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

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:
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) :|: X₄ < X₀ ∧ X₄ < X₁ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₄ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₄ ∧ X₁ ≤ X₃ ∧ X₀ ≤ X₂
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₂, X₃, X₂, X₃, X₄)
t₅: 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
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₃ ∧ X₀ ≤ X₂

MPRF for transition t₂: 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:

l3 [X₀-X₄-1 ]
l1 [X₀-X₄ ]

MPRF for transition t₅: 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)}

MPRF:

l3 [X₁-X₄ ]
l1 [X₁-X₄ ]

All Bounds

Timebounds

Overall timebound:2⋅X₄+X₂+X₃+5 {O(n)}
t₀: 1 {O(1)}
t₂: X₂+X₄ {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₅: X₃+X₄ {O(n)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₄+X₂+X₃+5 {O(n)}
t₀: 1 {O(1)}
t₂: X₂+X₄ {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₅: X₃+X₄ {O(n)}
t₆: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₂, X₀: X₂+X₃+X₄ {O(n)}
t₂, X₁: 2⋅X₃+X₄ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: 2⋅X₂+X₃+X₄ {O(n)}
t₃, X₁: 3⋅X₃+X₄ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₄, X₀: 2⋅X₂+X₃+X₄ {O(n)}
t₄, X₁: 3⋅X₃+X₄ {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₅, X₀: X₂+X₃+X₄ {O(n)}
t₅, X₁: 2⋅X₃+X₄ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₀: 2⋅X₃+2⋅X₄+4⋅X₂ {O(n)}
t₆, X₁: 2⋅X₄+6⋅X₃ {O(n)}
t₆, X₂: 4⋅X₂ {O(n)}
t₆, X₃: 4⋅X₃ {O(n)}
t₆, X₄: 4⋅X₄ {O(n)}