Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: H
Locations: f0, f10, f16, f28, f9
Transitions:
t₀: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f9(0, 0, H, X₃, X₄, X₅, X₆)
t₈: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f16(0, X₁, X₂, X₃, X₄, X₅, X₆) :|: 10 ≤ X₀
t₃: f10(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f9(1+X₀, 1+X₀, H, X₃, X₄, X₅, X₆) :|: X₀ ≤ 9
t₅: f16(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f16(1+X₀, X₁, X₂, X₃, X₀, H, H) :|: X₀ ≤ 9 ∧ 1+H ≤ 0
t₆: f16(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f16(1+X₀, X₁, X₂, X₃, X₀, H, H) :|: X₀ ≤ 9 ∧ 1 ≤ H
t₄: f16(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f28(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 10 ≤ X₀
t₇: f16(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f28(X₀, X₁, X₂, X₃, X₀, 0, 0) :|: X₀ ≤ 9
t₁: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f10(X₀, X₁, X₂, X₂, X₄, X₅, X₆) :|: 1+X₂ ≤ 0
t₂: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f10(X₀, X₁, X₂, X₂, X₄, X₅, X₆) :|: 1 ≤ X₂
t₉: f9(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → f16(0, X₁, 0, 0, X₄, X₅, X₆) :|: 0 ≤ X₂ ∧ X₂ ≤ 0

Preprocessing

Eliminate variables [X₁; X₃; X₄; X₅; X₆] that do not contribute to the problem

Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location f28

Found invariant 0 ≤ X₀ for location f10

Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location f16

Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location f9

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁
Temp_Vars: H
Locations: f0, f10, f16, f28, f9
Transitions:
t₂₀: f0(X₀, X₁) → f9(0, H)
t₂₁: f10(X₀, X₁) → f16(0, X₁) :|: 10 ≤ X₀ ∧ 0 ≤ X₀
t₂₂: f10(X₀, X₁) → f9(1+X₀, H) :|: X₀ ≤ 9 ∧ 0 ≤ X₀
t₂₃: f16(X₀, X₁) → f16(1+X₀, X₁) :|: X₀ ≤ 9 ∧ 1+H ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₄: f16(X₀, X₁) → f16(1+X₀, X₁) :|: X₀ ≤ 9 ∧ 1 ≤ H ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₅: f16(X₀, X₁) → f28(X₀, X₁) :|: 10 ≤ X₀ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₆: f16(X₀, X₁) → f28(X₀, X₁) :|: X₀ ≤ 9 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₇: f9(X₀, X₁) → f10(X₀, X₁) :|: 1+X₁ ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₈: f9(X₀, X₁) → f10(X₀, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₉: f9(X₀, X₁) → f16(0, 0) :|: 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀

MPRF for transition t₂₂: f10(X₀, X₁) → f9(1+X₀, H) :|: X₀ ≤ 9 ∧ 0 ≤ X₀ of depth 1:

new bound:

10 {O(1)}

• f10: [10-X₀]
• f9: [10-X₀]

MPRF for transition t₂₇: f9(X₀, X₁) → f10(X₀, X₁) :|: 1+X₁ ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

11 {O(1)}

• f10: [10-X₀]
• f9: [11-X₀]

MPRF for transition t₂₈: f9(X₀, X₁) → f10(X₀, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

11 {O(1)}

• f10: [10-X₀]
• f9: [11-X₀]

MPRF for transition t₂₃: f16(X₀, X₁) → f16(1+X₀, X₁) :|: X₀ ≤ 9 ∧ 1+H ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

22 {O(1)}

• f16: [11-X₀]

MPRF for transition t₂₄: f16(X₀, X₁) → f16(1+X₀, X₁) :|: X₀ ≤ 9 ∧ 1 ≤ H ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

22 {O(1)}

• f16: [11-X₀]

All Bounds

Timebounds

Overall timebound:81 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 10 {O(1)}
t₂₃: 22 {O(1)}
t₂₄: 22 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 11 {O(1)}
t₂₈: 11 {O(1)}
t₂₉: 1 {O(1)}

Costbounds

Overall costbound: 81 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 10 {O(1)}
t₂₃: 22 {O(1)}
t₂₄: 22 {O(1)}
t₂₅: 1 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 11 {O(1)}
t₂₈: 11 {O(1)}
t₂₉: 1 {O(1)}

Sizebounds

t₂₀, X₀: 0 {O(1)}
t₂₁, X₀: 0 {O(1)}
t₂₂, X₀: 10 {O(1)}
t₂₃, X₀: 10 {O(1)}
t₂₄, X₀: 10 {O(1)}
t₂₅, X₀: 10 {O(1)}
t₂₆, X₀: 9 {O(1)}
t₂₇, X₀: 10 {O(1)}
t₂₈, X₀: 10 {O(1)}
t₂₉, X₀: 0 {O(1)}
t₂₉, X₁: 0 {O(1)}