Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉
Temp_Vars: K, L
Locations: f0, f27, f5
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f5(K, 0, 0, X₃, X₄, X₅, X₆, X₇, X₈, X₉)
t₃: f5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f27(X₀, X₁, X₂, X₃, X₁, X₁, K, L, L, L) :|: 16 ≤ X₂
t₁: f5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f5(X₀, 1+X₁, 1+X₂, 1, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₂ ≤ 15
t₂: f5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉) → f5(X₀, X₁, 1+X₂, 0, X₄, X₅, X₆, X₇, X₈, X₉) :|: X₂ ≤ 15

Preprocessing

Eliminate variables [K; L; X₀; X₁; X₃; X₄; X₅; X₆; X₇; X₈; X₉] that do not contribute to the problem

Found invariant X₀ ≤ 16 ∧ 16 ≤ X₀ for location f27

Found invariant X₀ ≤ 16 ∧ 0 ≤ X₀ for location f5

Problem after Preprocessing

Start: f0
Program_Vars: X₀
Temp_Vars:
Locations: f0, f27, f5
Transitions:
t₈: f0(X₀) → f5(0)
t₉: f5(X₀) → f27(X₀) :|: 16 ≤ X₀ ∧ X₀ ≤ 16 ∧ 0 ≤ X₀
t₁₀: f5(X₀) → f5(1+X₀) :|: X₀ ≤ 15 ∧ X₀ ≤ 16 ∧ 0 ≤ X₀
t₁₁: f5(X₀) → f5(1+X₀) :|: X₀ ≤ 15 ∧ X₀ ≤ 16 ∧ 0 ≤ X₀

MPRF for transition t₁₀: f5(X₀) → f5(1+X₀) :|: X₀ ≤ 15 ∧ X₀ ≤ 16 ∧ 0 ≤ X₀ of depth 1:

new bound:

17 {O(1)}

• f5: [17-X₀]

MPRF for transition t₁₁: f5(X₀) → f5(1+X₀) :|: X₀ ≤ 15 ∧ X₀ ≤ 16 ∧ 0 ≤ X₀ of depth 1:

new bound:

17 {O(1)}

• f5: [17-X₀]

All Bounds

Timebounds

Overall timebound:36 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 17 {O(1)}
t₁₁: 17 {O(1)}

Costbounds

Overall costbound: 36 {O(1)}
t₈: 1 {O(1)}
t₉: 1 {O(1)}
t₁₀: 17 {O(1)}
t₁₁: 17 {O(1)}

Sizebounds

t₈, X₀: 0 {O(1)}
t₉, X₀: 16 {O(1)}
t₁₀, X₀: 16 {O(1)}
t₁₁, X₀: 16 {O(1)}