KoAT2 Proof Output

Initial Problem

Start: f1
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f1
Transitions:
t₁: f0(X₀, X₁) → f0(X₀+X₁, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₂: f0(X₀, X₁) → f0(X₀+X₁, X₁) :|: 1 ≤ X₀ ∧ 1+X₁ ≤ 0
t₀: f1(X₀, X₁) → f0(X₀, X₁)

Preprocessing

Problem after Preprocessing

MPRF for transition t₂: f0(X₀, X₁) → f0(X₀+X₁, X₁) :|: 1 ≤ X₀ ∧ 1+X₁ ≤ 0 of depth 1:

new bound:

X₀ {O(n)}

MPRF:

• f0: [X₀]

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location f0_v2

Found invariant 1+X₁ ≤ 0 ∧ 1+X₁ ≤ X₀ for location f0_v1

All Bounds

Timebounds

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

Costbounds

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

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: 2⋅X₁+X₀ {O(n)}
t₂, X₁: X₁ {O(n)}