Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: H
Locations: l0, l1, l2, l3, l4
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(0, 0, H, X₃, X₄, X₅, X₆)
t₉: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(0, X₁, 0, 0, X₄, X₅, X₆) :|: X₂ ≤ 0 ∧ 0 ≤ X₂
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₂, X₄, X₅, X₆) :|: X₂+1 ≤ 0
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l3(X₀, X₁, X₂, X₂, X₄, X₅, X₆) :|: 1 ≤ X₂
t₅: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀+1, X₁, X₂, X₃, X₀, H, H) :|: X₀ ≤ 9 ∧ H+1 ≤ 0
t₆: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(X₀+1, X₁, X₂, X₃, X₀, H, H) :|: X₀ ≤ 9 ∧ 1 ≤ H
t₄: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 10 ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l4(X₀, X₁, X₂, X₃, X₀, 0, 0) :|: X₀ ≤ 9
t₃: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l1(X₀+1, X₀+1, H, X₃, X₄, X₅, X₆) :|: X₀ ≤ 9
t₈: l3(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → l2(0, X₁, X₂, X₃, X₄, X₅, X₆) :|: 10 ≤ X₀

Preprocessing

Eliminate variables {X₁,X₃,X₄,X₅,X₆} that do not contribute to the problem

Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location l2

Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location l1

Found invariant X₀ ≤ 10 ∧ 0 ≤ X₀ for location l4

Found invariant 0 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: H
Locations: l0, l1, l2, l3, l4
Transitions:
t₂₀: l0(X₀, X₁) → l1(0, H)
t₂₁: l1(X₀, X₁) → l2(0, 0) :|: X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₂: l1(X₀, X₁) → l3(X₀, X₁) :|: X₁+1 ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₃: l1(X₀, X₁) → l3(X₀, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₄: l2(X₀, X₁) → l2(X₀+1, X₁) :|: X₀ ≤ 9 ∧ H+1 ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₅: l2(X₀, X₁) → l2(X₀+1, X₁) :|: X₀ ≤ 9 ∧ 1 ≤ H ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₆: l2(X₀, X₁) → l4(X₀, X₁) :|: 10 ≤ X₀ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₇: l2(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ 9 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀
t₂₈: l3(X₀, X₁) → l1(X₀+1, H) :|: X₀ ≤ 9 ∧ 0 ≤ X₀
t₂₉: l3(X₀, X₁) → l2(0, X₁) :|: 10 ≤ X₀ ∧ 0 ≤ X₀

MPRF for transition t₂₂: l1(X₀, X₁) → l3(X₀, X₁) :|: X₁+1 ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

11 {O(1)}

MPRF for transition t₂₃: l1(X₀, X₁) → l3(X₀, X₁) :|: 1 ≤ X₁ ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

11 {O(1)}

MPRF for transition t₂₈: l3(X₀, X₁) → l1(X₀+1, H) :|: X₀ ≤ 9 ∧ 0 ≤ X₀ of depth 1:

new bound:

10 {O(1)}

MPRF for transition t₂₄: l2(X₀, X₁) → l2(X₀+1, X₁) :|: X₀ ≤ 9 ∧ H+1 ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

20 {O(1)}

MPRF for transition t₂₅: l2(X₀, X₁) → l2(X₀+1, X₁) :|: X₀ ≤ 9 ∧ 1 ≤ H ∧ X₀ ≤ 10 ∧ 0 ≤ X₀ of depth 1:

new bound:

20 {O(1)}

All Bounds

Timebounds

Overall timebound:77 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 11 {O(1)}
t₂₃: 11 {O(1)}
t₂₄: 20 {O(1)}
t₂₅: 20 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 10 {O(1)}
t₂₉: 1 {O(1)}

Costbounds

Overall costbound: 77 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 11 {O(1)}
t₂₃: 11 {O(1)}
t₂₄: 20 {O(1)}
t₂₅: 20 {O(1)}
t₂₆: 1 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 10 {O(1)}
t₂₉: 1 {O(1)}

Sizebounds

t₂₀, X₀: 0 {O(1)}
t₂₁, X₀: 0 {O(1)}
t₂₁, X₁: 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: 10 {O(1)}
t₂₇, X₀: 9 {O(1)}
t₂₈, X₀: 10 {O(1)}
t₂₉, X₀: 0 {O(1)}