Initial Problem

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₃: l1(X₀, X₁) → l4(X₀, X₁)
t₁₀: l10(X₀, X₁) → l8(X₀, X₁)
t₁₂: l11(X₀, X₁) → l12(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, X₁)
t₆: l6(X₀, X₁) → l7(X₀, 0)
t₈: l7(X₀, X₁) → l11(X₀, X₁) :|: X₀ ≤ X₁
t₇: l7(X₀, X₁) → l9(X₀, X₁) :|: X₁ < X₀
t₁₁: l8(X₀, X₁) → l7(X₀, X₁+1)
t₉: l9(X₀, X₁) → l10(X₀, X₁)

Preprocessing

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l11

Found invariant 0 ≤ X₁ ∧ X₀ ≤ X₁ for location l12

Found invariant 0 ≤ X₁ for location l7

Found invariant 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l8

Found invariant 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l10

Found invariant 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l9

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁) → l2(X₀, X₁)
t₃: l1(X₀, X₁) → l4(X₀, X₁)
t₁₀: l10(X₀, X₁) → l8(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁₂: l11(X₀, X₁) → l12(X₀, X₁) :|: 0 ≤ X₁ ∧ 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, X₁)
t₆: l6(X₀, X₁) → l7(X₀, 0)
t₈: l7(X₀, X₁) → l11(X₀, X₁) :|: X₀ ≤ X₁ ∧ 0 ≤ X₁
t₇: l7(X₀, X₁) → l9(X₀, X₁) :|: X₁ < X₀ ∧ 0 ≤ X₁
t₁₁: l8(X₀, X₁) → l7(X₀, X₁+1) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₉: l9(X₀, X₁) → l10(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₇: l7(X₀, X₁) → l9(X₀, X₁) :|: X₁ < X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₀ {O(n)}

MPRF for transition t₉: l9(X₀, X₁) → l10(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF for transition t₁₀: l10(X₀, X₁) → l8(X₀, X₁) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

MPRF for transition t₁₁: l8(X₀, X₁) → l7(X₀, X₁+1) :|: 1+X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₀ {O(n)}

All Bounds

Timebounds

Overall timebound:4⋅X₀+9 {O(n)}
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: X₀ {O(n)}
t₈: 1 {O(1)}
t₉: X₀ {O(n)}
t₁₀: X₀ {O(n)}
t₁₁: X₀ {O(n)}
t₁₂: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₀+9 {O(n)}
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: X₀ {O(n)}
t₈: 1 {O(1)}
t₉: X₀ {O(n)}
t₁₀: X₀ {O(n)}
t₁₁: X₀ {O(n)}
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: X₁ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: 0 {O(1)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₀ {O(n)}
t₈, X₀: 2⋅X₀ {O(n)}
t₈, X₁: X₀ {O(n)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₀ {O(n)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₀ {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₀ {O(n)}
t₁₂, X₀: 2⋅X₀ {O(n)}
t₁₂, X₁: X₀ {O(n)}