Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: F
Locations: l0, l1, l2
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l1(F, F, 10, 0, X₄)
t₁: l1(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃+1, F) :|: X₃+1 ≤ X₂
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₃

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 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

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l2
Transitions:
t₆: l0(X₀, X₁) → l1(10, 0)
t₇: 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
t₈: l1(X₀, X₁) → l2(X₀, X₁) :|: X₀ ≤ X₁ ∧ X₁ ≤ 10 ∧ X₁ ≤ X₀ ∧ X₀+X₁ ≤ 20 ∧ 0 ≤ X₁ ∧ 10 ≤ X₀+X₁ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 10 ∧ 10 ≤ X₀

MPRF for transition t₇: 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)}

All Bounds

Timebounds

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

Costbounds

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