LTS Termination Proof

by T2Cert

Input

Integer Transition System

Initial Location: 6

Transitions: (pre-variables and post-variables)

0	0	1:	− 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 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − n9_post + n9_post ≤ 0 ∧ n9_post − n9_post ≤ 0 ∧ − n9_0 + n9_0 ≤ 0 ∧ n9_0 − n9_0 ≤ 0 ∧ − n12_post + n12_post ≤ 0 ∧ n12_post − n12_post ≤ 0 ∧ − n12_0 + n12_0 ≤ 0 ∧ n12_0 − n12_0 ≤ 0 ∧ − i13_post + i13_post ≤ 0 ∧ i13_post − i13_post ≤ 0 ∧ − i13_0 + i13_0 ≤ 0 ∧ i13_0 − i13_0 ≤ 0 ∧ − i10_post + i10_post ≤ 0 ∧ i10_post − i10_post ≤ 0 ∧ − i10_0 + i10_0 ≤ 0 ∧ i10_0 − i10_0 ≤ 0
2	1	3:	− i13_0 + n12_0 ≤ 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 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − n9_post + n9_post ≤ 0 ∧ n9_post − n9_post ≤ 0 ∧ − n9_0 + n9_0 ≤ 0 ∧ n9_0 − n9_0 ≤ 0 ∧ − n12_post + n12_post ≤ 0 ∧ n12_post − n12_post ≤ 0 ∧ − n12_0 + n12_0 ≤ 0 ∧ n12_0 − n12_0 ≤ 0 ∧ − i13_post + i13_post ≤ 0 ∧ i13_post − i13_post ≤ 0 ∧ − i13_0 + i13_0 ≤ 0 ∧ i13_0 − i13_0 ≤ 0 ∧ − i10_post + i10_post ≤ 0 ∧ i10_post − i10_post ≤ 0 ∧ − i10_0 + i10_0 ≤ 0 ∧ i10_0 − i10_0 ≤ 0
2	2	4:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + i13_0 − n12_0 ≤ 0 ∧ −1 − i13_0 + i13_post ≤ 0 ∧ 1 + i13_0 − i13_post ≤ 0 ∧ i13_0 − i13_post ≤ 0 ∧ − i13_0 + i13_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 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − n9_post + n9_post ≤ 0 ∧ n9_post − n9_post ≤ 0 ∧ − n9_0 + n9_0 ≤ 0 ∧ n9_0 − n9_0 ≤ 0 ∧ − n12_post + n12_post ≤ 0 ∧ n12_post − n12_post ≤ 0 ∧ − n12_0 + n12_0 ≤ 0 ∧ n12_0 − n12_0 ≤ 0 ∧ − i10_post + i10_post ≤ 0 ∧ i10_post − i10_post ≤ 0 ∧ − i10_0 + i10_0 ≤ 0 ∧ i10_0 − i10_0 ≤ 0
4	3	2:	− 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 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − n9_post + n9_post ≤ 0 ∧ n9_post − n9_post ≤ 0 ∧ − n9_0 + n9_0 ≤ 0 ∧ n9_0 − n9_0 ≤ 0 ∧ − n12_post + n12_post ≤ 0 ∧ n12_post − n12_post ≤ 0 ∧ − n12_0 + n12_0 ≤ 0 ∧ n12_0 − n12_0 ≤ 0 ∧ − i13_post + i13_post ≤ 0 ∧ i13_post − i13_post ≤ 0 ∧ − i13_0 + i13_0 ≤ 0 ∧ i13_0 − i13_0 ≤ 0 ∧ − i10_post + i10_post ≤ 0 ∧ i10_post − i10_post ≤ 0 ∧ − i10_0 + i10_0 ≤ 0 ∧ i10_0 − i10_0 ≤ 0
1	4	4:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − i10_0 + n9_0 ≤ 0 ∧ n12_post − n_0 ≤ 0 ∧ − n12_post + n_0 ≤ 0 ∧ i13_post ≤ 0 ∧ − i13_post ≤ 0 ∧ i13_0 − i13_post ≤ 0 ∧ − i13_0 + i13_post ≤ 0 ∧ n12_0 − n12_post ≤ 0 ∧ − n12_0 + n12_post ≤ 0 ∧ tmp___0_0 − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_post ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − n9_post + n9_post ≤ 0 ∧ n9_post − n9_post ≤ 0 ∧ − n9_0 + n9_0 ≤ 0 ∧ n9_0 − n9_0 ≤ 0 ∧ − i10_post + i10_post ≤ 0 ∧ i10_post − i10_post ≤ 0 ∧ − i10_0 + i10_0 ≤ 0 ∧ i10_0 − i10_0 ≤ 0
1	5	0:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + i10_0 − n9_0 ≤ 0 ∧ −1 − i10_0 + i10_post ≤ 0 ∧ 1 + i10_0 − i10_post ≤ 0 ∧ i10_0 − i10_post ≤ 0 ∧ − i10_0 + i10_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 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − n9_post + n9_post ≤ 0 ∧ n9_post − n9_post ≤ 0 ∧ − n9_0 + n9_0 ≤ 0 ∧ n9_0 − n9_0 ≤ 0 ∧ − n12_post + n12_post ≤ 0 ∧ n12_post − n12_post ≤ 0 ∧ − n12_0 + n12_0 ≤ 0 ∧ n12_0 − n12_0 ≤ 0 ∧ − i13_post + i13_post ≤ 0 ∧ i13_post − i13_post ≤ 0 ∧ − i13_0 + i13_0 ≤ 0 ∧ i13_0 − i13_0 ≤ 0
5	6	0:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ i10_post ≤ 0 ∧ − i10_post ≤ 0 ∧ i10_0 − i10_post ≤ 0 ∧ − i10_0 + i10_post ≤ 0 ∧ n9_0 − n9_post ≤ 0 ∧ − n9_0 + n9_post ≤ 0 ∧ n_0 − n_post ≤ 0 ∧ − n_0 + n_post ≤ 0 ∧ tmp_0 − tmp_post ≤ 0 ∧ − tmp_0 + 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 ∧ − n12_post + n12_post ≤ 0 ∧ n12_post − n12_post ≤ 0 ∧ − n12_0 + n12_0 ≤ 0 ∧ n12_0 − n12_0 ≤ 0 ∧ − i13_post + i13_post ≤ 0 ∧ i13_post − i13_post ≤ 0 ∧ − i13_0 + i13_0 ≤ 0 ∧ i13_0 − i13_0 ≤ 0
6	7	5:	− 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 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − n9_post + n9_post ≤ 0 ∧ n9_post − n9_post ≤ 0 ∧ − n9_0 + n9_0 ≤ 0 ∧ n9_0 − n9_0 ≤ 0 ∧ − n12_post + n12_post ≤ 0 ∧ n12_post − n12_post ≤ 0 ∧ − n12_0 + n12_0 ≤ 0 ∧ n12_0 − n12_0 ≤ 0 ∧ − i13_post + i13_post ≤ 0 ∧ i13_post − i13_post ≤ 0 ∧ − i13_0 + i13_0 ≤ 0 ∧ i13_0 − i13_0 ≤ 0 ∧ − i10_post + i10_post ≤ 0 ∧ i10_post − i10_post ≤ 0 ∧ − i10_0 + i10_0 ≤ 0 ∧ i10_0 − i10_0 ≤ 0

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

0	8	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 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − n9_post + n9_post ≤ 0 ∧ n9_post − n9_post ≤ 0 ∧ − n9_0 + n9_0 ≤ 0 ∧ n9_0 − n9_0 ≤ 0 ∧ − n12_post + n12_post ≤ 0 ∧ n12_post − n12_post ≤ 0 ∧ − n12_0 + n12_0 ≤ 0 ∧ n12_0 − n12_0 ≤ 0 ∧ − i13_post + i13_post ≤ 0 ∧ i13_post − i13_post ≤ 0 ∧ − i13_0 + i13_0 ≤ 0 ∧ i13_0 − i13_0 ≤ 0 ∧ − i10_post + i10_post ≤ 0 ∧ i10_post − i10_post ≤ 0 ∧ − i10_0 + i10_0 ≤ 0 ∧ i10_0 − i10_0 ≤ 0
4	15	4:	− 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 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − n9_post + n9_post ≤ 0 ∧ n9_post − n9_post ≤ 0 ∧ − n9_0 + n9_0 ≤ 0 ∧ n9_0 − n9_0 ≤ 0 ∧ − n12_post + n12_post ≤ 0 ∧ n12_post − n12_post ≤ 0 ∧ − n12_0 + n12_0 ≤ 0 ∧ n12_0 − n12_0 ≤ 0 ∧ − i13_post + i13_post ≤ 0 ∧ i13_post − i13_post ≤ 0 ∧ − i13_0 + i13_0 ≤ 0 ∧ i13_0 − i13_0 ≤ 0 ∧ − i10_post + i10_post ≤ 0 ∧ i10_post − i10_post ≤ 0 ∧ − i10_0 + i10_0 ≤ 0 ∧ i10_0 − i10_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

3 Location Addition

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

0* 11 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 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − n9_post + n9_post ≤ 0 ∧ n9_post − n9_post ≤ 0 ∧ − n9_0 + n9_0 ≤ 0 ∧ n9_0 − n9_0 ≤ 0 ∧ − n12_post + n12_post ≤ 0 ∧ n12_post − n12_post ≤ 0 ∧ − n12_0 + n12_0 ≤ 0 ∧ n12_0 − n12_0 ≤ 0 ∧ − i13_post + i13_post ≤ 0 ∧ i13_post − i13_post ≤ 0 ∧ − i13_0 + i13_0 ≤ 0 ∧ i13_0 − i13_0 ≤ 0 ∧ − i10_post + i10_post ≤ 0 ∧ i10_post − i10_post ≤ 0 ∧ − i10_0 + i10_0 ≤ 0 ∧ i10_0 − i10_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: − 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 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − n9_post + n9_post ≤ 0 ∧ n9_post − n9_post ≤ 0 ∧ − n9_0 + n9_0 ≤ 0 ∧ n9_0 − n9_0 ≤ 0 ∧ − n12_post + n12_post ≤ 0 ∧ n12_post − n12_post ≤ 0 ∧ − n12_0 + n12_0 ≤ 0 ∧ n12_0 − n12_0 ≤ 0 ∧ − i13_post + i13_post ≤ 0 ∧ i13_post − i13_post ≤ 0 ∧ − i13_0 + i13_0 ≤ 0 ∧ i13_0 − i13_0 ≤ 0 ∧ − i10_post + i10_post ≤ 0 ∧ i10_post − i10_post ≤ 0 ∧ − i10_0 + i10_0 ≤ 0 ∧ i10_0 − i10_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: − 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 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − n9_post + n9_post ≤ 0 ∧ n9_post − n9_post ≤ 0 ∧ − n9_0 + n9_0 ≤ 0 ∧ n9_0 − n9_0 ≤ 0 ∧ − n12_post + n12_post ≤ 0 ∧ n12_post − n12_post ≤ 0 ∧ − n12_0 + n12_0 ≤ 0 ∧ n12_0 − n12_0 ≤ 0 ∧ − i13_post + i13_post ≤ 0 ∧ i13_post − i13_post ≤ 0 ∧ − i13_0 + i13_0 ≤ 0 ∧ i13_0 − i13_0 ≤ 0 ∧ − i10_post + i10_post ≤ 0 ∧ i10_post − i10_post ≤ 0 ∧ − i10_0 + i10_0 ≤ 0 ∧ i10_0 − i10_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: − 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 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − n9_post + n9_post ≤ 0 ∧ n9_post − n9_post ≤ 0 ∧ − n9_0 + n9_0 ≤ 0 ∧ n9_0 − n9_0 ≤ 0 ∧ − n12_post + n12_post ≤ 0 ∧ n12_post − n12_post ≤ 0 ∧ − n12_0 + n12_0 ≤ 0 ∧ n12_0 − n12_0 ≤ 0 ∧ − i13_post + i13_post ≤ 0 ∧ i13_post − i13_post ≤ 0 ∧ − i13_0 + i13_0 ≤ 0 ∧ i13_0 − i13_0 ≤ 0 ∧ − i10_post + i10_post ≤ 0 ∧ i10_post − i10_post ≤ 0 ∧ − i10_0 + i10_0 ≤ 0 ∧ i10_0 − i10_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⋅i13_0 + 4⋅n12_0
4:	1 − 4⋅i13_0 + 4⋅n12_0
4_var_snapshot:	−4⋅i13_0 + 4⋅n12_0
4*:	2 − 4⋅i13_0 + 4⋅n12_0

7.1.2 Transition Removal

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

2:	−3
4:	−1
4_var_snapshot:	−2
4*:	0

7.1.3 Transition Removal

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

2:	0
4:	0
4_var_snapshot:	−1
4*:	0

7.1.4 Splitting Cut-Point Transitions

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

7.1.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 15.

7.1.4.1.1 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 3.

0:	2 − 4⋅i10_0 + 4⋅n9_0
1:	−4⋅i10_0 + 4⋅n9_0
0_var_snapshot:	1 − 4⋅i10_0 + 4⋅n9_0
0*:	3 − 4⋅i10_0 + 4⋅n9_0

7.2.2 Transition Removal

We remove transitions 11, 0 using the following ranking functions, which are bounded by −3.

0:	−1
1:	−3
0_var_snapshot:	−2
0*:	0

7.2.3 Transition Removal

We remove transition 9 using the following ranking functions, which are bounded by 0.

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

7.2.4 Splitting Cut-Point Transitions

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

7.2.4.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 8.

7.2.4.1.1 Splitting Cut-Point Transitions

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

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