_0 ≤ 0 ∧ ret_nPow12_0 − ret_nPow12_0 ≤ 0 ∧ − nx8_post + nx8_post ≤ 0 ∧ nx8_post − nx8_post ≤ 0 ∧ − nx8_0 + nx8_0 ≤ 0 ∧ nx8_0 − nx8_0 ≤ 0 ∧ − nx18_post + nx18_post ≤ 0 ∧ nx18_post − nx18_post ≤ 0 ∧ − nx18_0 + nx18_0 ≤ 0 ∧ nx18_0 − nx18_0 ≤ 0 ∧ − nx13_post + nx13_post ≤ 0 ∧ nx13_post − nx13_post ≤ 0 ∧ − nx13_0 + nx13_0 ≤ 0 ∧ nx13_0 − nx13_0 ≤ 0 ∧ − np9_post + np9_post ≤ 0 ∧ np9_post − np9_post ≤ 0 ∧ − np9_0 + np9_0 ≤ 0 ∧ np9_0 − np9_0 ≤ 0 ∧ − np19_post + np19_post ≤ 0 ∧ np19_post − np19_post ≤ 0 ∧ − np19_0 + np19_0 ≤ 0 ∧ np19_0 − np19_0 ≤ 0 ∧ − np14_post + np14_post ≤ 0 ∧ np14_post − np14_post ≤ 0 ∧ − np14_0 + np14_0 ≤ 0 ∧ np14_0 − np14_0 ≤ 0 ∧ − ni21_post + ni21_post ≤ 0 ∧ ni21_post − ni21_post ≤ 0 ∧ − ni21_0 + ni21_0 ≤ 0 ∧ ni21_0 − ni21_0 ≤ 0 ∧ − ni16_post + ni16_post ≤ 0 ∧ ni16_post − ni16_post ≤ 0 ∧ − ni16_0 + ni16_0 ≤ 0 ∧ ni16_0 − ni16_0 ≤ 0 ∧ − ni11_post + ni11_post ≤ 0 ∧ ni11_post − ni11_post ≤ 0 ∧ − ni11_0 + ni11_0 ≤ 0 ∧ ni11_0 − ni11_0 ≤ 0 ∧ − nc_0 + nc_0 ≤ 0 ∧ nc_0 − nc_0 ≤ 0 ∧ − nb_0 + nb_0 ≤ 0 ∧ nb_0 − nb_0 ≤ 0 ∧ − na_0 + na_0 ≤ 0 ∧ na_0 − na_0 ≤ 0 ∧ − nPow___020_post + nPow___020_post ≤ 0 ∧ nPow___020_post − nPow___020_post ≤ 0 ∧ − nPow___020_0 + nPow___020_0 ≤ 0 ∧ nPow___020_0 − nPow___020_0 ≤ 0 ∧ − nPow___015_post + nPow___015_post ≤ 0 ∧ nPow___015_post − nPow___015_post ≤ 0 ∧ − nPow___015_0 + nPow___015_0 ≤ 0 ∧ nPow___015_0 − nPow___015_0 ≤ 0 ∧ − nPow___010_post + nPow___010_post ≤ 0 ∧ nPow___010_post − nPow___010_post ≤ 0 ∧ − nPow___010_0 + nPow___010_0 ≤ 0 ∧ nPow___010_0 − nPow___010_0 ≤ 0 ∧ − nN_post + nN_post ≤ 0 ∧ nN_post − nN_post ≤ 0 ∧ − nN_0 + nN_0 ≤ 0 ∧ nN_0 − nN_0 ≤ 0

5 Location Addition

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

0 12 0_var_snapshot: − 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 ∧ − ret_nPow22_post + ret_nPow22_post ≤ 0 ∧ ret_nPow22_post − ret_nPow22_post ≤ 0 ∧ − ret_nPow22_0 + ret_nPow22_0 ≤ 0 ∧ ret_nPow22_0 − ret_nPow22_0 ≤ 0 ∧ − ret_nPow17_post + ret_nPow17_post ≤ 0 ∧ ret_nPow17_post − ret_nPow17_post ≤ 0 ∧ − ret_nPow17_0 + ret_nPow17_0 ≤ 0 ∧ ret_nPow17_0 − ret_nPow17_0 ≤ 0 ∧ − ret_nPow12_post + ret_nPow12_post ≤ 0 ∧ ret_nPow12_post − ret_nPow12_post ≤ 0 ∧ − ret_nPow12_0 + ret_nPow12_0 ≤ 0 ∧ ret_nPow12_0 − ret_nPow12_0 ≤ 0 ∧ − nx8_post + nx8_post ≤ 0 ∧ nx8_post − nx8_post ≤ 0 ∧ − nx8_0 + nx8_0 ≤ 0 ∧ nx8_0 − nx8_0 ≤ 0 ∧ − nx18_post + nx18_post ≤ 0 ∧ nx18_post − nx18_post ≤ 0 ∧ − nx18_0 + nx18_0 ≤ 0 ∧ nx18_0 − nx18_0 ≤ 0 ∧ − nx13_post + nx13_post ≤ 0 ∧ nx13_post − nx13_post ≤ 0 ∧ − nx13_0 + nx13_0 ≤ 0 ∧ nx13_0 − nx13_0 ≤ 0 ∧ − np9_post + np9_post ≤ 0 ∧ np9_post − np9_post ≤ 0 ∧ − np9_0 + np9_0 ≤ 0 ∧ np9_0 − np9_0 ≤ 0 ∧ − np19_post + np19_post ≤ 0 ∧ np19_post − np19_post ≤ 0 ∧ − np19_0 + np19_0 ≤ 0 ∧ np19_0 − np19_0 ≤ 0 ∧ − np14_post + np14_post ≤ 0 ∧ np14_post − np14_post ≤ 0 ∧ − np14_0 + np14_0 ≤ 0 ∧ np14_0 − np14_0 ≤ 0 ∧ − ni21_post + ni21_post ≤ 0 ∧ ni21_post − ni21_post ≤ 0 ∧ − ni21_0 + ni21_0 ≤ 0 ∧ ni21_0 − ni21_0 ≤ 0 ∧ − ni16_post + ni16_post ≤ 0 ∧ ni16_post − ni16_post ≤ 0 ∧ − ni16_0 + ni16_0 ≤ 0 ∧ ni16_0 − ni16_0 ≤ 0 ∧ − ni11_post + ni11_post ≤ 0 ∧ ni11_post − ni11_post ≤ 0 ∧ − ni11_0 + ni11_0 ≤ 0 ∧ ni11_0 − ni11_0 ≤ 0 ∧ − nc_0 + nc_0 ≤ 0 ∧ nc_0 − nc_0 ≤ 0 ∧ − nb_0 + nb_0 ≤ 0 ∧ nb_0 − nb_0 ≤ 0 ∧ − na_0 + na_0 ≤ 0 ∧ na_0 − na_0 ≤ 0 ∧ − nPow___020_post + nPow___020_post ≤ 0 ∧ nPow___020_post − nPow___020_post ≤ 0 ∧ − nPow___020_0 + nPow___020_0 ≤ 0 ∧ nPow___020_0 − nPow___020_0 ≤ 0 ∧ − nPow___015_post + nPow___015_post ≤ 0 ∧ nPow___015_post − nPow___015_post ≤ 0 ∧ − nPow___015_0 + nPow___015_0 ≤ 0 ∧ nPow___015_0 − nPow___015_0 ≤ 0 ∧ − nPow___010_post + nPow___010_post ≤ 0 ∧ nPow___010_post − nPow___010_post ≤ 0 ∧ − nPow___010_0 + nPow___010_0 ≤ 0 ∧ nPow___010_0 − nPow___010_0 ≤ 0 ∧ − nN_post + nN_post ≤ 0 ∧ nN_post − nN_post ≤ 0 ∧ − nN_0 + nN_0 ≤ 0 ∧ nN_0 − nN_0 ≤ 0

6 Location Addition

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

4* 21 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 ∧ − ret_nPow22_post + ret_nPow22_post ≤ 0 ∧ ret_nPow22_post − ret_nPow22_post ≤ 0 ∧ − ret_nPow22_0 + ret_nPow22_0 ≤ 0 ∧ ret_nPow22_0 − ret_nPow22_0 ≤ 0 ∧ − ret_nPow17_post + ret_nPow17_post ≤ 0 ∧ ret_nPow17_post − ret_nPow17_post ≤ 0 ∧ − ret_nPow17_0 + ret_nPow17_0 ≤ 0 ∧ ret_nPow17_0 − ret_nPow17_0 ≤ 0 ∧ − ret_nPow12_post + ret_nPow12_post ≤ 0 ∧ ret_nPow12_post − ret_nPow12_post ≤ 0 ∧ − ret_nPow12_0 + ret_nPow12_0 ≤ 0 ∧ ret_nPow12_0 − ret_nPow12_0 ≤ 0 ∧ − nx8_post + nx8_post ≤ 0 ∧ nx8_post − nx8_post ≤ 0 ∧ − nx8_0 + nx8_0 ≤ 0 ∧ nx8_0 − nx8_0 ≤ 0 ∧ − nx18_post + nx18_post ≤ 0 ∧ nx18_post − nx18_post ≤ 0 ∧ − nx18_0 + nx18_0 ≤ 0 ∧ nx18_0 − nx18_0 ≤ 0 ∧ − nx13_post + nx13_post ≤ 0 ∧ nx13_post − nx13_post ≤ 0 ∧ − nx13_0 + nx13_0 ≤ 0 ∧ nx13_0 − nx13_0 ≤ 0 ∧ − np9_post + np9_post ≤ 0 ∧ np9_post − np9_post ≤ 0 ∧ − np9_0 + np9_0 ≤ 0 ∧ np9_0 − np9_0 ≤ 0 ∧ − np19_post + np19_post ≤ 0 ∧ np19_post − np19_post ≤ 0 ∧ − np19_0 + np19_0 ≤ 0 ∧ np19_0 − np19_0 ≤ 0 ∧ − np14_post + np14_post ≤ 0 ∧ np14_post − np14_post ≤ 0 ∧ − np14_0 + np14_0 ≤ 0 ∧ np14_0 − np14_0 ≤ 0 ∧ − ni21_post + ni21_post ≤ 0 ∧ ni21_post − ni21_post ≤ 0 ∧ − ni21_0 + ni21_0 ≤ 0 ∧ ni21_0 − ni21_0 ≤ 0 ∧ − ni16_post + ni16_post ≤ 0 ∧ ni16_post − ni16_post ≤ 0 ∧ − ni16_0 + ni16_0 ≤ 0 ∧ ni16_0 − ni16_0 ≤ 0 ∧ − ni11_post + ni11_post ≤ 0 ∧ ni11_post − ni11_post ≤ 0 ∧ − ni11_0 + ni11_0 ≤ 0 ∧ ni11_0 − ni11_0 ≤ 0 ∧ − nc_0 + nc_0 ≤ 0 ∧ nc_0 − nc_0 ≤ 0 ∧ − nb_0 + nb_0 ≤ 0 ∧ nb_0 − nb_0 ≤ 0 ∧ − na_0 + na_0 ≤ 0 ∧ na_0 − na_0 ≤ 0 ∧ − nPow___020_post + nPow___020_post ≤ 0 ∧ nPow___020_post − nPow___020_post ≤ 0 ∧ − nPow___020_0 + nPow___020_0 ≤ 0 ∧ nPow___020_0 − nPow___020_0 ≤ 0 ∧ − nPow___015_post + nPow___015_post ≤ 0 ∧ nPow___015_post − nPow___015_post ≤ 0 ∧ − nPow___015_0 + nPow___015_0 ≤ 0 ∧ nPow___015_0 − nPow___015_0 ≤ 0 ∧ − nPow___010_post + nPow___010_post ≤ 0 ∧ nPow___010_post − nPow___010_post ≤ 0 ∧ − nPow___010_0 + nPow___010_0 ≤ 0 ∧ nPow___010_0 − nPow___010_0 ≤ 0 ∧ − nN_post + nN_post ≤ 0 ∧ nN_post − nN_post ≤ 0 ∧ − nN_0 + nN_0 ≤ 0 ∧ nN_0 − nN_0 ≤ 0

7 Location Addition

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

4 19 4_var_snapshot: − 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 ∧ − ret_nPow22_post + ret_nPow22_post ≤ 0 ∧ ret_nPow22_post − ret_nPow22_post ≤ 0 ∧ − ret_nPow22_0 + ret_nPow22_0 ≤ 0 ∧ ret_nPow22_0 − ret_nPow22_0 ≤ 0 ∧ − ret_nPow17_post + ret_nPow17_post ≤ 0 ∧ ret_nPow17_post − ret_nPow17_post ≤ 0 ∧ − ret_nPow17_0 + ret_nPow17_0 ≤ 0 ∧ ret_nPow17_0 − ret_nPow17_0 ≤ 0 ∧ − ret_nPow12_post + ret_nPow12_post ≤ 0 ∧ ret_nPow12_post − ret_nPow12_post ≤ 0 ∧ − ret_nPow12_0 + ret_nPow12_0 ≤ 0 ∧ ret_nPow12_0 − ret_nPow12_0 ≤ 0 ∧ − nx8_post + nx8_post ≤ 0 ∧ nx8_post − nx8_post ≤ 0 ∧ − nx8_0 + nx8_0 ≤ 0 ∧ nx8_0 − nx8_0 ≤ 0 ∧ − nx18_post + nx18_post ≤ 0 ∧ nx18_post − nx18_post ≤ 0 ∧ − nx18_0 + nx18_0 ≤ 0 ∧ nx18_0 − nx18_0 ≤ 0 ∧ − nx13_post + nx13_post ≤ 0 ∧ nx13_post − nx13_post ≤ 0 ∧ − nx13_0 + nx13_0 ≤ 0 ∧ nx13_0 − nx13_0 ≤ 0 ∧ − np9_post + np9_post ≤ 0 ∧ np9_post − np9_post ≤ 0 ∧ − np9_0 + np9_0 ≤ 0 ∧ np9_0 − np9_0 ≤ 0 ∧ − np19_post + np19_post ≤ 0 ∧ np19_post − np19_post ≤ 0 ∧ − np19_0 + np19_0 ≤ 0 ∧ np19_0 − np19_0 ≤ 0 ∧ − np14_post + np14_post ≤ 0 ∧ np14_post − np14_post ≤ 0 ∧ − np14_0 + np14_0 ≤ 0 ∧ np14_0 − np14_0 ≤ 0 ∧ − ni21_post + ni21_post ≤ 0 ∧ ni21_post − ni21_post ≤ 0 ∧ − ni21_0 + ni21_0 ≤ 0 ∧ ni21_0 − ni21_0 ≤ 0 ∧ − ni16_post + ni16_post ≤ 0 ∧ ni16_post − ni16_post ≤ 0 ∧ − ni16_0 + ni16_0 ≤ 0 ∧ ni16_0 − ni16_0 ≤ 0 ∧ − ni11_post + ni11_post ≤ 0 ∧ ni11_post − ni11_post ≤ 0 ∧ − ni11_0 + ni11_0 ≤ 0 ∧ ni11_0 − ni11_0 ≤ 0 ∧ − nc_0 + nc_0 ≤ 0 ∧ nc_0 − nc_0 ≤ 0 ∧ − nb_0 + nb_0 ≤ 0 ∧ nb_0 − nb_0 ≤ 0 ∧ − na_0 + na_0 ≤ 0 ∧ na_0 − na_0 ≤ 0 ∧ − nPow___020_post + nPow___020_post ≤ 0 ∧ nPow___020_post − nPow___020_post ≤ 0 ∧ − nPow___020_0 + nPow___020_0 ≤ 0 ∧ nPow___020_0 − nPow___020_0 ≤ 0 ∧ − nPow___015_post + nPow___015_post ≤ 0 ∧ nPow___015_post − nPow___015_post ≤ 0 ∧ − nPow___015_0 + nPow___015_0 ≤ 0 ∧ nPow___015_0 − nPow___015_0 ≤ 0 ∧ − nPow___010_post + nPow___010_post ≤ 0 ∧ nPow___010_post − nPow___010_post ≤ 0 ∧ − nPow___010_0 + nPow___010_0 ≤ 0 ∧ nPow___010_0 − nPow___010_0 ≤ 0 ∧ − nN_post + nN_post ≤ 0 ∧ nN_post − nN_post ≤ 0 ∧ − nN_0 + nN_0 ≤ 0 ∧ nN_0 − nN_0 ≤ 0

8 Location Addition

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

5* 28 5: − 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 ∧ − ret_nPow22_post + ret_nPow22_post ≤ 0 ∧ ret_nPow22_post − ret_nPow22_post ≤ 0 ∧ − ret_nPow22_0 + ret_nPow22_0 ≤ 0 ∧ ret_nPow22_0 − ret_nPow22_0 ≤ 0 ∧ − ret_nPow17_post + ret_nPow17_post ≤ 0 ∧ ret_nPow17_post − ret_nPow17_post ≤ 0 ∧ − ret_nPow17_0 + ret_nPow17_0 ≤ 0 ∧ ret_nPow17_0 − ret_nPow17_0 ≤ 0 ∧ − ret_nPow12_post + ret_nPow12_post ≤ 0 ∧ ret_nPow12_post − ret_nPow12_post ≤ 0 ∧ − ret_nPow12_0 + ret_nPow12_0 ≤ 0 ∧ ret_nPow12_0 − ret_nPow12_0 ≤ 0 ∧ − nx8_post + nx8_post ≤ 0 ∧ nx8_post − nx8_post ≤ 0 ∧ − nx8_0 + nx8_0 ≤ 0 ∧ nx8_0 − nx8_0 ≤ 0 ∧ − nx18_post + nx18_post ≤ 0 ∧ nx18_post − nx18_post ≤ 0 ∧ − nx18_0 + nx18_0 ≤ 0 ∧ nx18_0 − nx18_0 ≤ 0 ∧ − nx13_post + nx13_post ≤ 0 ∧ nx13_post − nx13_post ≤ 0 ∧ − nx13_0 + nx13_0 ≤ 0 ∧ nx13_0 − nx13_0 ≤ 0 ∧ − np9_post + np9_post ≤ 0 ∧ np9_post − np9_post ≤ 0 ∧ − np9_0 + np9_0 ≤ 0 ∧ np9_0 − np9_0 ≤ 0 ∧ − np19_post + np19_post ≤ 0 ∧ np19_post − np19_post ≤ 0 ∧ − np19_0 + np19_0 ≤ 0 ∧ np19_0 − np19_0 ≤ 0 ∧ − np14_post + np14_post ≤ 0 ∧ np14_post − np14_post ≤ 0 ∧ − np14_0 + np14_0 ≤ 0 ∧ np14_0 − np14_0 ≤ 0 ∧ − ni21_post + ni21_post ≤ 0 ∧ ni21_post − ni21_post ≤ 0 ∧ − ni21_0 + ni21_0 ≤ 0 ∧ ni21_0 − ni21_0 ≤ 0 ∧ − ni16_post + ni16_post ≤ 0 ∧ ni16_post − ni16_post ≤ 0 ∧ − ni16_0 + ni16_0 ≤ 0 ∧ ni16_0 − ni16_0 ≤ 0 ∧ − ni11_post + ni11_post ≤ 0 ∧ ni11_post − ni11_post ≤ 0 ∧ − ni11_0 + ni11_0 ≤ 0 ∧ ni11_0 − ni11_0 ≤ 0 ∧ − nc_0 + nc_0 ≤ 0 ∧ nc_0 − nc_0 ≤ 0 ∧ − nb_0 + nb_0 ≤ 0 ∧ nb_0 − nb_0 ≤ 0 ∧ − na_0 + na_0 ≤ 0 ∧ na_0 − na_0 ≤ 0 ∧ − nPow___020_post + nPow___020_post ≤ 0 ∧ nPow___020_post − nPow___020_post ≤ 0 ∧ − nPow___020_0 + nPow___020_0 ≤ 0 ∧ nPow___020_0 − nPow___020_0 ≤ 0 ∧ − nPow___015_post + nPow___015_post ≤ 0 ∧ nPow___015_post − nPow___015_post ≤ 0 ∧ − nPow___015_0 + nPow___015_0 ≤ 0 ∧ nPow___015_0 − nPow___015_0 ≤ 0 ∧ − nPow___010_post + nPow___010_post ≤ 0 ∧ nPow___010_post − nPow___010_post ≤ 0 ∧ − nPow___010_0 + nPow___010_0 ≤ 0 ∧ nPow___010_0 − nPow___010_0 ≤ 0 ∧ − nN_post + nN_post ≤ 0 ∧ nN_post − nN_post ≤ 0 ∧ − nN_0 + nN_0 ≤ 0 ∧ nN_0 − nN_0 ≤ 0

9 Location Addition

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

5 26 5_var_snapshot: − 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 ∧ − ret_nPow22_post + ret_nPow22_post ≤ 0 ∧ ret_nPow22_post − ret_nPow22_post ≤ 0 ∧ − ret_nPow22_0 + ret_nPow22_0 ≤ 0 ∧ ret_nPow22_0 − ret_nPow22_0 ≤ 0 ∧ − ret_nPow17_post + ret_nPow17_post ≤ 0 ∧ ret_nPow17_post − ret_nPow17_post ≤ 0 ∧ − ret_nPow17_0 + ret_nPow17_0 ≤ 0 ∧ ret_nPow17_0 − ret_nPow17_0 ≤ 0 ∧ − ret_nPow12_post + ret_nPow12_post ≤ 0 ∧ ret_nPow12_post − ret_nPow12_post ≤ 0 ∧ − ret_nPow12_0 + ret_nPow12_0 ≤ 0 ∧ ret_nPow12_0 − ret_nPow12_0 ≤ 0 ∧ − nx8_post + nx8_post ≤ 0 ∧ nx8_post − nx8_post ≤ 0 ∧ − nx8_0 + nx8_0 ≤ 0 ∧ nx8_0 − nx8_0 ≤ 0 ∧ − nx18_post + nx18_post ≤ 0 ∧ nx18_post − nx18_post ≤ 0 ∧ − nx18_0 + nx18_0 ≤ 0 ∧ nx18_0 − nx18_0 ≤ 0 ∧ − nx13_post + nx13_post ≤ 0 ∧ nx13_post − nx13_post ≤ 0 ∧ − nx13_0 + nx13_0 ≤ 0 ∧ nx13_0 − nx13_0 ≤ 0 ∧ − np9_post + np9_post ≤ 0 ∧ np9_post − np9_post ≤ 0 ∧ − np9_0 + np9_0 ≤ 0 ∧ np9_0 − np9_0 ≤ 0 ∧ − np19_post + np19_post ≤ 0 ∧ np19_post − np19_post ≤ 0 ∧ − np19_0 + np19_0 ≤ 0 ∧ np19_0 − np19_0 ≤ 0 ∧ − np14_post + np14_post ≤ 0 ∧ np14_post − np14_post ≤ 0 ∧ − np14_0 + np14_0 ≤ 0 ∧ np14_0 − np14_0 ≤ 0 ∧ − ni21_post + ni21_post ≤ 0 ∧ ni21_post − ni21_post ≤ 0 ∧ − ni21_0 + ni21_0 ≤ 0 ∧ ni21_0 − ni21_0 ≤ 0 ∧ − ni16_post + ni16_post ≤ 0 ∧ ni16_post − ni16_post ≤ 0 ∧ − ni16_0 + ni16_0 ≤ 0 ∧ ni16_0 − ni16_0 ≤ 0 ∧ − ni11_post + ni11_post ≤ 0 ∧ ni11_post − ni11_post ≤ 0 ∧ − ni11_0 + ni11_0 ≤ 0 ∧ ni11_0 − ni11_0 ≤ 0 ∧ − nc_0 + nc_0 ≤ 0 ∧ nc_0 − nc_0 ≤ 0 ∧ − nb_0 + nb_0 ≤ 0 ∧ nb_0 − nb_0 ≤ 0 ∧ − na_0 + na_0 ≤ 0 ∧ na_0 − na_0 ≤ 0 ∧ − nPow___020_post + nPow___020_post ≤ 0 ∧ nPow___020_post − nPow___020_post ≤ 0 ∧ − nPow___020_0 + nPow___020_0 ≤ 0 ∧ nPow___020_0 − nPow___020_0 ≤ 0 ∧ − nPow___015_post + nPow___015_post ≤ 0 ∧ nPow___015_post − nPow___015_post ≤ 0 ∧ − nPow___015_0 + nPow___015_0 ≤ 0 ∧ nPow___015_0 − nPow___015_0 ≤ 0 ∧ − nPow___010_post + nPow___010_post ≤ 0 ∧ nPow___010_post − nPow___010_post ≤ 0 ∧ − nPow___010_0 + nPow___010_0 ≤ 0 ∧ nPow___010_0 − nPow___010_0 ≤ 0 ∧ − nN_post + nN_post ≤ 0 ∧ nN_post − nN_post ≤ 0 ∧ − nN_0 + nN_0 ≤ 0 ∧ nN_0 − nN_0 ≤ 0

10 SCC Decomposition

We consider subproblems for each of the 3 SCC(s) of the program graph.

10.1 SCC Subproblem 1/3

Here we consider the SCC { 2, 4, 4_var_snapshot, 4* }.

10.1.1 Transition Removal

We remove transition 2 using the following ranking functions, which are bounded by −16.

2: − nN_0 − 6⋅ni21_0
4: 1 − 6⋅ni21_0
4_var_snapshot: −6⋅ni21_0
4*: 2 − 6⋅ni21_0

10.1.2 Transition Removal

We remove transitions 19, 21, 6 using the following ranking functions, which are bounded by −4.

2: −2⋅nN_0
4: 0
4_var_snapshot: − nN_0
4*: 1

10.1.3 Splitting Cut-Point Transitions

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

10.1.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 18.

10.1.3.1.1 Splitting Cut-Point Transitions

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

10.2 SCC Subproblem 2/3

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

10.2.1 Transition Removal

We remove transition 5 using the following ranking functions, which are bounded by −9.

5: 2 − 4⋅ni16_0
6: −4⋅ni16_0
5_var_snapshot: 1 − 4⋅ni16_0
5*: nN_0 − 4⋅ni16_0

10.2.2 Transition Removal

We remove transitions 26, 28, 3 using the following ranking functions, which are bounded by −4.

5: 0
6: − nN_0 − nN_post
5_var_snapshot: − nN_post
5*: nN_post

10.2.3 Splitting Cut-Point Transitions

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

10.2.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 25.

10.2.3.1.1 Splitting Cut-Point Transitions

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

10.3 SCC Subproblem 3/3

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

10.3.1 Transition Removal

We remove transition 8 using the following ranking functions, which are bounded by −15.

0: 6 − 7⋅ni11_0
1: −7⋅ni11_0
0_var_snapshot: 3 − 7⋅ni11_0
0*: 2⋅nN_0 − 7⋅ni11_0

10.3.2 Transition Removal

We remove transitions 12, 0 using the following ranking functions, which are bounded by −4.

0: 0
1: −1 − nN_post
0_var_snapshot: − nN_post
0*: nN_0

10.3.3 Transition Removal

We remove transition 14 using the following ranking functions, which are bounded by 2.

0: 0
1: 0
0_var_snapshot: 0
0*: nN_post

10.3.4 Splitting Cut-Point Transitions

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

10.3.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 11.

10.3.4.1.1 Splitting Cut-Point Transitions

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

Tool configuration

T2Cert