LTS Termination Proof

Input

Integer Transition System

Initial Location: l0, l2

Transitions: (pre-variables and post-variables)

l0	1	l1:		x1 = _iHAT0 ∧ x2 = _tmp10HAT0 ∧ x3 = _tmp13HAT0 ∧ x4 = _tmp___011HAT0 ∧ x5 = _tmp___014HAT0 ∧ x1 = _iHATpost ∧ x2 = _tmp10HATpost ∧ x3 = _tmp13HATpost ∧ x4 = _tmp___011HATpost ∧ x5 = _tmp___014HATpost ∧ _iHAT1 = 0 ∧ _tmp10HATpost = _iHAT1 ∧ _iHAT2 = 1 + _iHAT1 ∧ _tmp___011HATpost = _iHAT2 ∧ _iHAT3 = 1 + _iHAT2 ∧ _tmp13HATpost = _iHAT3 ∧ _iHAT4 = 1 + _iHAT3 ∧ _tmp___014HATpost = _iHAT4 ∧ _iHATpost = 1 + _iHAT4
l2	2	l0:		x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x1 = _x5 ∧ x2 = _x6 ∧ x3 = _x7 ∧ x4 = _x8 ∧ x5 = _x9 ∧ _x4 = _x9 ∧ _x3 = _x8 ∧ _x2 = _x7 ∧ _x1 = _x6 ∧ _x = _x5

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

l0	l0	l0:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5
l2	l2	l2:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5

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

2 SCC Decomposition

There exist no SCC in the program graph.

Tool configuration

version: AProVE Commit ID: unknown
strategy: Statistics for single proof: 100.00 % (2 real / 0 unknown / 0 assumptions / 2 total proof steps)