Initial Problem

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

Found invariant X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l1

Found invariant 10 ≤ X₁ ∧ 20 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l4

Found invariant 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2, l3, l4
Transitions:
t₁₆: l0(X₀, X₁) → l1(10, 0)
t₁₇: l1(X₀, X₁) → l1(X₀, X₁+1) :|: X₁+1 ≤ X₀ ∧ X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀
t₁₈: l1(X₀, X₁) → l2(X₀, 0) :|: X₀ ≤ X₁ ∧ X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀
t₁₉: l2(X₀, X₁) → l2(X₀, X₁+1) :|: X₁+1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀
t₂₀: l2(X₀, X₁) → l3(X₀, 0) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀
t₂₁: l3(X₀, X₁) → l3(X₀, X₁+1) :|: X₁+1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀
t₂₂: l3(X₀, X₁) → l4(X₀, X₁) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀

MPRF for transition t₁₇: l1(X₀, X₁) → l1(X₀, X₁+1) :|: X₁+1 ≤ X₀ ∧ X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ of depth 1:

new bound:

11 {O(1)}

MPRF for transition t₁₉: l2(X₀, X₁) → l2(X₀, X₁+1) :|: X₁+1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ of depth 1:

new bound:

10 {O(1)}

MPRF for transition t₂₁: l3(X₀, X₁) → l3(X₀, X₁+1) :|: X₁+1 ≤ X₀ ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀ of depth 1:

new bound:

10 {O(1)}

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)}