KoAT2 Proof Output

Initial Problem

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

Preprocessing

Problem after Preprocessing

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

new bound:

X₀ {O(n)}

MPRF:

• merge: [X₀]

MPRF for transition t₁: merge(X₀, X₁) → merge(X₀, X₁-1) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

• merge: [X₁]

All Bounds

Timebounds

Overall timebound:X₀+X₁+1 {O(n)}
t₀: X₀ {O(n)}
t₁: X₁ {O(n)}
t₂: 1 {O(1)}

Costbounds

Overall costbound: X₀+X₁+1 {O(n)}
t₀: X₀ {O(n)}
t₁: X₁ {O(n)}
t₂: 1 {O(1)}

Sizebounds

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