Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 < X₀
t₈: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₃, X₁, X₂, X₃) :|: 0 < X₂ ∧ X₂ < X₃
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ ≤ 0
t₃: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂
t₆: l4(X₀, X₁, X₂, X₃) → l1(X₀-1, X₁, X₂, X₃) :|: X₀ < X₂
t₇: l4(X₀, X₁, X₂, X₃) → l1(X₀-X₂, X₁, X₂, X₃) :|: X₂ ≤ X₀

Preprocessing

Eliminate variables {X₁} that do not contribute to the problem

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ for location l1

Found invariant 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l4

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₁₇: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₁₈: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁
t₁₉: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 0 < X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁
t₂₀: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₂₁: l3(X₀, X₁, X₂) → l1(X₂, X₁, X₂) :|: 0 < X₁ ∧ X₁ < X₂
t₂₂: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁ ≤ 0
t₂₃: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₂ ≤ X₁
t₂₄: l4(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₀ < X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₂₅: l4(X₀, X₁, X₂) → l1(X₀-X₁, X₁, X₂) :|: X₁ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₁₉: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 0 < X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ of depth 1:

new bound:

X₂ {O(n)}

MPRF for transition t₂₄: l4(X₀, X₁, X₂) → l1(X₀-1, X₁, X₂) :|: X₀ < X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF for transition t₂₅: l4(X₀, X₁, X₂) → l1(X₀-X₁, X₁, X₂) :|: X₁ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

All Bounds

Timebounds

Overall timebound:3⋅X₂+6 {O(n)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: X₂ {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: X₂ {O(n)}
t₂₅: X₂ {O(n)}

Costbounds

Overall costbound: 3⋅X₂+6 {O(n)}
t₁₇: 1 {O(1)}
t₁₈: 1 {O(1)}
t₁₉: X₂ {O(n)}
t₂₀: 1 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 1 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: X₂ {O(n)}
t₂₅: X₂ {O(n)}

Sizebounds

t₁₇, X₀: X₀ {O(n)}
t₁₇, X₁: X₁ {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₈, X₀: 2⋅X₂ {O(n)}
t₁₈, X₁: 2⋅X₁ {O(n)}
t₁₈, X₂: 2⋅X₂ {O(n)}
t₁₉, X₀: X₂ {O(n)}
t₁₉, X₁: X₁ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₂₀, X₀: 2⋅X₀+2⋅X₂ {O(n)}
t₂₀, X₁: 4⋅X₁ {O(n)}
t₂₀, X₂: 4⋅X₂ {O(n)}
t₂₁, X₀: X₂ {O(n)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₂, X₀: X₀ {O(n)}
t₂₂, X₁: X₁ {O(n)}
t₂₂, X₂: X₂ {O(n)}
t₂₃, X₀: X₀ {O(n)}
t₂₃, X₁: X₁ {O(n)}
t₂₃, X₂: X₂ {O(n)}
t₂₄, X₀: X₂ {O(n)}
t₂₄, X₁: X₁ {O(n)}
t₂₄, X₂: X₂ {O(n)}
t₂₅, X₀: X₂ {O(n)}
t₂₅, X₁: X₁ {O(n)}
t₂₅, X₂: X₂ {O(n)}