# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: l5, l4, l6, l1, l0, l2
• Transitions: (pre-variables and post-variables)  l0 1 l1: x1 = _aHAT0 ∧ x2 = _ret_returnOne3HAT0 ∧ x3 = _tmpHAT0 ∧ x1 = _aHATpost ∧ x2 = _ret_returnOne3HATpost ∧ x3 = _tmpHATpost ∧ _tmpHAT0 = _tmpHATpost ∧ _ret_returnOne3HAT0 = _ret_returnOne3HATpost ∧ _aHAT0 = _aHATpost ∧ 3 ≤ _aHAT0 l0 2 l1: x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x1 = _x3 ∧ x2 = _x4 ∧ x3 = _x5 ∧ _x2 = _x5 ∧ _x1 = _x4 ∧ _x = _x3 ∧ 1 + _x ≤ 2 l0 3 l2: x1 = _x6 ∧ x2 = _x7 ∧ x3 = _x8 ∧ x1 = _x9 ∧ x2 = _x10 ∧ x3 = _x11 ∧ _x7 = _x10 ∧ _x6 = _x9 ∧ _x11 = 1 ∧ 2 ≤ _x6 ∧ _x6 ≤ 2 l2 4 l3: x1 = _x12 ∧ x2 = _x13 ∧ x3 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ _x14 = _x17 ∧ _x13 = _x16 ∧ _x12 = _x15 l4 5 l0: x1 = _x18 ∧ x2 = _x19 ∧ x3 = _x20 ∧ x1 = _x21 ∧ x2 = _x22 ∧ x3 = _x23 ∧ _x20 = _x23 ∧ _x19 = _x22 ∧ _x18 = _x21 ∧ 2 ≤ _x18 l4 6 l0: x1 = _x24 ∧ x2 = _x25 ∧ x3 = _x26 ∧ x1 = _x27 ∧ x2 = _x28 ∧ x3 = _x29 ∧ _x26 = _x29 ∧ _x25 = _x28 ∧ _x24 = _x27 ∧ 1 + _x24 ≤ 1 l4 7 l2: x1 = _x30 ∧ x2 = _x31 ∧ x3 = _x32 ∧ x1 = _x33 ∧ x2 = _x34 ∧ x3 = _x35 ∧ _x31 = _x34 ∧ _x30 = _x33 ∧ _x35 = 1 ∧ 1 ≤ _x30 ∧ _x30 ≤ 1 l1 8 l2: x1 = _x36 ∧ x2 = _x37 ∧ x3 = _x38 ∧ x1 = _x39 ∧ x2 = _x40 ∧ x3 = _x41 ∧ _x37 = _x40 ∧ _x36 = _x39 ∧ _x41 = 0 l5 9 l4: x1 = _x42 ∧ x2 = _x43 ∧ x3 = _x44 ∧ x1 = _x45 ∧ x2 = _x46 ∧ x3 = _x47 ∧ _x48 = −1 ∧ _x46 = 1 ∧ _x45 = _x46 ∧ _x44 = _x47 l6 10 l5: x1 = _x49 ∧ x2 = _x50 ∧ x3 = _x51 ∧ x1 = _x52 ∧ x2 = _x53 ∧ x3 = _x54 ∧ _x51 = _x54 ∧ _x50 = _x53 ∧ _x49 = _x52

## Proof

### 1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 l5 l5 l5: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 l4 l4 l4: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 l6 l6 l6: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 l1 l1 l1: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 l0 l0 l0: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 l2 l2 l2: x1 = x1 ∧ x2 = x2 ∧ x3 = x3
and for every transition t, a duplicate t is considered.

### 2 SCC Decomposition

There exist no SCC in the program graph.

## Tool configuration

AProVE

• version: AProVE Commit ID: unknown
• strategy: Statistics for single proof: 100.00 % (2 real / 0 unknown / 0 assumptions / 2 total proof steps)