LTS Termination Proof

Input

Integer Transition System

Transitions: (pre-variables and post-variables)

f1_0_main_Load	1	f1_0_main_Load':	x1 = _arg1 ∧ x2 = _arg2 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ −1 ≤ _x2 − 1 ∧ 0 ≤ _arg2 − 1 ∧ 0 ≤ _arg1 − 1 ∧ _arg1 = _arg1P ∧ _arg2 = _arg2P
f1_0_main_Load'	2	f134_0_test_GT:	x1 = _x ∧ x2 = _x1 ∧ x1 = _x3 ∧ x2 = _x4 ∧ −1 ≤ _x5 − 1 ∧ 0 ≤ _x1 − 1 ∧ 0 ≤ _x − 1 ∧ _x5 − 100⋅_x6 ≤ 99 ∧ 0 ≤ _x5 − 100⋅_x6 ∧ _x5 − 100⋅_x6 = _x3 ∧ _x1 = _x4
f134_0_test_GT	3	f134_0_test_GT:	x1 = _x9 ∧ x2 = _x10 ∧ x1 = _x11 ∧ x2 = _x12 ∧ _x10 = _x12 ∧ _x9 − 1 = _x11 ∧ 0 ≤ _x9 − 1 ∧ _x9 − 1 ≤ _x9 − 1 ∧ 0 ≤ _x10 − 1
__init	4	f1_0_main_Load:	x1 = _x13 ∧ x2 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ 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 { f134_0_test_GT }.

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

f134_0_test_GT:

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 % (4 real / 0 unknown / 0 assumptions / 4 total proof steps)