Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: nondef_0
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₃: l1(X₀, X₁) → l4(X₀, X₁)
t₁: l2(X₀, X₁) → l3(X₀, X₁)
t₂: l3(X₀, X₁) → l1(X₀, X₁)
t₄: l4(X₀, X₁) → l5(X₀, X₁)
t₅: l5(X₀, X₁) → l6(X₀, 0)
t₆: l6(X₀, X₁) → l8(X₀, X₁)
t₈: l7(X₀, X₁) → l6(X₀, X₀) :|: X₀ ≤ X₁+2 ∧ 1+X₁ ≤ X₀ ∧ X₀ < 10
t₉: l7(X₀, X₁) → l9(X₀, X₁) :|: 2+X₁ < X₀
t₁₀: l7(X₀, X₁) → l9(X₀, X₁) :|: X₀ < X₁+1
t₁₁: l7(X₀, X₁) → l9(X₀, X₁) :|: 10 ≤ X₀
t₇: l8(X₀, X₁) → l7(nondef_0, X₁)
t₁₂: l9(X₀, X₁) → l10(X₀, X₁)

Preprocessing

Found invariant X₁ ≤ 9 ∧ 0 ≤ X₁ for location l6

Found invariant 0 ≤ X₁ for location l7

Found invariant 0 ≤ X₁ for location l8

Found invariant 0 ≤ X₁ for location l10

Found invariant 0 ≤ X₁ for location l9

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: nondef_0
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₃: l1(X₀, X₁) → l4(X₀, X₁)
t₁: l2(X₀, X₁) → l3(X₀, X₁)
t₂: l3(X₀, X₁) → l1(X₀, X₁)
t₄: l4(X₀, X₁) → l5(X₀, X₁)
t₅: l5(X₀, X₁) → l6(X₀, 0)
t₆: l6(X₀, X₁) → l8(X₀, X₁) :|: X₁ ≤ 9 ∧ 0 ≤ X₁
t₈: l7(X₀, X₁) → l6(X₀, X₀) :|: X₀ ≤ X₁+2 ∧ 1+X₁ ≤ X₀ ∧ X₀ < 10 ∧ 0 ≤ X₁
t₉: l7(X₀, X₁) → l9(X₀, X₁) :|: 2+X₁ < X₀ ∧ 0 ≤ X₁
t₁₀: l7(X₀, X₁) → l9(X₀, X₁) :|: X₀ < X₁+1 ∧ 0 ≤ X₁
t₁₁: l7(X₀, X₁) → l9(X₀, X₁) :|: 10 ≤ X₀ ∧ 0 ≤ X₁
t₇: l8(X₀, X₁) → l7(nondef_0, X₁) :|: 0 ≤ X₁
t₁₂: l9(X₀, X₁) → l10(X₀, X₁) :|: 0 ≤ X₁

MPRF for transition t₆: l6(X₀, X₁) → l8(X₀, X₁) :|: X₁ ≤ 9 ∧ 0 ≤ X₁ of depth 1:

new bound:

10 {O(1)}

MPRF for transition t₈: l7(X₀, X₁) → l6(X₀, X₀) :|: X₀ ≤ X₁+2 ∧ 1+X₁ ≤ X₀ ∧ X₀ < 10 ∧ 0 ≤ X₁ of depth 1:

new bound:

9 {O(1)}

knowledge_propagation leads to new time bound 10 {O(1)} for transition t₇: l8(X₀, X₁) → l7(nondef_0, X₁) :|: 0 ≤ X₁

All Bounds

Timebounds

Overall timebound:39 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 10 {O(1)}
t₇: 10 {O(1)}
t₈: 9 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}

Costbounds

Overall costbound: 39 {O(1)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 10 {O(1)}
t₇: 10 {O(1)}
t₈: 9 {O(1)}
t₉: 1 {O(1)}
t₁₀: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁₂: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: 0 {O(1)}
t₆, X₀: X₀+9 {O(n)}
t₆, X₁: 9 {O(1)}
t₇, X₁: 9 {O(1)}
t₈, X₀: 9 {O(1)}
t₈, X₁: 9 {O(1)}
t₉, X₁: 9 {O(1)}
t₁₀, X₁: 9 {O(1)}
t₁₁, X₁: 9 {O(1)}
t₁₂, X₁: 27 {O(1)}