LTS Termination Proof

by T2Cert

Input

Integer Transition System

Initial Location: 5

Transitions: (pre-variables and post-variables)

0	0	1:	− tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − tmp10_post + tmp10_post ≤ 0 ∧ tmp10_post − tmp10_post ≤ 0 ∧ − tmp10_0 + tmp10_0 ≤ 0 ∧ tmp10_0 − tmp10_0 ≤ 0 ∧ − ___val8_post + ___val8_post ≤ 0 ∧ ___val8_post − ___val8_post ≤ 0 ∧ − ___val8_0 + ___val8_0 ≤ 0 ∧ ___val8_0 − ___val8_0 ≤ 0 ∧ − ___len9_post + ___len9_post ≤ 0 ∧ ___len9_post − ___len9_post ≤ 0 ∧ − ___len9_0 + ___len9_0 ≤ 0 ∧ ___len9_0 − ___len9_0 ≤ 0
2	1	0:	0 ≤ 0 ∧ 0 ≤ 0 ∧ tmp___0_0 − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_post ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − tmp10_post + tmp10_post ≤ 0 ∧ tmp10_post − tmp10_post ≤ 0 ∧ − tmp10_0 + tmp10_0 ≤ 0 ∧ tmp10_0 − tmp10_0 ≤ 0 ∧ − ___val8_post + ___val8_post ≤ 0 ∧ ___val8_post − ___val8_post ≤ 0 ∧ − ___val8_0 + ___val8_0 ≤ 0 ∧ ___val8_0 − ___val8_0 ≤ 0 ∧ − ___len9_post + ___len9_post ≤ 0 ∧ ___len9_post − ___len9_post ≤ 0 ∧ − ___len9_0 + ___len9_0 ≤ 0 ∧ ___len9_0 − ___len9_0 ≤ 0
3	2	0:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 1 + tmp___1_0 ≤ 0 ∧ −1 − tmp___1_0 ≤ 0 ∧ ___val8_post ≤ 0 ∧ − ___val8_post ≤ 0 ∧ ___len9_0 − ___len9_post ≤ 0 ∧ − ___len9_0 + ___len9_post ≤ 0 ∧ ___val8_0 − ___val8_post ≤ 0 ∧ − ___val8_0 + ___val8_post ≤ 0 ∧ tmp10_0 − tmp10_post ≤ 0 ∧ − tmp10_0 + tmp10_post ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0
3	3	2:	− tmp___1_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − tmp10_post + tmp10_post ≤ 0 ∧ tmp10_post − tmp10_post ≤ 0 ∧ − tmp10_0 + tmp10_0 ≤ 0 ∧ tmp10_0 − tmp10_0 ≤ 0 ∧ − ___val8_post + ___val8_post ≤ 0 ∧ ___val8_post − ___val8_post ≤ 0 ∧ − ___val8_0 + ___val8_0 ≤ 0 ∧ ___val8_0 − ___val8_0 ≤ 0 ∧ − ___len9_post + ___len9_post ≤ 0 ∧ ___len9_post − ___len9_post ≤ 0 ∧ − ___len9_0 + ___len9_0 ≤ 0 ∧ ___len9_0 − ___len9_0 ≤ 0
3	4	2:	2 + tmp___1_0 ≤ 0 ∧ − tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − tmp10_post + tmp10_post ≤ 0 ∧ tmp10_post − tmp10_post ≤ 0 ∧ − tmp10_0 + tmp10_0 ≤ 0 ∧ tmp10_0 − tmp10_0 ≤ 0 ∧ − ___val8_post + ___val8_post ≤ 0 ∧ ___val8_post − ___val8_post ≤ 0 ∧ − ___val8_0 + ___val8_0 ≤ 0 ∧ ___val8_0 − ___val8_0 ≤ 0 ∧ − ___len9_post + ___len9_post ≤ 0 ∧ ___len9_post − ___len9_post ≤ 0 ∧ − ___len9_0 + ___len9_0 ≤ 0 ∧ ___len9_0 − ___len9_0 ≤ 0
4	5	3:	0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ tmp_0 − tmp_post ≤ 0 ∧ − tmp_0 + tmp_post ≤ 0 ∧ tmp___1_0 − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_post ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp10_post + tmp10_post ≤ 0 ∧ tmp10_post − tmp10_post ≤ 0 ∧ − tmp10_0 + tmp10_0 ≤ 0 ∧ tmp10_0 − tmp10_0 ≤ 0 ∧ − ___val8_post + ___val8_post ≤ 0 ∧ ___val8_post − ___val8_post ≤ 0 ∧ − ___val8_0 + ___val8_0 ≤ 0 ∧ ___val8_0 − ___val8_0 ≤ 0 ∧ − ___len9_post + ___len9_post ≤ 0 ∧ ___len9_post − ___len9_post ≤ 0 ∧ − ___len9_0 + ___len9_0 ≤ 0 ∧ ___len9_0 − ___len9_0 ≤ 0
5	6	4:	− tmp_post + tmp_post ≤ 0 ∧ tmp_post − tmp_post ≤ 0 ∧ − tmp___1_post + tmp___1_post ≤ 0 ∧ tmp___1_post − tmp___1_post ≤ 0 ∧ − tmp___1_0 + tmp___1_0 ≤ 0 ∧ tmp___1_0 − tmp___1_0 ≤ 0 ∧ − tmp___0_post + tmp___0_post ≤ 0 ∧ tmp___0_post − tmp___0_post ≤ 0 ∧ − tmp___0_0 + tmp___0_0 ≤ 0 ∧ tmp___0_0 − tmp___0_0 ≤ 0 ∧ − tmp_0 + tmp_0 ≤ 0 ∧ tmp_0 − tmp_0 ≤ 0 ∧ − tmp10_post + tmp10_post ≤ 0 ∧ tmp10_post − tmp10_post ≤ 0 ∧ − tmp10_0 + tmp10_0 ≤ 0 ∧ tmp10_0 − tmp10_0 ≤ 0 ∧ − ___val8_post + ___val8_post ≤ 0 ∧ ___val8_post − ___val8_post ≤ 0 ∧ − ___val8_0 + ___val8_0 ≤ 0 ∧ ___val8_0 − ___val8_0 ≤ 0 ∧ − ___len9_post + ___len9_post ≤ 0 ∧ ___len9_post − ___len9_post ≤ 0 ∧ − ___len9_0 + ___len9_0 ≤ 0 ∧ ___len9_0 − ___len9_0 ≤ 0

Proof

1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:

and for every transition t, a duplicate t is considered.

2 Transition Removal

We remove transitions 0, 1, 2, 3, 4, 5, 6 using the following ranking functions, which are bounded by −14.

5:	0
4:	0
3:	0
2:	0
0:	0
1:	0
5:	−7
4:	−8
3:	−9
2:	−10
0:	−11
1:	−12

3 SCC Decomposition

There exist no SCC in the program graph.

Tool configuration

T2Cert

version: 1.0