Initial Problem

Start: f0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: f0, f10, f18, f4
Transitions:
t₀: f0(X₀, X₁) → f4(0, X₁)
t₂: f10(X₀, X₁) → f10(X₀, 1+X₁) :|: X₁ ≤ 1
t₃: f10(X₀, X₁) → f18(X₀, X₁) :|: 1+C ≤ 0 ∧ 2 ≤ X₁
t₄: f10(X₀, X₁) → f18(X₀, X₁) :|: 2 ≤ X₁
t₅: f4(X₀, X₁) → f10(X₀, 0) :|: 2 ≤ X₀
t₁: f4(X₀, X₁) → f4(1+X₀, X₁) :|: X₀ ≤ 1

Preprocessing

Found invariant X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location f18

Found invariant X₁ ≤ 2 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ 0 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 2 ∧ 2 ≤ X₀ for location f10

Found invariant X₀ ≤ 2 ∧ 0 ≤ X₀ for location f4

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars: C
Locations: f0, f10, f18, f4
Transitions:
t₀: f0(X₀, X₁) → f4(0, X₁)
t₂: f10(X₀, X₁) → f10(X₀, 1+X₁) :|: X₁ ≤ 1 ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₁ ≤ 2 ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₃: f10(X₀, X₁) → f18(X₀, X₁) :|: 1+C ≤ 0 ∧ 2 ≤ X₁ ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₁ ≤ 2 ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₄: f10(X₀, X₁) → f18(X₀, X₁) :|: 2 ≤ X₁ ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₁ ≤ 2 ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₅: f4(X₀, X₁) → f10(X₀, 0) :|: 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ X₀
t₁: f4(X₀, X₁) → f4(1+X₀, X₁) :|: X₀ ≤ 1 ∧ X₀ ≤ 2 ∧ 0 ≤ X₀

MPRF for transition t₁: f4(X₀, X₁) → f4(1+X₀, X₁) :|: X₀ ≤ 1 ∧ X₀ ≤ 2 ∧ 0 ≤ X₀ of depth 1:

new bound:

3 {O(1)}

• f4: [3-X₀]

MPRF for transition t₂: f10(X₀, X₁) → f10(X₀, 1+X₁) :|: X₁ ≤ 1 ∧ X₀+X₁ ≤ 4 ∧ X₀ ≤ 2 ∧ X₀ ≤ 2+X₁ ∧ X₁ ≤ 2 ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

3 {O(1)}

• f10: [1+X₀-X₁]

All Bounds

Timebounds

Overall timebound:10 {O(1)}
t₀: 1 {O(1)}
t₁: 3 {O(1)}
t₂: 3 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}

Costbounds

Overall costbound: 10 {O(1)}
t₀: 1 {O(1)}
t₁: 3 {O(1)}
t₂: 3 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}

Sizebounds

t₀, X₀: 0 {O(1)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: 2 {O(1)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: 2 {O(1)}
t₂, X₁: 2 {O(1)}
t₃, X₀: 2 {O(1)}
t₃, X₁: 2 {O(1)}
t₄, X₀: 2 {O(1)}
t₄, X₁: 2 {O(1)}
t₅, X₀: 2 {O(1)}
t₅, X₁: 0 {O(1)}