LTS Termination Proof

Input

Integer Transition System

Initial Location: f48_0_rec_GE, f77_0_descend_LE, f1_0_main_Load, f33_0_rec_Cmp, __init

Transitions: (pre-variables and post-variables)

f1_0_main_Load	1	f33_0_rec_Cmp:	x1 = _arg1 ∧ x2 = _arg2 ∧ x3 = _arg3 ∧ x1 = _arg1P ∧ x2 = _arg2P ∧ x3 = _arg3P ∧ _arg2 = _arg1P ∧ −1 ≤ _arg2 − 1 ∧ 0 ≤ _arg1 − 1
f33_0_rec_Cmp	2	f48_0_rec_GE:	x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ _x = _x5 ∧ _x = _x4 ∧ _x = _x3
f48_0_rec_GE	3	f33_0_rec_Cmp:	x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ _x6 − 1 = _x9 ∧ _x7 = _x8 ∧ 99 ≤ _x7 − 1 ∧ 0 ≤ _x6 − 1 ∧ _x6 − 1 ≤ _x6 − 1
f48_0_rec_GE	4	f77_0_descend_LE:	x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ _x13 = _x15 ∧ _x13 = _x14 ∧ _x13 ≤ 99 ∧ 0 ≤ _x13 − 1
f48_0_rec_GE	5	f77_0_descend_LE:	x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ x3 = _x23 ∧ _x19 = _x21 ∧ _x19 = _x20 ∧ 0 ≤ _x19 − 1 ∧ _x19 ≤ 99
f48_0_rec_GE	6	f48_0_rec_GE:	x1 = _x24 ∧ x2 = _x25 ∧ x3 = _x26 ∧ x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ _x25 + 1 = _x29 ∧ _x25 + 1 = _x28 ∧ _x24 = _x27 ∧ _x25 = _x26 ∧ 0 ≤ _x25 − 1 ∧ _x25 ≤ 99
f77_0_descend_LE	7	f77_0_descend_LE:	x1 = _x30 ∧ x2 = _x31 ∧ x3 = _x32 ∧ x1 = _x33 ∧ x2 = _x34 ∧ x3 = _x35 ∧ _x30 − 1 = _x33 ∧ _x30 − 1 ≤ _x30 − 1 ∧ 0 ≤ _x30 − 1
__init	8	f1_0_main_Load:	x1 = _x36 ∧ x2 = _x37 ∧ x3 = _x38 ∧ x1 = _x39 ∧ x2 = _x40 ∧ x3 = _x41 ∧ 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 { f48_0_rec_GE, f33_0_rec_Cmp }.

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

f33_0_rec_Cmp:	−1 + x1
f48_0_rec_GE:	−1 + x1

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

f33_0_rec_Cmp:	99 − x1
f48_0_rec_GE:	99 − x2

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

f33_0_rec_Cmp:	0
f48_0_rec_GE:	−1

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

Here we consider the SCC { f77_0_descend_LE }.

We remove transition 7 using the following ranking functions, which are bounded by 0.

f77_0_descend_LE:

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 % (10 real / 0 unknown / 0 assumptions / 10 total proof steps)