KoAT2 Proof Output

Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars:
Locations: l0, l1
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄, X₅) → l1(X₀, X₁, X₂, X₃, X₄, X₅)
t₁: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(3⋅X₀+2⋅X₁, -5⋅X₀-3⋅X₁, X₂, -2⋅X₃, (X₂)²+X₄+(X₄)², (X₂)²+2⋅(X₄)²+3⋅X₅-4⋅X₄) :|: 1+(X₃)²+X₅ ≤ (X₂)⁵+2⋅X₄ ∧ 1+X₃ ≤ 0
t₂: l1(X₀, X₁, X₂, X₃, X₄, X₅) → l1(3⋅X₀+2⋅X₁, -5⋅X₀-3⋅X₁, X₂, -2⋅X₃, (X₂)²+X₄+(X₄)², (X₂)²+2⋅(X₄)²+3⋅X₅-4⋅X₄) :|: 1+(X₃)²+X₅ ≤ (X₂)⁵+2⋅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, X₃
Temp_Vars:
Locations: l0, l1
Transitions:
t₆: l0(X₀, X₁, X₂, X₃) → l1(X₀, X₁, X₂, X₃)
t₇: l1(X₀, X₁, X₂, X₃) → l1(X₀, -2⋅X₁, (X₀)²+X₂+(X₂)², (X₀)²+2⋅(X₂)²+3⋅X₃-4⋅X₂) :|: 1+(X₁)²+X₃ ≤ (X₀)⁵+2⋅X₂ ∧ 1+X₁ ≤ 0
t₈: l1(X₀, X₁, X₂, X₃) → l1(X₀, -2⋅X₁, (X₀)²+X₂+(X₂)², (X₀)²+2⋅(X₂)²+3⋅X₃-4⋅X₂) :|: 1+(X₁)²+X₃ ≤ (X₀)⁵+2⋅X₂ ∧ 1 ≤ X₁

TWN: t₇: l1→l1

cycle: [t₇: l1→l1; t₈: l1→l1]
original loop: (1+Temp_Int₇₇₇+(X₁)² ≤ (X₀)⁵ ∧ 1+X₁ ≤ 0 ∨ 1+Temp_Int₇₇₇+(X₁)² ≤ (X₀)⁵ ∧ 1 ≤ X₁,(Temp_Int₇₇₇,X₀,X₁) -> (3⋅Temp_Int₇₇₇-(X₀)²,X₀,-2⋅X₁))
transformed loop: (1+Temp_Int₇₇₇+(X₁)² ≤ (X₀)⁵ ∧ 1+X₁ ≤ 0 ∨ 1+Temp_Int₇₇₇+(X₁)² ≤ (X₀)⁵ ∧ 1 ≤ X₁,(Temp_Int₇₇₇,X₀,X₁) -> (3⋅Temp_Int₇₇₇-(X₀)²,X₀,-2⋅X₁))
loop: (1+Temp_Int₇₇₇+(X₁)² ≤ (X₀)⁵ ∧ 1+X₁ ≤ 0 ∨ 1+Temp_Int₇₇₇+(X₁)² ≤ (X₀)⁵ ∧ 1 ≤ X₁,(Temp_Int₇₇₇,X₀,X₁) -> (3⋅Temp_Int₇₇₇-(X₀)²,X₀,-2⋅X₁))
order: [X₀; X₁; Temp_Int₇₇₇]
closed-form:

X₀: X₀
X₁: X₁⋅(4)^n
Temp_Int₇₇₇: Temp_Int₇₇₇⋅(9)^n + [[n != 0]]⋅-1/2⋅(X₀)²⋅(9)^n + [[n != 0]]⋅1/2⋅(X₀)²

Termination: true
Formula:

2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1+2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1+2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1+2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1+2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1+6⋅Temp_Int₇₇₇ ≤ 3⋅(X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1+6⋅Temp_Int₇₇₇ ≤ 3⋅(X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1+6⋅Temp_Int₇₇₇ ≤ 3⋅(X₀)² ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1+6⋅Temp_Int₇₇₇ ≤ 3⋅(X₀)² ∧ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 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 ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 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 ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 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 ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 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 ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 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 ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 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 ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 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 ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 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 ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 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 ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 2⋅(X₀)⁵ ≤ 2+(X₀)² ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 2+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 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 ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 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 ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 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 ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 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 ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 1+6⋅Temp_Int₇₇₇ ≤ 3⋅(X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 1+6⋅Temp_Int₇₇₇ ≤ 3⋅(X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 1+6⋅Temp_Int₇₇₇ ≤ 3⋅(X₀)² ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 1+6⋅Temp_Int₇₇₇ ≤ 3⋅(X₀)² ∧ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 1+8⋅(X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+6⋅Temp_Int₇₇₇ ≤ 3⋅(X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 1+2⋅(X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+6⋅Temp_Int₇₇₇ ≤ 3⋅(X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+6⋅Temp_Int₇₇₇ ≤ 3⋅(X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 1+2⋅(X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+6⋅Temp_Int₇₇₇ ≤ 3⋅(X₀)² ∧ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+6⋅Temp_Int₇₇₇ ≤ 3⋅(X₀)² ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 1+2⋅(X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+6⋅Temp_Int₇₇₇ ≤ 3⋅(X₀)² ∧ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+6⋅Temp_Int₇₇₇ ≤ 3⋅(X₀)² ∧ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 1+2⋅(X₁)² ≤ 0 ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+6⋅Temp_Int₇₇₇ ≤ 3⋅(X₀)² ∧ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 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 ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 1+8⋅(X₁)² ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 2⋅X₁ ∧ 1 ≤ X₁ ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 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 ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ 2⋅X₁ ∧ 1+X₁ ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 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 ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1 ≤ X₁ ∧ 1+2⋅X₁ ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 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 ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 1+8⋅(X₁)² ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0
∨ 1+X₁ ≤ 0 ∧ 1+2⋅X₁ ≤ 0 ∧ 3+(X₀)² ≤ 2⋅(X₀)⁵ ∧ (X₀)² ≤ 2⋅Temp_Int₇₇₇ ∧ 2⋅Temp_Int₇₇₇ ≤ (X₀)² ∧ 0 ≤ (X₁)² ∧ (X₁)² ≤ 0

Stabilization-Threshold for: 1+3⋅Temp_Int₇₇₇+4⋅(X₁)² ≤ (X₀)²+(X₀)⁵

alphas_abs: 6⋅Temp_Int₇₇₇+3⋅(X₀)²+2⋅(X₀)⁵
M': 1
N: 1
Bound: 7⋅log(X₀)+log(Temp_Int₇₇₇)+10 {O(log(n))}

Stabilization-Threshold for: 1+Temp_Int₇₇₇+(X₁)² ≤ (X₀)⁵

alphas_abs: 2⋅Temp_Int₇₇₇+(X₀)²+2⋅(X₀)⁵
M': 1
N: 1
Bound: 7⋅log(X₀)+log(Temp_Int₇₇₇)+6 {O(log(n))}

TWN - Lifting for [7: l1->l1; 8: l1->l1] of 28⋅log(X₀)+4⋅log(X₂)+4⋅log(X₃)+41 {O(log(n))}

relevant size-bounds w.r.t. t₆: l0→l1:
X₀: X₀ {O(n)}
X₂: X₂ {O(n)}
X₃: X₃ {O(n)}
Runtime-bound of t₆: 1 {O(1)}
Results in: 28⋅log(X₀)+4⋅log(X₂)+4⋅log(X₃)+41 {O(log(n))}

All Bounds

Timebounds

Overall timebound:56⋅log(X₀)+8⋅log(X₂)+8⋅log(X₃)+83 {O(log(n))}
t₆: 1 {O(1)}
t₇: 28⋅log(X₀)+4⋅log(X₂)+4⋅log(X₃)+41 {O(log(n))}
t₈: 28⋅log(X₀)+4⋅log(X₂)+4⋅log(X₃)+41 {O(log(n))}

Costbounds

Overall costbound: 56⋅log(X₀)+8⋅log(X₂)+8⋅log(X₃)+83 {O(log(n))}
t₆: 1 {O(1)}
t₇: 28⋅log(X₀)+4⋅log(X₂)+4⋅log(X₃)+41 {O(log(n))}
t₈: 28⋅log(X₀)+4⋅log(X₂)+4⋅log(X₃)+41 {O(log(n))}

Sizebounds

t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: 2^(28⋅log(X₀))⋅2^(28⋅log(X₀))⋅2^(4⋅log(X₂))⋅2^(4⋅log(X₂))⋅2^(4⋅log(X₃))⋅2^(4⋅log(X₃))⋅4835703278458516698824704⋅X₁ {O(EXP)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: 2^(28⋅log(X₀))⋅2^(28⋅log(X₀))⋅2^(4⋅log(X₂))⋅2^(4⋅log(X₂))⋅2^(4⋅log(X₃))⋅2^(4⋅log(X₃))⋅4835703278458516698824704⋅X₁ {O(EXP)}