LTS Termination Proof

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Input

Integer Transition System

Proof

1 Invariant Updates

The following invariants are asserted.

0: −1 + a_post ≤ 0−1 + ret_returnOne3_post ≤ 01 − ret_returnOne3_post ≤ 01 + a_1 ≤ 0−1 − a_1 ≤ 0−1 + a_0 ≤ 0−1 + ret_returnOne3_0 ≤ 01 − ret_returnOne3_0 ≤ 0
1: −1 + a_post ≤ 0−1 + ret_returnOne3_post ≤ 01 − ret_returnOne3_post ≤ 01 + a_1 ≤ 0−1 − a_1 ≤ 0−1 + a_0 ≤ 0−1 + ret_returnOne3_0 ≤ 01 − ret_returnOne3_0 ≤ 0
2: −1 + a_post ≤ 0−1 + ret_returnOne3_post ≤ 01 − ret_returnOne3_post ≤ 01 + a_1 ≤ 0−1 − a_1 ≤ 0−1 + a_0 ≤ 0−1 + ret_returnOne3_0 ≤ 01 − ret_returnOne3_0 ≤ 0−1 + tmp_post ≤ 0−1 + tmp_0 ≤ 0
3: −1 + a_post ≤ 0−1 + ret_returnOne3_post ≤ 01 − ret_returnOne3_post ≤ 01 + a_1 ≤ 0−1 − a_1 ≤ 0−1 + a_0 ≤ 0−1 + ret_returnOne3_0 ≤ 01 − ret_returnOne3_0 ≤ 0−1 + tmp_post ≤ 0−1 + tmp_0 ≤ 0
4: −1 + a_post ≤ 0−1 + ret_returnOne3_post ≤ 01 − ret_returnOne3_post ≤ 01 + a_1 ≤ 0−1 − a_1 ≤ 0−1 + a_0 ≤ 0−1 + ret_returnOne3_0 ≤ 01 − ret_returnOne3_0 ≤ 0
5: TRUE
6: TRUE

The invariants are proved as follows.

IMPACT Invariant Proof

2 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
and for every transition t, a duplicate t is considered.

3 Transition Removal

We remove transitions 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 using the following ranking functions, which are bounded by −16.

6: 0
5: 0
4: 0
0: 0
1: 0
2: 0
3: 0
6: −8
5: −9
4: −10
0: −11
1: −12
2: −13
3: −14

4 SCC Decomposition

There exist no SCC in the program graph.

Tool configuration

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