Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: 0 < X₀ ∧ 0 < X₁
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 0
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 0
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₄, X₂, X₃, X₄)
t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀-1, X₁-1, X₂, X₃, X₄)
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)

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 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₃, X₄
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₄: l0(X₀, X₁, X₃, X₄) → l2(X₀, X₁, X₃, X₄)
t₁₅: l1(X₀, X₁, X₃, X₄) → l3(X₀, X₁, X₃, X₄) :|: 0 < X₀ ∧ 0 < X₁ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃
t₁₆: l1(X₀, X₁, X₃, X₄) → l4(X₀, X₁, X₃, X₄) :|: X₀ ≤ 0 ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃
t₁₇: l1(X₀, X₁, X₃, X₄) → l4(X₀, X₁, X₃, X₄) :|: X₁ ≤ 0 ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃
t₁₈: l2(X₀, X₁, X₃, X₄) → l1(X₃, X₄, X₃, X₄)
t₁₉: l3(X₀, X₁, X₃, X₄) → l1(X₀-1, X₁-1, X₃, X₄) :|: 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₀: l4(X₀, X₁, X₃, X₄) → l5(X₀, X₁, X₃, X₄) :|: X₁ ≤ X₄ ∧ X₀ ≤ X₃

MPRF for transition t₁₅: l1(X₀, X₁, X₃, X₄) → l3(X₀, X₁, X₃, X₄) :|: 0 < X₀ ∧ 0 < X₁ ∧ X₁ ≤ X₄ ∧ X₀ ≤ X₃ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l3 [X₁-1 ]
l1 [X₁ ]

MPRF for transition t₁₉: l3(X₀, X₁, X₃, X₄) → l1(X₀-1, X₁-1, X₃, X₄) :|: 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l3 [X₁ ]
l1 [X₁ ]

All Bounds

Timebounds

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

Costbounds

Overall costbound: 2⋅X₄+5 {O(n)}
t₁₄: 1 {O(1)}
t₁₅: X₄ {O(n)}
t₁₆: 1 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: 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)}
t₁₅, X₀: X₃ {O(n)}
t₁₅, X₁: X₄ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₆, X₀: 2⋅X₃ {O(n)}
t₁₆, X₁: 2⋅X₄ {O(n)}
t₁₆, X₃: 2⋅X₃ {O(n)}
t₁₆, X₄: 2⋅X₄ {O(n)}
t₁₇, X₀: 2⋅X₃ {O(n)}
t₁₇, X₁: 2⋅X₄ {O(n)}
t₁₇, X₃: 2⋅X₃ {O(n)}
t₁₇, X₄: 2⋅X₄ {O(n)}
t₁₈, X₀: X₃ {O(n)}
t₁₈, X₁: X₄ {O(n)}
t₁₈, X₃: X₃ {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₉, X₀: X₃ {O(n)}
t₁₉, X₁: X₄ {O(n)}
t₁₉, X₃: X₃ {O(n)}
t₁₉, X₄: X₄ {O(n)}
t₂₀, X₀: 4⋅X₃ {O(n)}
t₂₀, X₁: 4⋅X₄ {O(n)}
t₂₀, X₃: 4⋅X₃ {O(n)}
t₂₀, X₄: 4⋅X₄ {O(n)}