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 ≤ X₄ ∧ X₀ ≤ X₃ for location l5

Found invariant X₁ ≤ X₄ ∧ X₀ ≤ X₃ for location l1

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

Found invariant 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ 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) :|: X₅ < X₀ ∧ X₅ < X₁ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃
t₁₆: l1(X₀, X₁, X₃, X₄, X₅) → l4(X₀, X₁, X₃, X₄, X₅) :|: X₀ ≤ X₅ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃
t₁₇: l1(X₀, X₁, X₃, X₄, X₅) → l4(X₀, X₁, X₃, X₄, X₅) :|: X₁ ≤ X₅ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃
t₁₈: l2(X₀, X₁, X₃, X₄, X₅) → l1(X₃, X₄, X₃, X₄, X₅)
t₁₉: l3(X₀, X₁, X₃, X₄, X₅) → l1(X₀-1, X₁-1, X₃, X₄, X₅) :|: 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₁ ∧ 1+X₅ ≤ X₀ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃
t₂₀: l4(X₀, X₁, X₃, X₄, X₅) → l5(X₀, X₁, X₃, X₄, X₅) :|: X₁ ≤ X₄ ∧ X₀ ≤ X₃

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

new bound:

X₃+X₅ {O(n)}

MPRF:

l3 [X₀-X₅-1 ]
l1 [X₀-X₅ ]

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

new bound:

X₄+X₅ {O(n)}

MPRF:

l3 [X₁-X₅ ]
l1 [X₁-X₅ ]

All Bounds

Timebounds

Overall timebound:2⋅X₅+X₃+X₄+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: X₄+X₅ {O(n)}
t₂₀: 1 {O(1)}

Costbounds

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