LTS Termination Proof

by T2Cert

Input

Integer Transition System

Initial Location: 2

Transitions: (pre-variables and post-variables)

0	0	1:		0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ 0 ≤ 0 ∧ − cnt_59_0 + lt_47_post ≤ 0 ∧ cnt_59_0 − lt_47_post ≤ 0 ∧ Result_4_0 − Result_4_post ≤ 0 ∧ − Result_4_0 + Result_4_post ≤ 0 ∧ devExt_7_0 − devExt_7_post ≤ 0 ∧ − devExt_7_0 + devExt_7_post ≤ 0 ∧ i_12_0 − i_12_post ≤ 0 ∧ − i_12_0 + i_12_post ≤ 0 ∧ irp_11_0 − irp_11_post ≤ 0 ∧ − irp_11_0 + irp_11_post ≤ 0 ∧ loop_count_14_0 − loop_count_14_post ≤ 0 ∧ − loop_count_14_0 + loop_count_14_post ≤ 0 ∧ loop_max_13_0 − loop_max_13_post ≤ 0 ∧ − loop_max_13_0 + loop_max_13_post ≤ 0 ∧ lt_47_0 − lt_47_post ≤ 0 ∧ − lt_47_0 + lt_47_post ≤ 0 ∧ nPacketsOld_9_0 − nPacketsOld_9_post ≤ 0 ∧ − nPacketsOld_9_0 + nPacketsOld_9_post ≤ 0 ∧ nPackets_10_0 − nPackets_10_post ≤ 0 ∧ − nPackets_10_0 + nPackets_10_post ≤ 0 ∧ request_8_0 − request_8_post ≤ 0 ∧ − request_8_0 + request_8_post ≤ 0 ∧ − cnt_59_0 + cnt_59_0 ≤ 0 ∧ cnt_59_0 − cnt_59_0 ≤ 0
2	1	0:		− request_8_post + request_8_post ≤ 0 ∧ request_8_post − request_8_post ≤ 0 ∧ − request_8_0 + request_8_0 ≤ 0 ∧ request_8_0 − request_8_0 ≤ 0 ∧ − nPackets_10_post + nPackets_10_post ≤ 0 ∧ nPackets_10_post − nPackets_10_post ≤ 0 ∧ − nPackets_10_0 + nPackets_10_0 ≤ 0 ∧ nPackets_10_0 − nPackets_10_0 ≤ 0 ∧ − nPacketsOld_9_post + nPacketsOld_9_post ≤ 0 ∧ nPacketsOld_9_post − nPacketsOld_9_post ≤ 0 ∧ − nPacketsOld_9_0 + nPacketsOld_9_0 ≤ 0 ∧ nPacketsOld_9_0 − nPacketsOld_9_0 ≤ 0 ∧ − lt_47_post + lt_47_post ≤ 0 ∧ lt_47_post − lt_47_post ≤ 0 ∧ − lt_47_0 + lt_47_0 ≤ 0 ∧ lt_47_0 − lt_47_0 ≤ 0 ∧ − loop_max_13_post + loop_max_13_post ≤ 0 ∧ loop_max_13_post − loop_max_13_post ≤ 0 ∧ − loop_max_13_0 + loop_max_13_0 ≤ 0 ∧ loop_max_13_0 − loop_max_13_0 ≤ 0 ∧ − loop_count_14_post + loop_count_14_post ≤ 0 ∧ loop_count_14_post − loop_count_14_post ≤ 0 ∧ − loop_count_14_0 + loop_count_14_0 ≤ 0 ∧ loop_count_14_0 − loop_count_14_0 ≤ 0 ∧ − irp_11_post + irp_11_post ≤ 0 ∧ irp_11_post − irp_11_post ≤ 0 ∧ − irp_11_0 + irp_11_0 ≤ 0 ∧ irp_11_0 − irp_11_0 ≤ 0 ∧ − i_12_post + i_12_post ≤ 0 ∧ i_12_post − i_12_post ≤ 0 ∧ − i_12_0 + i_12_0 ≤ 0 ∧ i_12_0 − i_12_0 ≤ 0 ∧ − devExt_7_post + devExt_7_post ≤ 0 ∧ devExt_7_post − devExt_7_post ≤ 0 ∧ − devExt_7_0 + devExt_7_0 ≤ 0 ∧ devExt_7_0 − devExt_7_0 ≤ 0 ∧ − cnt_59_0 + cnt_59_0 ≤ 0 ∧ cnt_59_0 − cnt_59_0 ≤ 0 ∧ − Result_4_post + Result_4_post ≤ 0 ∧ Result_4_post − Result_4_post ≤ 0 ∧ − Result_4_0 + Result_4_0 ≤ 0 ∧ Result_4_0 − Result_4_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 using the following ranking functions, which are bounded by −8.

2:	0
0:	0
1:	0
2:	−4
0:	−5
1:	−6

3 SCC Decomposition

There exist no SCC in the program graph.

Tool configuration

T2Cert

version: 1.0