# LTS Termination Proof

by AProVE

## Input

Integer Transition System
• Initial Location: l4, l0, l2
• Transitions: (pre-variables and post-variables)  l0 1 l1: x1 = ____patmp1HAT0 ∧ x2 = ____patmp2HAT0 ∧ x3 = _k_208HAT0 ∧ x4 = _k_243HAT0 ∧ x5 = _len_263HAT0 ∧ x1 = ____patmp1HATpost ∧ x2 = ____patmp2HATpost ∧ x3 = _k_208HATpost ∧ x4 = _k_243HATpost ∧ x5 = _len_263HATpost ∧ _k_208HAT0 = _k_208HATpost ∧ 0 ≤ −1 + _k_243HATpost ∧ _k_243HATpost = ____patmp2HATpost ∧ _len_263HATpost = ____patmp1HATpost ∧ ____patmp2HATpost = _k_208HAT0 ∧ ____patmp1HATpost = 1 ∧ 0 ≤ _k_208HAT0 l2 2 l3: x1 = _x ∧ x2 = _x1 ∧ x3 = _x2 ∧ x4 = _x3 ∧ x5 = _x4 ∧ x1 = _x5 ∧ x2 = _x6 ∧ x3 = _x7 ∧ x4 = _x8 ∧ x5 = _x9 ∧ _x4 = _x9 ∧ _x3 = _x8 ∧ _x2 = _x7 ∧ _x1 = _x6 ∧ _x = _x5 l4 3 l0: x1 = _x10 ∧ x2 = _x11 ∧ x3 = _x12 ∧ x4 = _x13 ∧ x5 = _x14 ∧ x1 = _x15 ∧ x2 = _x16 ∧ x3 = _x17 ∧ x4 = _x18 ∧ x5 = _x19 ∧ _x14 = _x19 ∧ _x13 = _x18 ∧ _x12 = _x17 ∧ _x11 = _x16 ∧ _x10 = _x15

## Proof

### 1 Switch to Cooperation Termination Proof

We consider the following cutpoint-transitions:
 l4 l4 l4: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 l0 l0 l0: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5 l2 l2 l2: x1 = x1 ∧ x2 = x2 ∧ x3 = x3 ∧ x4 = x4 ∧ x5 = x5
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)