LTS Termination Proof

by T2Cert

Input

Integer Transition System

Initial Location: 6

Transitions: (pre-variables and post-variables)

0	0	1:	− x79_post + x79_post ≤ 0 ∧ x79_post − x79_post ≤ 0 ∧ − x79_0 + x79_0 ≤ 0 ∧ x79_0 − x79_0 ≤ 0 ∧ − x35_post + x35_post ≤ 0 ∧ x35_post − x35_post ≤ 0 ∧ − x35_0 + x35_0 ≤ 0 ∧ x35_0 − x35_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − i911_post + i911_post ≤ 0 ∧ i911_post − i911_post ≤ 0 ∧ − i911_0 + i911_0 ≤ 0 ∧ i911_0 − i911_0 ≤ 0 ∧ − i57_post + i57_post ≤ 0 ∧ i57_post − i57_post ≤ 0 ∧ − i57_0 + i57_0 ≤ 0 ∧ i57_0 − i57_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
2	1	3:	___const_10_0 − i911_0 ≤ 0 ∧ − x79_post + x79_post ≤ 0 ∧ x79_post − x79_post ≤ 0 ∧ − x79_0 + x79_0 ≤ 0 ∧ x79_0 − x79_0 ≤ 0 ∧ − x35_post + x35_post ≤ 0 ∧ x35_post − x35_post ≤ 0 ∧ − x35_0 + x35_0 ≤ 0 ∧ x35_0 − x35_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − i911_post + i911_post ≤ 0 ∧ i911_post − i911_post ≤ 0 ∧ − i911_0 + i911_0 ≤ 0 ∧ i911_0 − i911_0 ≤ 0 ∧ − i57_post + i57_post ≤ 0 ∧ i57_post − i57_post ≤ 0 ∧ − i57_0 + i57_0 ≤ 0 ∧ i57_0 − i57_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
2	2	4:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − ___const_10_0 + i911_0 ≤ 0 ∧ −1 − i911_0 + i911_post ≤ 0 ∧ 1 + i911_0 − i911_post ≤ 0 ∧ i911_0 − i911_post ≤ 0 ∧ − i911_0 + i911_post ≤ 0 ∧ − x79_post + x79_post ≤ 0 ∧ x79_post − x79_post ≤ 0 ∧ − x79_0 + x79_0 ≤ 0 ∧ x79_0 − x79_0 ≤ 0 ∧ − x35_post + x35_post ≤ 0 ∧ x35_post − x35_post ≤ 0 ∧ − x35_0 + x35_0 ≤ 0 ∧ x35_0 − x35_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − i57_post + i57_post ≤ 0 ∧ i57_post − i57_post ≤ 0 ∧ − i57_0 + i57_0 ≤ 0 ∧ i57_0 − i57_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
4	3	2:	− x79_post + x79_post ≤ 0 ∧ x79_post − x79_post ≤ 0 ∧ − x79_0 + x79_0 ≤ 0 ∧ x79_0 − x79_0 ≤ 0 ∧ − x35_post + x35_post ≤ 0 ∧ x35_post − x35_post ≤ 0 ∧ − x35_0 + x35_0 ≤ 0 ∧ x35_0 − x35_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − i911_post + i911_post ≤ 0 ∧ i911_post − i911_post ≤ 0 ∧ − i911_0 + i911_0 ≤ 0 ∧ i911_0 − i911_0 ≤ 0 ∧ − i57_post + i57_post ≤ 0 ∧ i57_post − i57_post ≤ 0 ∧ − i57_0 + i57_0 ≤ 0 ∧ i57_0 − i57_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
1	4	4:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ ___const_10_0 − i57_0 ≤ 0 ∧ i911_post ≤ 0 ∧ − i911_post ≤ 0 ∧ i911_0 − i911_post ≤ 0 ∧ − i911_0 + i911_post ≤ 0 ∧ x79_0 − x79_post ≤ 0 ∧ − x79_0 + x79_post ≤ 0 ∧ − x35_post + x35_post ≤ 0 ∧ x35_post − x35_post ≤ 0 ∧ − x35_0 + x35_0 ≤ 0 ∧ x35_0 − x35_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − i57_post + i57_post ≤ 0 ∧ i57_post − i57_post ≤ 0 ∧ − i57_0 + i57_0 ≤ 0 ∧ i57_0 − i57_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
1	5	0:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − ___const_10_0 + i57_0 ≤ 0 ∧ −1 − i57_0 + i57_post ≤ 0 ∧ 1 + i57_0 − i57_post ≤ 0 ∧ i57_0 − i57_post ≤ 0 ∧ − i57_0 + i57_post ≤ 0 ∧ − x79_post + x79_post ≤ 0 ∧ x79_post − x79_post ≤ 0 ∧ − x79_0 + x79_0 ≤ 0 ∧ x79_0 − x79_0 ≤ 0 ∧ − x35_post + x35_post ≤ 0 ∧ x35_post − x35_post ≤ 0 ∧ − x35_0 + x35_0 ≤ 0 ∧ x35_0 − x35_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − i911_post + i911_post ≤ 0 ∧ i911_post − i911_post ≤ 0 ∧ − i911_0 + i911_0 ≤ 0 ∧ i911_0 − i911_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
5	6	0:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ i57_post ≤ 0 ∧ − i57_post ≤ 0 ∧ i57_0 − i57_post ≤ 0 ∧ − i57_0 + i57_post ≤ 0 ∧ tmp_0 − tmp_post ≤ 0 ∧ − tmp_0 + tmp_post ≤ 0 ∧ x35_0 − x35_post ≤ 0 ∧ − x35_0 + x35_post ≤ 0 ∧ − x79_post + x79_post ≤ 0 ∧ x79_post − x79_post ≤ 0 ∧ − x79_0 + x79_0 ≤ 0 ∧ x79_0 − x79_0 ≤ 0 ∧ − i911_post + i911_post ≤ 0 ∧ i911_post − i911_post ≤ 0 ∧ − i911_0 + i911_0 ≤ 0 ∧ i911_0 − i911_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
6	7	5:	− x79_post + x79_post ≤ 0 ∧ x79_post − x79_post ≤ 0 ∧ − x79_0 + x79_0 ≤ 0 ∧ x79_0 − x79_0 ≤ 0 ∧ − x35_post + x35_post ≤ 0 ∧ x35_post − x35_post ≤ 0 ∧ − x35_0 + x35_0 ≤ 0 ∧ x35_0 − x35_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − i911_post + i911_post ≤ 0 ∧ i911_post − i911_post ≤ 0 ∧ − i911_0 + i911_0 ≤ 0 ∧ i911_0 − i911_0 ≤ 0 ∧ − i57_post + i57_post ≤ 0 ∧ i57_post − i57_post ≤ 0 ∧ − i57_0 + i57_0 ≤ 0 ∧ i57_0 − i57_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

0	8	0:	− x79_post + x79_post ≤ 0 ∧ x79_post − x79_post ≤ 0 ∧ − x79_0 + x79_0 ≤ 0 ∧ x79_0 − x79_0 ≤ 0 ∧ − x35_post + x35_post ≤ 0 ∧ x35_post − x35_post ≤ 0 ∧ − x35_0 + x35_0 ≤ 0 ∧ x35_0 − x35_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − i911_post + i911_post ≤ 0 ∧ i911_post − i911_post ≤ 0 ∧ − i911_0 + i911_0 ≤ 0 ∧ i911_0 − i911_0 ≤ 0 ∧ − i57_post + i57_post ≤ 0 ∧ i57_post − i57_post ≤ 0 ∧ − i57_0 + i57_0 ≤ 0 ∧ i57_0 − i57_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0
4	15	4:	− x79_post + x79_post ≤ 0 ∧ x79_post − x79_post ≤ 0 ∧ − x79_0 + x79_0 ≤ 0 ∧ x79_0 − x79_0 ≤ 0 ∧ − x35_post + x35_post ≤ 0 ∧ x35_post − x35_post ≤ 0 ∧ − x35_0 + x35_0 ≤ 0 ∧ x35_0 − x35_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − i911_post + i911_post ≤ 0 ∧ i911_post − i911_post ≤ 0 ∧ − i911_0 + i911_0 ≤ 0 ∧ i911_0 − i911_0 ≤ 0 ∧ − i57_post + i57_post ≤ 0 ∧ i57_post − i57_post ≤ 0 ∧ − i57_0 + i57_0 ≤ 0 ∧ i57_0 − i57_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0

and for every transition t, a duplicate t is considered.

2 Transition Removal

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

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

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] ]
16	lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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, 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] ]
3	lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]
5	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] ]
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] ]
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] ]
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] ]
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] ]

3 Location Addition

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

0* 11 0: − x79_post + x79_post ≤ 0 ∧ x79_post − x79_post ≤ 0 ∧ − x79_0 + x79_0 ≤ 0 ∧ x79_0 − x79_0 ≤ 0 ∧ − x35_post + x35_post ≤ 0 ∧ x35_post − x35_post ≤ 0 ∧ − x35_0 + x35_0 ≤ 0 ∧ x35_0 − x35_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − i911_post + i911_post ≤ 0 ∧ i911_post − i911_post ≤ 0 ∧ − i911_0 + i911_0 ≤ 0 ∧ i911_0 − i911_0 ≤ 0 ∧ − i57_post + i57_post ≤ 0 ∧ i57_post − i57_post ≤ 0 ∧ − i57_0 + i57_0 ≤ 0 ∧ i57_0 − i57_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0

4 Location Addition

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

0 9 0_var_snapshot: − x79_post + x79_post ≤ 0 ∧ x79_post − x79_post ≤ 0 ∧ − x79_0 + x79_0 ≤ 0 ∧ x79_0 − x79_0 ≤ 0 ∧ − x35_post + x35_post ≤ 0 ∧ x35_post − x35_post ≤ 0 ∧ − x35_0 + x35_0 ≤ 0 ∧ x35_0 − x35_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − i911_post + i911_post ≤ 0 ∧ i911_post − i911_post ≤ 0 ∧ − i911_0 + i911_0 ≤ 0 ∧ i911_0 − i911_0 ≤ 0 ∧ − i57_post + i57_post ≤ 0 ∧ i57_post − i57_post ≤ 0 ∧ − i57_0 + i57_0 ≤ 0 ∧ i57_0 − i57_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0

5 Location Addition

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

4* 18 4: − x79_post + x79_post ≤ 0 ∧ x79_post − x79_post ≤ 0 ∧ − x79_0 + x79_0 ≤ 0 ∧ x79_0 − x79_0 ≤ 0 ∧ − x35_post + x35_post ≤ 0 ∧ x35_post − x35_post ≤ 0 ∧ − x35_0 + x35_0 ≤ 0 ∧ x35_0 − x35_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − i911_post + i911_post ≤ 0 ∧ i911_post − i911_post ≤ 0 ∧ − i911_0 + i911_0 ≤ 0 ∧ i911_0 − i911_0 ≤ 0 ∧ − i57_post + i57_post ≤ 0 ∧ i57_post − i57_post ≤ 0 ∧ − i57_0 + i57_0 ≤ 0 ∧ i57_0 − i57_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0

6 Location Addition

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

4 16 4_var_snapshot: − x79_post + x79_post ≤ 0 ∧ x79_post − x79_post ≤ 0 ∧ − x79_0 + x79_0 ≤ 0 ∧ x79_0 − x79_0 ≤ 0 ∧ − x35_post + x35_post ≤ 0 ∧ x35_post − x35_post ≤ 0 ∧ − x35_0 + x35_0 ≤ 0 ∧ x35_0 − x35_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − i911_post + i911_post ≤ 0 ∧ i911_post − i911_post ≤ 0 ∧ − i911_0 + i911_0 ≤ 0 ∧ i911_0 − i911_0 ≤ 0 ∧ − i57_post + i57_post ≤ 0 ∧ i57_post − i57_post ≤ 0 ∧ − i57_0 + i57_0 ≤ 0 ∧ i57_0 − i57_0 ≤ 0 ∧ − ___const_10_0 + ___const_10_0 ≤ 0 ∧ ___const_10_0 − ___const_10_0 ≤ 0

7 SCC Decomposition

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

7.1 SCC Subproblem 1/2

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

7.1.1 Transition Removal

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

2:	−1 + 4⋅___const_10_0 − 4⋅i911_0
4:	1 + 4⋅___const_10_0 − 4⋅i911_0
4_var_snapshot:	4⋅___const_10_0 − 4⋅i911_0
4*:	2 + 4⋅___const_10_0 − 4⋅i911_0

Hints:

16	lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0] ]
18	lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0, 0, 0, 0, 4, 0] ]
2	lexStrict[ [0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0] , [0, 0, 4, 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, 4, 0, 0, 0, 0, 4, 0] ]

7.1.2 Transition Removal

We remove transitions 16, 18, 3 using the following ranking functions, which are bounded by −1.

2:	−1
4:	1
4_var_snapshot:	0
4*:	2

Hints:

16	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] ]
18	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] ]
3	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] ]

7.1.3 Splitting Cut-Point Transitions

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

7.1.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 15.

7.1.3.1.1 Splitting Cut-Point Transitions

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

7.2 SCC Subproblem 2/2

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

7.2.1 Transition Removal

We remove transition 5 using the following ranking functions, which are bounded by 1.

0:	4⋅___const_10_0 − 4⋅i57_0
1:	−2 + 4⋅___const_10_0 − 4⋅i57_0
0_var_snapshot:	−1 + 4⋅___const_10_0 − 4⋅i57_0
0*:	1 + 4⋅___const_10_0 − 4⋅i57_0

Hints:

9	lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0] ]
11	lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0] ]
0	lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 4, 0] ]
5	lexStrict[ [0, 0, 0, 0, 4, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4, 0] , [0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ]

7.2.2 Transition Removal

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

0:	1
1:	−1
0_var_snapshot:	0
0*:	2

Hints:

9	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] ]
11	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	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] ]

7.2.3 Splitting Cut-Point Transitions

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

7.2.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 8.

7.2.3.1.1 Splitting Cut-Point Transitions

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

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