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) :|: X₀ < X₃ ∧ X₁ < X₃
t₃: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l4(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₄, X₅, 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 X₅ ≤ X₁ ∧ X₄ ≤ X₀ for location l5

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ for location l1

Found invariant X₅ ≤ X₁ ∧ X₄ ≤ X₀ for location l4

Found invariant 1+X₅ ≤ X₃ ∧ X₅ ≤ X₁ ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₄: l0(X₀, X₁, X₃, X₄, X₅) → l2(X₀, X₁, X₃, X₄, X₅)
t₁₅: l1(X₀, X₁, X₃, X₄, X₅) → l3(X₀, X₁, X₃, X₄, X₅) :|: X₀ < X₃ ∧ X₁ < X₃ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₀
t₁₆: l1(X₀, X₁, X₃, X₄, X₅) → l4(X₀, X₁, X₃, X₄, X₅) :|: X₃ ≤ X₀ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₀
t₁₇: l1(X₀, X₁, X₃, X₄, X₅) → l4(X₀, X₁, X₃, X₄, X₅) :|: X₃ ≤ X₁ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₀
t₁₈: l2(X₀, X₁, X₃, X₄, X₅) → l1(X₄, X₅, X₃, X₄, X₅)
t₁₉: l3(X₀, X₁, X₃, X₄, X₅) → l1(X₀+1, X₁+1, X₃, X₄, X₅) :|: 1+X₅ ≤ X₃ ∧ X₅ ≤ X₁ ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃
t₂₀: l4(X₀, X₁, X₃, X₄, X₅) → l5(X₀, X₁, X₃, X₄, X₅) :|: X₅ ≤ X₁ ∧ X₄ ≤ X₀

MPRF for transition t₁₅: l1(X₀, X₁, X₃, X₄, X₅) → l3(X₀, X₁, X₃, X₄, X₅) :|: X₀ < X₃ ∧ X₁ < X₃ ∧ X₅ ≤ X₁ ∧ X₄ ≤ X₀ of depth 1:

new bound:

X₃+X₅ {O(n)}

MPRF:

l3 [X₃-X₁-1 ]
l1 [X₃-X₁ ]

MPRF for transition t₁₉: l3(X₀, X₁, X₃, X₄, X₅) → l1(X₀+1, X₁+1, X₃, X₄, X₅) :|: 1+X₅ ≤ X₃ ∧ X₅ ≤ X₁ ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ 1+X₀ ≤ X₃ of depth 1:

new bound:

X₃+X₄ {O(n)}

MPRF:

l3 [X₃-X₀ ]
l1 [X₃-X₀ ]

All Bounds

Timebounds

Overall timebound:2⋅X₃+X₄+X₅+5 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: X₃+X₅ {O(n)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: X₃+X₄ {O(n)}
t₂₀: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₃+X₄+X₅+5 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: X₃+X₅ {O(n)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: X₃+X₄ {O(n)}
t₂₀: 1 {O(1)}

Sizebounds

t₁₄, X₀: X₀ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₄, X₅: X₅ {O(n)}
t₁₅, X₀: 2⋅X₄+X₃ {O(n)}
t₁₅, X₁: X₃+X₄+X₅ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₅, X₅: X₅ {O(n)}
t₁₆, X₀: 3⋅X₄+X₃ {O(n)}
t₁₆, X₁: 2⋅X₅+X₃+X₄ {O(n)}
t₁₆, X₃: 2⋅X₃ {O(n)}
t₁₆, X₄: 2⋅X₄ {O(n)}
t₁₆, X₅: 2⋅X₅ {O(n)}
t₁₇, X₀: 3⋅X₄+X₃ {O(n)}
t₁₇, X₁: 2⋅X₅+X₃+X₄ {O(n)}
t₁₇, X₃: 2⋅X₃ {O(n)}
t₁₇, X₄: 2⋅X₄ {O(n)}
t₁₇, X₅: 2⋅X₅ {O(n)}
t₁₈, X₀: X₄ {O(n)}
t₁₈, X₁: X₅ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₈, X₅: X₅ {O(n)}
t₁₉, X₀: 2⋅X₄+X₃ {O(n)}
t₁₉, X₁: X₃+X₄+X₅ {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₁₉, X₄: X₄ {O(n)}
t₁₉, X₅: X₅ {O(n)}
t₂₀, X₀: 2⋅X₃+6⋅X₄ {O(n)}
t₂₀, X₁: 2⋅X₃+2⋅X₄+4⋅X₅ {O(n)}
t₂₀, X₃: 4⋅X₃ {O(n)}
t₂₀, X₄: 4⋅X₄ {O(n)}
t₂₀, X₅: 4⋅X₅ {O(n)}