Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₉: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃) :|: 0 < X₀ ∧ 0 < X₀
t₁₀: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₂-1, X₂, X₃) :|: 0 < X₀ ∧ X₀ ≤ 0
t₁₁: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₁, X₃) :|: X₀ ≤ 0 ∧ 0 < X₀
t₁₂: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₂-1, X₁, X₃) :|: X₀ ≤ 0 ∧ X₀ ≤ 0
t₆: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃)
t₈: l3(X₀, X₁, X₂, X₃) → l1(nondef.0, X₁, X₂, X₃)
t₄: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁
t₅: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ < X₃
t₃: l5(X₀, X₁, X₂, X₃) → l4(X₀, 2⋅X₃, 2⋅X₃, X₃)
t₁₃: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₁: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃
t₂: l7(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₃ < 0

Preprocessing

Cut unsatisfiable transition t₁₀: l1→l4

Cut unsatisfiable transition t₁₁: l1→l4

Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l2

Found invariant 0 ≤ X₃ for location l5

Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l1

Found invariant X₃ ≤ X₂ ∧ X₃ ≤ 1+X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₁ for location l4

Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ for location l3

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: nondef.0
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l7(X₀, X₁, X₂, X₃)
t₉: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃) :|: 0 < X₀ ∧ 0 < X₀ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₁₂: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₂-1, X₁, X₃) :|: X₀ ≤ 0 ∧ X₀ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₆: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₈: l3(X₀, X₁, X₂, X₃) → l1(nondef.0, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁
t₄: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₁
t₅: l4(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₁ < X₃ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₁
t₃: l5(X₀, X₁, X₂, X₃) → l4(X₀, 2⋅X₃, 2⋅X₃, X₃) :|: 0 ≤ X₃
t₁₃: l6(X₀, X₁, X₂, X₃) → l8(X₀, X₁, X₂, X₃)
t₁: l7(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: 0 ≤ X₃
t₂: l7(X₀, X₁, X₂, X₃) → l6(X₀, X₁, X₂, X₃) :|: X₃ < 0

MPRF for transition t₄: l4(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ 1+X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ 1+X₁+X₂ ∧ 0 ≤ 1+X₁ of depth 1:

new bound:

4⋅X₃+2 {O(n)}

MPRF for transition t₆: l2(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

4⋅X₃+1 {O(n)}

MPRF for transition t₈: l3(X₀, X₁, X₂, X₃) → l1(nondef.0, X₁, X₂, X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

4⋅X₃+1 {O(n)}

MPRF for transition t₉: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁-1, X₂, X₃) :|: 0 < X₀ ∧ 0 < X₀ ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

4⋅X₃+1 {O(n)}

MPRF for transition t₁₂: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₂-1, X₁, X₃) :|: X₀ ≤ 0 ∧ X₀ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁ of depth 1:

new bound:

4⋅X₃+1 {O(n)}

All Bounds

Timebounds

Overall timebound:20⋅X₃+12 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 4⋅X₃+2 {O(n)}
t₅: 1 {O(1)}
t₆: 4⋅X₃+1 {O(n)}
t₈: 4⋅X₃+1 {O(n)}
t₉: 4⋅X₃+1 {O(n)}
t₁₂: 4⋅X₃+1 {O(n)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 20⋅X₃+12 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 4⋅X₃+2 {O(n)}
t₅: 1 {O(1)}
t₆: 4⋅X₃+1 {O(n)}
t₈: 4⋅X₃+1 {O(n)}
t₉: 4⋅X₃+1 {O(n)}
t₁₂: 4⋅X₃+1 {O(n)}
t₁₃: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: 2⋅X₃ {O(n)}
t₃, X₂: 2⋅X₃ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₁: 4⋅X₃+1 {O(n)}
t₄, X₂: 4⋅X₃+1 {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₁: 8⋅X₃+2 {O(n)}
t₅, X₂: 8⋅X₃+2 {O(n)}
t₅, X₃: 2⋅X₃ {O(n)}
t₆, X₁: 4⋅X₃+1 {O(n)}
t₆, X₂: 4⋅X₃+1 {O(n)}
t₆, X₃: X₃ {O(n)}
t₈, X₁: 4⋅X₃+1 {O(n)}
t₈, X₂: 4⋅X₃+1 {O(n)}
t₈, X₃: X₃ {O(n)}
t₉, X₁: 4⋅X₃+1 {O(n)}
t₉, X₂: 4⋅X₃+1 {O(n)}
t₉, X₃: X₃ {O(n)}
t₁₂, X₁: 4⋅X₃+1 {O(n)}
t₁₂, X₂: 4⋅X₃+1 {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₃, X₁: 8⋅X₃+X₁+2 {O(n)}
t₁₃, X₂: 8⋅X₃+X₂+2 {O(n)}
t₁₃, X₃: 3⋅X₃ {O(n)}