Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: G, H
Locations: f0, f18, f24, f31, f39
Transitions:
t₆: f0(X₀, X₁, X₂, X₃, X₄, X₅) → f18(10, 0, 10, G, 10, H)
t₀: f18(X₀, X₁, X₂, X₃, X₄, X₅) → f18(X₀, 1+X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₀
t₅: f18(X₀, X₁, X₂, X₃, X₄, X₅) → f24(X₀, 0, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₁
t₁: f24(X₀, X₁, X₂, X₃, X₄, X₅) → f24(X₀, 1+X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₀
t₄: f24(X₀, X₁, X₂, X₃, X₄, X₅) → f31(X₀, 0, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₁
t₂: f31(X₀, X₁, X₂, X₃, X₄, X₅) → f31(X₀, 1+X₁, X₂, X₃, X₄, X₅) :|: 1+X₁ ≤ X₀
t₃: f31(X₀, X₁, X₂, X₃, X₄, X₅) → f39(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₁

Preprocessing

Eliminate variables [G; H; X₂; X₃; X₄; X₅] that do not contribute to the problem

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location f18

Found invariant 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location f24

Found invariant 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location f31

Found invariant 10 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location f39

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: f0, f18, f24, f31, f39
Transitions:
t₁₆: f0(X₀, X₁) → f18(10, 0)
t₁₇: f18(X₀, X₁) → f18(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
t₁₈: f18(X₀, X₁) → f24(X₀, 0) :|: X₀ ≤ X₁ ∧ X₀+X₁ ≤ 20 ∧ X₀ ≤ 10 ∧ X₀ ≤ 10+X₁ ∧ X₁ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁
t₁₉: f24(X₀, X₁) → f24(X₀, 1+X₁) :|: 1+X₁ ≤ X₀ ∧ X₀ ≤ 10 ∧ X₀ ≤ 10+X₁ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₀: f24(X₀, X₁) → f31(X₀, 0) :|: X₀ ≤ X₁ ∧ X₀ ≤ 10 ∧ X₀ ≤ 10+X₁ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₁: f31(X₀, X₁) → f31(X₀, 1+X₁) :|: 1+X₁ ≤ X₀ ∧ X₀ ≤ 10 ∧ X₀ ≤ 10+X₁ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₂: f31(X₀, X₁) → f39(X₀, X₁) :|: X₀ ≤ X₁ ∧ X₀ ≤ 10 ∧ X₀ ≤ 10+X₁ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₁ ∧ 0 ≤ X₁

MPRF for transition t₁₇: f18(X₀, X₁) → f18(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)}

• f18: [11-X₁]

MPRF for transition t₁₉: f24(X₀, X₁) → f24(X₀, 1+X₁) :|: 1+X₁ ≤ X₀ ∧ X₀ ≤ 10 ∧ X₀ ≤ 10+X₁ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

10 {O(1)}

• f24: [X₀-X₁]

MPRF for transition t₂₁: f31(X₀, X₁) → f31(X₀, 1+X₁) :|: 1+X₁ ≤ X₀ ∧ X₀ ≤ 10 ∧ X₀ ≤ 10+X₁ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₁ ∧ 0 ≤ X₁ of depth 1:

new bound:

10 {O(1)}

• f31: [X₀-X₁]

All Bounds

Timebounds

Overall timebound:35 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 11 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 10 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 10 {O(1)}
t₂₂: 1 {O(1)}

Costbounds

Overall costbound: 35 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 11 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 10 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 10 {O(1)}
t₂₂: 1 {O(1)}

Sizebounds

t₁₆, X₀: 10 {O(1)}
t₁₆, X₁: 0 {O(1)}
t₁₇, X₀: 10 {O(1)}
t₁₇, X₁: 10 {O(1)}
t₁₈, X₀: 10 {O(1)}
t₁₈, X₁: 0 {O(1)}
t₁₉, X₀: 10 {O(1)}
t₁₉, X₁: 10 {O(1)}
t₂₀, X₀: 10 {O(1)}
t₂₀, X₁: 0 {O(1)}
t₂₁, X₀: 10 {O(1)}
t₂₁, X₁: 10 {O(1)}
t₂₂, X₀: 10 {O(1)}
t₂₂, X₁: 10 {O(1)}