KoAT2 Proof Output

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)
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁+X₀ < 0
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁+X₀
t₆: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃) :|: 2 ≤ X₂
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ < 2
t₅: l4(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁-X₀, X₂, X₃)

Preprocessing

Found invariant X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 2 ≤ X₀ for location l1

Found invariant X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 0 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l4

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) → l3(X₀, X₁, X₂, X₃)
t₄: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₁+X₀ < 0 ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 2 ≤ X₀
t₃: l1(X₀, X₁, X₂, X₃) → l4(X₀, X₁, X₂, X₃) :|: 0 ≤ X₁+X₀ ∧ X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 2 ≤ X₀
t₆: l2(X₀, X₁, X₂, X₃) → l5(X₀, X₁, X₂, X₃)
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃) :|: 2 ≤ X₂
t₂: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₂ < 2
t₅: l4(X₀, X₁, X₂, X₃) → l1(X₀+1, X₁-X₀, X₂, X₃) :|: X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 0 ≤ X₀+X₁ ∧ 2 ≤ X₀

Found invariant X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 2 ≤ X₀ for location l1

Found invariant X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 0 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l4

Time-Bound by TWN-Loops:

TWN-Loops: t₃ 4⋅X₃+11 {O(n)}

TWN-Loops:

entry: t₁: l3(X₀, X₁, X₂, X₃) → l1(X₂, X₃, X₂, X₃) :|: 2 ≤ X₂

results in twn-loop: twn:Inv: [X₁ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 2 ≤ X₀ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 0 ≤ X₀+X₁ ∧ 2 ≤ X₀] , (X₀,X₁,X₂,X₃) -> (X₀+1,X₁-X₀,X₂,X₃) :|: 0 ≤ X₁+X₀

order: [X₀; X₁; X₂; X₃]
closed-form:

X₀: X₀ + [[n != 0]] * n^1
X₁: X₁ + [[n != 0]] * -X₀ * n^1 + [[n != 0, n != 1]] * -1/2 * n^2 + [[n != 0, n != 1]] * 1/2 * n^1
X₂: X₂
X₃: X₃

Termination: true
Formula:

0 < 1 ∧ 1 < 0
∨ 1 < 0 ∧ 0 < 1 ∧ 2⋅X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 0 < 1 ∧ 0 < 2⋅X₀+2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀
∨ 1 < 0 ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₀+2⋅X₁ ∧ 2⋅X₀+2⋅X₁ ≤ 0
∨ 1 < 2⋅X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ 1 < 0 ∧ 1 < 2⋅X₀ ∧ 2⋅X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 < 2⋅X₀ ∧ 0 < 2⋅X₀+2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀
∨ 1 < 0 ∧ 1 < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₀+2⋅X₁ ∧ 2⋅X₀+2⋅X₁ ≤ 0
∨ 2⋅X₁ < 2⋅X₃ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 1 < 0
∨ 1 < 0 ∧ 2⋅X₁ < 2⋅X₃ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 2⋅X₁ < 2⋅X₃ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 0 < 2⋅X₀+2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀
∨ 1 < 0 ∧ 2⋅X₁ < 2⋅X₃ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₀+2⋅X₁ ∧ 2⋅X₀+2⋅X₁ ≤ 0
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₁ ≤ 2⋅X₃ ∧ 2⋅X₃ ≤ 2⋅X₁ ∧ 1 < 0
∨ 1 < 0 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₁ ≤ 2⋅X₃ ∧ 2⋅X₃ ≤ 2⋅X₁ ∧ 2⋅X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 1 < 0 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₁ ≤ 2⋅X₃ ∧ 2⋅X₃ ≤ 2⋅X₁ ∧ 0 < 2⋅X₀+2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀
∨ 1 < 0 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₁ ≤ 2⋅X₃ ∧ 2⋅X₃ ≤ 2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₀+2⋅X₁ ∧ 2⋅X₀+2⋅X₁ ≤ 0
∨ 2⋅X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 0 < 1 ∧ 1 < 0
∨ 2⋅X₀ < 3 ∧ 0 < 1 ∧ 2⋅X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₀ < 3 ∧ 0 < 1 ∧ 0 < 2⋅X₀+2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀
∨ 2⋅X₀ < 3 ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₀+2⋅X₁ ∧ 2⋅X₀+2⋅X₁ ≤ 0
∨ 2⋅X₀ < 3 ∧ 1 < 2⋅X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ 2⋅X₀ < 3 ∧ 1 < 2⋅X₀ ∧ 2⋅X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₀ < 3 ∧ 1 < 2⋅X₀ ∧ 0 < 2⋅X₀+2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀
∨ 2⋅X₀ < 3 ∧ 1 < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₀+2⋅X₁ ∧ 2⋅X₀+2⋅X₁ ≤ 0
∨ 2⋅X₀ < 3 ∧ 2⋅X₁ < 2⋅X₃ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 1 < 0
∨ 2⋅X₀ < 3 ∧ 2⋅X₁ < 2⋅X₃ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₀ < 3 ∧ 2⋅X₁ < 2⋅X₃ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 0 < 2⋅X₀+2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀
∨ 2⋅X₀ < 3 ∧ 2⋅X₁ < 2⋅X₃ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₀+2⋅X₁ ∧ 2⋅X₀+2⋅X₁ ≤ 0
∨ 2⋅X₀ < 3 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₁ ≤ 2⋅X₃ ∧ 2⋅X₃ ≤ 2⋅X₁ ∧ 1 < 0
∨ 2⋅X₀ < 3 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₁ ≤ 2⋅X₃ ∧ 2⋅X₃ ≤ 2⋅X₁ ∧ 2⋅X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₀ < 3 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₁ ≤ 2⋅X₃ ∧ 2⋅X₃ ≤ 2⋅X₁ ∧ 0 < 2⋅X₀+2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀
∨ 2⋅X₀ < 3 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₁ ≤ 2⋅X₃ ∧ 2⋅X₃ ≤ 2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₀+2⋅X₁ ∧ 2⋅X₀+2⋅X₁ ≤ 0
∨ 0 < 2⋅X₁+2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 < 1 ∧ 1 < 0
∨ 0 < 2⋅X₁+2⋅X₀ ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 < 1 ∧ 2⋅X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 2⋅X₁+2⋅X₀ ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 < 1 ∧ 0 < 2⋅X₀+2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀
∨ 0 < 2⋅X₁+2⋅X₀ ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₀+2⋅X₁ ∧ 2⋅X₀+2⋅X₁ ≤ 0
∨ 0 < 2⋅X₁+2⋅X₀ ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 1 < 2⋅X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ 0 < 2⋅X₁+2⋅X₀ ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 1 < 2⋅X₀ ∧ 2⋅X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 2⋅X₁+2⋅X₀ ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 1 < 2⋅X₀ ∧ 0 < 2⋅X₀+2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀
∨ 0 < 2⋅X₁+2⋅X₀ ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 1 < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₀+2⋅X₁ ∧ 2⋅X₀+2⋅X₁ ≤ 0
∨ 0 < 2⋅X₁+2⋅X₀ ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 2⋅X₁ < 2⋅X₃ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 1 < 0
∨ 0 < 2⋅X₁+2⋅X₀ ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 2⋅X₁ < 2⋅X₃ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 2⋅X₁+2⋅X₀ ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 2⋅X₁ < 2⋅X₃ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 0 < 2⋅X₀+2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀
∨ 0 < 2⋅X₁+2⋅X₀ ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 2⋅X₁ < 2⋅X₃ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₀+2⋅X₁ ∧ 2⋅X₀+2⋅X₁ ≤ 0
∨ 0 < 2⋅X₁+2⋅X₀ ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₁ ≤ 2⋅X₃ ∧ 2⋅X₃ ≤ 2⋅X₁ ∧ 1 < 0
∨ 0 < 2⋅X₁+2⋅X₀ ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₁ ≤ 2⋅X₃ ∧ 2⋅X₃ ≤ 2⋅X₁ ∧ 2⋅X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 0 < 2⋅X₁+2⋅X₀ ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₁ ≤ 2⋅X₃ ∧ 2⋅X₃ ≤ 2⋅X₁ ∧ 0 < 2⋅X₀+2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀
∨ 0 < 2⋅X₁+2⋅X₀ ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₁ ≤ 2⋅X₃ ∧ 2⋅X₃ ≤ 2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₀+2⋅X₁ ∧ 2⋅X₀+2⋅X₁ ≤ 0
∨ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₁+2⋅X₀ ∧ 2⋅X₁+2⋅X₀ ≤ 0 ∧ 0 < 1 ∧ 1 < 0
∨ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₁+2⋅X₀ ∧ 2⋅X₁+2⋅X₀ ≤ 0 ∧ 0 < 1 ∧ 2⋅X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₁+2⋅X₀ ∧ 2⋅X₁+2⋅X₀ ≤ 0 ∧ 0 < 1 ∧ 0 < 2⋅X₀+2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀
∨ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₁+2⋅X₀ ∧ 2⋅X₁+2⋅X₀ ≤ 0 ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₀+2⋅X₁ ∧ 2⋅X₀+2⋅X₁ ≤ 0
∨ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₁+2⋅X₀ ∧ 2⋅X₁+2⋅X₀ ≤ 0 ∧ 1 < 2⋅X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₁+2⋅X₀ ∧ 2⋅X₁+2⋅X₀ ≤ 0 ∧ 1 < 2⋅X₀ ∧ 2⋅X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₁+2⋅X₀ ∧ 2⋅X₁+2⋅X₀ ≤ 0 ∧ 1 < 2⋅X₀ ∧ 0 < 2⋅X₀+2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀
∨ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₁+2⋅X₀ ∧ 2⋅X₁+2⋅X₀ ≤ 0 ∧ 1 < 2⋅X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₀+2⋅X₁ ∧ 2⋅X₀+2⋅X₁ ≤ 0
∨ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₁+2⋅X₀ ∧ 2⋅X₁+2⋅X₀ ≤ 0 ∧ 2⋅X₁ < 2⋅X₃ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 1 < 0
∨ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₁+2⋅X₀ ∧ 2⋅X₁+2⋅X₀ ≤ 0 ∧ 2⋅X₁ < 2⋅X₃ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₁+2⋅X₀ ∧ 2⋅X₁+2⋅X₀ ≤ 0 ∧ 2⋅X₁ < 2⋅X₃ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 0 < 2⋅X₀+2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀
∨ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₁+2⋅X₀ ∧ 2⋅X₁+2⋅X₀ ≤ 0 ∧ 2⋅X₁ < 2⋅X₃ ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₀+2⋅X₁ ∧ 2⋅X₀+2⋅X₁ ≤ 0
∨ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₁+2⋅X₀ ∧ 2⋅X₁+2⋅X₀ ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₁ ≤ 2⋅X₃ ∧ 2⋅X₃ ≤ 2⋅X₁ ∧ 1 < 0
∨ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₁+2⋅X₀ ∧ 2⋅X₁+2⋅X₀ ≤ 0 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₁ ≤ 2⋅X₃ ∧ 2⋅X₃ ≤ 2⋅X₁ ∧ 2⋅X₀ < 3 ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₁+2⋅X₀ ∧ 2⋅X₁+2⋅X₀ ≤ 0 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₁ ≤ 2⋅X₃ ∧ 2⋅X₃ ≤ 2⋅X₁ ∧ 0 < 2⋅X₀+2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀
∨ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₁+2⋅X₀ ∧ 2⋅X₁+2⋅X₀ ≤ 0 ∧ 1 ≤ 2⋅X₀ ∧ 2⋅X₀ ≤ 1 ∧ 2⋅X₁ ≤ 2⋅X₃ ∧ 2⋅X₃ ≤ 2⋅X₁ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2⋅X₀ ≤ 3 ∧ 3 ≤ 2⋅X₀ ∧ 0 ≤ 2⋅X₀+2⋅X₁ ∧ 2⋅X₀+2⋅X₁ ≤ 0

Stabilization-Threshold for: 0 ≤ X₁+X₀

alphas_abs: 3+2⋅X₁
M: 0
N: 2
Bound: 4⋅X₁+9 {O(n)}

relevant size-bounds w.r.t. t₁:
X₁: X₃ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 4⋅X₃+11 {O(n)}

4⋅X₃+11 {O(n)}

Time-Bound by TWN-Loops:

TWN-Loops: t₅ 4⋅X₃+11 {O(n)}

relevant size-bounds w.r.t. t₁:
X₁: X₃ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 4⋅X₃+11 {O(n)}

4⋅X₃+11 {O(n)}

All Bounds

Timebounds

Overall timebound:8⋅X₃+27 {O(n)}
t₀: 1 {O(1)}
t₃: 4⋅X₃+11 {O(n)}
t₄: 1 {O(1)}
t₆: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: 4⋅X₃+11 {O(n)}

Costbounds

Overall costbound: 8⋅X₃+27 {O(n)}
t₀: 1 {O(1)}
t₃: 4⋅X₃+11 {O(n)}
t₄: 1 {O(1)}
t₆: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: 4⋅X₃+11 {O(n)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₃, X₀: 4⋅X₃+X₂+11 {O(n)}
t₃, X₁: 16⋅X₃⋅X₃+4⋅X₂⋅X₃+12⋅X₂+93⋅X₃+132 {O(n^2)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₄, X₀: 2⋅X₂+4⋅X₃+11 {O(n)}
t₄, X₁: 16⋅X₃⋅X₃+4⋅X₂⋅X₃+12⋅X₂+94⋅X₃+132 {O(n^2)}
t₄, X₂: 2⋅X₂ {O(n)}
t₄, X₃: 2⋅X₃ {O(n)}
t₆, X₀: 2⋅X₂+4⋅X₃+X₀+11 {O(n)}
t₆, X₁: 16⋅X₃⋅X₃+4⋅X₂⋅X₃+12⋅X₂+94⋅X₃+X₁+132 {O(n^2)}
t₆, X₂: 3⋅X₂ {O(n)}
t₆, X₃: 3⋅X₃ {O(n)}
t₁, X₀: X₂ {O(n)}
t₁, X₁: X₃ {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)}
t₅, X₀: 4⋅X₃+X₂+11 {O(n)}
t₅, X₁: 16⋅X₃⋅X₃+4⋅X₂⋅X₃+12⋅X₂+93⋅X₃+132 {O(n^2)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}