LTS Termination Proof

Input

Integer Transition System

Transitions: (pre-variables and post-variables)

l0	1	l1:	x1 = _cHAT0 ∧ x2 = _oxHAT0 ∧ x3 = _xHAT0 ∧ x1 = _cHATpost ∧ x2 = _oxHATpost ∧ x3 = _xHATpost ∧ _xHAT0 = _xHATpost ∧ _oxHAT0 = _oxHATpost ∧ _cHAT0 = _cHATpost ∧ 1 + _xHAT0 ≤ _oxHAT0
l0	2	l2:	x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ _x2 = _x5 ∧ _x1 = _x4 ∧ _x = _x3 ∧ _x1 ≤ _x2
l3	3	l1:	x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ _x8 = _x11 ∧ _x7 = _x10 ∧ _x6 = _x9 ∧ _x6 ≤ 0
l3	4	l1:	x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ _x14 = _x17 ∧ _x15 = 1 ∧ _x16 = _x14
l4	5	l3:	x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ x3 = _x23 ∧ _x20 = _x23 ∧ _x19 = _x22 ∧ _x18 = _x21 ∧ _x18 ≤ 0
l4	6	l0:	x1 = _x24 ∧ x2 = _x25 ∧ x3 = _x26 ∧ x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ _x26 = _x29 ∧ _x25 = _x28 ∧ _x24 = _x27 ∧ 1 ≤ _x24
l1	7	l4:	x1 = _x30 ∧ x2 = _x31 ∧ x3 = _x32 ∧ x1 = _x33 ∧ x2 = _x34 ∧ x3 = _x35 ∧ _x31 = _x34 ∧ _x30 = _x33 ∧ _x35 = −1 + _x32 ∧ 1 ≤ _x32
l5	8	l1:	x1 = _x36 ∧ x2 = _x37 ∧ x3 = _x38 ∧ x1 = _x39 ∧ x2 = _x40 ∧ x3 = _x41 ∧ _x38 = _x41 ∧ _x37 = _x40 ∧ _x36 = _x39 ∧ _x36 ≤ 0
l6	9	l5:	x1 = _x42 ∧ x2 = _x43 ∧ x3 = _x44 ∧ x1 = _x45 ∧ x2 = _x46 ∧ x3 = _x47 ∧ _x44 = _x47 ∧ _x43 = _x46 ∧ _x42 = _x45

We consider the following cutpoint-transitions:

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

We consider subproblems for each of the 1 SCC(s) of the program graph.

Here we consider the SCC { l4, l1, l3, l0 }.

We remove transition 7 using the following ranking functions, which are bounded by 0.

We remove transitions 1, 6, 4, 3, 5 using the following ranking functions, which are bounded by 0.

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 % (5 real / 0 unknown / 0 assumptions / 5 total proof steps)