LTS Termination Proof

Input

Integer Transition System

Transitions: (pre-variables and post-variables)

f1_0_main_Load	1	f115_0_main_EQ:	x1 = _arg1 ∧ x2 = _arg2 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ 0 ≤ _arg1 − 1 ∧ −1 ≤ _arg2 − 1 ∧ 0 ≤ _arg1P − 1
f115_0_main_EQ	2	f115_0_main_EQ':	x1 = _x ∧ x2 = _x1 ∧ x1 = _x2 ∧ x2 = _x3 ∧ _x − 2⋅_x4 = 1 ∧ 0 ≤ _x − 1 ∧ _x = _x2
f115_0_main_EQ'	3	f115_0_main_EQ:	x1 = _x5 ∧ x2 = _x7 ∧ x1 = _x9 ∧ x2 = _x12 ∧ 0 ≤ _x5 − 1 ∧ _x5 − 2⋅_x13 = 1 ∧ _x5 − 2⋅_x13 ≤ 1 ∧ 0 ≤ _x5 − 2⋅_x13 ∧ _x5 − 1 = _x9
f115_0_main_EQ	4	f115_0_main_EQ':	x1 = _x15 ∧ x2 = _x16 ∧ x1 = _x17 ∧ x2 = _x18 ∧ _x15 − 2⋅_x19 = 0 ∧ _x20 ≤ _x15 − 1 ∧ 0 ≤ _x15 − 1 ∧ _x15 = _x17
f115_0_main_EQ'	5	f115_0_main_EQ:	x1 = _x21 ∧ x2 = _x22 ∧ x1 = _x23 ∧ x2 = _x24 ∧ _x21 − 2⋅_x25 = 0 ∧ 0 ≤ _x21 − 1 ∧ _x23 ≤ _x21 − 1 ∧ 0 ≤ _x21 − 2⋅_x25 ∧ _x21 − 2⋅_x25 ≤ 1 ∧ _x21 − 2⋅_x23 ≤ 1 ∧ 0 ≤ _x21 − 2⋅_x23
__init	6	f1_0_main_Load:	x1 = _x26 ∧ x2 = _x27 ∧ x1 = _x28 ∧ x2 = _x29 ∧ 0 ≤ 0

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 { f115_0_main_EQ, f115_0_main_EQ' }.

We remove transitions 2, 3, 4, 5 using the following ranking functions, which are bounded by 0.

f115_0_main_EQ:	1 + 2⋅x1
f115_0_main_EQ':	2⋅x1

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)