Initial Problem

Start: f0
Program_Vars: X₀
Temp_Vars: B
Locations: f0, f11, f14, f4, f5
Transitions:
t₂: f0(X₀) → f4(0)
t₆: f11(X₀) → f14(X₀) :|: X₀ ≤ 1
t₇: f11(X₀) → f14(X₀) :|: 2 ≤ X₀
t₄: f4(X₀) → f11(X₀)
t₀: f4(X₀) → f5(X₀) :|: 1+B ≤ 0
t₁: f4(X₀) → f5(X₀)
t₃: f5(X₀) → f11(X₀) :|: 3 ≤ X₀
t₅: f5(X₀) → f4(1+X₀) :|: X₀ ≤ 2

Preprocessing

Found invariant X₀ ≤ 3 ∧ 0 ≤ X₀ for location f14

Found invariant X₀ ≤ 3 ∧ 0 ≤ X₀ for location f11

Found invariant X₀ ≤ 3 ∧ 0 ≤ X₀ for location f5

Found invariant X₀ ≤ 3 ∧ 0 ≤ X₀ for location f4

Problem after Preprocessing

Start: f0
Program_Vars: X₀
Temp_Vars: B
Locations: f0, f11, f14, f4, f5
Transitions:
t₂: f0(X₀) → f4(0)
t₆: f11(X₀) → f14(X₀) :|: X₀ ≤ 1 ∧ X₀ ≤ 3 ∧ 0 ≤ X₀
t₇: f11(X₀) → f14(X₀) :|: 2 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 ≤ X₀
t₄: f4(X₀) → f11(X₀) :|: X₀ ≤ 3 ∧ 0 ≤ X₀
t₀: f4(X₀) → f5(X₀) :|: 1+B ≤ 0 ∧ X₀ ≤ 3 ∧ 0 ≤ X₀
t₁: f4(X₀) → f5(X₀) :|: X₀ ≤ 3 ∧ 0 ≤ X₀
t₃: f5(X₀) → f11(X₀) :|: 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 ≤ X₀
t₅: f5(X₀) → f4(1+X₀) :|: X₀ ≤ 2 ∧ X₀ ≤ 3 ∧ 0 ≤ X₀

MPRF for transition t₀: f4(X₀) → f5(X₀) :|: 1+B ≤ 0 ∧ X₀ ≤ 3 ∧ 0 ≤ X₀ of depth 1:

new bound:

4 {O(1)}

• f4: [4-X₀]
• f5: [3-X₀]

MPRF for transition t₁: f4(X₀) → f5(X₀) :|: X₀ ≤ 3 ∧ 0 ≤ X₀ of depth 1:

new bound:

4 {O(1)}

• f4: [4-X₀]
• f5: [3-X₀]

MPRF for transition t₅: f5(X₀) → f4(1+X₀) :|: X₀ ≤ 2 ∧ X₀ ≤ 3 ∧ 0 ≤ X₀ of depth 1:

new bound:

4 {O(1)}

• f4: [4-X₀]
• f5: [4-X₀]

All Bounds

Timebounds

Overall timebound:17 {O(1)}
t₀: 4 {O(1)}
t₁: 4 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 4 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}

Costbounds

Overall costbound: 17 {O(1)}
t₀: 4 {O(1)}
t₁: 4 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 4 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}

Sizebounds

t₀, X₀: 3 {O(1)}
t₁, X₀: 3 {O(1)}
t₂, X₀: 0 {O(1)}
t₃, X₀: 3 {O(1)}
t₄, X₀: 3 {O(1)}
t₅, X₀: 3 {O(1)}
t₆, X₀: 1 {O(1)}
t₇, X₀: 3 {O(1)}