LTS Termination Proof

Input

Integer Transition System

Transitions: (pre-variables and post-variables)

l0	1	l1:	x1 = _iHAT0 ∧ x2 = _jHAT0 ∧ x1 = _iHATpost ∧ x2 = _jHATpost ∧ _iHAT0 = _iHATpost ∧ _jHATpost = 0 ∧ 2 ≤ _iHAT0
l0	2	l2:	x1 = _x ∧ x2 = _x1 ∧ x1 = _x2 ∧ x2 = _x3 ∧ _x1 = _x3 ∧ _x2 = 1 + _x ∧ 1 + _x ≤ 2
l2	3	l0:	x1 = _x4 ∧ x2 = _x5 ∧ x1 = _x6 ∧ x2 = _x7 ∧ _x5 = _x7 ∧ _x4 = _x6
l1	4	l3:	x1 = _x8 ∧ x2 = _x9 ∧ x1 = _x10 ∧ x2 = _x11 ∧ _x9 = _x11 ∧ _x8 = _x10
l4	5	l5:	x1 = _x12 ∧ x2 = _x13 ∧ x1 = _x14 ∧ x2 = _x15 ∧ _x13 = _x15 ∧ _x12 = _x14
l6	6	l4:	x1 = _x16 ∧ x2 = _x17 ∧ x1 = _x18 ∧ x2 = _x19 ∧ _x17 = _x19 ∧ _x16 = _x18
l3	7	l6:	x1 = _x20 ∧ x2 = _x21 ∧ x1 = _x22 ∧ x2 = _x23 ∧ _x21 = _x23 ∧ _x20 = _x22 ∧ 2 ≤ _x21
l3	8	l1:	x1 = _x24 ∧ x2 = _x25 ∧ x1 = _x26 ∧ x2 = _x27 ∧ _x24 = _x26 ∧ _x27 = 1 + _x25 ∧ 1 + _x25 ≤ 2
l7	9	l2:	x1 = _x28 ∧ x2 = _x29 ∧ x1 = _x30 ∧ x2 = _x31 ∧ _x29 = _x31 ∧ _x30 = 0
l8	10	l7:	x1 = _x32 ∧ x2 = _x33 ∧ x1 = _x34 ∧ x2 = _x35 ∧ _x33 = _x35 ∧ _x32 = _x34

We consider the following cutpoint-transitions:

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

We consider subproblems for each of the 2 SCC(s) of the program graph.

Here we consider the SCC { l0, l2 }.

We remove transition 2 using the following ranking functions, which are bounded by 0.

l0:	1 − x1
l2:	1 − x1

We remove transition 3 using the following ranking functions, which are bounded by 0.

l2:	0
l0:	−1

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

Here we consider the SCC { l1, l3 }.

We remove transition 8 using the following ranking functions, which are bounded by 0.

l1:	1 − x2
l3:	1 − x2

We remove transition 4 using the following ranking functions, which are bounded by 0.

l1:	0
l3:	−1

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

version: AProVE Commit ID: unknown
strategy: Statistics for single proof: 100.00 % (8 real / 0 unknown / 0 assumptions / 8 total proof steps)