Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: nondef_0
Locations: l0, l1, l10, l11, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₃: l1(X₀, X₁) → l4(X₀, X₁)
t₁₃: l10(X₀, X₁) → l11(X₀, X₁)
t₁: l2(X₀, X₁) → l3(nondef_0, X₁)
t₂: l3(X₀, X₁) → l1(X₀, X₁)
t₄: l4(X₀, X₁) → l5(X₀, X₁)
t₅: l5(X₀, X₁) → l6(X₀, X₁)
t₆: l6(X₀, X₁) → l7(X₀, X₁)
t₇: l7(X₀, X₁) → l8(X₀, 0)
t₉: l8(X₀, X₁) → l10(X₀, X₁) :|: 40 ≤ X₁
t₈: l8(X₀, X₁) → l9(X₀, X₁) :|: X₁ < 40
t₁₀: l9(X₀, X₁) → l8(X₀, X₁+1) :|: X₀ ≤ 0 ∧ 0 ≤ X₀
t₁₁: l9(X₀, X₁) → l8(X₀, X₁+2) :|: X₀ < 0
t₁₂: l9(X₀, X₁) → l8(X₀, X₁+2) :|: 0 < X₀

Preprocessing

Found invariant 40 ≤ X₁ for location l11

Found invariant 0 ≤ X₁ for location l8

Found invariant 40 ≤ X₁ for location l10

Found invariant X₁ ≤ 39 ∧ 0 ≤ X₁ for location l9

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars: nondef_0
Locations: l0, l1, l10, l11, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₃: l1(X₀, X₁) → l4(X₀, X₁)
t₁₃: l10(X₀, X₁) → l11(X₀, X₁) :|: 40 ≤ X₁
t₁: l2(X₀, X₁) → l3(nondef_0, X₁)
t₂: l3(X₀, X₁) → l1(X₀, X₁)
t₄: l4(X₀, X₁) → l5(X₀, X₁)
t₅: l5(X₀, X₁) → l6(X₀, X₁)
t₆: l6(X₀, X₁) → l7(X₀, X₁)
t₇: l7(X₀, X₁) → l8(X₀, 0)
t₉: l8(X₀, X₁) → l10(X₀, X₁) :|: 40 ≤ X₁ ∧ 0 ≤ X₁
t₈: l8(X₀, X₁) → l9(X₀, X₁) :|: X₁ < 40 ∧ 0 ≤ X₁
t₁₀: l9(X₀, X₁) → l8(X₀, X₁+1) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 39 ∧ 0 ≤ X₁
t₁₁: l9(X₀, X₁) → l8(X₀, X₁+2) :|: X₀ < 0 ∧ X₁ ≤ 39 ∧ 0 ≤ X₁
t₁₂: l9(X₀, X₁) → l8(X₀, X₁+2) :|: 0 < X₀ ∧ X₁ ≤ 39 ∧ 0 ≤ X₁

MPRF for transition t₈: l8(X₀, X₁) → l9(X₀, X₁) :|: X₁ < 40 ∧ 0 ≤ X₁ of depth 1:

new bound:

40 {O(1)}

MPRF for transition t₁₀: l9(X₀, X₁) → l8(X₀, X₁+1) :|: X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₁ ≤ 39 ∧ 0 ≤ X₁ of depth 1:

new bound:

40 {O(1)}

MPRF for transition t₁₁: l9(X₀, X₁) → l8(X₀, X₁+2) :|: X₀ < 0 ∧ X₁ ≤ 39 ∧ 0 ≤ X₁ of depth 1:

new bound:

40 {O(1)}

MPRF for transition t₁₂: l9(X₀, X₁) → l8(X₀, X₁+2) :|: 0 < X₀ ∧ X₁ ≤ 39 ∧ 0 ≤ X₁ of depth 1:

new bound:

40 {O(1)}

All Bounds

Timebounds

Overall timebound:170 {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: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 40 {O(1)}
t₉: 1 {O(1)}
t₁₀: 40 {O(1)}
t₁₁: 40 {O(1)}
t₁₂: 40 {O(1)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 170 {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: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 40 {O(1)}
t₉: 1 {O(1)}
t₁₀: 40 {O(1)}
t₁₁: 40 {O(1)}
t₁₂: 40 {O(1)}
t₁₃: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₂, X₁: X₁ {O(n)}
t₃, X₁: X₁ {O(n)}
t₄, X₁: X₁ {O(n)}
t₅, X₁: X₁ {O(n)}
t₆, X₁: X₁ {O(n)}
t₇, X₁: 0 {O(1)}
t₈, X₁: 39 {O(1)}
t₉, X₁: 122 {O(1)}
t₁₀, X₀: 0 {O(1)}
t₁₀, X₁: 40 {O(1)}
t₁₁, X₁: 41 {O(1)}
t₁₂, X₁: 41 {O(1)}
t₁₃, X₁: 122 {O(1)}