Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: f0, f23, f8
Transitions:
t₀: f0(X₀, X₁, X₂, X₃) → f8(0, X₁, X₂, X₃)
t₃: f8(X₀, X₁, X₂, X₃) → f23(X₀, X₁, X₂, X₃) :|: 1+E ≤ 0 ∧ 4 ≤ X₀
t₄: f8(X₀, X₁, X₂, X₃) → f23(X₀, X₁, X₂, X₃) :|: 4 ≤ X₀
t₁: f8(X₀, X₁, X₂, X₃) → f8(1+X₀, X₁, X₂, X₃) :|: X₀ ≤ 3
t₂: f8(X₀, X₁, X₂, X₃) → f8(1+X₀, X₀, 1+X₀, E) :|: X₀ ≤ 3

Preprocessing

Eliminate variables [X₁; X₂; X₃] that do not contribute to the problem

Found invariant X₀ ≤ 4 ∧ 0 ≤ X₀ for location f8

Found invariant X₀ ≤ 4 ∧ 4 ≤ X₀ for location f23

Problem after Preprocessing

Start: f0
Program_Vars: X₀
Temp_Vars: E
Locations: f0, f23, f8
Transitions:
t₁₀: f0(X₀) → f8(0)
t₁₁: f8(X₀) → f23(X₀) :|: 1+E ≤ 0 ∧ 4 ≤ X₀ ∧ X₀ ≤ 4 ∧ 0 ≤ X₀
t₁₂: f8(X₀) → f23(X₀) :|: 4 ≤ X₀ ∧ X₀ ≤ 4 ∧ 0 ≤ X₀
t₁₃: f8(X₀) → f8(1+X₀) :|: X₀ ≤ 3 ∧ X₀ ≤ 4 ∧ 0 ≤ X₀
t₁₄: f8(X₀) → f8(1+X₀) :|: X₀ ≤ 3 ∧ X₀ ≤ 4 ∧ 0 ≤ X₀

MPRF for transition t₁₃: f8(X₀) → f8(1+X₀) :|: X₀ ≤ 3 ∧ X₀ ≤ 4 ∧ 0 ≤ X₀ of depth 1:

new bound:

5 {O(1)}

• f8: [5-X₀]

MPRF for transition t₁₄: f8(X₀) → f8(1+X₀) :|: X₀ ≤ 3 ∧ X₀ ≤ 4 ∧ 0 ≤ X₀ of depth 1:

new bound:

5 {O(1)}

• f8: [5-X₀]

All Bounds

Timebounds

Overall timebound:13 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 5 {O(1)}
t₁₄: 5 {O(1)}

Costbounds

Overall costbound: 13 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}
t₁₃: 5 {O(1)}
t₁₄: 5 {O(1)}

Sizebounds

t₁₀, X₀: 0 {O(1)}
t₁₁, X₀: 4 {O(1)}
t₁₂, X₀: 4 {O(1)}
t₁₃, X₀: 4 {O(1)}
t₁₄, X₀: 4 {O(1)}