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) :|: X₁ < X₀
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ X₁
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l1(X₃, X₄, X₂, X₃, X₄)
t₄: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀+1, X₁+2, X₂, X₃, X₄)
t₅: 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 X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₁ for location l5

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

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

Found invariant X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ 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:
t₁₂: l0(X₀, X₁, X₃, X₄) → l2(X₀, X₁, X₃, X₄)
t₁₃: l1(X₀, X₁, X₃, X₄) → l3(X₀, X₁, X₃, X₄) :|: X₁ < X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀
t₁₄: l1(X₀, X₁, X₃, X₄) → l4(X₀, X₁, X₃, X₄) :|: X₀ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀
t₁₅: l2(X₀, X₁, X₃, X₄) → l1(X₃, X₄, X₃, X₄)
t₁₆: l3(X₀, X₁, X₃, X₄) → l1(X₀+1, X₁+2, X₃, X₄) :|: X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀
t₁₇: l4(X₀, X₁, X₃, X₄) → l5(X₀, X₁, X₃, X₄) :|: X₄ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₁

MPRF for transition t₁₃: l1(X₀, X₁, X₃, X₄) → l3(X₀, X₁, X₃, X₄) :|: X₁ < X₀ ∧ X₄ ≤ X₁ ∧ X₃ ≤ X₀ of depth 1:

new bound:

X₃+X₄ {O(n)}

MPRF:

l3 [X₀-X₁-1 ]
l1 [X₀-X₁ ]

MPRF for transition t₁₆: l3(X₀, X₁, X₃, X₄) → l1(X₀+1, X₁+2, X₃, X₄) :|: X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ X₃ ≤ X₀ ∧ 1+X₁ ≤ X₀ of depth 1:

new bound:

X₃+X₄ {O(n)}

MPRF:

l3 [X₀-X₁ ]
l1 [X₀-X₁ ]

All Bounds

Timebounds

Overall timebound:2⋅X₃+2⋅X₄+4 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: X₃+X₄ {O(n)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: X₃+X₄ {O(n)}
t₁₇: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₃+2⋅X₄+4 {O(n)}
t₁₂: 1 {O(1)}
t₁₃: X₃+X₄ {O(n)}
t₁₄: 1 {O(1)}
t₁₅: 1 {O(1)}
t₁₆: X₃+X₄ {O(n)}
t₁₇: 1 {O(1)}

Sizebounds

t₁₂, X₀: X₀ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₃, X₀: 2⋅X₃+X₄ {O(n)}
t₁₃, X₁: 2⋅X₃+3⋅X₄ {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₄, X₀: 3⋅X₃+X₄ {O(n)}
t₁₄, X₁: 2⋅X₃+4⋅X₄ {O(n)}
t₁₄, X₃: 2⋅X₃ {O(n)}
t₁₄, X₄: 2⋅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+X₄ {O(n)}
t₁₆, X₁: 2⋅X₃+3⋅X₄ {O(n)}
t₁₆, X₃: X₃ {O(n)}
t₁₆, X₄: X₄ {O(n)}
t₁₇, X₀: 3⋅X₃+X₄ {O(n)}
t₁₇, X₁: 2⋅X₃+4⋅X₄ {O(n)}
t₁₇, X₃: 2⋅X₃ {O(n)}
t₁₇, X₄: 2⋅X₄ {O(n)}