Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, 1, 0)
t₁: l1(X₀, X₁, X₂) → l2(X₀-1, X₁, X₁) :|: 0 < X₀
t₃: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₀ ≤ 0
t₂: l2(X₀, X₁, X₂) → l1(X₀, X₂+X₁, X₂)
t₄: l3(X₀, X₁, X₂) → l3(X₀, X₁-1, X₂) :|: 0 < X₁
Preprocessing
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l1
Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₀: l0(X₀, X₁, X₂) → l1(X₀, 1, 0)
t₁: l1(X₀, X₁, X₂) → l2(X₀-1, X₁, X₁) :|: 0 < X₀ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₃: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
t₂: l2(X₀, X₁, X₂) → l1(X₀, X₂+X₁, X₂) :|: X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₄: l3(X₀, X₁, X₂) → l3(X₀, X₁-1, X₂) :|: 0 < X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l1
Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l3
Time-Bound by TWN-Loops:
TWN-Loops: t₁ 2⋅X₀+4 {O(n)}
TWN-Loops:
entry: t₀: l0(X₀, X₁, X₂) → l1(X₀, 1, 0)
results in twn-loop: twn:Inv: [1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ ∧ 0 ≤ 0 ∧ 1 ≤ X₁ ∧ 2 ≤ 2⋅X₁ ∧ 0 ≤ 0 ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀] , (X₀,X₁,X₂) -> (X₀-1,2⋅X₁,X₁) :|: 0 < X₀
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀ + [[n != 0]] * -1 * n^1
X₁: X₁ * 2^n
X₂: [[n == 0]] * X₂ + [[n != 0]] * 1/2⋅X₁ * 2^n
Termination: true
Formula:
1 < 0 ∧ 0 < 3⋅X₁ ∧ 0 < X₁
∨ 1 < 0 ∧ 0 < X₁ ∧ 0 < 3⋅X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 0 < X₁ ∧ 0 < 3⋅X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁
∨ 1 < 0 ∧ 0 < X₁ ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 < X₁
∨ 1 < 0 ∧ 0 < X₁ ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 0 < X₁ ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < 3⋅X₁ ∧ 0 < X₁
∨ 1 < 0 ∧ 0 < 3⋅X₁ ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 0 < 3⋅X₁ ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 0 < 3⋅X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 1 < 0 ∧ 0 < 3⋅X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 0 < 3⋅X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁
∨ 1 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 1 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 < X₁
∨ 1 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 1 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 3⋅X₁ ∧ 0 < X₁
∨ 1 < 0 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 3⋅X₁ ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 3⋅X₁ ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 3⋅X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 1 < 0 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 3⋅X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 3⋅X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁
∨ 1 < 0 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 1 < 0 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 2 < X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 < X₁
∨ 1 < 0 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 1 < 0 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 < 3⋅X₁ ∧ 0 < X₁
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 < 3⋅X₁ ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 < 3⋅X₁ ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 < 3⋅X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 < 3⋅X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 < 3⋅X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 < X₁
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 3⋅X₁ ∧ 0 < X₁
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 3⋅X₁ ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 3⋅X₁ ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 3⋅X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₁ ∧ 0 < 3⋅X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₁ ∧ 0 < 3⋅X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₁ ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 < X₁
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₁ ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₁ ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < 3⋅X₁ ∧ 0 < X₁
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 < 3⋅X₁ ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 < 3⋅X₁ ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 < 3⋅X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 < 3⋅X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 < 3⋅X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 < X₁
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 2 < X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 3⋅X₁ ∧ 0 < X₁
∨ 0 < X₀ ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 3⋅X₁ ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 3⋅X₁ ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 3⋅X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 0 < X₀ ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 3⋅X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 3⋅X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 2 < X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁
∨ 0 < X₀ ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 0 < X₀ ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 2 < X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 < X₁
∨ 0 < X₀ ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 0 < X₀ ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 2 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 < 3⋅X₁ ∧ 0 < X₁
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 < 3⋅X₁ ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 < 3⋅X₁ ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 < 3⋅X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 < 3⋅X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 < 3⋅X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 2 < 0 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 < X₁
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 < X₁ ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 < X₁ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 0 < X₁
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2 ∧ 2 < 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
∨ 0 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₀ ∧ X₀ ≤ 2 ∧ 0 ≤ 3⋅X₁ ∧ 3⋅X₁ ≤ 0 ∧ 0 ≤ X₁ ∧ X₁ ≤ 0 ∧ 2 ≤ 0 ∧ 0 ≤ 2
Stabilization-Threshold for: 0 < X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
relevant size-bounds w.r.t. t₀:
X₀: X₀ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 2⋅X₀+4 {O(n)}
2⋅X₀+4 {O(n)}
Time-Bound by TWN-Loops:
TWN-Loops: t₂ 2⋅X₀+4 {O(n)}
relevant size-bounds w.r.t. t₀:
X₀: X₀ {O(n)}
Runtime-bound of t₀: 1 {O(1)}
Results in: 2⋅X₀+4 {O(n)}
2⋅X₀+4 {O(n)}
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l1
Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l3
Time-Bound by TWN-Loops:
TWN-Loops: t₄ 2⋅2^(2⋅X₀+4)+6 {O(EXP)}
TWN-Loops:
entry: t₃: l1(X₀, X₁, X₂) → l3(X₀, X₁, X₂) :|: X₀ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁
results in twn-loop: twn:Inv: [0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0] , (X₀,X₁,X₂) -> (X₀,X₁-1,X₂) :|: 0 < X₁
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * -1 * n^1
X₂: X₂
Termination: true
Formula:
1 < 0
∨ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1
Stabilization-Threshold for: 0 < X₁
alphas_abs: X₁
M: 0
N: 1
Bound: 2⋅X₁+2 {O(n)}
relevant size-bounds w.r.t. t₃:
X₁: 2^(2⋅X₀+4)+1 {O(EXP)}
Runtime-bound of t₃: 1 {O(1)}
Results in: 2⋅2^(2⋅X₀+4)+6 {O(EXP)}
2⋅2^(2⋅X₀+4)+6 {O(EXP)}
Analysing control-flow refined program
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l3___2
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l1
Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l3___1
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l3
Found invariant X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l2
Found invariant X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l3___2
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location l1
Found invariant 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0 for location n_l3___1
Found invariant 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ X₀ ≤ 0 for location l3
Time-Bound by TWN-Loops:
TWN-Loops: t₅₀ 2⋅2^(2⋅X₀+4)+8 {O(EXP)}
TWN-Loops:
entry: t₅₁: n_l3___2(X₀, X₁, X₂) → n_l3___1(X₀, X₁-1, X₂) :|: X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₁ ∧ X₀ ≤ 0 ∧ X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0
results in twn-loop: twn:Inv: [0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₀ ≤ 0] , (X₀,X₁,X₂) -> (X₀,X₁-1,X₂) :|: X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 < X₁ ∧ X₀ ≤ 0
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀
X₁: X₁ + [[n != 0]] * -1 * n^1
X₂: X₂
Termination: true
Formula:
X₀ < 0 ∧ 1 < 0 ∧ 0 < X₂
∨ X₀ < 0 ∧ 1 < 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ < 0 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₂
∨ X₀ < 0 ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0 ∧ 0 < X₂
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 1 < 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < X₂
∨ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0
Stabilization-Threshold for: 0 < X₁
alphas_abs: X₁
M: 0
N: 1
Bound: 2⋅X₁+2 {O(n)}
relevant size-bounds w.r.t. t₅₁:
X₁: 2^(2⋅X₀+4)+1 {O(EXP)}
Runtime-bound of t₅₁: 1 {O(1)}
Results in: 2⋅2^(2⋅X₀+4)+8 {O(EXP)}
2⋅2^(2⋅X₀+4)+8 {O(EXP)}
CFR did not improve the program. Rolling back
All Bounds
Timebounds
Overall timebound:2⋅2^(2⋅X₀+4)+4⋅X₀+16 {O(EXP)}
t₀: 1 {O(1)}
t₁: 2⋅X₀+4 {O(n)}
t₃: 1 {O(1)}
t₂: 2⋅X₀+4 {O(n)}
t₄: 2⋅2^(2⋅X₀+4)+6 {O(EXP)}
Costbounds
Overall costbound: 2⋅2^(2⋅X₀+4)+4⋅X₀+16 {O(EXP)}
t₀: 1 {O(1)}
t₁: 2⋅X₀+4 {O(n)}
t₃: 1 {O(1)}
t₂: 2⋅X₀+4 {O(n)}
t₄: 2⋅2^(2⋅X₀+4)+6 {O(EXP)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: 1 {O(1)}
t₀, X₂: 0 {O(1)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: 2^(2⋅X₀+4) {O(EXP)}
t₁, X₂: 2^(2⋅X₀+4)+1 {O(EXP)}
t₃, X₀: 2⋅X₀ {O(n)}
t₃, X₁: 2^(2⋅X₀+4)+1 {O(EXP)}
t₃, X₂: 2^(2⋅X₀+4)+1 {O(EXP)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: 2^(2⋅X₀+4) {O(EXP)}
t₂, X₂: 2^(2⋅X₀+4)+1 {O(EXP)}
t₄, X₀: 2⋅X₀ {O(n)}
t₄, X₁: 2^(2⋅X₀+4)+1 {O(EXP)}
t₄, X₂: 2^(2⋅X₀+4)+1 {O(EXP)}