LTS Termination Proof

by T2Cert

Input

Integer Transition System

Proof

1 Invariant Updates

The following invariants are asserted.

0: TRUE
1: TRUE
2: TRUE
3: Result_4_post ≤ 0___cil_tmp4_8_post ≤ 0___retres3_7_post ≤ 0___retres3_7_post ≤ 0Result_4_0 ≤ 0___cil_tmp4_8_0 ≤ 0___retres3_7_0 ≤ 0___retres3_7_0 ≤ 0
4: TRUE
5: Result_4_post ≤ 0___cil_tmp4_8_post ≤ 0___retres3_7_post ≤ 0___retres3_7_post ≤ 0Result_4_0 ≤ 0___cil_tmp4_8_0 ≤ 0___retres3_7_0 ≤ 0___retres3_7_0 ≤ 0___cil_tmp2_10_post ≤ 0___retres1_9_post ≤ 0___retres1_9_post ≤ 0___cil_tmp2_10_0 ≤ 0___retres1_9_0 ≤ 0___retres1_9_0 ≤ 0
6: TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
2 8 2: ___retres1_9_post + ___retres1_9_post ≤ 0___retres1_9_post___retres1_9_post ≤ 0___retres1_9_0 + ___retres1_9_0 ≤ 0___retres1_9_0___retres1_9_0 ≤ 0___cil_tmp2_10_post + ___cil_tmp2_10_post ≤ 0___cil_tmp2_10_post___cil_tmp2_10_post ≤ 0___cil_tmp2_10_0 + ___cil_tmp2_10_0 ≤ 0___cil_tmp2_10_0___cil_tmp2_10_0 ≤ 0i_5_post + i_5_post ≤ 0i_5_posti_5_post ≤ 0d_6_0 + d_6_0 ≤ 0d_6_0d_6_0 ≤ 0i_5_0 + i_5_0 ≤ 0i_5_0i_5_0 ≤ 0___retres3_7_post + ___retres3_7_post ≤ 0___retres3_7_post___retres3_7_post ≤ 0___retres3_7_0 + ___retres3_7_0 ≤ 0___retres3_7_0___retres3_7_0 ≤ 0___cil_tmp4_8_post + ___cil_tmp4_8_post ≤ 0___cil_tmp4_8_post___cil_tmp4_8_post ≤ 0___cil_tmp4_8_0 + ___cil_tmp4_8_0 ≤ 0___cil_tmp4_8_0___cil_tmp4_8_0 ≤ 0Result_4_post + Result_4_post ≤ 0Result_4_postResult_4_post ≤ 0Result_4_0 + Result_4_0 ≤ 0Result_4_0Result_4_0 ≤ 0
and for every transition t, a duplicate t is considered.

3 Transition Removal

We remove transitions 0, 1, 4, 5, 6, 7 using the following ranking functions, which are bounded by −17.

6: 0
0: 0
1: 0
2: 0
4: 0
3: 0
5: 0
6: −7
0: −8
1: −9
2: −10
4: −10
2_var_snapshot: −10
2*: −10
3: −14
5: −15
Hints:
9 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
2 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
3 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
0 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
1 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
4 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
5 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
6 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
7 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

4 Location Addition

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

2* 11 2: ___retres1_9_post + ___retres1_9_post ≤ 0___retres1_9_post___retres1_9_post ≤ 0___retres1_9_0 + ___retres1_9_0 ≤ 0___retres1_9_0___retres1_9_0 ≤ 0___cil_tmp2_10_post + ___cil_tmp2_10_post ≤ 0___cil_tmp2_10_post___cil_tmp2_10_post ≤ 0___cil_tmp2_10_0 + ___cil_tmp2_10_0 ≤ 0___cil_tmp2_10_0___cil_tmp2_10_0 ≤ 0i_5_post + i_5_post ≤ 0i_5_posti_5_post ≤ 0d_6_0 + d_6_0 ≤ 0d_6_0d_6_0 ≤ 0i_5_0 + i_5_0 ≤ 0i_5_0i_5_0 ≤ 0___retres3_7_post + ___retres3_7_post ≤ 0___retres3_7_post___retres3_7_post ≤ 0___retres3_7_0 + ___retres3_7_0 ≤ 0___retres3_7_0___retres3_7_0 ≤ 0___cil_tmp4_8_post + ___cil_tmp4_8_post ≤ 0___cil_tmp4_8_post___cil_tmp4_8_post ≤ 0___cil_tmp4_8_0 + ___cil_tmp4_8_0 ≤ 0___cil_tmp4_8_0___cil_tmp4_8_0 ≤ 0Result_4_post + Result_4_post ≤ 0Result_4_postResult_4_post ≤ 0Result_4_0 + Result_4_0 ≤ 0Result_4_0Result_4_0 ≤ 0

5 Location Addition

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

2 9 2_var_snapshot: ___retres1_9_post + ___retres1_9_post ≤ 0___retres1_9_post___retres1_9_post ≤ 0___retres1_9_0 + ___retres1_9_0 ≤ 0___retres1_9_0___retres1_9_0 ≤ 0___cil_tmp2_10_post + ___cil_tmp2_10_post ≤ 0___cil_tmp2_10_post___cil_tmp2_10_post ≤ 0___cil_tmp2_10_0 + ___cil_tmp2_10_0 ≤ 0___cil_tmp2_10_0___cil_tmp2_10_0 ≤ 0i_5_post + i_5_post ≤ 0i_5_posti_5_post ≤ 0d_6_0 + d_6_0 ≤ 0d_6_0d_6_0 ≤ 0i_5_0 + i_5_0 ≤ 0i_5_0i_5_0 ≤ 0___retres3_7_post + ___retres3_7_post ≤ 0___retres3_7_post___retres3_7_post ≤ 0___retres3_7_0 + ___retres3_7_0 ≤ 0___retres3_7_0___retres3_7_0 ≤ 0___cil_tmp4_8_post + ___cil_tmp4_8_post ≤ 0___cil_tmp4_8_post___cil_tmp4_8_post ≤ 0___cil_tmp4_8_0 + ___cil_tmp4_8_0 ≤ 0___cil_tmp4_8_0___cil_tmp4_8_0 ≤ 0Result_4_post + Result_4_post ≤ 0Result_4_postResult_4_post ≤ 0Result_4_0 + Result_4_0 ≤ 0Result_4_0Result_4_0 ≤ 0

6 SCC Decomposition

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

6.1 SCC Subproblem 1/1

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

6.1.1 Splitting Cut-Point Transitions

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

6.1.1.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 8.

6.1.1.1.1 Fresh Variable Addition

The new variable __snapshot_2____retres1_9_post is introduced. The transition formulas are extended as follows:

9: __snapshot_2____retres1_9_post___retres1_9_post___retres1_9_post__snapshot_2____retres1_9_post
11: __snapshot_2____retres1_9_post__snapshot_2____retres1_9_post__snapshot_2____retres1_9_post__snapshot_2____retres1_9_post
2: __snapshot_2____retres1_9_post__snapshot_2____retres1_9_post__snapshot_2____retres1_9_post__snapshot_2____retres1_9_post
3: __snapshot_2____retres1_9_post__snapshot_2____retres1_9_post__snapshot_2____retres1_9_post__snapshot_2____retres1_9_post

6.1.1.1.2 Fresh Variable Addition

The new variable __snapshot_2____retres1_9_0 is introduced. The transition formulas are extended as follows:

9: __snapshot_2____retres1_9_0___retres1_9_0___retres1_9_0__snapshot_2____retres1_9_0
11: __snapshot_2____retres1_9_0__snapshot_2____retres1_9_0__snapshot_2____retres1_9_0__snapshot_2____retres1_9_0
2: __snapshot_2____retres1_9_0__snapshot_2____retres1_9_0__snapshot_2____retres1_9_0__snapshot_2____retres1_9_0
3: __snapshot_2____retres1_9_0__snapshot_2____retres1_9_0__snapshot_2____retres1_9_0__snapshot_2____retres1_9_0

6.1.1.1.3 Fresh Variable Addition

The new variable __snapshot_2____cil_tmp2_10_post is introduced. The transition formulas are extended as follows:

9: __snapshot_2____cil_tmp2_10_post___cil_tmp2_10_post___cil_tmp2_10_post__snapshot_2____cil_tmp2_10_post
11: __snapshot_2____cil_tmp2_10_post__snapshot_2____cil_tmp2_10_post__snapshot_2____cil_tmp2_10_post__snapshot_2____cil_tmp2_10_post
2: __snapshot_2____cil_tmp2_10_post__snapshot_2____cil_tmp2_10_post__snapshot_2____cil_tmp2_10_post__snapshot_2____cil_tmp2_10_post
3: __snapshot_2____cil_tmp2_10_post__snapshot_2____cil_tmp2_10_post__snapshot_2____cil_tmp2_10_post__snapshot_2____cil_tmp2_10_post

6.1.1.1.4 Fresh Variable Addition

The new variable __snapshot_2____cil_tmp2_10_0 is introduced. The transition formulas are extended as follows:

9: __snapshot_2____cil_tmp2_10_0___cil_tmp2_10_0___cil_tmp2_10_0__snapshot_2____cil_tmp2_10_0
11: __snapshot_2____cil_tmp2_10_0__snapshot_2____cil_tmp2_10_0__snapshot_2____cil_tmp2_10_0__snapshot_2____cil_tmp2_10_0
2: __snapshot_2____cil_tmp2_10_0__snapshot_2____cil_tmp2_10_0__snapshot_2____cil_tmp2_10_0__snapshot_2____cil_tmp2_10_0
3: __snapshot_2____cil_tmp2_10_0__snapshot_2____cil_tmp2_10_0__snapshot_2____cil_tmp2_10_0__snapshot_2____cil_tmp2_10_0

6.1.1.1.5 Fresh Variable Addition

The new variable __snapshot_2_i_5_post is introduced. The transition formulas are extended as follows:

9: __snapshot_2_i_5_posti_5_posti_5_post__snapshot_2_i_5_post
11: __snapshot_2_i_5_post__snapshot_2_i_5_post__snapshot_2_i_5_post__snapshot_2_i_5_post
2: __snapshot_2_i_5_post__snapshot_2_i_5_post__snapshot_2_i_5_post__snapshot_2_i_5_post
3: __snapshot_2_i_5_post__snapshot_2_i_5_post__snapshot_2_i_5_post__snapshot_2_i_5_post

6.1.1.1.6 Fresh Variable Addition

The new variable __snapshot_2_d_6_0 is introduced. The transition formulas are extended as follows:

9: __snapshot_2_d_6_0d_6_0d_6_0__snapshot_2_d_6_0
11: __snapshot_2_d_6_0__snapshot_2_d_6_0__snapshot_2_d_6_0__snapshot_2_d_6_0
2: __snapshot_2_d_6_0__snapshot_2_d_6_0__snapshot_2_d_6_0__snapshot_2_d_6_0
3: __snapshot_2_d_6_0__snapshot_2_d_6_0__snapshot_2_d_6_0__snapshot_2_d_6_0

6.1.1.1.7 Fresh Variable Addition

The new variable __snapshot_2_i_5_0 is introduced. The transition formulas are extended as follows:

9: __snapshot_2_i_5_0i_5_0i_5_0__snapshot_2_i_5_0
11: __snapshot_2_i_5_0__snapshot_2_i_5_0__snapshot_2_i_5_0__snapshot_2_i_5_0
2: __snapshot_2_i_5_0__snapshot_2_i_5_0__snapshot_2_i_5_0__snapshot_2_i_5_0
3: __snapshot_2_i_5_0__snapshot_2_i_5_0__snapshot_2_i_5_0__snapshot_2_i_5_0

6.1.1.1.8 Fresh Variable Addition

The new variable __snapshot_2____retres3_7_post is introduced. The transition formulas are extended as follows:

9: __snapshot_2____retres3_7_post___retres3_7_post___retres3_7_post__snapshot_2____retres3_7_post
11: __snapshot_2____retres3_7_post__snapshot_2____retres3_7_post__snapshot_2____retres3_7_post__snapshot_2____retres3_7_post
2: __snapshot_2____retres3_7_post__snapshot_2____retres3_7_post__snapshot_2____retres3_7_post__snapshot_2____retres3_7_post
3: __snapshot_2____retres3_7_post__snapshot_2____retres3_7_post__snapshot_2____retres3_7_post__snapshot_2____retres3_7_post

6.1.1.1.9 Fresh Variable Addition

The new variable __snapshot_2____retres3_7_0 is introduced. The transition formulas are extended as follows:

9: __snapshot_2____retres3_7_0___retres3_7_0___retres3_7_0__snapshot_2____retres3_7_0
11: __snapshot_2____retres3_7_0__snapshot_2____retres3_7_0__snapshot_2____retres3_7_0__snapshot_2____retres3_7_0
2: __snapshot_2____retres3_7_0__snapshot_2____retres3_7_0__snapshot_2____retres3_7_0__snapshot_2____retres3_7_0
3: __snapshot_2____retres3_7_0__snapshot_2____retres3_7_0__snapshot_2____retres3_7_0__snapshot_2____retres3_7_0

6.1.1.1.10 Fresh Variable Addition

The new variable __snapshot_2____cil_tmp4_8_post is introduced. The transition formulas are extended as follows:

9: __snapshot_2____cil_tmp4_8_post___cil_tmp4_8_post___cil_tmp4_8_post__snapshot_2____cil_tmp4_8_post
11: __snapshot_2____cil_tmp4_8_post__snapshot_2____cil_tmp4_8_post__snapshot_2____cil_tmp4_8_post__snapshot_2____cil_tmp4_8_post
2: __snapshot_2____cil_tmp4_8_post__snapshot_2____cil_tmp4_8_post__snapshot_2____cil_tmp4_8_post__snapshot_2____cil_tmp4_8_post
3: __snapshot_2____cil_tmp4_8_post__snapshot_2____cil_tmp4_8_post__snapshot_2____cil_tmp4_8_post__snapshot_2____cil_tmp4_8_post

6.1.1.1.11 Fresh Variable Addition

The new variable __snapshot_2____cil_tmp4_8_0 is introduced. The transition formulas are extended as follows:

9: __snapshot_2____cil_tmp4_8_0___cil_tmp4_8_0___cil_tmp4_8_0__snapshot_2____cil_tmp4_8_0
11: __snapshot_2____cil_tmp4_8_0__snapshot_2____cil_tmp4_8_0__snapshot_2____cil_tmp4_8_0__snapshot_2____cil_tmp4_8_0
2: __snapshot_2____cil_tmp4_8_0__snapshot_2____cil_tmp4_8_0__snapshot_2____cil_tmp4_8_0__snapshot_2____cil_tmp4_8_0
3: __snapshot_2____cil_tmp4_8_0__snapshot_2____cil_tmp4_8_0__snapshot_2____cil_tmp4_8_0__snapshot_2____cil_tmp4_8_0

6.1.1.1.12 Fresh Variable Addition

The new variable __snapshot_2_Result_4_post is introduced. The transition formulas are extended as follows:

9: __snapshot_2_Result_4_postResult_4_postResult_4_post__snapshot_2_Result_4_post
11: __snapshot_2_Result_4_post__snapshot_2_Result_4_post__snapshot_2_Result_4_post__snapshot_2_Result_4_post
2: __snapshot_2_Result_4_post__snapshot_2_Result_4_post__snapshot_2_Result_4_post__snapshot_2_Result_4_post
3: __snapshot_2_Result_4_post__snapshot_2_Result_4_post__snapshot_2_Result_4_post__snapshot_2_Result_4_post

6.1.1.1.13 Fresh Variable Addition

The new variable __snapshot_2_Result_4_0 is introduced. The transition formulas are extended as follows:

9: __snapshot_2_Result_4_0Result_4_0Result_4_0__snapshot_2_Result_4_0
11: __snapshot_2_Result_4_0__snapshot_2_Result_4_0__snapshot_2_Result_4_0__snapshot_2_Result_4_0
2: __snapshot_2_Result_4_0__snapshot_2_Result_4_0__snapshot_2_Result_4_0__snapshot_2_Result_4_0
3: __snapshot_2_Result_4_0__snapshot_2_Result_4_0__snapshot_2_Result_4_0__snapshot_2_Result_4_0

6.1.1.1.14 Invariant Updates

The following invariants are asserted.

0: TRUE
1: TRUE
2: 1 + d_6_0 ≤ 0
3: Result_4_post ≤ 0___cil_tmp4_8_post ≤ 0___retres3_7_post ≤ 0___retres3_7_post ≤ 0Result_4_0 ≤ 0___cil_tmp4_8_0 ≤ 0___retres3_7_0 ≤ 0___retres3_7_0 ≤ 0
4: 1 + d_6_0 ≤ 0
5: Result_4_post ≤ 0___cil_tmp4_8_post ≤ 0___retres3_7_post ≤ 0___retres3_7_post ≤ 0Result_4_0 ≤ 0___cil_tmp4_8_0 ≤ 0___retres3_7_0 ≤ 0___retres3_7_0 ≤ 0___cil_tmp2_10_post ≤ 0___retres1_9_post ≤ 0___retres1_9_post ≤ 0___cil_tmp2_10_0 ≤ 0___retres1_9_0 ≤ 0___retres1_9_0 ≤ 0
6: TRUE
2: 1 + d_6_0 ≤ 01 + d_6_0 ≤ 01 − __snapshot_2_i_5_0 + i_5_0 ≤ 0__snapshot_2_i_5_0 ≤ 0
4: 1 + d_6_0 ≤ 01 − __snapshot_2_i_5_0 + i_5_0 ≤ 0__snapshot_2_i_5_0 ≤ 0
2_var_snapshot: 1 + d_6_0 ≤ 0__snapshot_2_i_5_0 + i_5_0 ≤ 01 − __snapshot_2_i_5_0 + d_6_0 + i_5_0 ≤ 0
2*: 1 + d_6_0 ≤ 01 − __snapshot_2_i_5_0 + i_5_0 ≤ 0__snapshot_2_i_5_0 ≤ 0

The invariants are proved as follows.

IMPACT Invariant Proof

6.1.1.1.15 Transition Removal

We remove transition 11 using the following ranking functions, which are bounded by −2.

2: i_5_0
4: __snapshot_2_i_5_0
2_var_snapshot: __snapshot_2_i_5_0
2*: __snapshot_2_i_5_0
Hints:
9 distribute assertion
lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
11 lexStrict[ [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
2 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
3 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

6.1.1.1.16 Transition Removal

We remove transition 9 using the following ranking functions, which are bounded by −6.

2: −1
2_var_snapshot: −2
4: −3
2*: −4
Hints:
9 distribute assertion
lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
2 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
3 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

6.1.1.1.17 Splitting Cut-Point Transitions

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

Tool configuration

T2Cert