LTS Termination Proof

by T2Cert

Input

Integer Transition System

Transitions: (pre-variables and post-variables)

0	0	1:		0 ≤ 0 ∧ 0 ≤ 0 ∧ x_promoted_1_post ≤ 0 ∧ − x_promoted_1_post ≤ 0 ∧ x_promoted_1_0 − x_promoted_1_post ≤ 0 ∧ − x_promoted_1_0 + x_promoted_1_post ≤ 0
2	1	0:		0 ≤ 0 ∧ 0 ≤ 0 ∧ − x_promoted_1_post + x_promoted_1_post ≤ 0 ∧ x_promoted_1_post − x_promoted_1_post ≤ 0 ∧ − x_promoted_1_0 + x_promoted_1_0 ≤ 0 ∧ x_promoted_1_0 − x_promoted_1_0 ≤ 0

The following invariants are asserted.

0:	TRUE
1:	x_promoted_1_0 ≤ 0 ∧ − x_promoted_1_0 ≤ 0 ∧ x_promoted_1_post ≤ 0 ∧ − x_promoted_1_post ≤ 0
2:	TRUE

The invariants are proved as follows.

nodes (location) invariant:

0	(0)	TRUE
1	(1)	x_promoted_1_0 ≤ 0 ∧ − x_promoted_1_0 ≤ 0 ∧ x_promoted_1_post ≤ 0 ∧ − x_promoted_1_post ≤ 0
2	(2)	TRUE

We consider the following cutpoint-transitions:

and for every transition t, a duplicate t is considered.

We remove transitions 0, 1 using the following ranking functions, which are bounded by −8.

Hints:

0	lexStrict[ [0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0] ]
1	lexStrict[ [0, 0, 0, 0, 0, 0] , [0, 0, 0, 0, 0, 0] ]

There exist no SCC in the program graph.

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