Initial Problem
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₄: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ < 0
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 0 ≤ X₀
t₆: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₁: l3(X₀, X₁, X₂) → l1(X₁, X₁, X₂) :|: 1 ≤ 2⋅X₂
t₂: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 2⋅X₂ < 1
t₅: l4(X₀, X₁, X₂) → l1(X₀+1-2⋅X₂, X₁, X₂)
Preprocessing
Found invariant 1 ≤ X₂ ∧ X₀ ≤ X₁ for location l1
Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l4
Problem after Preprocessing
Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₄: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ < 0 ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 0 ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁
t₆: l2(X₀, X₁, X₂) → l5(X₀, X₁, X₂)
t₁: l3(X₀, X₁, X₂) → l1(X₁, X₁, X₂) :|: 1 ≤ 2⋅X₂
t₂: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: 2⋅X₂ < 1
t₅: l4(X₀, X₁, X₂) → l1(X₀+1-2⋅X₂, X₁, X₂) :|: 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀
Found invariant 1 ≤ X₂ ∧ X₀ ≤ X₁ for location l1
Found invariant 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l4
Time-Bound by TWN-Loops:
TWN-Loops: t₃ 2⋅X₁+4 {O(n)}
TWN-Loops:
entry: t₁: l3(X₀, X₁, X₂) → l1(X₁, X₁, X₂) :|: 1 ≤ 2⋅X₂
results in twn-loop: twn:Inv: [1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₀] , (X₀,X₁,X₂) -> (X₀+1-2⋅X₂,X₁,X₂) :|: 0 ≤ X₀
order: [X₂; X₀; X₁]
closed-form:
X₂: X₂
X₀: X₀ + [[n != 0]] * 1-2⋅X₂ * n^1
X₁: X₁
Termination: true
Formula:
1 < 2⋅X₂ ∧ 2⋅X₂ < 1
∨ 1 < 2⋅X₂ ∧ 2⋅X₂ < 1 ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 1 < 2⋅X₂ ∧ 2⋅X₂ < 1 ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 1 < 2⋅X₂ ∧ 0 < X₀+X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 2⋅X₂ < 1
∨ 2⋅X₂ < 1 ∧ 1 < 2⋅X₂ ∧ 0 < X₀+X₁ ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 2⋅X₂ < 1 ∧ 1 < 2⋅X₂ ∧ 0 < X₀+X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 1 < 2⋅X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 2⋅X₂ < 1
∨ 2⋅X₂ < 1 ∧ 1 < 2⋅X₂ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 2⋅X₂ < 1 ∧ 1 < 2⋅X₂ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ X₀ < X₁ ∧ 1 ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ 1 ∧ 2⋅X₂ < 1
∨ X₀ < X₁ ∧ 2⋅X₂ < 1 ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ X₀ < X₁ ∧ 2⋅X₂ < 1 ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ X₀ < X₁ ∧ 0 < X₀+X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 2⋅X₂ < 1
∨ 2⋅X₂ < 1 ∧ X₀ < X₁ ∧ 0 < X₀+X₁ ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 2⋅X₂ < 1 ∧ X₀ < X₁ ∧ 0 < X₀+X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ X₀ < X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 2⋅X₂ < 1
∨ 2⋅X₂ < 1 ∧ X₀ < X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 2⋅X₂ < 1 ∧ X₀ < X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 1 ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 2⋅X₂ < 1
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 2⋅X₂ < 1 ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 2⋅X₂ < 1 ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀+X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 2⋅X₂ < 1
∨ 2⋅X₂ < 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀+X₁ ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 2⋅X₂ < 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀+X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 2⋅X₂ < 1
∨ 2⋅X₂ < 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 2⋅X₂ < 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 0 < X₀ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 < 2⋅X₂ ∧ 2⋅X₂ < 1
∨ 0 < X₀ ∧ 1 < 2⋅X₂ ∧ 2⋅X₂ < 1 ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 0 < X₀ ∧ 1 < 2⋅X₂ ∧ 2⋅X₂ < 1 ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 0 < X₀ ∧ 1 < 2⋅X₂ ∧ 0 < X₀+X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 2⋅X₂ < 1
∨ 0 < X₀ ∧ 1 < 2⋅X₂ ∧ 0 < X₀+X₁ ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 0 < X₀ ∧ 1 < 2⋅X₂ ∧ 0 < X₀+X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 0 < X₀ ∧ 1 < 2⋅X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 2⋅X₂ < 1
∨ 0 < X₀ ∧ 1 < 2⋅X₂ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 0 < X₀ ∧ 1 < 2⋅X₂ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 0 < X₀ ∧ X₀ < X₁ ∧ 1 ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ 1 ∧ 2⋅X₂ < 1
∨ 0 < X₀ ∧ X₀ < X₁ ∧ 2⋅X₂ < 1 ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 0 < X₀ ∧ X₀ < X₁ ∧ 2⋅X₂ < 1 ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 0 < X₀ ∧ X₀ < X₁ ∧ 0 < X₀+X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 2⋅X₂ < 1
∨ 0 < X₀ ∧ X₀ < X₁ ∧ 0 < X₀+X₁ ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 0 < X₀ ∧ X₀ < X₁ ∧ 0 < X₀+X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 0 < X₀ ∧ X₀ < X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 2⋅X₂ < 1
∨ 0 < X₀ ∧ X₀ < X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 0 < X₀ ∧ X₀ < X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 0 < X₀ ∧ 1 ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 2⋅X₂ < 1
∨ 0 < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 2⋅X₂ < 1 ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 0 < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 2⋅X₂ < 1 ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 0 < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀+X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 2⋅X₂ < 1
∨ 0 < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀+X₁ ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 0 < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀+X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 0 < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 2⋅X₂ < 1
∨ 0 < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 0 < X₀ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 2⋅X₂ ∧ 2⋅X₂ < 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 2⋅X₂ ∧ 2⋅X₂ < 1 ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 2⋅X₂ ∧ 2⋅X₂ < 1 ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 2⋅X₂ ∧ 0 < X₀+X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 2⋅X₂ < 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 2⋅X₂ ∧ 0 < X₀+X₁ ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 2⋅X₂ ∧ 0 < X₀+X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 2⋅X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 2⋅X₂ < 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 2⋅X₂ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 < 2⋅X₂ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ < X₁ ∧ 1 ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ 1 ∧ 2⋅X₂ < 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ < X₁ ∧ 2⋅X₂ < 1 ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ < X₁ ∧ 2⋅X₂ < 1 ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ < X₁ ∧ 0 < X₀+X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 2⋅X₂ < 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ < X₁ ∧ 0 < X₀+X₁ ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ < X₁ ∧ 0 < X₀+X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ < X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 2⋅X₂ < 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ < X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ < X₁ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ 2⋅X₂ ∧ 2⋅X₂ ≤ 1 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 2⋅X₂ < 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 2⋅X₂ < 1 ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 2⋅X₂ < 1 ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀+X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 2⋅X₂ < 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀+X₁ ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 < X₀+X₁ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 2⋅X₂ < 1
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 1 < X₀+X₂ ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂
∨ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ X₀+X₁ ≤ 0 ∧ 2⋅X₂ ≤ 1 ∧ 1 ≤ 2⋅X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀+X₂ ≤ 1
Stabilization-Threshold for: 0 ≤ X₀
alphas_abs: X₀
M: 0
N: 1
Bound: 2⋅X₀+2 {O(n)}
relevant size-bounds w.r.t. t₁:
X₀: X₁ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₁+4 {O(n)}
2⋅X₁+4 {O(n)}
Time-Bound by TWN-Loops:
TWN-Loops: t₅ 2⋅X₁+4 {O(n)}
relevant size-bounds w.r.t. t₁:
X₀: X₁ {O(n)}
Runtime-bound of t₁: 1 {O(1)}
Results in: 2⋅X₁+4 {O(n)}
2⋅X₁+4 {O(n)}
All Bounds
Timebounds
Overall timebound:4⋅X₁+13 {O(n)}
t₀: 1 {O(1)}
t₃: 2⋅X₁+4 {O(n)}
t₄: 1 {O(1)}
t₆: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: 2⋅X₁+4 {O(n)}
Costbounds
Overall costbound: 4⋅X₁+13 {O(n)}
t₀: 1 {O(1)}
t₃: 2⋅X₁+4 {O(n)}
t₄: 1 {O(1)}
t₆: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: 2⋅X₁+4 {O(n)}
Sizebounds
t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₃, X₀: 2⋅2^(2⋅X₁+4)⋅X₁⋅X₂+2^(2⋅X₁+4)⋅5⋅X₂+2^(2⋅X₁+4)⋅X₁ {O(EXP)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₄, X₀: 2⋅2^(2⋅X₁+4)⋅X₁⋅X₂+2^(2⋅X₁+4)⋅5⋅X₂+2^(2⋅X₁+4)⋅X₁+X₁ {O(EXP)}
t₄, X₁: 2⋅X₁ {O(n)}
t₄, X₂: 2⋅X₂ {O(n)}
t₆, X₀: 2⋅2^(2⋅X₁+4)⋅X₁⋅X₂+2^(2⋅X₁+4)⋅5⋅X₂+2^(2⋅X₁+4)⋅X₁+X₀+X₁ {O(EXP)}
t₆, X₁: 3⋅X₁ {O(n)}
t₆, X₂: 3⋅X₂ {O(n)}
t₁, X₀: X₁ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₅, X₀: 2⋅2^(2⋅X₁+4)⋅X₁⋅X₂+2^(2⋅X₁+4)⋅5⋅X₂+2^(2⋅X₁+4)⋅X₁ {O(EXP)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}