LTS Termination Proof

Input

Integer Transition System

Initial Location: f152_0_createList_LE, f196_0_reverse_NULL, f1_0_main_Load, __init

Transitions: (pre-variables and post-variables)

f1_0_main_Load	1	f152_0_createList_LE:	x1 = _arg1 ∧ x2 = _arg2 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ 0 ≤ _arg2 − 1 ∧ −1 ≤ _x3 − 1 ∧ _arg1P + 1 ≤ _arg1 ∧ 0 ≤ _arg1 − 1 ∧ −1 ≤ _arg1P − 1 ∧ _x3 − 1 = _arg2P
f152_0_createList_LE	2	f196_0_reverse_NULL:	x1 = _x ∧ x2 = _x1 ∧ x1 = _x2 ∧ x2 = _x4 ∧ −1 ≤ _x2 − 1 ∧ −1 ≤ _x − 1 ∧ _x1 ≤ 0 ∧ _x2 ≤ _x
f152_0_createList_LE	3	f152_0_createList_LE:	x1 = _x5 ∧ x2 = _x6 ∧ x1 = _x7 ∧ x2 = _x8 ∧ _x6 − 1 = _x8 ∧ 0 ≤ _x7 − 1 ∧ −1 ≤ _x5 − 1 ∧ 0 ≤ _x6 − 1 ∧ _x7 − 2 ≤ _x5
f196_0_reverse_NULL	4	f196_0_reverse_NULL:	x1 = _x9 ∧ x2 = _x10 ∧ x1 = _x11 ∧ x2 = _x12 ∧ −1 ≤ _x11 − 1 ∧ 0 ≤ _x9 − 1 ∧ _x11 + 1 ≤ _x9
__init	5	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 2 SCC(s) of the program graph.

Here we consider the SCC { f152_0_createList_LE }.

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

f152_0_createList_LE:

There are no more "sharp" transitions in the cooperation program. Hence the cooperation termination is proved.

Here we consider the SCC { f196_0_reverse_NULL }.

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

f196_0_reverse_NULL:

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 % (7 real / 0 unknown / 0 assumptions / 7 total proof steps)