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

Found invariant X₄ ≤ X₁ ∧ X₃ ≤ X₀ for location l5

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

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

Found invariant 1+X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+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) :|: X₀ < X₂ ∧ X₁ < X₂ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀
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) :|: 1+X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂
t₆: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₁ ∧ X₃ ≤ X₀

MPRF for transition t₂: l1(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄) :|: X₀ < X₂ ∧ X₁ < X₂ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₂+X₄ {O(n)}

MPRF for transition t₅: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀+1, X₁+1, X₂, X₃, X₄) :|: 1+X₄ ≤ X₂ ∧ X₄ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ of depth 1:

new bound:

X₂+X₃ {O(n)}

All Bounds

Timebounds

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

Costbounds

Overall costbound: 2⋅X₂+X₃+X₄+5 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂+X₄ {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: X₂+X₃ {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)}
t₁, X₀: X₃ {O(n)}
t₁, X₁: X₄ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: 2⋅X₃+X₂ {O(n)}
t₂, X₁: X₂+X₃+X₄ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: 3⋅X₃+X₂ {O(n)}
t₃, X₁: 2⋅X₄+X₂+X₃ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₃ {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₄, X₀: 3⋅X₃+X₂ {O(n)}
t₄, X₁: 2⋅X₄+X₂+X₃ {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₄, X₄: 2⋅X₄ {O(n)}
t₅, X₀: 2⋅X₃+X₂ {O(n)}
t₅, X₁: X₂+X₃+X₄ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₀: 2⋅X₂+6⋅X₃ {O(n)}
t₆, X₁: 2⋅X₂+2⋅X₃+4⋅X₄ {O(n)}
t₆, X₂: 4⋅X₂ {O(n)}
t₆, X₃: 4⋅X₃ {O(n)}
t₆, X₄: 4⋅X₄ {O(n)}