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) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ X₀ < X₁
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(2⋅X₀, X₁+1, X₂, X₃)
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
Preprocessing
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location l5
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location l1
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location l4
Found invariant X₃ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3
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) → l2(X₀, X₁, X₂, X₃)
t₂: l1(X₀, X₁, X₂, X₃) → l3(X₀, X₁, X₂, X₃) :|: 0 < X₀ ∧ X₀ < X₁ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 0 ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
t₅: l3(X₀, X₁, X₂, X₃) → l1(2⋅X₀, X₁+1, X₂, X₃) :|: X₃ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀
t₆: l4(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃) :|: X₃ ≤ X₁ ∧ X₂ ≤ X₀
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location l5
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location l1
Found invariant X₃ ≤ X₁ ∧ X₂ ≤ X₀ for location l4
Found invariant X₃ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location l3
Time-Bound by TWN-Loops:
TWN-Loops: t₂ 2⋅X₃+11 {O(n)}
TWN-Loops:
entry: t₁: l2(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃)
results in twn-loop: twn:Inv: [X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀] , (X₀,X₁,X₂,X₃) -> (2⋅X₀,X₁+1,X₂,X₃) :|: 0 < X₀ ∧ X₀ < X₁
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀ * 2^n
X₁: X₁ + [[n != 0]] * n^1
X₂: X₂
X₃: X₃
Termination: true
Formula:
X₀ < 0 ∧ 0 < X₀
∨ 0 < X₀ ∧ X₀ < 0 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < X₀ ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ X₀ < 0 ∧ 0 < 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ X₀ < 0 ∧ 0 < X₀ ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 0 < X₀ ∧ 0 < 1 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 0 ∧ 0 < X₀ ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ X₀ < 0 ∧ 1 < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 0 < X₀ ∧ 1 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 0 < X₀ ∧ 1 < X₁ ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 0 ∧ 0 < X₀ ∧ 1 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ X₀ < 0 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀
∨ X₀ < 0 ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 0 < X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 0 ∧ 0 < X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ X₂ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ < 0 ∧ 0 < X₀
∨ 0 < X₀ ∧ X₂ < 0 ∧ X₀ < 0 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < X₀ ∧ X₂ < 0 ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ X₀ < 0 ∧ X₂ < 0 ∧ 0 < 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ X₀ < 0 ∧ 0 < X₀ ∧ X₂ < 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 0 < X₀ ∧ X₂ < 0 ∧ 0 < 1 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 0 ∧ 0 < X₀ ∧ X₂ < 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ X₀ < 0 ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 0 < X₀ ∧ X₂ < 0 ∧ 1 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 0 < X₀ ∧ X₂ < 0 ∧ 1 < X₁ ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 0 ∧ 0 < X₀ ∧ X₂ < 0 ∧ 1 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ X₀ < 0 ∧ X₂ < 0 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀
∨ X₀ < 0 ∧ 0 < X₀ ∧ X₂ < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 0 < X₀ ∧ X₂ < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 0 ∧ 0 < X₀ ∧ X₂ < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ < 0 ∧ 0 < X₀
∨ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ < 0 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ X₀ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ X₀ < 0 ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < 1 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 0 ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ X₀ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₀
∨ X₀ < 0 ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 < X₁ ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 0 ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ X₀ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀
∨ X₀ < 0 ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ X₀ < 0 ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ X₀ < 0 ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ < 0 ∧ 0 < X₀
∨ 0 < X₀ ∧ X₀ < 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < 1 ∧ 0 < X₀ ∧ X₀ < 0 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < 1 ∧ 0 < X₀ ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ 0 < X₀ ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₀ ∧ 0 < 1 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < X₀ ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < 1 ∧ 1 < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₀
∨ 0 < X₀ ∧ 1 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < 1 ∧ 0 < X₀ ∧ 1 < X₁ ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < 1 ∧ 0 < X₀ ∧ 1 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀
∨ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < 1 ∧ 0 < X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < 1 ∧ 0 < X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < 1 ∧ X₂ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ < 0 ∧ 0 < X₀
∨ 0 < X₀ ∧ X₂ < 0 ∧ X₀ < 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < 1 ∧ 0 < X₀ ∧ X₂ < 0 ∧ X₀ < 0 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < 1 ∧ 0 < X₀ ∧ X₂ < 0 ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ X₂ < 0 ∧ 0 < 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ 0 < X₀ ∧ X₂ < 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₀ ∧ X₂ < 0 ∧ 0 < 1 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < X₀ ∧ X₂ < 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < 1 ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₀
∨ 0 < X₀ ∧ X₂ < 0 ∧ 1 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < 1 ∧ 0 < X₀ ∧ X₂ < 0 ∧ 1 < X₁ ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < 1 ∧ 0 < X₀ ∧ X₂ < 0 ∧ 1 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < 1 ∧ X₂ < 0 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀
∨ 0 < X₀ ∧ X₂ < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < 1 ∧ 0 < X₀ ∧ X₂ < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < 1 ∧ 0 < X₀ ∧ X₂ < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ < 0 ∧ 0 < X₀
∨ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ < 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < 1 ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ < 0 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < 1 ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < 1 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₀
∨ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < 1 ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 < X₁ ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < 1 ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀
∨ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < 1 ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < 1 ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₀ < 0 ∧ 0 < X₀
∨ 0 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₀ ∧ X₀ < 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₀ < 0 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ 0 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₀ ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ 0 < 1 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < X₁ ∧ 1 < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₀
∨ 0 < X₁ ∧ 0 < X₀ ∧ 1 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ 1 < X₁ ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ 1 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀
∨ 0 < X₁ ∧ 0 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₂ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ < 0 ∧ 0 < X₀
∨ 0 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₀ ∧ X₂ < 0 ∧ X₀ < 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ < 0 ∧ X₀ < 0 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ < 0 ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₂ < 0 ∧ 0 < 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ 0 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₀ ∧ X₂ < 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ < 0 ∧ 0 < 1 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ < 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < X₁ ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₀
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ < 0 ∧ 1 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ < 0 ∧ 1 < X₁ ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ < 0 ∧ 1 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < X₁ ∧ X₂ < 0 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ < 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ < 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ < 0 ∧ 0 < X₀
∨ 0 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ < 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ < 0 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ < 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < 1 ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 < X₀
∨ 0 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < 1 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 < X₁ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < X₀
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 < X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 < X₁ ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
∨ 0 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₀ ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < X₀
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 < 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 3 < X₁ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0
∨ 0 < X₁ ∧ 0 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3
Stabilization-Threshold for: X₀ < X₁
alphas_abs: 1+X₁
M: 5
N: 2
Bound: 2⋅X₁+8 {O(n)}
relevant size-bounds w.r.t. t₁:
X₁: X₃ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₃+11 {O(n)}
2⋅X₃+11 {O(n)}
Time-Bound by TWN-Loops:
TWN-Loops: t₅ 2⋅X₃+11 {O(n)}
relevant size-bounds w.r.t. t₁:
X₁: X₃ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₃+11 {O(n)}
2⋅X₃+11 {O(n)}
All Bounds
Timebounds
Overall timebound:4⋅X₃+27 {O(n)}
t₀: 1 {O(1)}
t₂: 2⋅X₃+11 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₅: 2⋅X₃+11 {O(n)}
t₆: 1 {O(1)}
Costbounds
Overall costbound: 4⋅X₃+27 {O(n)}
t₀: 1 {O(1)}
t₂: 2⋅X₃+11 {O(n)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₁: 1 {O(1)}
t₅: 2⋅X₃+11 {O(n)}
t₆: 1 {O(1)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₂, X₀: 2^(2⋅X₃+11)⋅X₂ {O(EXP)}
t₂, X₁: 3⋅X₃+11 {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: 2^(2⋅X₃+11)⋅X₂+X₂ {O(EXP)}
t₄, X₁: 4⋅X₃+11 {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₅, X₀: 2^(2⋅X₃+11)⋅X₂ {O(EXP)}
t₅, X₁: 3⋅X₃+11 {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₆, X₀: 2^(2⋅X₃+11)⋅X₂+2⋅X₂ {O(EXP)}
t₆, X₁: 5⋅X₃+11 {O(n)}
t₆, X₂: 3⋅X₂ {O(n)}
t₆, X₃: 3⋅X₃ {O(n)}