Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: F
Locations: f0, f19, f7
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄) → f7(F, F, 10, 0, X₄)
t₂: f7(X₀, X₁, X₂, X₃, X₄) → f19(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₃
t₁: f7(X₀, X₁, X₂, X₃, X₄) → f7(X₀, X₁, X₂, 1+X₃, F) :|: 1+X₃ ≤ X₂

Preprocessing

Eliminate variables [F; X₀; X₁; X₄] that do not contribute to the problem

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 10 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location f19

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location f7

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f19, f7
Transitions:
t₆: f0(X₀, X₁) → f7(10, 0)
t₇: f7(X₀, X₁) → f19(X₀, X₁) :|: X₀ ≤ X₁ ∧ X₀+X₁ ≤ 20 ∧ X₀ ≤ 10 ∧ X₀ ≤ 10+X₁ ∧ X₁ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₈: f7(X₀, X₁) → f7(X₀, 1+X₁) :|: 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ X₀ ≤ 10 ∧ X₀ ≤ 10+X₁ ∧ X₁ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁

MPRF for transition t₈: f7(X₀, X₁) → f7(X₀, 1+X₁) :|: 1+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ X₀ ≤ 10 ∧ X₀ ≤ 10+X₁ ∧ X₁ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

11 {O(1)}

MPRF:

• f7: [11-X₁]

All Bounds

Timebounds

Overall timebound:13 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 11 {O(1)}

Costbounds

Overall costbound: 13 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 11 {O(1)}

Sizebounds

t₆, X₀: 10 {O(1)}
t₆, X₁: 0 {O(1)}
t₇, X₀: 10 {O(1)}
t₇, X₁: 10 {O(1)}
t₈, X₀: 10 {O(1)}
t₈, X₁: 10 {O(1)}