LTS Termination Proof

Input

Integer Transition System

Transitions: (pre-variables and post-variables)

f1_0_main_Load	1	f291_0_solve_GE:	x1 = _arg1 ∧ x2 = _arg2 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ 0 = _arg2P ∧ 0 = _arg1P ∧ 0 = _arg2 ∧ 0 ≤ _arg1 − 1
f1_0_main_Load	2	f291_0_solve_GE:	x1 = _x ∧ x2 = _x1 ∧ x1 = _x2 ∧ x2 = _x3 ∧ 1 = _x3 ∧ 0 ≤ _x − 1 ∧ 0 ≤ _x1 − 1 ∧ −1 ≤ _x2 − 1
f291_0_solve_GE	3	f291_0_solve_GE:	x1 = _x4 ∧ x2 = _x5 ∧ x1 = _x6 ∧ x2 = _x7 ∧ _x5 = _x7 ∧ _x4 − 1 = _x6 ∧ 1 ≤ _x4 − 1 ∧ _x5 ≤ 1 ∧ _x4 − 1 ≤ _x4 − 1
f291_0_solve_GE	4	f291_0_solve_GE:	x1 = _x8 ∧ x2 = _x9 ∧ x1 = _x10 ∧ x2 = _x11 ∧ _x9 = _x11 ∧ _x8 − 1 = _x10 ∧ 1 ≤ _x8 − 1 ∧ _x8 − 1 ≤ _x8 − 1 ∧ _x9 ≤ 1
__init	5	f1_0_main_Load:	x1 = _x12 ∧ x2 = _x13 ∧ x1 = _x14 ∧ x2 = _x15 ∧ 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 { f291_0_solve_GE }.

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

f291_0_solve_GE:

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)