LTS Termination Proof

Input

Integer Transition System

Initial Location: l4, l0, l2

Transitions: (pre-variables and post-variables)

l0	1	l1:		x1 = ___patmp1HAT0 ∧ x2 = ___patmp2HAT0 ∧ x3 = _k_208HAT0 ∧ x4 = _k_243HAT0 ∧ x5 = _len_263HAT0 ∧ x1 = ___patmp1HATpost ∧ x2 = ___patmp2HATpost ∧ x3 = _k_208HATpost ∧ x4 = _k_243HATpost ∧ x5 = _len_263HATpost ∧ _k_208HAT0 = _k_208HATpost ∧ 0 ≤ −1 + _k_243HATpost ∧ _k_243HATpost = ___patmp2HATpost ∧ _len_263HATpost = ___patmp1HATpost ∧ ___patmp2HATpost = _k_208HAT0 ∧ ___patmp1HATpost = 1 ∧ 0 ≤ _k_208HAT0
l2	2	l3:		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
l4	3	l0:		x1 = _x10 ∧ x2 = _x11 ∧ x3 = _x12 ∧ x4 = _x13 ∧ x5 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ x4 = _x18 ∧ x5 = _x19 ∧ _x14 = _x19 ∧ _x13 = _x18 ∧ _x12 = _x17 ∧ _x11 = _x16 ∧ _x10 = _x15

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

l4	l4	l4:	x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5
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)