# LTS Termination Proof

by T2Cert

## Input

Integer Transition System
• Initial Location: 3
• Transitions: (pre-variables and post-variables)  0 0 1: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg3P ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg2P ≤ 0 ∧ 1 − arg1 ≤ 0 ∧ − arg1P ≤ 0 ∧ arg1P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 1 1 2: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg2 + arg3 ≤ 0 ∧ 1 − arg3 ≤ 0 ∧ − arg1P + arg3 ≤ 0 ∧ arg1P − arg3 ≤ 0 ∧ arg1 − arg2P ≤ 0 ∧ − arg1 + arg2P ≤ 0 ∧ arg2 − arg3P ≤ 0 ∧ − arg2 + arg3P ≤ 0 ∧ arg3 − arg4P ≤ 0 ∧ − arg3 + arg4P ≤ 0 ∧ arg3 − arg5P ≤ 0 ∧ − arg3 + arg5P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 2 2 2: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + arg4 ≤ 0 ∧ arg4 ≤ 0 ∧ arg4 − arg5 ≤ 0 ∧ − arg4 + arg5 ≤ 0 ∧ 1 − arg3P + arg3 ≤ 0 ∧ −1 + arg3P − arg3 ≤ 0 ∧ 1 − arg4P + arg4 ≤ 0 ∧ −1 + arg4P − arg4 ≤ 0 ∧ 1 + arg4 − arg5P ≤ 0 ∧ −1 − arg4 + arg5P ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0 2 3 2: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ arg4 ≤ 0 ∧ arg4 − arg5 ≤ 0 ∧ − arg4 + arg5 ≤ 0 ∧ 1 − arg3P + arg3 ≤ 0 ∧ −1 + arg3P − arg3 ≤ 0 ∧ 1 − arg4P + arg4 ≤ 0 ∧ −1 + arg4P − arg4 ≤ 0 ∧ 1 + arg4 − arg5P ≤ 0 ∧ −1 − arg4 + arg5P ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0 2 4 2: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 − arg4 ≤ 0 ∧ arg4 − arg5 ≤ 0 ∧ − arg4 + arg5 ≤ 0 ∧ −1 − arg3P + arg3 ≤ 0 ∧ 1 + arg3P − arg3 ≤ 0 ∧ −1 − arg4P + arg4 ≤ 0 ∧ 1 + arg4P − arg4 ≤ 0 ∧ −1 + arg4 − arg5P ≤ 0 ∧ 1 − arg4 + arg5P ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0 2 5 1: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg2 ≤ 0 ∧ − arg4 ≤ 0 ∧ arg4 ≤ 0 ∧ − arg5 ≤ 0 ∧ arg5 ≤ 0 ∧ 1 − arg1P + arg2 ≤ 0 ∧ −1 + arg1P − arg2 ≤ 0 ∧ − arg2P + arg3 ≤ 0 ∧ arg2P − arg3 ≤ 0 ∧ arg1 − arg3P ≤ 0 ∧ − arg1 + arg3P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0 3 6 0: 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0 ∧ − arg2P + arg2 ≤ 0 ∧ arg2P − arg2 ≤ 0 ∧ − arg3P + arg3 ≤ 0 ∧ arg3P − arg3 ≤ 0 ∧ − arg4P + arg4 ≤ 0 ∧ arg4P − arg4 ≤ 0 ∧ − arg5P + arg5 ≤ 0 ∧ arg5P − arg5 ≤ 0

## Proof

### 1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 1 7 1: − arg5P + arg5P ≤ 0 ∧ arg5P − arg5P ≤ 0 ∧ − arg5 + arg5 ≤ 0 ∧ arg5 − arg5 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0 2 14 2: − arg5P + arg5P ≤ 0 ∧ arg5P − arg5P ≤ 0 ∧ − arg5 + arg5 ≤ 0 ∧ arg5 − arg5 ≤ 0 ∧ − arg4P + arg4P ≤ 0 ∧ arg4P − arg4P ≤ 0 ∧ − arg4 + arg4 ≤ 0 ∧ arg4 − arg4 ≤ 0 ∧ − arg3P + arg3P ≤ 0 ∧ arg3P − arg3P ≤ 0 ∧ − arg3 + arg3 ≤ 0 ∧ arg3 − arg3 ≤ 0 ∧ − arg2P + arg2P ≤ 0 ∧ arg2P − arg2P ≤ 0 ∧ − arg2 + arg2 ≤ 0 ∧ arg2 − arg2 ≤ 0 ∧ − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0
and for every transition t, a duplicate t is considered.

### 2 Transition Removal

We remove transitions 0, 6 using the following ranking functions, which are bounded by −13.

 3: 0 0: 0 1: 0 2: 0 3: −4 0: −5 1: −6 2: −6 1_var_snapshot: −6 1*: −6 2_var_snapshot: −6 2*: −6

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

1* 10 1: arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

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

1 8 1_var_snapshot: arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

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

2* 17 2: arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

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

2 15 2_var_snapshot: arg5P + arg5P ≤ 0arg5Parg5P ≤ 0arg5 + arg5 ≤ 0arg5arg5 ≤ 0arg4P + arg4P ≤ 0arg4Parg4P ≤ 0arg4 + arg4 ≤ 0arg4arg4 ≤ 0arg3P + arg3P ≤ 0arg3Parg3P ≤ 0arg3 + arg3 ≤ 0arg3arg3 ≤ 0arg2P + arg2P ≤ 0arg2Parg2P ≤ 0arg2 + arg2 ≤ 0arg2arg2 ≤ 0arg1P + arg1P ≤ 0arg1Parg1P ≤ 0arg1 + arg1 ≤ 0arg1arg1 ≤ 0

### 7 SCC Decomposition

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

### 7.1 SCC Subproblem 1/1

Here we consider the SCC { 1, 2, 1_var_snapshot, 1*, 2_var_snapshot, 2* }.

### 7.1.1 Transition Removal

We remove transition 1 using the following ranking functions, which are bounded by 0.

 1: −2 + 4⋅arg2 2: 4⋅arg3 − arg4 − 3⋅arg5 1_var_snapshot: −3 + 4⋅arg2 1*: −1 + 4⋅arg2 2_var_snapshot: 4⋅arg3 − arg4 − 3⋅arg5 2*: 4⋅arg3 − arg4 − 3⋅arg5

### 7.1.2 Transition Removal

We remove transitions 8, 10, 3, 5 using the following ranking functions, which are bounded by −3.

 1: −2 2: 0 1_var_snapshot: −3 1*: −1 2_var_snapshot: 0 2*: 0

### 7.1.3 Splitting Cut-Point Transitions

We consider 2 subproblems corresponding to sets of cut-point transitions as follows.

### 7.1.3.1 Cut-Point Subproblem 1/2

Here we consider cut-point transition 7.

### 7.1.3.1.1 Splitting Cut-Point Transitions

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

### 7.1.3.2 Cut-Point Subproblem 2/2

Here we consider cut-point transition 14.

The new variable __snapshot_2_arg5P is introduced. The transition formulas are extended as follows:

 8: __snapshot_2_arg5P ≤ __snapshot_2_arg5P ∧ __snapshot_2_arg5P ≤ __snapshot_2_arg5P 15: __snapshot_2_arg5P ≤ arg5P ∧ arg5P ≤ __snapshot_2_arg5P 17: __snapshot_2_arg5P ≤ __snapshot_2_arg5P ∧ __snapshot_2_arg5P ≤ __snapshot_2_arg5P 2: __snapshot_2_arg5P ≤ __snapshot_2_arg5P ∧ __snapshot_2_arg5P ≤ __snapshot_2_arg5P 4: __snapshot_2_arg5P ≤ __snapshot_2_arg5P ∧ __snapshot_2_arg5P ≤ __snapshot_2_arg5P

The new variable __snapshot_2_arg5 is introduced. The transition formulas are extended as follows:

 8: __snapshot_2_arg5 ≤ __snapshot_2_arg5 ∧ __snapshot_2_arg5 ≤ __snapshot_2_arg5 15: __snapshot_2_arg5 ≤ arg5 ∧ arg5 ≤ __snapshot_2_arg5 17: __snapshot_2_arg5 ≤ __snapshot_2_arg5 ∧ __snapshot_2_arg5 ≤ __snapshot_2_arg5 2: __snapshot_2_arg5 ≤ __snapshot_2_arg5 ∧ __snapshot_2_arg5 ≤ __snapshot_2_arg5 4: __snapshot_2_arg5 ≤ __snapshot_2_arg5 ∧ __snapshot_2_arg5 ≤ __snapshot_2_arg5

The new variable __snapshot_2_arg4P is introduced. The transition formulas are extended as follows:

 8: __snapshot_2_arg4P ≤ __snapshot_2_arg4P ∧ __snapshot_2_arg4P ≤ __snapshot_2_arg4P 15: __snapshot_2_arg4P ≤ arg4P ∧ arg4P ≤ __snapshot_2_arg4P 17: __snapshot_2_arg4P ≤ __snapshot_2_arg4P ∧ __snapshot_2_arg4P ≤ __snapshot_2_arg4P 2: __snapshot_2_arg4P ≤ __snapshot_2_arg4P ∧ __snapshot_2_arg4P ≤ __snapshot_2_arg4P 4: __snapshot_2_arg4P ≤ __snapshot_2_arg4P ∧ __snapshot_2_arg4P ≤ __snapshot_2_arg4P

The new variable __snapshot_2_arg4 is introduced. The transition formulas are extended as follows:

 8: __snapshot_2_arg4 ≤ __snapshot_2_arg4 ∧ __snapshot_2_arg4 ≤ __snapshot_2_arg4 15: __snapshot_2_arg4 ≤ arg4 ∧ arg4 ≤ __snapshot_2_arg4 17: __snapshot_2_arg4 ≤ __snapshot_2_arg4 ∧ __snapshot_2_arg4 ≤ __snapshot_2_arg4 2: __snapshot_2_arg4 ≤ __snapshot_2_arg4 ∧ __snapshot_2_arg4 ≤ __snapshot_2_arg4 4: __snapshot_2_arg4 ≤ __snapshot_2_arg4 ∧ __snapshot_2_arg4 ≤ __snapshot_2_arg4

The new variable __snapshot_2_arg3P is introduced. The transition formulas are extended as follows:

 8: __snapshot_2_arg3P ≤ __snapshot_2_arg3P ∧ __snapshot_2_arg3P ≤ __snapshot_2_arg3P 15: __snapshot_2_arg3P ≤ arg3P ∧ arg3P ≤ __snapshot_2_arg3P 17: __snapshot_2_arg3P ≤ __snapshot_2_arg3P ∧ __snapshot_2_arg3P ≤ __snapshot_2_arg3P 2: __snapshot_2_arg3P ≤ __snapshot_2_arg3P ∧ __snapshot_2_arg3P ≤ __snapshot_2_arg3P 4: __snapshot_2_arg3P ≤ __snapshot_2_arg3P ∧ __snapshot_2_arg3P ≤ __snapshot_2_arg3P

The new variable __snapshot_2_arg3 is introduced. The transition formulas are extended as follows:

 8: __snapshot_2_arg3 ≤ __snapshot_2_arg3 ∧ __snapshot_2_arg3 ≤ __snapshot_2_arg3 15: __snapshot_2_arg3 ≤ arg3 ∧ arg3 ≤ __snapshot_2_arg3 17: __snapshot_2_arg3 ≤ __snapshot_2_arg3 ∧ __snapshot_2_arg3 ≤ __snapshot_2_arg3 2: __snapshot_2_arg3 ≤ __snapshot_2_arg3 ∧ __snapshot_2_arg3 ≤ __snapshot_2_arg3 4: __snapshot_2_arg3 ≤ __snapshot_2_arg3 ∧ __snapshot_2_arg3 ≤ __snapshot_2_arg3

The new variable __snapshot_2_arg2P is introduced. The transition formulas are extended as follows:

 8: __snapshot_2_arg2P ≤ __snapshot_2_arg2P ∧ __snapshot_2_arg2P ≤ __snapshot_2_arg2P 15: __snapshot_2_arg2P ≤ arg2P ∧ arg2P ≤ __snapshot_2_arg2P 17: __snapshot_2_arg2P ≤ __snapshot_2_arg2P ∧ __snapshot_2_arg2P ≤ __snapshot_2_arg2P 2: __snapshot_2_arg2P ≤ __snapshot_2_arg2P ∧ __snapshot_2_arg2P ≤ __snapshot_2_arg2P 4: __snapshot_2_arg2P ≤ __snapshot_2_arg2P ∧ __snapshot_2_arg2P ≤ __snapshot_2_arg2P

The new variable __snapshot_2_arg2 is introduced. The transition formulas are extended as follows:

 8: __snapshot_2_arg2 ≤ __snapshot_2_arg2 ∧ __snapshot_2_arg2 ≤ __snapshot_2_arg2 15: __snapshot_2_arg2 ≤ arg2 ∧ arg2 ≤ __snapshot_2_arg2 17: __snapshot_2_arg2 ≤ __snapshot_2_arg2 ∧ __snapshot_2_arg2 ≤ __snapshot_2_arg2 2: __snapshot_2_arg2 ≤ __snapshot_2_arg2 ∧ __snapshot_2_arg2 ≤ __snapshot_2_arg2 4: __snapshot_2_arg2 ≤ __snapshot_2_arg2 ∧ __snapshot_2_arg2 ≤ __snapshot_2_arg2

The new variable __snapshot_2_arg1P is introduced. The transition formulas are extended as follows:

 8: __snapshot_2_arg1P ≤ __snapshot_2_arg1P ∧ __snapshot_2_arg1P ≤ __snapshot_2_arg1P 15: __snapshot_2_arg1P ≤ arg1P ∧ arg1P ≤ __snapshot_2_arg1P 17: __snapshot_2_arg1P ≤ __snapshot_2_arg1P ∧ __snapshot_2_arg1P ≤ __snapshot_2_arg1P 2: __snapshot_2_arg1P ≤ __snapshot_2_arg1P ∧ __snapshot_2_arg1P ≤ __snapshot_2_arg1P 4: __snapshot_2_arg1P ≤ __snapshot_2_arg1P ∧ __snapshot_2_arg1P ≤ __snapshot_2_arg1P

The new variable __snapshot_2_arg1 is introduced. The transition formulas are extended as follows:

 8: __snapshot_2_arg1 ≤ __snapshot_2_arg1 ∧ __snapshot_2_arg1 ≤ __snapshot_2_arg1 15: __snapshot_2_arg1 ≤ arg1 ∧ arg1 ≤ __snapshot_2_arg1 17: __snapshot_2_arg1 ≤ __snapshot_2_arg1 ∧ __snapshot_2_arg1 ≤ __snapshot_2_arg1 2: __snapshot_2_arg1 ≤ __snapshot_2_arg1 ∧ __snapshot_2_arg1 ≤ __snapshot_2_arg1 4: __snapshot_2_arg1 ≤ __snapshot_2_arg1 ∧ __snapshot_2_arg1 ≤ __snapshot_2_arg1

The following invariants are asserted.

 0: TRUE 1: TRUE 2: 1 − arg4 ≤ 0 ∨ 1 ≤ 0 ∨ − arg5 ≤ 0 3: TRUE 1: FALSE 2: 1 − arg4 ≤ 0 ∨ 1 − __snapshot_2_arg4 + arg4 ≤ 0 ∧ 1 − __snapshot_2_arg4 ≤ 0 ∧ − arg5 ≤ 0 ∨ − arg5 ≤ 0 1_var_snapshot: 1 ≤ 0 1*: 1 ≤ 0 2_var_snapshot: − __snapshot_2_arg4 + arg4 ≤ 0 ∧ 1 − __snapshot_2_arg4 ≤ 0 ∧ 1 − arg4 ≤ 0 ∨ − __snapshot_2_arg4 + arg4 ≤ 0 ∧ − arg5 ≤ 0 2*: 1 ≤ 0 ∨ 1 − __snapshot_2_arg4 + arg4 ≤ 0 ∧ 1 − __snapshot_2_arg4 ≤ 0 ∧ − arg5 ≤ 0

The invariants are proved as follows.

### IMPACT Invariant Proof

• nodes (location) invariant:  0 (3) TRUE 1 (0) TRUE 2 (1) TRUE 3 (2) 1 − arg4 ≤ 0 8 (2) 1 ≤ 0 9 (2) 1 ≤ 0 10 (2) − arg5 ≤ 0 11 (1) TRUE 12 (2) 1 − arg4 ≤ 0 13 (2_var_snapshot) − __snapshot_2_arg4 + arg4 ≤ 0 ∧ 1 − __snapshot_2_arg4 ≤ 0 ∧ 1 − arg4 ≤ 0 18 (2*) 1 ≤ 0 19 (2*) 1 − __snapshot_2_arg4 + arg4 ≤ 0 ∧ 1 − __snapshot_2_arg4 ≤ 0 ∧ − arg5 ≤ 0 20 (2) 1 − __snapshot_2_arg4 + arg4 ≤ 0 ∧ 1 − __snapshot_2_arg4 ≤ 0 ∧ − arg5 ≤ 0 21 (2_var_snapshot) − __snapshot_2_arg4 + arg4 ≤ 0 ∧ − arg5 ≤ 0 22 (2_var_snapshot) − __snapshot_2_arg4 + arg4 ≤ 0 ∧ − arg5 ≤ 0 30 (2) 1 ≤ 0 31 (2) 1 ≤ 0 32 (2) − arg5 ≤ 0 33 (1) TRUE 34 (2) − arg5 ≤ 0 35 (2_var_snapshot) − __snapshot_2_arg4 + arg4 ≤ 0 ∧ − arg5 ≤ 0 38 (2*) 1 ≤ 0 39 (2*) 1 − __snapshot_2_arg4 + arg4 ≤ 0 ∧ 1 − __snapshot_2_arg4 ≤ 0 ∧ − arg5 ≤ 0
• initial node: 0
• cover edges:  11 → 2 21 → 22 32 → 10 33 → 2 35 → 22 39 → 19
• transition edges:  0 6 1 1 0 2 2 1 3 3 2 8 3 3 9 3 4 10 3 5 11 3 14 12 10 2 30 10 3 31 10 4 32 10 5 33 10 14 34 12 15 13 13 2 18 13 4 19 19 17 20 20 15 21 20 15 22 22 2 38 22 4 39 34 15 35

### 7.1.3.2.12 Transition Removal

We remove transition 17 using the following ranking functions, which are bounded by −1.

 1: __snapshot_2_arg4 2: arg4 1_var_snapshot: __snapshot_2_arg4 1*: __snapshot_2_arg4 2_var_snapshot: __snapshot_2_arg4 2*: __snapshot_2_arg4

### 7.1.3.2.13 Transition Removal

We remove transition 15 using the following ranking functions, which are bounded by −8.

 1: −1 2: −2 1_var_snapshot: −3 1*: −4 2_var_snapshot: −5 2*: −6

### 7.1.3.2.14 Splitting Cut-Point Transitions

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

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