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) → l4(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 2+X₁ < X₀
t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 2+X₀ < X₁
t₆: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁+2 ∧ X₁ ≤ X₀+2
t₇: l2(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₀ < X₁ ∧ X₀ < X₁
t₈: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃) :|: X₀ < X₁ ∧ X₁ ≤ X₀
t₉: l2(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁+1, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₀ < X₁
t₁₀: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₁ ≤ X₀
t₁₁: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₃: l4(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃) :|: 0 ≤ X₂ ∧ 0 ≤ X₃
t₁: l4(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₂ < 0
t₂: l4(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃ < 0
Preprocessing
Cut unsatisfiable transition t₈: l2→l1
Cut unsatisfiable transition t₉: l2→l1
Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l1
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 2+X₁ < X₀ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 2+X₀ < X₁ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₆: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₀ ≤ X₁+2 ∧ X₁ ≤ X₀+2 ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₇: l2(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₀ < X₁ ∧ X₀ < X₁ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₀: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₁: l3(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₃: l4(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃) :|: 0 ≤ X₂ ∧ 0 ≤ X₃
t₁: l4(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₂ < 0
t₂: l4(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: X₃ < 0
MPRF for transition t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 2+X₁ < X₀ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₂+X₃+2 {O(n)}
MPRF for transition t₅: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 2+X₀ < X₁ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₂+X₃+4 {O(n)}
MPRF for transition t₇: l2(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁, X₂, X₃) :|: X₀ < X₁ ∧ X₀ < X₁ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₂+X₃+1 {O(n)}
MPRF for transition t₁₀: l2(X₀, X₁, X₂, X₃) → l1(X₀, X₁+1, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:
new bound:
X₂+X₃+1 {O(n)}
All Bounds
Timebounds
Overall timebound:4⋅X₂+4⋅X₃+14 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: X₂+X₃+2 {O(n)}
t₅: X₂+X₃+4 {O(n)}
t₆: 1 {O(1)}
t₇: X₂+X₃+1 {O(n)}
t₁₀: X₂+X₃+1 {O(n)}
t₁₁: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₂+4⋅X₃+14 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: X₂+X₃+2 {O(n)}
t₅: X₂+X₃+4 {O(n)}
t₆: 1 {O(1)}
t₇: X₂+X₃+1 {O(n)}
t₁₀: X₂+X₃+1 {O(n)}
t₁₁: 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: X₂ {O(n)}
t₃, X₁: X₃ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: X₂ {O(n)}
t₄, X₁: 2⋅X₃+X₂+1 {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₅, X₀: 2⋅X₂+X₃+1 {O(n)}
t₅, X₁: X₃ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: 4⋅X₂+X₃+1 {O(n)}
t₆, X₁: 4⋅X₃+X₂+1 {O(n)}
t₆, X₂: 3⋅X₂ {O(n)}
t₆, X₃: 3⋅X₃ {O(n)}
t₇, X₀: 2⋅X₂+X₃+1 {O(n)}
t₇, X₁: X₃ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₁₀, X₀: X₂ {O(n)}
t₁₀, X₁: 2⋅X₃+X₂+1 {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₁, X₀: 2⋅X₀+4⋅X₂+X₃+1 {O(n)}
t₁₁, X₁: 2⋅X₁+4⋅X₃+X₂+1 {O(n)}
t₁₁, X₂: 5⋅X₂ {O(n)}
t₁₁, X₃: 5⋅X₃ {O(n)}