LTS Termination Proof

by T2Cert

Input

• Initial Location: 2
• Transitions: (pre-variables and post-variables)

  0	0	1:		0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg1P ≤ 0 ∧ arg1P ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0
  1	1	1:		0 ≤ 0 ∧ 0 ≤ 0 ∧ −10 + arg1 ≤ 0 ∧ −19 + arg1 ≤ 0 ∧ 2 − arg1P + arg1 ≤ 0 ∧ −2 + arg1P − arg1 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0
  1	2	1:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 11 − arg1 ≤ 0 ∧ −19 + arg1 ≤ 0 ∧ 2 − arg1P + arg1 ≤ 0 ∧ −2 + arg1P − arg1 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0
  2	3	0:		0 ≤ 0 ∧ 0 ≤ 0 ∧ − arg1P + arg1 ≤ 0 ∧ arg1P − arg1 ≤ 0

Proof

1 Switch to Cooperation Termination Proof

2 Transition Removal

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

3 Location Addition

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

1* 7 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 5 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 transitions 1, 2 using the following ranking functions, which are bounded by −20.

5.1.2 Transition Removal

We remove transitions 5, 7 using the following ranking functions, which are bounded by −1.

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

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

T2Cert

• version: 1.0