Initial Problem

Start: f1
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f1, f2
Transitions:
t₀: f1(X₀, X₁) → f2(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: f2(X₀, X₁) → f2(X₀-1, X₁) :|: 1 ≤ X₁ ∧ 2 ≤ X₀
t₂: f2(X₀, X₁) → f2(X₀, X₁-1) :|: 1 ≤ X₀ ∧ 2 ≤ X₁

Preprocessing

Found invariant 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location f2

Problem after Preprocessing

Start: f1
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f1, f2
Transitions:
t₀: f1(X₀, X₁) → f2(X₀, X₁) :|: 1 ≤ X₀ ∧ 1 ≤ X₁
t₁: f2(X₀, X₁) → f2(X₀-1, X₁) :|: 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀+X₁
t₂: f2(X₀, X₁) → f2(X₀, X₁-1) :|: 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁

MPRF for transition t₁: f2(X₀, X₁) → f2(X₀-1, X₁) :|: 1 ≤ X₁ ∧ 2 ≤ X₀ ∧ 1 ≤ X₀ ∧ 2 ≤ X₀+X₁ of depth 1:

new bound:

X₀ {O(n)}

• f2: [X₀]

MPRF for transition t₂: f2(X₀, X₁) → f2(X₀, X₁-1) :|: 1 ≤ X₀ ∧ 2 ≤ X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ of depth 1:

new bound:

X₁ {O(n)}

• f2: [X₁]

All Bounds

Timebounds

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

Costbounds

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

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)}