KoAT2 Proof Output

Initial Problem

Start: start
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: ack, start
Transitions:
t₀: ack(X₀, X₁) → ack(X₀-1, C) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: ack(X₀, X₁) → ack(X₀, X₁-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₂: start(X₀, X₁) → ack(X₀, X₁)

Preprocessing

Problem after Preprocessing

MPRF for transition t₀: ack(X₀, X₁) → ack(X₀-1, C) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

• ack: [X₀]

Found invariant 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location ack_v1

Found invariant 0 ≤ X₀ for location ack_v2

All Bounds

Timebounds

Overall timebound:inf {Infinity}
t₀: X₀ {O(n)}
t₁: inf {Infinity}
t₂: 1 {O(1)}

Costbounds

Overall costbound: inf {Infinity}
t₀: X₀ {O(n)}
t₁: inf {Infinity}
t₂: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₁, X₀: X₀ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}