Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁₂: l10(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃)
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₂, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ < X₃
t₇: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₃, X₂, X₃) :|: X₃ ≤ X₀
t₈: l7(X₀, X₁, X₂, X₃) → l6(X₀+1, X₁, X₂, X₃)
t₁₀: l8(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁
t₉: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₁ < X₀
t₁₁: l9(X₀, X₁, X₂, X₃) → l8(X₀, X₁+1, X₂, X₃)

Preprocessing

Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l11

Found invariant X₂ ≤ X₀ for location l6

Found invariant 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ for location l7

Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ for location l8

Found invariant X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ for location l10

Found invariant X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ for location l9

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l10, l11, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃)
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₁₂: l10(X₀, X₁, X₂, X₃) → l11(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₂: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₅: l5(X₀, X₁, X₂, X₃) → l6(X₂, X₁, X₂, X₃)
t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ < X₃ ∧ X₂ ≤ X₀
t₇: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₃, X₂, X₃) :|: X₃ ≤ X₀ ∧ X₂ ≤ X₀
t₈: l7(X₀, X₁, X₂, X₃) → l6(X₀+1, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀
t₁₀: l8(X₀, X₁, X₂, X₃) → l10(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀
t₉: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀
t₁₁: l9(X₀, X₁, X₂, X₃) → l8(X₀, X₁+1, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀

MPRF for transition t₆: l6(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃) :|: X₀ < X₃ ∧ X₂ ≤ X₀ of depth 1:

new bound:

X₂+X₃ {O(n)}

MPRF for transition t₈: l7(X₀, X₁, X₂, X₃) → l6(X₀+1, X₁, X₂, X₃) :|: 1+X₂ ≤ X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ of depth 1:

new bound:

X₂+X₃ {O(n)}

MPRF for transition t₉: l8(X₀, X₁, X₂, X₃) → l9(X₀, X₁, X₂, X₃) :|: X₁ < X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₀ of depth 1:

new bound:

3⋅X₂+3⋅X₃+1 {O(n)}

MPRF for transition t₁₁: l9(X₀, X₁, X₂, X₃) → l8(X₀, X₁+1, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

3⋅X₂+3⋅X₃ {O(n)}

All Bounds

Timebounds

Overall timebound:8⋅X₂+8⋅X₃+10 {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: X₂+X₃ {O(n)}
t₇: 1 {O(1)}
t₈: X₂+X₃ {O(n)}
t₉: 3⋅X₂+3⋅X₃+1 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: 3⋅X₂+3⋅X₃ {O(n)}
t₁₂: 1 {O(1)}

Costbounds

Overall costbound: 8⋅X₂+8⋅X₃+10 {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: X₂+X₃ {O(n)}
t₇: 1 {O(1)}
t₈: X₂+X₃ {O(n)}
t₉: 3⋅X₂+3⋅X₃+1 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: 3⋅X₂+3⋅X₃ {O(n)}
t₁₂: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: X₂ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: 2⋅X₂+X₃ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: 3⋅X₂+X₃ {O(n)}
t₇, X₁: 2⋅X₃ {O(n)}
t₇, X₂: 2⋅X₂ {O(n)}
t₇, X₃: 2⋅X₃ {O(n)}
t₈, X₀: 2⋅X₂+X₃ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: X₃ {O(n)}
t₉, X₀: 3⋅X₂+X₃ {O(n)}
t₉, X₁: 3⋅X₂+5⋅X₃ {O(n)}
t₉, X₂: 2⋅X₂ {O(n)}
t₉, X₃: 2⋅X₃ {O(n)}
t₁₀, X₀: 2⋅X₃+6⋅X₂ {O(n)}
t₁₀, X₁: 3⋅X₂+7⋅X₃ {O(n)}
t₁₀, X₂: 4⋅X₂ {O(n)}
t₁₀, X₃: 4⋅X₃ {O(n)}
t₁₁, X₀: 3⋅X₂+X₃ {O(n)}
t₁₁, X₁: 3⋅X₂+5⋅X₃ {O(n)}
t₁₁, X₂: 2⋅X₂ {O(n)}
t₁₁, X₃: 2⋅X₃ {O(n)}
t₁₂, X₀: 2⋅X₃+6⋅X₂ {O(n)}
t₁₂, X₁: 3⋅X₂+7⋅X₃ {O(n)}
t₁₂, X₂: 4⋅X₂ {O(n)}
t₁₂, X₃: 4⋅X₃ {O(n)}