LTS Termination Proof

by T2Cert

Input

Integer Transition System

Proof

1 Invariant Updates

The following invariants are asserted.

0: −8 + lx2_post ≤ 08 − lx2_post ≤ 0−8 + lx2_0 ≤ 08 − lx2_0 ≤ 0
1: −8 + lx2_post ≤ 08 − lx2_post ≤ 0−8 + lx2_0 ≤ 08 − lx2_0 ≤ 0
2: −8 + lx2_post ≤ 08 − lx2_post ≤ 0−8 + lx2_0 ≤ 08 − lx2_0 ≤ 0
3: −8 + lx2_post ≤ 08 − lx2_post ≤ 0−8 + lx2_0 ≤ 08 − lx2_0 ≤ 0
4: −8 + lx2_post ≤ 08 − lx2_post ≤ 08 − i20_0 ≤ 0−8 + lx2_0 ≤ 08 − lx2_0 ≤ 0
5: TRUE
6: TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
1 8 1: z519_post + z519_post ≤ 0z519_postz519_post ≤ 0z519_0 + z519_0 ≤ 0z519_0z519_0 ≤ 0z418_post + z418_post ≤ 0z418_postz418_post ≤ 0z418_2 + z418_2 ≤ 0z418_2z418_2 ≤ 0z418_1 + z418_1 ≤ 0z418_1z418_1 ≤ 0z418_0 + z418_0 ≤ 0z418_0z418_0 ≤ 0z317_post + z317_post ≤ 0z317_postz317_post ≤ 0z317_2 + z317_2 ≤ 0z317_2z317_2 ≤ 0z317_1 + z317_1 ≤ 0z317_1z317_1 ≤ 0z317_0 + z317_0 ≤ 0z317_0z317_0 ≤ 0z216_post + z216_post ≤ 0z216_postz216_post ≤ 0z216_1 + z216_1 ≤ 0z216_1z216_1 ≤ 0z216_0 + z216_0 ≤ 0z216_0z216_0 ≤ 0z115_post + z115_post ≤ 0z115_postz115_post ≤ 0z115_2 + z115_2 ≤ 0z115_2z115_2 ≤ 0z115_1 + z115_1 ≤ 0z115_1z115_1 ≤ 0z115_0 + z115_0 ≤ 0z115_0z115_0 ≤ 0tmp710_post + tmp710_post ≤ 0tmp710_posttmp710_post ≤ 0tmp710_1 + tmp710_1 ≤ 0tmp710_1tmp710_1 ≤ 0tmp710_0 + tmp710_0 ≤ 0tmp710_0tmp710_0 ≤ 0tmp69_post + tmp69_post ≤ 0tmp69_posttmp69_post ≤ 0tmp69_1 + tmp69_1 ≤ 0tmp69_1tmp69_1 ≤ 0tmp69_0 + tmp69_0 ≤ 0tmp69_0tmp69_0 ≤ 0tmp58_post + tmp58_post ≤ 0tmp58_posttmp58_post ≤ 0tmp58_1 + tmp58_1 ≤ 0tmp58_1tmp58_1 ≤ 0tmp58_0 + tmp58_0 ≤ 0tmp58_0tmp58_0 ≤ 0tmp47_post + tmp47_post ≤ 0tmp47_posttmp47_post ≤ 0tmp47_1 + tmp47_1 ≤ 0tmp47_1tmp47_1 ≤ 0tmp47_0 + tmp47_0 ≤ 0tmp47_0tmp47_0 ≤ 0tmp36_post + tmp36_post ≤ 0tmp36_posttmp36_post ≤ 0tmp36_0 + tmp36_0 ≤ 0tmp36_0tmp36_0 ≤ 0tmp25_post + tmp25_post ≤ 0tmp25_posttmp25_post ≤ 0tmp25_0 + tmp25_0 ≤ 0tmp25_0tmp25_0 ≤ 0tmp14_post + tmp14_post ≤ 0tmp14_posttmp14_post ≤ 0tmp14_0 + tmp14_0 ≤ 0tmp14_0tmp14_0 ≤ 0tmp1314_post + tmp1314_post ≤ 0tmp1314_posttmp1314_post ≤ 0tmp1314_0 + tmp1314_0 ≤ 0tmp1314_0tmp1314_0 ≤ 0tmp1213_post + tmp1213_post ≤ 0tmp1213_posttmp1213_post ≤ 0tmp1213_0 + tmp1213_0 ≤ 0tmp1213_0tmp1213_0 ≤ 0tmp1112_post + tmp1112_post ≤ 0tmp1112_posttmp1112_post ≤ 0tmp1112_0 + tmp1112_0 ≤ 0tmp1112_0tmp1112_0 ≤ 0tmp1011_post + tmp1011_post ≤ 0tmp1011_posttmp1011_post ≤ 0tmp1011_0 + tmp1011_0 ≤ 0tmp1011_0tmp1011_0 ≤ 0tmp03_post + tmp03_post ≤ 0tmp03_posttmp03_post ≤ 0tmp03_0 + tmp03_0 ≤ 0tmp03_0tmp03_0 ≤ 0lx2_post + lx2_post ≤ 0lx2_postlx2_post ≤ 0lx2_0 + lx2_0 ≤ 0lx2_0lx2_0 ≤ 0i20_post + i20_post ≤ 0i20_posti20_post ≤ 0i20_0 + i20_0 ≤ 0i20_0i20_0 ≤ 0constant22_post + constant22_post ≤ 0constant22_postconstant22_post ≤ 0constant22_9 + constant22_9 ≤ 0constant22_9constant22_9 ≤ 0constant22_8 + constant22_8 ≤ 0constant22_8constant22_8 ≤ 0constant22_7 + constant22_7 ≤ 0constant22_7constant22_7 ≤ 0constant22_6 + constant22_6 ≤ 0constant22_6constant22_6 ≤ 0constant22_5 + constant22_5 ≤ 0constant22_5constant22_5 ≤ 0constant22_4 + constant22_4 ≤ 0constant22_4constant22_4 ≤ 0constant22_3 + constant22_3 ≤ 0constant22_3constant22_3 ≤ 0constant22_2 + constant22_2 ≤ 0constant22_2constant22_2 ≤ 0constant22_11 + constant22_11 ≤ 0constant22_11constant22_11 ≤ 0constant22_10 + constant22_10 ≤ 0constant22_10constant22_10 ≤ 0constant22_1 + constant22_1 ≤ 0constant22_1constant22_1 ≤ 0constant22_0 + constant22_0 ≤ 0constant22_0constant22_0 ≤ 0
2 15 2: z519_post + z519_post ≤ 0z519_postz519_post ≤ 0z519_0 + z519_0 ≤ 0z519_0z519_0 ≤ 0z418_post + z418_post ≤ 0z418_postz418_post ≤ 0z418_2 + z418_2 ≤ 0z418_2z418_2 ≤ 0z418_1 + z418_1 ≤ 0z418_1z418_1 ≤ 0z418_0 + z418_0 ≤ 0z418_0z418_0 ≤ 0z317_post + z317_post ≤ 0z317_postz317_post ≤ 0z317_2 + z317_2 ≤ 0z317_2z317_2 ≤ 0z317_1 + z317_1 ≤ 0z317_1z317_1 ≤ 0z317_0 + z317_0 ≤ 0z317_0z317_0 ≤ 0z216_post + z216_post ≤ 0z216_postz216_post ≤ 0z216_1 + z216_1 ≤ 0z216_1z216_1 ≤ 0z216_0 + z216_0 ≤ 0z216_0z216_0 ≤ 0z115_post + z115_post ≤ 0z115_postz115_post ≤ 0z115_2 + z115_2 ≤ 0z115_2z115_2 ≤ 0z115_1 + z115_1 ≤ 0z115_1z115_1 ≤ 0z115_0 + z115_0 ≤ 0z115_0z115_0 ≤ 0tmp710_post + tmp710_post ≤ 0tmp710_posttmp710_post ≤ 0tmp710_1 + tmp710_1 ≤ 0tmp710_1tmp710_1 ≤ 0tmp710_0 + tmp710_0 ≤ 0tmp710_0tmp710_0 ≤ 0tmp69_post + tmp69_post ≤ 0tmp69_posttmp69_post ≤ 0tmp69_1 + tmp69_1 ≤ 0tmp69_1tmp69_1 ≤ 0tmp69_0 + tmp69_0 ≤ 0tmp69_0tmp69_0 ≤ 0tmp58_post + tmp58_post ≤ 0tmp58_posttmp58_post ≤ 0tmp58_1 + tmp58_1 ≤ 0tmp58_1tmp58_1 ≤ 0tmp58_0 + tmp58_0 ≤ 0tmp58_0tmp58_0 ≤ 0tmp47_post + tmp47_post ≤ 0tmp47_posttmp47_post ≤ 0tmp47_1 + tmp47_1 ≤ 0tmp47_1tmp47_1 ≤ 0tmp47_0 + tmp47_0 ≤ 0tmp47_0tmp47_0 ≤ 0tmp36_post + tmp36_post ≤ 0tmp36_posttmp36_post ≤ 0tmp36_0 + tmp36_0 ≤ 0tmp36_0tmp36_0 ≤ 0tmp25_post + tmp25_post ≤ 0tmp25_posttmp25_post ≤ 0tmp25_0 + tmp25_0 ≤ 0tmp25_0tmp25_0 ≤ 0tmp14_post + tmp14_post ≤ 0tmp14_posttmp14_post ≤ 0tmp14_0 + tmp14_0 ≤ 0tmp14_0tmp14_0 ≤ 0tmp1314_post + tmp1314_post ≤ 0tmp1314_posttmp1314_post ≤ 0tmp1314_0 + tmp1314_0 ≤ 0tmp1314_0tmp1314_0 ≤ 0tmp1213_post + tmp1213_post ≤ 0tmp1213_posttmp1213_post ≤ 0tmp1213_0 + tmp1213_0 ≤ 0tmp1213_0tmp1213_0 ≤ 0tmp1112_post + tmp1112_post ≤ 0tmp1112_posttmp1112_post ≤ 0tmp1112_0 + tmp1112_0 ≤ 0tmp1112_0tmp1112_0 ≤ 0tmp1011_post + tmp1011_post ≤ 0tmp1011_posttmp1011_post ≤ 0tmp1011_0 + tmp1011_0 ≤ 0tmp1011_0tmp1011_0 ≤ 0tmp03_post + tmp03_post ≤ 0tmp03_posttmp03_post ≤ 0tmp03_0 + tmp03_0 ≤ 0tmp03_0tmp03_0 ≤ 0lx2_post + lx2_post ≤ 0lx2_postlx2_post ≤ 0lx2_0 + lx2_0 ≤ 0lx2_0lx2_0 ≤ 0i20_post + i20_post ≤ 0i20_posti20_post ≤ 0i20_0 + i20_0 ≤ 0i20_0i20_0 ≤ 0constant22_post + constant22_post ≤ 0constant22_postconstant22_post ≤ 0constant22_9 + constant22_9 ≤ 0constant22_9constant22_9 ≤ 0constant22_8 + constant22_8 ≤ 0constant22_8constant22_8 ≤ 0constant22_7 + constant22_7 ≤ 0constant22_7constant22_7 ≤ 0constant22_6 + constant22_6 ≤ 0constant22_6constant22_6 ≤ 0constant22_5 + constant22_5 ≤ 0constant22_5constant22_5 ≤ 0constant22_4 + constant22_4 ≤ 0constant22_4constant22_4 ≤ 0constant22_3 + constant22_3 ≤ 0constant22_3constant22_3 ≤ 0constant22_2 + constant22_2 ≤ 0constant22_2constant22_2 ≤ 0constant22_11 + constant22_11 ≤ 0constant22_11constant22_11 ≤ 0constant22_10 + constant22_10 ≤ 0constant22_10constant22_10 ≤ 0constant22_1 + constant22_1 ≤ 0constant22_1constant22_1 ≤ 0constant22_0 + constant22_0 ≤ 0constant22_0constant22_0 ≤ 0
and for every transition t, a duplicate t is considered.

3 Transition Removal

We remove transitions 0, 2, 6, 7 using the following ranking functions, which are bounded by −17.

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

4 Location Addition

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

1* 11 1: z519_post + z519_post ≤ 0z519_postz519_post ≤ 0z519_0 + z519_0 ≤ 0z519_0z519_0 ≤ 0z418_post + z418_post ≤ 0z418_postz418_post ≤ 0z418_2 + z418_2 ≤ 0z418_2z418_2 ≤ 0z418_1 + z418_1 ≤ 0z418_1z418_1 ≤ 0z418_0 + z418_0 ≤ 0z418_0z418_0 ≤ 0z317_post + z317_post ≤ 0z317_postz317_post ≤ 0z317_2 + z317_2 ≤ 0z317_2z317_2 ≤ 0z317_1 + z317_1 ≤ 0z317_1z317_1 ≤ 0z317_0 + z317_0 ≤ 0z317_0z317_0 ≤ 0z216_post + z216_post ≤ 0z216_postz216_post ≤ 0z216_1 + z216_1 ≤ 0z216_1z216_1 ≤ 0z216_0 + z216_0 ≤ 0z216_0z216_0 ≤ 0z115_post + z115_post ≤ 0z115_postz115_post ≤ 0z115_2 + z115_2 ≤ 0z115_2z115_2 ≤ 0z115_1 + z115_1 ≤ 0z115_1z115_1 ≤ 0z115_0 + z115_0 ≤ 0z115_0z115_0 ≤ 0tmp710_post + tmp710_post ≤ 0tmp710_posttmp710_post ≤ 0tmp710_1 + tmp710_1 ≤ 0tmp710_1tmp710_1 ≤ 0tmp710_0 + tmp710_0 ≤ 0tmp710_0tmp710_0 ≤ 0tmp69_post + tmp69_post ≤ 0tmp69_posttmp69_post ≤ 0tmp69_1 + tmp69_1 ≤ 0tmp69_1tmp69_1 ≤ 0tmp69_0 + tmp69_0 ≤ 0tmp69_0tmp69_0 ≤ 0tmp58_post + tmp58_post ≤ 0tmp58_posttmp58_post ≤ 0tmp58_1 + tmp58_1 ≤ 0tmp58_1tmp58_1 ≤ 0tmp58_0 + tmp58_0 ≤ 0tmp58_0tmp58_0 ≤ 0tmp47_post + tmp47_post ≤ 0tmp47_posttmp47_post ≤ 0tmp47_1 + tmp47_1 ≤ 0tmp47_1tmp47_1 ≤ 0tmp47_0 + tmp47_0 ≤ 0tmp47_0tmp47_0 ≤ 0tmp36_post + tmp36_post ≤ 0tmp36_posttmp36_post ≤ 0tmp36_0 + tmp36_0 ≤ 0tmp36_0tmp36_0 ≤ 0tmp25_post + tmp25_post ≤ 0tmp25_posttmp25_post ≤ 0tmp25_0 + tmp25_0 ≤ 0tmp25_0tmp25_0 ≤ 0tmp14_post + tmp14_post ≤ 0tmp14_posttmp14_post ≤ 0tmp14_0 + tmp14_0 ≤ 0tmp14_0tmp14_0 ≤ 0tmp1314_post + tmp1314_post ≤ 0tmp1314_posttmp1314_post ≤ 0tmp1314_0 + tmp1314_0 ≤ 0tmp1314_0tmp1314_0 ≤ 0tmp1213_post + tmp1213_post ≤ 0tmp1213_posttmp1213_post ≤ 0tmp1213_0 + tmp1213_0 ≤ 0tmp1213_0tmp1213_0 ≤ 0tmp1112_post + tmp1112_post ≤ 0tmp1112_posttmp1112_post ≤ 0tmp1112_0 + tmp1112_0 ≤ 0tmp1112_0tmp1112_0 ≤ 0tmp1011_post + tmp1011_post ≤ 0tmp1011_posttmp1011_post ≤ 0tmp1011_0 + tmp1011_0 ≤ 0tmp1011_0tmp1011_0 ≤ 0tmp03_post + tmp03_post ≤ 0tmp03_posttmp03_post ≤ 0tmp03_0 + tmp03_0 ≤ 0tmp03_0tmp03_0 ≤ 0lx2_post + lx2_post ≤ 0lx2_postlx2_post ≤ 0lx2_0 + lx2_0 ≤ 0lx2_0lx2_0 ≤ 0i20_post + i20_post ≤ 0i20_posti20_post ≤ 0i20_0 + i20_0 ≤ 0i20_0i20_0 ≤ 0constant22_post + constant22_post ≤ 0constant22_postconstant22_post ≤ 0constant22_9 + constant22_9 ≤ 0constant22_9constant22_9 ≤ 0constant22_8 + constant22_8 ≤ 0constant22_8constant22_8 ≤ 0constant22_7 + constant22_7 ≤ 0constant22_7constant22_7 ≤ 0constant22_6 + constant22_6 ≤ 0constant22_6constant22_6 ≤ 0constant22_5 + constant22_5 ≤ 0constant22_5constant22_5 ≤ 0constant22_4 + constant22_4 ≤ 0constant22_4constant22_4 ≤ 0constant22_3 + constant22_3 ≤ 0constant22_3constant22_3 ≤ 0constant22_2 + constant22_2 ≤ 0constant22_2constant22_2 ≤ 0constant22_11 + constant22_11 ≤ 0constant22_11constant22_11 ≤ 0constant22_10 + constant22_10 ≤ 0constant22_10constant22_10 ≤ 0constant22_1 + constant22_1 ≤ 0constant22_1constant22_1 ≤ 0constant22_0 + constant22_0 ≤ 0constant22_0constant22_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: z519_post + z519_post ≤ 0z519_postz519_post ≤ 0z519_0 + z519_0 ≤ 0z519_0z519_0 ≤ 0z418_post + z418_post ≤ 0z418_postz418_post ≤ 0z418_2 + z418_2 ≤ 0z418_2z418_2 ≤ 0z418_1 + z418_1 ≤ 0z418_1z418_1 ≤ 0z418_0 + z418_0 ≤ 0z418_0z418_0 ≤ 0z317_post + z317_post ≤ 0z317_postz317_post ≤ 0z317_2 + z317_2 ≤ 0z317_2z317_2 ≤ 0z317_1 + z317_1 ≤ 0z317_1z317_1 ≤ 0z317_0 + z317_0 ≤ 0z317_0z317_0 ≤ 0z216_post + z216_post ≤ 0z216_postz216_post ≤ 0z216_1 + z216_1 ≤ 0z216_1z216_1 ≤ 0z216_0 + z216_0 ≤ 0z216_0z216_0 ≤ 0z115_post + z115_post ≤ 0z115_postz115_post ≤ 0z115_2 + z115_2 ≤ 0z115_2z115_2 ≤ 0z115_1 + z115_1 ≤ 0z115_1z115_1 ≤ 0z115_0 + z115_0 ≤ 0z115_0z115_0 ≤ 0tmp710_post + tmp710_post ≤ 0tmp710_posttmp710_post ≤ 0tmp710_1 + tmp710_1 ≤ 0tmp710_1tmp710_1 ≤ 0tmp710_0 + tmp710_0 ≤ 0tmp710_0tmp710_0 ≤ 0tmp69_post + tmp69_post ≤ 0tmp69_posttmp69_post ≤ 0tmp69_1 + tmp69_1 ≤ 0tmp69_1tmp69_1 ≤ 0tmp69_0 + tmp69_0 ≤ 0tmp69_0tmp69_0 ≤ 0tmp58_post + tmp58_post ≤ 0tmp58_posttmp58_post ≤ 0tmp58_1 + tmp58_1 ≤ 0tmp58_1tmp58_1 ≤ 0tmp58_0 + tmp58_0 ≤ 0tmp58_0tmp58_0 ≤ 0tmp47_post + tmp47_post ≤ 0tmp47_posttmp47_post ≤ 0tmp47_1 + tmp47_1 ≤ 0tmp47_1tmp47_1 ≤ 0tmp47_0 + tmp47_0 ≤ 0tmp47_0tmp47_0 ≤ 0tmp36_post + tmp36_post ≤ 0tmp36_posttmp36_post ≤ 0tmp36_0 + tmp36_0 ≤ 0tmp36_0tmp36_0 ≤ 0tmp25_post + tmp25_post ≤ 0tmp25_posttmp25_post ≤ 0tmp25_0 + tmp25_0 ≤ 0tmp25_0tmp25_0 ≤ 0tmp14_post + tmp14_post ≤ 0tmp14_posttmp14_post ≤ 0tmp14_0 + tmp14_0 ≤ 0tmp14_0tmp14_0 ≤ 0tmp1314_post + tmp1314_post ≤ 0tmp1314_posttmp1314_post ≤ 0tmp1314_0 + tmp1314_0 ≤ 0tmp1314_0tmp1314_0 ≤ 0tmp1213_post + tmp1213_post ≤ 0tmp1213_posttmp1213_post ≤ 0tmp1213_0 + tmp1213_0 ≤ 0tmp1213_0tmp1213_0 ≤ 0tmp1112_post + tmp1112_post ≤ 0tmp1112_posttmp1112_post ≤ 0tmp1112_0 + tmp1112_0 ≤ 0tmp1112_0tmp1112_0 ≤ 0tmp1011_post + tmp1011_post ≤ 0tmp1011_posttmp1011_post ≤ 0tmp1011_0 + tmp1011_0 ≤ 0tmp1011_0tmp1011_0 ≤ 0tmp03_post + tmp03_post ≤ 0tmp03_posttmp03_post ≤ 0tmp03_0 + tmp03_0 ≤ 0tmp03_0tmp03_0 ≤ 0lx2_post + lx2_post ≤ 0lx2_postlx2_post ≤ 0lx2_0 + lx2_0 ≤ 0lx2_0lx2_0 ≤ 0i20_post + i20_post ≤ 0i20_posti20_post ≤ 0i20_0 + i20_0 ≤ 0i20_0i20_0 ≤ 0constant22_post + constant22_post ≤ 0constant22_postconstant22_post ≤ 0constant22_9 + constant22_9 ≤ 0constant22_9constant22_9 ≤ 0constant22_8 + constant22_8 ≤ 0constant22_8constant22_8 ≤ 0constant22_7 + constant22_7 ≤ 0constant22_7constant22_7 ≤ 0constant22_6 + constant22_6 ≤ 0constant22_6constant22_6 ≤ 0constant22_5 + constant22_5 ≤ 0constant22_5constant22_5 ≤ 0constant22_4 + constant22_4 ≤ 0constant22_4constant22_4 ≤ 0constant22_3 + constant22_3 ≤ 0constant22_3constant22_3 ≤ 0constant22_2 + constant22_2 ≤ 0constant22_2constant22_2 ≤ 0constant22_11 + constant22_11 ≤ 0constant22_11constant22_11 ≤ 0constant22_10 + constant22_10 ≤ 0constant22_10constant22_10 ≤ 0constant22_1 + constant22_1 ≤ 0constant22_1constant22_1 ≤ 0constant22_0 + constant22_0 ≤ 0constant22_0constant22_0 ≤ 0

6 Location Addition

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

2* 18 2: z519_post + z519_post ≤ 0z519_postz519_post ≤ 0z519_0 + z519_0 ≤ 0z519_0z519_0 ≤ 0z418_post + z418_post ≤ 0z418_postz418_post ≤ 0z418_2 + z418_2 ≤ 0z418_2z418_2 ≤ 0z418_1 + z418_1 ≤ 0z418_1z418_1 ≤ 0z418_0 + z418_0 ≤ 0z418_0z418_0 ≤ 0z317_post + z317_post ≤ 0z317_postz317_post ≤ 0z317_2 + z317_2 ≤ 0z317_2z317_2 ≤ 0z317_1 + z317_1 ≤ 0z317_1z317_1 ≤ 0z317_0 + z317_0 ≤ 0z317_0z317_0 ≤ 0z216_post + z216_post ≤ 0z216_postz216_post ≤ 0z216_1 + z216_1 ≤ 0z216_1z216_1 ≤ 0z216_0 + z216_0 ≤ 0z216_0z216_0 ≤ 0z115_post + z115_post ≤ 0z115_postz115_post ≤ 0z115_2 + z115_2 ≤ 0z115_2z115_2 ≤ 0z115_1 + z115_1 ≤ 0z115_1z115_1 ≤ 0z115_0 + z115_0 ≤ 0z115_0z115_0 ≤ 0tmp710_post + tmp710_post ≤ 0tmp710_posttmp710_post ≤ 0tmp710_1 + tmp710_1 ≤ 0tmp710_1tmp710_1 ≤ 0tmp710_0 + tmp710_0 ≤ 0tmp710_0tmp710_0 ≤ 0tmp69_post + tmp69_post ≤ 0tmp69_posttmp69_post ≤ 0tmp69_1 + tmp69_1 ≤ 0tmp69_1tmp69_1 ≤ 0tmp69_0 + tmp69_0 ≤ 0tmp69_0tmp69_0 ≤ 0tmp58_post + tmp58_post ≤ 0tmp58_posttmp58_post ≤ 0tmp58_1 + tmp58_1 ≤ 0tmp58_1tmp58_1 ≤ 0tmp58_0 + tmp58_0 ≤ 0tmp58_0tmp58_0 ≤ 0tmp47_post + tmp47_post ≤ 0tmp47_posttmp47_post ≤ 0tmp47_1 + tmp47_1 ≤ 0tmp47_1tmp47_1 ≤ 0tmp47_0 + tmp47_0 ≤ 0tmp47_0tmp47_0 ≤ 0tmp36_post + tmp36_post ≤ 0tmp36_posttmp36_post ≤ 0tmp36_0 + tmp36_0 ≤ 0tmp36_0tmp36_0 ≤ 0tmp25_post + tmp25_post ≤ 0tmp25_posttmp25_post ≤ 0tmp25_0 + tmp25_0 ≤ 0tmp25_0tmp25_0 ≤ 0tmp14_post + tmp14_post ≤ 0tmp14_posttmp14_post ≤ 0tmp14_0 + tmp14_0 ≤ 0tmp14_0tmp14_0 ≤ 0tmp1314_post + tmp1314_post ≤ 0tmp1314_posttmp1314_post ≤ 0tmp1314_0 + tmp1314_0 ≤ 0tmp1314_0tmp1314_0 ≤ 0tmp1213_post + tmp1213_post ≤ 0tmp1213_posttmp1213_post ≤ 0tmp1213_0 + tmp1213_0 ≤ 0tmp1213_0tmp1213_0 ≤ 0tmp1112_post + tmp1112_post ≤ 0tmp1112_posttmp1112_post ≤ 0tmp1112_0 + tmp1112_0 ≤ 0tmp1112_0tmp1112_0 ≤ 0tmp1011_post + tmp1011_post ≤ 0tmp1011_posttmp1011_post ≤ 0tmp1011_0 + tmp1011_0 ≤ 0tmp1011_0tmp1011_0 ≤ 0tmp03_post + tmp03_post ≤ 0tmp03_posttmp03_post ≤ 0tmp03_0 + tmp03_0 ≤ 0tmp03_0tmp03_0 ≤ 0lx2_post + lx2_post ≤ 0lx2_postlx2_post ≤ 0lx2_0 + lx2_0 ≤ 0lx2_0lx2_0 ≤ 0i20_post + i20_post ≤ 0i20_posti20_post ≤ 0i20_0 + i20_0 ≤ 0i20_0i20_0 ≤ 0constant22_post + constant22_post ≤ 0constant22_postconstant22_post ≤ 0constant22_9 + constant22_9 ≤ 0constant22_9constant22_9 ≤ 0constant22_8 + constant22_8 ≤ 0constant22_8constant22_8 ≤ 0constant22_7 + constant22_7 ≤ 0constant22_7constant22_7 ≤ 0constant22_6 + constant22_6 ≤ 0constant22_6constant22_6 ≤ 0constant22_5 + constant22_5 ≤ 0constant22_5constant22_5 ≤ 0constant22_4 + constant22_4 ≤ 0constant22_4constant22_4 ≤ 0constant22_3 + constant22_3 ≤ 0constant22_3constant22_3 ≤ 0constant22_2 + constant22_2 ≤ 0constant22_2constant22_2 ≤ 0constant22_11 + constant22_11 ≤ 0constant22_11constant22_11 ≤ 0constant22_10 + constant22_10 ≤ 0constant22_10constant22_10 ≤ 0constant22_1 + constant22_1 ≤ 0constant22_1constant22_1 ≤ 0constant22_0 + constant22_0 ≤ 0constant22_0constant22_0 ≤ 0

7 Location Addition

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

2 16 2_var_snapshot: z519_post + z519_post ≤ 0z519_postz519_post ≤ 0z519_0 + z519_0 ≤ 0z519_0z519_0 ≤ 0z418_post + z418_post ≤ 0z418_postz418_post ≤ 0z418_2 + z418_2 ≤ 0z418_2z418_2 ≤ 0z418_1 + z418_1 ≤ 0z418_1z418_1 ≤ 0z418_0 + z418_0 ≤ 0z418_0z418_0 ≤ 0z317_post + z317_post ≤ 0z317_postz317_post ≤ 0z317_2 + z317_2 ≤ 0z317_2z317_2 ≤ 0z317_1 + z317_1 ≤ 0z317_1z317_1 ≤ 0z317_0 + z317_0 ≤ 0z317_0z317_0 ≤ 0z216_post + z216_post ≤ 0z216_postz216_post ≤ 0z216_1 + z216_1 ≤ 0z216_1z216_1 ≤ 0z216_0 + z216_0 ≤ 0z216_0z216_0 ≤ 0z115_post + z115_post ≤ 0z115_postz115_post ≤ 0z115_2 + z115_2 ≤ 0z115_2z115_2 ≤ 0z115_1 + z115_1 ≤ 0z115_1z115_1 ≤ 0z115_0 + z115_0 ≤ 0z115_0z115_0 ≤ 0tmp710_post + tmp710_post ≤ 0tmp710_posttmp710_post ≤ 0tmp710_1 + tmp710_1 ≤ 0tmp710_1tmp710_1 ≤ 0tmp710_0 + tmp710_0 ≤ 0tmp710_0tmp710_0 ≤ 0tmp69_post + tmp69_post ≤ 0tmp69_posttmp69_post ≤ 0tmp69_1 + tmp69_1 ≤ 0tmp69_1tmp69_1 ≤ 0tmp69_0 + tmp69_0 ≤ 0tmp69_0tmp69_0 ≤ 0tmp58_post + tmp58_post ≤ 0tmp58_posttmp58_post ≤ 0tmp58_1 + tmp58_1 ≤ 0tmp58_1tmp58_1 ≤ 0tmp58_0 + tmp58_0 ≤ 0tmp58_0tmp58_0 ≤ 0tmp47_post + tmp47_post ≤ 0tmp47_posttmp47_post ≤ 0tmp47_1 + tmp47_1 ≤ 0tmp47_1tmp47_1 ≤ 0tmp47_0 + tmp47_0 ≤ 0tmp47_0tmp47_0 ≤ 0tmp36_post + tmp36_post ≤ 0tmp36_posttmp36_post ≤ 0tmp36_0 + tmp36_0 ≤ 0tmp36_0tmp36_0 ≤ 0tmp25_post + tmp25_post ≤ 0tmp25_posttmp25_post ≤ 0tmp25_0 + tmp25_0 ≤ 0tmp25_0tmp25_0 ≤ 0tmp14_post + tmp14_post ≤ 0tmp14_posttmp14_post ≤ 0tmp14_0 + tmp14_0 ≤ 0tmp14_0tmp14_0 ≤ 0tmp1314_post + tmp1314_post ≤ 0tmp1314_posttmp1314_post ≤ 0tmp1314_0 + tmp1314_0 ≤ 0tmp1314_0tmp1314_0 ≤ 0tmp1213_post + tmp1213_post ≤ 0tmp1213_posttmp1213_post ≤ 0tmp1213_0 + tmp1213_0 ≤ 0tmp1213_0tmp1213_0 ≤ 0tmp1112_post + tmp1112_post ≤ 0tmp1112_posttmp1112_post ≤ 0tmp1112_0 + tmp1112_0 ≤ 0tmp1112_0tmp1112_0 ≤ 0tmp1011_post + tmp1011_post ≤ 0tmp1011_posttmp1011_post ≤ 0tmp1011_0 + tmp1011_0 ≤ 0tmp1011_0tmp1011_0 ≤ 0tmp03_post + tmp03_post ≤ 0tmp03_posttmp03_post ≤ 0tmp03_0 + tmp03_0 ≤ 0tmp03_0tmp03_0 ≤ 0lx2_post + lx2_post ≤ 0lx2_postlx2_post ≤ 0lx2_0 + lx2_0 ≤ 0lx2_0lx2_0 ≤ 0i20_post + i20_post ≤ 0i20_posti20_post ≤ 0i20_0 + i20_0 ≤ 0i20_0i20_0 ≤ 0constant22_post + constant22_post ≤ 0constant22_postconstant22_post ≤ 0constant22_9 + constant22_9 ≤ 0constant22_9constant22_9 ≤ 0constant22_8 + constant22_8 ≤ 0constant22_8constant22_8 ≤ 0constant22_7 + constant22_7 ≤ 0constant22_7constant22_7 ≤ 0constant22_6 + constant22_6 ≤ 0constant22_6constant22_6 ≤ 0constant22_5 + constant22_5 ≤ 0constant22_5constant22_5 ≤ 0constant22_4 + constant22_4 ≤ 0constant22_4constant22_4 ≤ 0constant22_3 + constant22_3 ≤ 0constant22_3constant22_3 ≤ 0constant22_2 + constant22_2 ≤ 0constant22_2constant22_2 ≤ 0constant22_11 + constant22_11 ≤ 0constant22_11constant22_11 ≤ 0constant22_10 + constant22_10 ≤ 0constant22_10constant22_10 ≤ 0constant22_1 + constant22_1 ≤ 0constant22_1constant22_1 ≤ 0constant22_0 + constant22_0 ≤ 0constant22_0constant22_0 ≤ 0

8 SCC Decomposition

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

8.1 SCC Subproblem 1/2

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

8.1.1 Transition Removal

We remove transition 3 using the following ranking functions, which are bounded by −200.

1: −25⋅i20_0lx2_0
3: −25⋅i20_0lx2_0 − 2⋅lx2_post
1_var_snapshot: −25⋅i20_0 − 2⋅lx2_post
1*: −25⋅i20_0

8.1.2 Transition Removal

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

1: 0
3: −2⋅lx2_post
1_var_snapshot: lx2_post
1*: lx2_0

8.1.3 Transition Removal

We remove transition 11 using the following ranking functions, which are bounded by 0.

1: 0
3: 0
1_var_snapshot: 0
1*: 1

8.1.4 Splitting Cut-Point Transitions

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

8.1.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 8.

8.1.4.1.1 Splitting Cut-Point Transitions

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

8.2 SCC Subproblem 2/2

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

8.2.1 Transition Removal

We remove transition 1 using the following ranking functions, which are bounded by −200.

0: −25⋅i20_0lx2_0 − 2⋅lx2_post
2: −8 − 25⋅i20_0
2_var_snapshot: −25⋅i20_0 − 2⋅lx2_post
2*: −25⋅i20_0

8.2.2 Transition Removal

We remove transitions 16, 4 using the following ranking functions, which are bounded by −9.

0: −2⋅lx2_post
2: 0
2_var_snapshot: lx2_post
2*: 1

8.2.3 Transition Removal

We remove transition 18 using the following ranking functions, which are bounded by 7.

0: 0
2: 0
2_var_snapshot: 0
2*: lx2_0

8.2.4 Splitting Cut-Point Transitions

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

8.2.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 15.

8.2.4.1.1 Splitting Cut-Point Transitions

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

Tool configuration

T2Cert