# 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.

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