LTS Termination Proof

Input

Integer Transition System

Transitions: (pre-variables and post-variables)

f1_0_main_Load	1	f152_0_gcd_EQ:	x1 = _arg1 ∧ x2 = _arg2 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ 0 ≤ _arg1 − 1 ∧ −1 ≤ _arg1P − 1 ∧ −1 ≤ _arg2 − 1 ∧ −1 ≤ _arg2P − 1
f152_0_gcd_EQ	2	f198_0_mod_LE:	x1 = _x ∧ x2 = _x1 ∧ x1 = _x2 ∧ x2 = _x3 ∧ _x1 = _x3 ∧ _x = _x2 ∧ 0 ≤ _x1 − 1 ∧ −1 ≤ _x − 1 ∧ _x ≤ _x1 − 1
f152_0_gcd_EQ	3	f198_0_mod_LE:	x1 = _x4 ∧ x2 = _x5 ∧ x1 = _x6 ∧ x2 = _x7 ∧ _x5 = _x7 ∧ _x4 = _x6 ∧ 0 ≤ _x5 − 1 ∧ −1 ≤ _x4 − 1 ∧ _x5 ≤ _x4 − 1
f198_0_mod_LE	4	f198_0_mod_LE:	x1 = _x8 ∧ x2 = _x9 ∧ x1 = _x10 ∧ x2 = _x11 ∧ _x9 = _x11 ∧ _x8 − _x9 = _x10 ∧ 0 ≤ _x9 − 1 ∧ 0 ≤ _x8 − 1 ∧ _x9 ≤ _x8 − 1
f152_0_gcd_EQ	5	f152_0_gcd_EQ:	x1 = _x12 ∧ x2 = _x13 ∧ x1 = _x14 ∧ x2 = _x15 ∧ 0 = _x15 ∧ _x12 = _x14 ∧ _x12 = _x13 ∧ 0 ≤ _x12 − 1
f198_0_mod_LE	6	f152_0_gcd_EQ:	x1 = _x16 ∧ x2 = _x17 ∧ x1 = _x18 ∧ x2 = _x19 ∧ _x16 = _x19 ∧ _x17 = _x18 ∧ _x16 ≤ _x17 − 1
__init	7	f1_0_main_Load:	x1 = _x20 ∧ x2 = _x21 ∧ x1 = _x22 ∧ x2 = _x23 ∧ 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 { f152_0_gcd_EQ, f198_0_mod_LE }.

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

f152_0_gcd_EQ:	−2 + x1 + x2
f198_0_mod_LE:	−2 + x1 + x2

We remove transitions 2, 6 using the following ranking functions, which are bounded by 0.

f152_0_gcd_EQ:	− x1 + x2
f198_0_mod_LE:	−1 − x1 + x2

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

f152_0_gcd_EQ:	0
f198_0_mod_LE:	−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 % (6 real / 0 unknown / 0 assumptions / 6 total proof steps)