Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₄: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₂, X₂, X₀)
t₃: l1(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1) :|: 2 ≤ X₃ ∧ 1 ≤ X₃ ∧ X₃+1 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁
t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 2 ≤ X₀ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1) :|: 2 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
t₀: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃
Preprocessing
Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l2
Found invariant 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀ for location l1
Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l3
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: l0, l1, l2, l3
Transitions:
t₄: l0(X₀, X₁, X₂, X₃) → l3(X₀, X₂, X₂, X₀)
t₃: l1(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1) :|: 2 ≤ X₃ ∧ 1 ≤ X₃ ∧ X₃+1 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀
t₂: l1(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: 2 ≤ X₀ ∧ X₃ ≤ 1 ∧ 1 ≤ X₃ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀
t₁: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1) :|: 2 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₀: l3(X₀, X₁, X₂, X₃) → l2(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1 ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₀ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l2
Found invariant 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀ for location l1
Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location l3
Time-Bound by TWN-Loops:
TWN-Loops: t₃ 8⋅X₀+18 {O(n)}
TWN-Loops:
entry: t₁: l3(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃-1) :|: 2 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
results in twn-loop: twn:Inv: [1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀] , (X₀,X₁,X₂,X₃) -> (X₀,X₁,X₂,X₃-1) :|: 2 ≤ X₃ ∧ 1 ≤ X₃ ∧ X₃+1 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁
order: [X₀; X₁; X₂; X₃]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂
X₃: X₃ + [[n != 0]] * -1 * n^1
Termination: true
Formula:
X₂ < X₁ ∧ X₁ < X₂ ∧ 0 < 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ 0 < 1 ∧ 1 < 0 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ 0 < 1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ 0 < 1 ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ 0 < 1 ∧ 1 < X₃ ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ 0 < 1 ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ 0 < 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ 0 < 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ X₃+1 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ X₃+1 < X₀ ∧ 1 < 0 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ X₃+1 < X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ X₃+1 < X₀ ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ X₃+1 < X₀ ∧ 1 < X₃ ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ X₃+1 < X₀ ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ X₃+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ X₃+1 < X₀ ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ X₃+1 < X₀ ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < 0
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < 0 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < X₃ ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ X₁ < X₂ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < 1 ∧ 1 < 0 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < 1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < 1 ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < 1 ∧ 1 < X₃ ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < 1 ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 < X₀ ∧ 1 < 0 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 < X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 < X₀ ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 < X₀ ∧ 1 < X₃ ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 < X₀ ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 < X₀ ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 < X₀ ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < 0
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < 0 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < X₃ ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 < 0
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ < X₁ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ 0 < 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ 0 < 1 ∧ 1 < 0 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ 0 < 1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ 0 < 1 ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ 0 < 1 ∧ 1 < X₃ ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ 0 < 1 ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ 0 < 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ 0 < 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ X₃+1 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ X₃+1 < X₀ ∧ 1 < 0 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ X₃+1 < X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ X₃+1 < X₀ ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ X₃+1 < X₀ ∧ 1 < X₃ ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ X₃+1 < X₀ ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ X₃+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ X₃+1 < X₀ ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ X₃+1 < X₀ ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < 0 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < X₃ ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ < X₂ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < 1 ∧ 1 < 0 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < 1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < 1 ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < 1 ∧ 1 < X₃ ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < 1 ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 < 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 < X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 < X₀ ∧ 1 < 0 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 < X₀ ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 < X₀ ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 < X₀ ∧ 1 < X₃ ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 < X₀ ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 < X₀ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 < X₀ ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 < X₀ ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < 0 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < 0 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < X₃ ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 < 0
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 2 < X₃ ∧ 1 ≤ 0 ∧ 0 ≤ 1
∨ X₂ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₂ ∧ X₂ ≤ X₁ ∧ X₃+1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1 ≤ X₃ ∧ X₃ ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ 1 ∧ 2 ≤ X₃ ∧ X₃ ≤ 2
Stabilization-Threshold for: X₃+1 ≤ X₀
alphas_abs: X₃+1+X₀
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₃+4 {O(n)}
Stabilization-Threshold for: 1 ≤ X₃
alphas_abs: 1+X₃
M: 0
N: 1
Bound: 2⋅X₃+4 {O(n)}
Stabilization-Threshold for: 2 ≤ X₃
alphas_abs: 2+X₃
M: 0
N: 1
Bound: 2⋅X₃+6 {O(n)}
relevant size-bounds w.r.t. t₁:
X₀: X₀ {O(n)}
X₃: X₀ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 8⋅X₀+18 {O(n)}
8⋅X₀+18 {O(n)}
All Bounds
Timebounds
Overall timebound:8⋅X₀+22 {O(n)}
t₄: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 8⋅X₀+18 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
Costbounds
Overall costbound: 8⋅X₀+22 {O(n)}
t₄: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 8⋅X₀+18 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
Sizebounds
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₂ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₀ {O(n)}
t₂, X₀: 2⋅X₀ {O(n)}
t₂, X₁: 2⋅X₂ {O(n)}
t₂, X₂: 2⋅X₂ {O(n)}
t₂, X₃: 1 {O(1)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₂ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₀ {O(n)}
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₂ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₀ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₂ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₀ {O(n)}