Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
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) :|: X₅ < X₀ ∧ X₅ < X₁
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₅
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ X₅
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₃, X₄, X₂, X₃, X₄, X₅)
t₅: l3(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀-1, X₁-1, X₂, X₃, X₄, X₅)
t₆: l4(X₀, X₁, X₂, X₃, X₄, X₅) → l5(X₀, X₁, X₂, X₃, X₄, X₅)

Preprocessing

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

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ for location l5

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ for location l1

Found invariant X₁ ≤ X₃ ∧ X₀ ≤ X₂ for location l4

Found invariant 1+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₃: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₁₄: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₄ < X₀ ∧ X₄ < X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₁₅: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₄ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₁₆: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₄ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₁₇: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₃, X₂, X₃, X₄)
t₁₈: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁-1, X₂, X₃, X₄) :|: 1+X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₁₉: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂

MPRF for transition t₁₄: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₄ < X₀ ∧ X₄ < X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂ of depth 1:

new bound:

X₂+X₄ {O(n)}

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

new bound:

X₃+X₄ {O(n)}

All Bounds

Timebounds

Overall timebound:2⋅X₄+X₂+X₃+5 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₂+X₄ {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: X₃+X₄ {O(n)}
t₁₉: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₄+X₂+X₃+5 {O(n)}
t₁₃: 1 {O(1)}
t₁₄: X₂+X₄ {O(n)}
t₁₅: 1 {O(1)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: X₃+X₄ {O(n)}
t₁₉: 1 {O(1)}

Sizebounds

t₁₃, X₀: X₀ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₄, X₀: X₂+X₃+X₄ {O(n)}
t₁₄, X₁: 2⋅X₃+X₄ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₅, X₀: 2⋅X₂+X₃+X₄ {O(n)}
t₁₅, X₁: 3⋅X₃+X₄ {O(n)}
t₁₅, X₂: 2⋅X₂ {O(n)}
t₁₅, X₃: 2⋅X₃ {O(n)}
t₁₅, X₄: 2⋅X₄ {O(n)}
t₁₆, X₀: 2⋅X₂+X₃+X₄ {O(n)}
t₁₆, X₁: 3⋅X₃+X₄ {O(n)}
t₁₆, X₂: 2⋅X₂ {O(n)}
t₁₆, X₃: 2⋅X₃ {O(n)}
t₁₆, X₄: 2⋅X₄ {O(n)}
t₁₇, X₀: X₂ {O(n)}
t₁₇, X₁: X₃ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₃ {O(n)}
t₁₇, X₄: X₄ {O(n)}
t₁₈, X₀: X₂+X₃+X₄ {O(n)}
t₁₈, X₁: 2⋅X₃+X₄ {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₉, X₀: 2⋅X₃+2⋅X₄+4⋅X₂ {O(n)}
t₁₉, X₁: 2⋅X₄+6⋅X₃ {O(n)}
t₁₉, X₂: 4⋅X₂ {O(n)}
t₁₉, X₃: 4⋅X₃ {O(n)}
t₁₉, X₄: 4⋅X₄ {O(n)}