LTS Termination Proof

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Input

Integer Transition System

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
1 3 1: − 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, 2 using the following ranking functions, which are bounded by −11.

2: 0
0: 0
1: 0
2: −4
0: −5
1: −6
1_var_snapshot: −6
1*: −6
Hints:
4 lexWeak[ [0, 0, 0, 0] ]
1 lexWeak[ [0, 0, 0, 0, 0, 0, 0] ]
0 lexStrict[ [0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0] ]
2 lexStrict[ [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.

1* 6 1: − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0

4 Location Addition

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

1 4 1_var_snapshot: − arg1P + arg1P ≤ 0 ∧ arg1P − arg1P ≤ 0 ∧ − arg1 + arg1 ≤ 0 ∧ arg1 − arg1 ≤ 0

5 SCC Decomposition

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

5.1 SCC Subproblem 1/1

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

5.1.1 Transition Removal

We remove transition 1 using the following ranking functions, which are bounded by 2.

1: 1 + 3⋅arg1
1_var_snapshot: 3⋅arg1
1*: 2 + 3⋅arg1
Hints:
4 lexWeak[ [0, 0, 3, 0] ]
6 lexWeak[ [0, 0, 3, 0] ]
1 lexStrict[ [0, 0, 0, 0, 3, 3, 0] , [0, 0, 3, 0, 0, 0, 0] ]

5.1.2 Transition Removal

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

1: 0
1_var_snapshot: −1
1*: 1
Hints:
4 lexStrict[ [0, 0, 0, 0] , [0, 0, 0, 0] ]
6 lexStrict[ [0, 0, 0, 0] , [0, 0, 0, 0] ]

5.1.3 Splitting Cut-Point Transitions

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

5.1.3.1 Cut-Point Subproblem 1/1

Here we consider cut-point transition 3.

5.1.3.1.1 Splitting Cut-Point Transitions

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

Tool configuration

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