Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l2(X₀, X₁, X₂, X₃, X₄, X₅)
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ < X₄
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₀, X₂, X₃, X₄, X₅) :|: X₄ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₅, X₁, X₂, X₃, X₄, X₅)
t₄: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀+1, X₁, X₂, X₃, X₄, X₅)
t₅: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ < X₃
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l6(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ X₁
t₇: l5(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁+1, X₂, X₃, X₄, X₅)
t₈: l6(X₀, X₁, X₂, X₃, X₄, X₅) → l7(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

Eliminate variables {X₂} that do not contribute to the problem

Found invariant X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ for location l6

Found invariant X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁ for location l7

Found invariant 1+X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ X₁ for location l5

Found invariant X₄ ≤ X₀ for location l1

Found invariant X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₁ for location l4

Found invariant 1+X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1+X₀ ≤ X₃ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7
Transitions:
t₁₇: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₁₈: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀ < X₃ ∧ X₄ ≤ X₀
t₁₉: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₀, X₂, X₃, X₄) :|: X₃ ≤ X₀ ∧ X₄ ≤ X₀
t₂₀: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₄, X₁, X₂, X₃, X₄)
t₂₁: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀+1, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1+X₀ ≤ X₃
t₂₂: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₁ < X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₁
t₂₃: l4(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₁
t₂₄: l5(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁+1, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ X₁
t₂₅: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₀ ≤ X₁

MPRF for transition t₁₈: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀ < X₃ ∧ X₄ ≤ X₀ of depth 1:

new bound:

X₃+X₄ {O(n)}

MPRF for transition t₂₁: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀+1, X₁, X₂, X₃, X₄) :|: 1+X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1+X₀ ≤ X₃ of depth 1:

new bound:

X₃+X₄ {O(n)}

MPRF for transition t₂₂: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₁ < X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₁ of depth 1:

new bound:

2⋅X₂+3⋅X₄+X₃ {O(n)}

MPRF for transition t₂₄: l5(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁+1, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ X₀ ≤ X₁ of depth 1:

new bound:

2⋅X₂+3⋅X₄+X₃ {O(n)}

All Bounds

Timebounds

Overall timebound:4⋅X₂+4⋅X₃+8⋅X₄+5 {O(n)}
t₁₇: 1 {O(1)}
t₁₈: X₃+X₄ {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₃+X₄ {O(n)}
t₂₂: 2⋅X₂+3⋅X₄+X₃ {O(n)}
t₂₃: 1 {O(1)}
t₂₄: 2⋅X₂+3⋅X₄+X₃ {O(n)}
t₂₅: 1 {O(1)}

Costbounds

Overall costbound: 4⋅X₂+4⋅X₃+8⋅X₄+5 {O(n)}
t₁₇: 1 {O(1)}
t₁₈: X₃+X₄ {O(n)}
t₁₉: 1 {O(1)}
t₂₀: 1 {O(1)}
t₂₁: X₃+X₄ {O(n)}
t₂₂: 2⋅X₂+3⋅X₄+X₃ {O(n)}
t₂₃: 1 {O(1)}
t₂₄: 2⋅X₂+3⋅X₄+X₃ {O(n)}
t₂₅: 1 {O(1)}

Sizebounds

t₁₇, X₀: X₀ {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₇, X₄: X₄ {O(n)}
t₁₈, X₀: 2⋅X₄+X₃ {O(n)}
t₁₈, X₁: X₁ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₉, X₀: 3⋅X₄+X₃ {O(n)}
t₁₉, X₁: 3⋅X₄+X₃ {O(n)}
t₁₉, X₂: 2⋅X₂ {O(n)}
t₁₉, X₃: 2⋅X₃ {O(n)}
t₁₉, X₄: 2⋅X₄ {O(n)}
t₂₀, X₀: X₄ {O(n)}
t₂₀, X₁: X₁ {O(n)}
t₂₀, X₂: X₂ {O(n)}
t₂₀, X₃: X₃ {O(n)}
t₂₀, X₄: X₄ {O(n)}
t₂₁, X₀: 2⋅X₄+X₃ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₁, X₄: X₄ {O(n)}
t₂₂, X₀: 3⋅X₄+X₃ {O(n)}
t₂₂, X₁: 2⋅X₂+2⋅X₃+6⋅X₄ {O(n)}
t₂₂, X₂: 2⋅X₂ {O(n)}
t₂₂, X₃: 2⋅X₃ {O(n)}
t₂₂, X₄: 2⋅X₄ {O(n)}
t₂₃, X₀: 2⋅X₃+6⋅X₄ {O(n)}
t₂₃, X₁: 2⋅X₂+3⋅X₃+9⋅X₄ {O(n)}
t₂₃, X₂: 4⋅X₂ {O(n)}
t₂₃, X₃: 4⋅X₃ {O(n)}
t₂₃, X₄: 4⋅X₄ {O(n)}
t₂₄, X₀: 3⋅X₄+X₃ {O(n)}
t₂₄, X₁: 2⋅X₂+2⋅X₃+6⋅X₄ {O(n)}
t₂₄, X₂: 2⋅X₂ {O(n)}
t₂₄, X₃: 2⋅X₃ {O(n)}
t₂₄, X₄: 2⋅X₄ {O(n)}
t₂₅, X₀: 2⋅X₃+6⋅X₄ {O(n)}
t₂₅, X₁: 2⋅X₂+3⋅X₃+9⋅X₄ {O(n)}
t₂₅, X₂: 4⋅X₂ {O(n)}
t₂₅, X₃: 4⋅X₃ {O(n)}
t₂₅, X₄: 4⋅X₄ {O(n)}