# LTS Termination Proof

by T2Cert

## Input

Integer Transition System
• Initial Location: 7
• Transitions: (pre-variables and post-variables)  0 0 1: 1 − copied_0 ≤ 0 ∧ − e_0 + olde_0 ≤ 0 ∧ n_0 − oldn_0 ≤ 0 ∧ − oldn_post + oldn_post ≤ 0 ∧ oldn_post − oldn_post ≤ 0 ∧ − oldn_0 + oldn_0 ≤ 0 ∧ oldn_0 − oldn_0 ≤ 0 ∧ − olde_post + olde_post ≤ 0 ∧ olde_post − olde_post ≤ 0 ∧ − olde_0 + olde_0 ≤ 0 ∧ olde_0 − olde_0 ≤ 0 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − e_post + e_post ≤ 0 ∧ e_post − e_post ≤ 0 ∧ − e_0 + e_0 ≤ 0 ∧ e_0 − e_0 ≤ 0 ∧ − copied_post + copied_post ≤ 0 ∧ copied_post − copied_post ≤ 0 ∧ − copied_0 + copied_0 ≤ 0 ∧ copied_0 − copied_0 ≤ 0 0 1 2: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ copied_0 ≤ 0 ∧ −1 + copied_post ≤ 0 ∧ 1 − copied_post ≤ 0 ∧ − n_0 + oldn_post ≤ 0 ∧ n_0 − oldn_post ≤ 0 ∧ − e_0 + olde_post ≤ 0 ∧ e_0 − olde_post ≤ 0 ∧ 1 − e_0 ≤ 0 ∧ −100 + n_0 ≤ 0 ∧ −11 − n_0 + n_post ≤ 0 ∧ 11 + n_0 − n_post ≤ 0 ∧ −1 − e_0 + e_post ≤ 0 ∧ 1 + e_0 − e_post ≤ 0 ∧ copied_0 − copied_post ≤ 0 ∧ − copied_0 + copied_post ≤ 0 ∧ e_0 − e_post ≤ 0 ∧ − e_0 + e_post ≤ 0 ∧ n_0 − n_post ≤ 0 ∧ − n_0 + n_post ≤ 0 ∧ olde_0 − olde_post ≤ 0 ∧ − olde_0 + olde_post ≤ 0 ∧ oldn_0 − oldn_post ≤ 0 ∧ − oldn_0 + oldn_post ≤ 0 2 2 0: − oldn_post + oldn_post ≤ 0 ∧ oldn_post − oldn_post ≤ 0 ∧ − oldn_0 + oldn_0 ≤ 0 ∧ oldn_0 − oldn_0 ≤ 0 ∧ − olde_post + olde_post ≤ 0 ∧ olde_post − olde_post ≤ 0 ∧ − olde_0 + olde_0 ≤ 0 ∧ olde_0 − olde_0 ≤ 0 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − e_post + e_post ≤ 0 ∧ e_post − e_post ≤ 0 ∧ − e_0 + e_0 ≤ 0 ∧ e_0 − e_0 ≤ 0 ∧ − copied_post + copied_post ≤ 0 ∧ copied_post − copied_post ≤ 0 ∧ − copied_0 + copied_0 ≤ 0 ∧ copied_0 − copied_0 ≤ 0 0 3 3: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ copied_0 ≤ 0 ∧ −1 + copied_post ≤ 0 ∧ 1 − copied_post ≤ 0 ∧ − n_0 + oldn_post ≤ 0 ∧ n_0 − oldn_post ≤ 0 ∧ − e_0 + olde_post ≤ 0 ∧ e_0 − olde_post ≤ 0 ∧ 1 − e_0 ≤ 0 ∧ 101 − n_0 ≤ 0 ∧ 10 − n_0 + n_post ≤ 0 ∧ −10 + n_0 − n_post ≤ 0 ∧ 1 − e_0 + e_post ≤ 0 ∧ −1 + e_0 − e_post ≤ 0 ∧ copied_0 − copied_post ≤ 0 ∧ − copied_0 + copied_post ≤ 0 ∧ e_0 − e_post ≤ 0 ∧ − e_0 + e_post ≤ 0 ∧ n_0 − n_post ≤ 0 ∧ − n_0 + n_post ≤ 0 ∧ olde_0 − olde_post ≤ 0 ∧ − olde_0 + olde_post ≤ 0 ∧ oldn_0 − oldn_post ≤ 0 ∧ − oldn_0 + oldn_post ≤ 0 3 4 0: − oldn_post + oldn_post ≤ 0 ∧ oldn_post − oldn_post ≤ 0 ∧ − oldn_0 + oldn_0 ≤ 0 ∧ oldn_0 − oldn_0 ≤ 0 ∧ − olde_post + olde_post ≤ 0 ∧ olde_post − olde_post ≤ 0 ∧ − olde_0 + olde_0 ≤ 0 ∧ olde_0 − olde_0 ≤ 0 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − e_post + e_post ≤ 0 ∧ e_post − e_post ≤ 0 ∧ − e_0 + e_0 ≤ 0 ∧ e_0 − e_0 ≤ 0 ∧ − copied_post + copied_post ≤ 0 ∧ copied_post − copied_post ≤ 0 ∧ − copied_0 + copied_0 ≤ 0 ∧ copied_0 − copied_0 ≤ 0 0 5 4: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − e_0 ≤ 0 ∧ −100 + n_0 ≤ 0 ∧ −11 − n_0 + n_post ≤ 0 ∧ 11 + n_0 − n_post ≤ 0 ∧ −1 − e_0 + e_post ≤ 0 ∧ 1 + e_0 − e_post ≤ 0 ∧ e_0 − e_post ≤ 0 ∧ − e_0 + e_post ≤ 0 ∧ n_0 − n_post ≤ 0 ∧ − n_0 + n_post ≤ 0 ∧ − oldn_post + oldn_post ≤ 0 ∧ oldn_post − oldn_post ≤ 0 ∧ − oldn_0 + oldn_0 ≤ 0 ∧ oldn_0 − oldn_0 ≤ 0 ∧ − olde_post + olde_post ≤ 0 ∧ olde_post − olde_post ≤ 0 ∧ − olde_0 + olde_0 ≤ 0 ∧ olde_0 − olde_0 ≤ 0 ∧ − copied_post + copied_post ≤ 0 ∧ copied_post − copied_post ≤ 0 ∧ − copied_0 + copied_0 ≤ 0 ∧ copied_0 − copied_0 ≤ 0 4 6 0: − oldn_post + oldn_post ≤ 0 ∧ oldn_post − oldn_post ≤ 0 ∧ − oldn_0 + oldn_0 ≤ 0 ∧ oldn_0 − oldn_0 ≤ 0 ∧ − olde_post + olde_post ≤ 0 ∧ olde_post − olde_post ≤ 0 ∧ − olde_0 + olde_0 ≤ 0 ∧ olde_0 − olde_0 ≤ 0 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − e_post + e_post ≤ 0 ∧ e_post − e_post ≤ 0 ∧ − e_0 + e_0 ≤ 0 ∧ e_0 − e_0 ≤ 0 ∧ − copied_post + copied_post ≤ 0 ∧ copied_post − copied_post ≤ 0 ∧ − copied_0 + copied_0 ≤ 0 ∧ copied_0 − copied_0 ≤ 0 0 7 5: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − e_0 ≤ 0 ∧ 101 − n_0 ≤ 0 ∧ 10 − n_0 + n_post ≤ 0 ∧ −10 + n_0 − n_post ≤ 0 ∧ 1 − e_0 + e_post ≤ 0 ∧ −1 + e_0 − e_post ≤ 0 ∧ e_0 − e_post ≤ 0 ∧ − e_0 + e_post ≤ 0 ∧ n_0 − n_post ≤ 0 ∧ − n_0 + n_post ≤ 0 ∧ − oldn_post + oldn_post ≤ 0 ∧ oldn_post − oldn_post ≤ 0 ∧ − oldn_0 + oldn_0 ≤ 0 ∧ oldn_0 − oldn_0 ≤ 0 ∧ − olde_post + olde_post ≤ 0 ∧ olde_post − olde_post ≤ 0 ∧ − olde_0 + olde_0 ≤ 0 ∧ olde_0 − olde_0 ≤ 0 ∧ − copied_post + copied_post ≤ 0 ∧ copied_post − copied_post ≤ 0 ∧ − copied_0 + copied_0 ≤ 0 ∧ copied_0 − copied_0 ≤ 0 5 8 0: − oldn_post + oldn_post ≤ 0 ∧ oldn_post − oldn_post ≤ 0 ∧ − oldn_0 + oldn_0 ≤ 0 ∧ oldn_0 − oldn_0 ≤ 0 ∧ − olde_post + olde_post ≤ 0 ∧ olde_post − olde_post ≤ 0 ∧ − olde_0 + olde_0 ≤ 0 ∧ olde_0 − olde_0 ≤ 0 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − e_post + e_post ≤ 0 ∧ e_post − e_post ≤ 0 ∧ − e_0 + e_0 ≤ 0 ∧ e_0 − e_0 ≤ 0 ∧ − copied_post + copied_post ≤ 0 ∧ copied_post − copied_post ≤ 0 ∧ − copied_0 + copied_0 ≤ 0 ∧ copied_0 − copied_0 ≤ 0 6 9 0: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ −1 + e_post ≤ 0 ∧ 1 − e_post ≤ 0 ∧ copied_post ≤ 0 ∧ − copied_post ≤ 0 ∧ copied_0 − copied_post ≤ 0 ∧ − copied_0 + copied_post ≤ 0 ∧ e_0 − e_post ≤ 0 ∧ − e_0 + e_post ≤ 0 ∧ n_0 − n_post ≤ 0 ∧ − n_0 + n_post ≤ 0 ∧ − oldn_post + oldn_post ≤ 0 ∧ oldn_post − oldn_post ≤ 0 ∧ − oldn_0 + oldn_0 ≤ 0 ∧ oldn_0 − oldn_0 ≤ 0 ∧ − olde_post + olde_post ≤ 0 ∧ olde_post − olde_post ≤ 0 ∧ − olde_0 + olde_0 ≤ 0 ∧ olde_0 − olde_0 ≤ 0 7 10 6: − oldn_post + oldn_post ≤ 0 ∧ oldn_post − oldn_post ≤ 0 ∧ − oldn_0 + oldn_0 ≤ 0 ∧ oldn_0 − oldn_0 ≤ 0 ∧ − olde_post + olde_post ≤ 0 ∧ olde_post − olde_post ≤ 0 ∧ − olde_0 + olde_0 ≤ 0 ∧ olde_0 − olde_0 ≤ 0 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − e_post + e_post ≤ 0 ∧ e_post − e_post ≤ 0 ∧ − e_0 + e_0 ≤ 0 ∧ e_0 − e_0 ≤ 0 ∧ − copied_post + copied_post ≤ 0 ∧ copied_post − copied_post ≤ 0 ∧ − copied_0 + copied_0 ≤ 0 ∧ copied_0 − copied_0 ≤ 0

## Proof

The following invariants are asserted.

 0: − copied_post ≤ 0 ∧ − copied_0 ≤ 0 1: − copied_post ≤ 0 ∧ 1 − copied_0 ≤ 0 2: −1 + copied_post ≤ 0 ∧ 1 − copied_post ≤ 0 ∧ −1 + copied_0 ≤ 0 ∧ 1 − copied_0 ≤ 0 3: −1 + copied_post ≤ 0 ∧ 1 − copied_post ≤ 0 ∧ −1 + copied_0 ≤ 0 ∧ 1 − copied_0 ≤ 0 4: − copied_post ≤ 0 ∧ − copied_0 ≤ 0 5: − copied_post ≤ 0 ∧ − copied_0 ≤ 0 6: TRUE 7: TRUE

The invariants are proved as follows.

### IMPACT Invariant Proof

• nodes (location) invariant:  0 (0) − copied_post ≤ 0 ∧ − copied_0 ≤ 0 1 (1) − copied_post ≤ 0 ∧ 1 − copied_0 ≤ 0 2 (2) −1 + copied_post ≤ 0 ∧ 1 − copied_post ≤ 0 ∧ −1 + copied_0 ≤ 0 ∧ 1 − copied_0 ≤ 0 3 (3) −1 + copied_post ≤ 0 ∧ 1 − copied_post ≤ 0 ∧ −1 + copied_0 ≤ 0 ∧ 1 − copied_0 ≤ 0 4 (4) − copied_post ≤ 0 ∧ − copied_0 ≤ 0 5 (5) − copied_post ≤ 0 ∧ − copied_0 ≤ 0 6 (6) TRUE 7 (7) TRUE
• initial node: 7
• cover edges:
• transition edges:  0 0 1 0 1 2 0 3 3 0 5 4 0 7 5 2 2 0 3 4 0 4 6 0 5 8 0 6 9 0 7 10 6

### 2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 0 11 0: − oldn_post + oldn_post ≤ 0 ∧ oldn_post − oldn_post ≤ 0 ∧ − oldn_0 + oldn_0 ≤ 0 ∧ oldn_0 − oldn_0 ≤ 0 ∧ − olde_post + olde_post ≤ 0 ∧ olde_post − olde_post ≤ 0 ∧ − olde_0 + olde_0 ≤ 0 ∧ olde_0 − olde_0 ≤ 0 ∧ − n_post + n_post ≤ 0 ∧ n_post − n_post ≤ 0 ∧ − n_0 + n_0 ≤ 0 ∧ n_0 − n_0 ≤ 0 ∧ − e_post + e_post ≤ 0 ∧ e_post − e_post ≤ 0 ∧ − e_0 + e_0 ≤ 0 ∧ e_0 − e_0 ≤ 0 ∧ − copied_post + copied_post ≤ 0 ∧ copied_post − copied_post ≤ 0 ∧ − copied_0 + copied_0 ≤ 0 ∧ copied_0 − copied_0 ≤ 0
and for every transition t, a duplicate t is considered.

### 3 Transition Removal

We remove transitions 0, 9, 10 using the following ranking functions, which are bounded by −13.

 7: 0 6: 0 0: 0 2: 0 3: 0 4: 0 5: 0 1: 0 7: −5 6: −6 0: −7 2: −7 3: −7 4: −7 5: −7 0_var_snapshot: −7 0*: −7 1: −11
Hints:
 12 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 1 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] ] 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] ] 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] ] 4 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] ] 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, 0, 0, 0] ] 6 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 7 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] ] 8 lexWeak[ [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] ] 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, 0, 0, 0, 0] ] 10 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] ]

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

0* 14 0: oldn_post + oldn_post ≤ 0oldn_postoldn_post ≤ 0oldn_0 + oldn_0 ≤ 0oldn_0oldn_0 ≤ 0olde_post + olde_post ≤ 0olde_postolde_post ≤ 0olde_0 + olde_0 ≤ 0olde_0olde_0 ≤ 0n_post + n_post ≤ 0n_postn_post ≤ 0n_0 + n_0 ≤ 0n_0n_0 ≤ 0e_post + e_post ≤ 0e_poste_post ≤ 0e_0 + e_0 ≤ 0e_0e_0 ≤ 0copied_post + copied_post ≤ 0copied_postcopied_post ≤ 0copied_0 + copied_0 ≤ 0copied_0copied_0 ≤ 0

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

0 12 0_var_snapshot: oldn_post + oldn_post ≤ 0oldn_postoldn_post ≤ 0oldn_0 + oldn_0 ≤ 0oldn_0oldn_0 ≤ 0olde_post + olde_post ≤ 0olde_postolde_post ≤ 0olde_0 + olde_0 ≤ 0olde_0olde_0 ≤ 0n_post + n_post ≤ 0n_postn_post ≤ 0n_0 + n_0 ≤ 0n_0n_0 ≤ 0e_post + e_post ≤ 0e_poste_post ≤ 0e_0 + e_0 ≤ 0e_0e_0 ≤ 0copied_post + copied_post ≤ 0copied_postcopied_post ≤ 0copied_0 + copied_0 ≤ 0copied_0copied_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 { 0, 2, 3, 4, 5, 0_var_snapshot, 0* }.

### 6.1.1 Transition Removal

We remove transitions 1, 5 using the following ranking functions, which are bounded by −719.

 0: −1 + 84⋅e_0 − 8⋅n_0 2: copied_post + 84⋅e_0 − 8⋅n_0 3: 1 + 84⋅e_0 − 8⋅n_0 4: 1 + 84⋅e_0 − 8⋅n_0 5: 1 + 84⋅e_0 − 8⋅n_0 0_var_snapshot: −2 + 84⋅e_0 − 8⋅n_0 0*: 84⋅e_0 − 8⋅n_0
Hints:
 12 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 84, 0, 0, 0, 0, 0] ] 14 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 84, 0, 0, 0, 0, 0] ] 1 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 8, 84, 0, 0, 0, 84, 0, 0, 8, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 84, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 2 lexWeak[ [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 84, 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, 8, 84, 0, 0, 0, 84, 0, 0, 8, 0, 0, 0, 0] ] 4 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 84, 0, 0, 0, 0, 0] ] 5 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 84, 0, 84, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 84, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 6 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 84, 0, 0, 0, 0, 0] ] 7 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 84, 0, 84, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 8 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 84, 0, 0, 0, 0, 0] ]

### 6.1.2 Transition Removal

We remove transition 7 using the following ranking functions, which are bounded by 19.

 0: 30⋅e_0 2: 1 + 30⋅e_0 3: copied_post + 30⋅e_0 4: 1 + 30⋅e_0 5: 10 + 30⋅e_0 0_var_snapshot: −10 + 30⋅e_0 0*: 30⋅e_0
Hints:
 12 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0] ] 14 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 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, 30, 0, 0, 0, 0, 0] ] 3 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0] ] 4 lexWeak[ [0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0] ] 6 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0] ] 7 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 8 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 30, 0, 0, 0, 0, 0] ]

### 6.1.3 Transition Removal

We remove transitions 2, 3, 4, 8 using the following ranking functions, which are bounded by −4.

 0: −1 − 4⋅copied_0 2: 1 − 4⋅copied_0 3: −3⋅copied_0 4: 1 − 4⋅copied_0 5: 1 0_var_snapshot: −2 − 4⋅copied_0 0*: −4⋅copied_0
Hints:
 12 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4] ] 14 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4] ] 2 lexStrict[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4] , [0, 0, 4, 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, 4, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0, 0, 0, 0, 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] ] 4 lexStrict[ [0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4] , [0, 0, 3, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0] ] 6 lexWeak[ [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 4] ] 8 lexStrict[ [0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 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] ]

### 6.1.4 Transition Removal

We remove transitions 12, 6 using the following ranking functions, which are bounded by −1.

 0: 0 2: 0 3: 0 4: 2 5: 0 0_var_snapshot: −1 0*: 1
Hints:
 12 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] ] 14 lexWeak[ [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] ]

### 6.1.5 Transition Removal

We remove transition 14 using the following ranking functions, which are bounded by 0.

 0: 0 2: 0 3: 0 4: 0 5: 0 0_var_snapshot: 0 0*: 1
Hints:
 14 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] ]

### 6.1.6 Splitting Cut-Point Transitions

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

### 6.1.6.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 11.

### 6.1.6.1.1 Splitting Cut-Point Transitions

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

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