Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₁: l1(X₀, X₁, X₂, X₃, X₄) → l1(3⋅X₀+2⋅X₁, -5⋅X₀-3⋅X₁, X₂, -2⋅X₃, (X₂)²+3⋅X₄) :|: 1+(X₃)² ≤ (X₂)⁵+X₄ ∧ 1+X₃ ≤ 0
t₂: l1(X₀, X₁, X₂, X₃, X₄) → l1(3⋅X₀+2⋅X₁, -5⋅X₀-3⋅X₁, X₂, -2⋅X₃, (X₂)²+3⋅X₄) :|: 1+(X₃)² ≤ (X₂)⁵+X₄ ∧ 1 ≤ X₃

Preprocessing

Eliminate variables [X₀; X₁] that do not contribute to the problem

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1
Transitions:
t₆: l0(X₀, X₁, X₂) → l1(X₀, X₁, X₂)
t₇: l1(X₀, X₁, X₂) → l1(X₀, -2⋅X₁, (X₀)²+3⋅X₂) :|: 1+(X₁)² ≤ (X₀)⁵+X₂ ∧ 1+X₁ ≤ 0
t₈: l1(X₀, X₁, X₂) → l1(X₀, -2⋅X₁, (X₀)²+3⋅X₂) :|: 1+(X₁)² ≤ (X₀)⁵+X₂ ∧ 1 ≤ X₁

TWN: t₇: l1→l1

cycle: [t₇: l1→l1; t₈: l1→l1]
original loop: (1+(X₁)² ≤ (X₀)⁵+X₂ ∧ 1+X₁ ≤ 0 ∨ 1+(X₁)² ≤ (X₀)⁵+X₂ ∧ 1 ≤ X₁,(X₀,X₁,X₂) -> (X₀,-2⋅X₁,(X₀)²+3⋅X₂))
transformed loop: (1+(X₁)² ≤ (X₀)⁵+X₂ ∧ 1+X₁ ≤ 0 ∨ 1+(X₁)² ≤ (X₀)⁵+X₂ ∧ 1 ≤ X₁,(X₀,X₁,X₂) -> (X₀,-2⋅X₁,(X₀)²+3⋅X₂))
loop: (1+(X₁)² ≤ (X₀)⁵+X₂ ∧ 1+X₁ ≤ 0 ∨ 1+(X₁)² ≤ (X₀)⁵+X₂ ∧ 1 ≤ X₁,(X₀,X₁,X₂) -> (X₀,-2⋅X₁,(X₀)²+3⋅X₂))
order: [X₀; X₂; X₁]
closed-form:
X₀: X₀
X₂: X₂⋅(9)^n + [[n != 0]]⋅1/2⋅(X₀)²⋅(9)^n + [[n != 0]]⋅-1/2⋅(X₀)²
X₁: X₁⋅(4)^n

Termination: true
Formula:

2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ 3⋅(X₀)²+6⋅X₂ ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ 3⋅(X₀)²+6⋅X₂ ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ 3⋅(X₀)²+6⋅X₂ ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ 3⋅(X₀)²+6⋅X₂ ∧ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ (X₀)²+2⋅X₂ ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ (X₀)²+2⋅X₂ ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ (X₀)²+2⋅X₂ ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ (X₀)²+2⋅X₂ ∧ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 1+2⋅(X₁)² ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 1+8⋅(X₁)² ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 1+2⋅(X₁)² ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 1+2⋅(X₁)² ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 1+2⋅(X₁)² ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 3⋅(X₀)²+6⋅X₂ ∧ 1 ≤ (X₀)²+2⋅X₂ ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 3⋅(X₀)²+6⋅X₂ ∧ 1 ≤ (X₀)²+2⋅X₂ ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 3⋅(X₀)²+6⋅X₂ ∧ 1 ≤ (X₀)²+2⋅X₂ ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 3⋅(X₀)²+6⋅X₂ ∧ 1 ≤ (X₀)²+2⋅X₂ ∧ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 3⋅(X₀)²+6⋅X₂ ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 1+2⋅(X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 3⋅(X₀)²+6⋅X₂ ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 3⋅(X₀)²+6⋅X₂ ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 1+2⋅(X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 3⋅(X₀)²+6⋅X₂ ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 3⋅(X₀)²+6⋅X₂ ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 1+2⋅(X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 3⋅(X₀)²+6⋅X₂ ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 3⋅(X₀)²+6⋅X₂ ∧ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 1+2⋅(X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 3⋅(X₀)²+6⋅X₂ ∧ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ (X₀)²+2⋅X₂ ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 1+8⋅(X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ (X₀)²+2⋅X₂ ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ (X₀)²+2⋅X₂ ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ (X₀)²+2⋅X₂ ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ (X₀)²+2⋅X₂ ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ (X₀)²+2⋅X₂ ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ (X₀)²+2⋅X₂ ∧ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ (X₀)²+2⋅X₂ ∧ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 1+2⋅(X₁)² ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0
∨ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 1+2⋅(X₁)² ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 1+8⋅(X₁)² ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 1+2⋅(X₁)² ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0
∨ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 1+2⋅(X₁)² ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 1+2⋅(X₁)² ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0
∨ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 1+2⋅(X₁)² ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 1+2⋅(X₁)² ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0
∨ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 1+2⋅(X₁)² ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ 0 ≤ (X₀)²+2⋅X₂ ∧ (X₀)²+2⋅X₂ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0

Stabilization-Threshold for: 1+4⋅(X₁)² ≤ (X₀)²+(X₀)⁵+3⋅X₂
alphas_abs: 3⋅(X₀)²+2⋅(X₀)⁵+6⋅X₂
M': 1
N: 1
Bound: 7⋅log(X₀)+log(X₂)+10 {O(log(n))}
Stabilization-Threshold for: 1+(X₁)² ≤ (X₀)⁵+X₂
alphas_abs: (X₀)²+2⋅(X₀)⁵+2⋅X₂
M': 1
N: 1
Bound: 7⋅log(X₀)+log(X₂)+6 {O(log(n))}

TWN - Lifting for [7: l1->l1; 8: l1->l1] of 28⋅log(X₀)+4⋅log(X₂)+37 {O(log(n))}

relevant size-bounds w.r.t. t₆: l0→l1:
X₀: X₀ {O(n)}
X₂: X₂ {O(n)}
Runtime-bound of t₆: 1 {O(1)}
Results in: 28⋅log(X₀)+4⋅log(X₂)+37 {O(log(n))}

All Bounds

Timebounds

Overall timebound:56⋅log(X₀)+8⋅log(X₂)+75 {O(log(n))}
t₆: 1 {O(1)}
t₇: 28⋅log(X₀)+4⋅log(X₂)+37 {O(log(n))}
t₈: 28⋅log(X₀)+4⋅log(X₂)+37 {O(log(n))}

Costbounds

Overall costbound: 56⋅log(X₀)+8⋅log(X₂)+75 {O(log(n))}
t₆: 1 {O(1)}
t₇: 28⋅log(X₀)+4⋅log(X₂)+37 {O(log(n))}
t₈: 28⋅log(X₀)+4⋅log(X₂)+37 {O(log(n))}

Sizebounds

t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: 2475880078570760549798248448⋅2^(16⋅log(X₀))⋅2^(56⋅log(X₀))⋅2^(8⋅log(X₂))⋅X₁ {O(EXP)}
t₇, X₂: 17455927136175424851782794958953454680082898⋅3^(16⋅log(X₀))⋅3^(56⋅log(X₀))⋅3^(8⋅log(X₂))⋅X₀⋅X₀+26183890704263137277674192438430182020124347⋅3^(16⋅log(X₀))⋅3^(56⋅log(X₀))⋅3^(8⋅log(X₂))⋅X₂+X₀⋅X₀ {O(EXP)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: 2475880078570760549798248448⋅2^(16⋅log(X₀))⋅2^(56⋅log(X₀))⋅2^(8⋅log(X₂))⋅X₁ {O(EXP)}
t₈, X₂: 17455927136175424851782794958953454680082898⋅3^(16⋅log(X₀))⋅3^(56⋅log(X₀))⋅3^(8⋅log(X₂))⋅X₀⋅X₀+26183890704263137277674192438430182020124347⋅3^(16⋅log(X₀))⋅3^(56⋅log(X₀))⋅3^(8⋅log(X₂))⋅X₂+X₀⋅X₀ {O(EXP)}