Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: l0, l1, l2, l3, l4, l5, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₄: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁ < 0
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 0 ≤ X₁
t₁₁: l2(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₁: l3(X₀, X₁, X₂) → l1(X₀, X₀, X₂) :|: 0 ≤ X₀
t₂: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ < 0
t₆: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ 1
t₅: l4(X₀, X₁, X₂) → l6(X₀, X₁, 1) :|: 1 < X₁
t₁₀: l5(X₀, X₁, X₂) → l1(X₀, X₁-1, X₂)
t₈: l6(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ X₂
t₇: l6(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ < X₁
t₉: l7(X₀, X₁, X₂) → l6(X₀, X₁, 2⋅X₂)

Preprocessing

Found invariant 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l6

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l7

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₁ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ for location l1

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ 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, l6, l7, l8
Transitions:
t₀: l0(X₀, X₁, X₂) → l3(X₀, X₁, X₂)
t₄: l1(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₁ < 0 ∧ X₁ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀
t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 0 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀
t₁₁: l2(X₀, X₁, X₂) → l8(X₀, X₁, X₂)
t₁: l3(X₀, X₁, X₂) → l1(X₀, X₀, X₂) :|: 0 ≤ X₀
t₂: l3(X₀, X₁, X₂) → l2(X₀, X₁, X₂) :|: X₀ < 0
t₆: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₅: l4(X₀, X₁, X₂) → l6(X₀, X₁, 1) :|: 1 < X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₁₀: l5(X₀, X₁, X₂) → l1(X₀, X₁-1, X₂) :|: X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
t₈: l6(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₇: l6(X₀, X₁, X₂) → l7(X₀, X₁, X₂) :|: X₂ < X₁ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀
t₉: l7(X₀, X₁, X₂) → l6(X₀, X₁, 2⋅X₂) :|: 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀

MPRF for transition t₃: l1(X₀, X₁, X₂) → l4(X₀, X₁, X₂) :|: 0 ≤ X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l4 [X₁ ]
l1 [X₁+1 ]
l5 [X₁ ]
l7 [X₁ ]
l6 [X₁ ]

MPRF for transition t₅: l4(X₀, X₁, X₂) → l6(X₀, X₁, 1) :|: 1 < X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l4 [X₁+1 ]
l1 [X₁+1 ]
l5 [X₁ ]
l7 [X₁ ]
l6 [X₁ ]

MPRF for transition t₆: l4(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ 1 ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l4 [X₁+1 ]
l1 [X₁+1 ]
l5 [X₁ ]
l7 [X₁ ]
l6 [X₁ ]

MPRF for transition t₁₀: l5(X₀, X₁, X₂) → l1(X₀, X₁-1, X₂) :|: X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l4 [X₁+1 ]
l1 [X₁+1 ]
l5 [X₁+1 ]
l7 [X₁+1 ]
l6 [X₁+1 ]

MPRF for transition t₈: l6(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l4 [X₁+1 ]
l1 [X₁+1 ]
l5 [X₁ ]
l7 [X₁+1 ]
l6 [X₁+1 ]

Found invariant 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l6

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l7

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₁ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ for location l1

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l4

Time-Bound by TWN-Loops:

TWN-Loops: t₇ 2⋅X₀⋅X₀+10⋅X₀+8 {O(n^2)}

TWN-Loops:

entry: t₅: l4(X₀, X₁, X₂) → l6(X₀, X₁, 1) :|: 1 < X₁ ∧ X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀
results in twn-loop: twn:Inv: [1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀] , (X₀,X₁,X₂) -> (X₀,X₁,2⋅X₂) :|: X₂ < X₁
order: [X₀; X₁; X₂]
closed-form:
X₀: X₀
X₁: X₁
X₂: X₂ * 2^n

Termination: true
Formula:

0 < X₂ ∧ X₂ < 0
∨ 0 < X₂ ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₂ ∧ X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₂ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
∨ X₂ < 0 ∧ 0 < X₂ ∧ 1 < X₀ ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ X₂ < 0 ∧ 0 < X₂ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ < 0
∨ X₂ < 0 ∧ 0 < X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ X₂ < 0 ∧ 0 < X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₂ ∧ 3 < X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ < 0
∨ 0 < X₂ ∧ 3 < X₁ ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₂ ∧ 3 < X₁ ∧ X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₂ ∧ 3 < X₁ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
∨ X₂ < 0 ∧ 0 < X₂ ∧ 3 < X₁ ∧ 1 < X₀ ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ X₂ < 0 ∧ 0 < X₂ ∧ 3 < X₁ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₂ ∧ 3 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ < 0
∨ X₂ < 0 ∧ 0 < X₂ ∧ 3 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ X₂ < 0 ∧ 0 < X₂ ∧ 3 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ < 0
∨ 0 < X₂ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₂ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₂ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
∨ X₂ < 0 ∧ 0 < X₂ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 < X₀ ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ X₂ < 0 ∧ 0 < X₂ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₂ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ < 0
∨ X₂ < 0 ∧ 0 < X₂ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ X₂ < 0 ∧ 0 < X₂ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 3 < X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 < X₂ ∧ X₂ < 0
∨ 3 < X₀ ∧ 0 < X₂ ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 3 < X₀ ∧ 0 < X₂ ∧ X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 3 < X₀ ∧ 0 < X₂ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
∨ X₂ < 0 ∧ 3 < X₀ ∧ 0 < X₂ ∧ 1 < X₀ ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ X₂ < 0 ∧ 3 < X₀ ∧ 0 < X₂ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 3 < X₀ ∧ 0 < X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ < 0
∨ X₂ < 0 ∧ 3 < X₀ ∧ 0 < X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ X₂ < 0 ∧ 3 < X₀ ∧ 0 < X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 3 < X₀ ∧ 3 < X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ < 0
∨ 3 < X₀ ∧ 3 < X₁ ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 3 < X₀ ∧ 3 < X₁ ∧ X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 3 < X₀ ∧ 3 < X₁ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
∨ X₂ < 0 ∧ 3 < X₀ ∧ 3 < X₁ ∧ 1 < X₀ ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ X₂ < 0 ∧ 3 < X₀ ∧ 3 < X₁ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 3 < X₀ ∧ 3 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ < 0
∨ X₂ < 0 ∧ 3 < X₀ ∧ 3 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ X₂ < 0 ∧ 3 < X₀ ∧ 3 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 3 < X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ < 0
∨ 3 < X₀ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 3 < X₀ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 3 < X₀ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
∨ X₂ < 0 ∧ 3 < X₀ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 < X₀ ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ X₂ < 0 ∧ 3 < X₀ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 3 < X₀ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ < 0
∨ X₂ < 0 ∧ 3 < X₀ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ X₂ < 0 ∧ 3 < X₀ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 < X₂ ∧ X₂ < 0
∨ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 < X₂ ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 < X₂ ∧ X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 < X₂ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
∨ X₂ < 0 ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 < X₂ ∧ 1 < X₀ ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ X₂ < 0 ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 < X₂ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 < X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ < 0
∨ X₂ < 0 ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 < X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ X₂ < 0 ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 < X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 < X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ < 0
∨ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 < X₁ ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 < X₁ ∧ X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 < X₁ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
∨ X₂ < 0 ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 < X₁ ∧ 1 < X₀ ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ X₂ < 0 ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 < X₁ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ < 0
∨ X₂ < 0 ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ X₂ < 0 ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ < 0
∨ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
∨ X₂ < 0 ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 < X₀ ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ X₂ < 0 ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ < 0
∨ X₂ < 0 ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ X₂ < 0 ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 < X₂ ∧ X₂ < 0
∨ 0 < X₁ ∧ 0 < X₂ ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 0 < X₂ ∧ X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 0 < X₂ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
∨ 0 < X₁ ∧ 0 < X₂ ∧ 1 < X₀ ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 0 < X₂ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 0 < X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ < 0
∨ 0 < X₁ ∧ 0 < X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 0 < X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 0 < X₂ ∧ 3 < X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ < 0
∨ 0 < X₁ ∧ 0 < X₂ ∧ 3 < X₁ ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 0 < X₂ ∧ 3 < X₁ ∧ X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 0 < X₂ ∧ 3 < X₁ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
∨ 0 < X₁ ∧ 0 < X₂ ∧ 3 < X₁ ∧ 1 < X₀ ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 0 < X₂ ∧ 3 < X₁ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 0 < X₂ ∧ 3 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ < 0
∨ 0 < X₁ ∧ 0 < X₂ ∧ 3 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 0 < X₂ ∧ 3 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 0 < X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ < 0
∨ 0 < X₁ ∧ 0 < X₂ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 0 < X₂ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 0 < X₂ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
∨ 0 < X₁ ∧ 0 < X₂ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 < X₀ ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 0 < X₂ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 0 < X₂ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ < 0
∨ 0 < X₁ ∧ 0 < X₂ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 0 < X₂ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 3 < X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 < X₂ ∧ X₂ < 0
∨ 0 < X₁ ∧ 3 < X₀ ∧ 0 < X₂ ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 3 < X₀ ∧ 0 < X₂ ∧ X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 3 < X₀ ∧ 0 < X₂ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
∨ 0 < X₁ ∧ 3 < X₀ ∧ 0 < X₂ ∧ 1 < X₀ ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 3 < X₀ ∧ 0 < X₂ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 3 < X₀ ∧ 0 < X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ < 0
∨ 0 < X₁ ∧ 3 < X₀ ∧ 0 < X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 3 < X₀ ∧ 0 < X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 3 < X₀ ∧ 3 < X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ < 0
∨ 0 < X₁ ∧ 3 < X₀ ∧ 3 < X₁ ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 3 < X₀ ∧ 3 < X₁ ∧ X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 3 < X₀ ∧ 3 < X₁ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
∨ 0 < X₁ ∧ 3 < X₀ ∧ 3 < X₁ ∧ 1 < X₀ ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 3 < X₀ ∧ 3 < X₁ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 3 < X₀ ∧ 3 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ < 0
∨ 0 < X₁ ∧ 3 < X₀ ∧ 3 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 3 < X₀ ∧ 3 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 3 < X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ < 0
∨ 0 < X₁ ∧ 3 < X₀ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 3 < X₀ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 3 < X₀ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
∨ 0 < X₁ ∧ 3 < X₀ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 < X₀ ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 3 < X₀ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 3 < X₀ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ < 0
∨ 0 < X₁ ∧ 3 < X₀ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 3 < X₀ ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 < X₂ ∧ X₂ < 0
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 < X₂ ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 < X₂ ∧ X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 < X₂ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 < X₂ ∧ 1 < X₀ ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 < X₂ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 < X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ < 0
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 < X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 < X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 < X₁ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ X₂ < 0
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 < X₁ ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 < X₁ ∧ X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 < X₁ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 < X₁ ∧ 1 < X₀ ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 < X₁ ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ < 0
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 < X₁ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ < 0
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ < 0 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ < 0 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ < 0
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 < X₀ ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 < X₀ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ < 0
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ 1 < X₁ ∧ X₂ ≤ 0 ∧ 0 ≤ X₂
∨ 0 < X₁ ∧ 3 ≤ X₀ ∧ X₀ ≤ 3 ∧ 3 ≤ X₁ ∧ X₁ ≤ 3 ∧ 1 ≤ X₀ ∧ X₀ ≤ 1 ∧ X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ 1

Stabilization-Threshold for: X₂ < X₁
alphas_abs: X₁
M: 0
N: 1
Bound: 2⋅X₁+2 {O(n)}

relevant size-bounds w.r.t. t₅:
X₁: X₀+2 {O(n)}
Runtime-bound of t₅: X₀+1 {O(n)}
Results in: 2⋅X₀⋅X₀+10⋅X₀+8 {O(n^2)}

2⋅X₀⋅X₀+10⋅X₀+8 {O(n^2)}

Time-Bound by TWN-Loops:

TWN-Loops: t₉ 2⋅X₀⋅X₀+10⋅X₀+8 {O(n^2)}

relevant size-bounds w.r.t. t₅:
X₁: X₀+2 {O(n)}
Runtime-bound of t₅: X₀+1 {O(n)}
Results in: 2⋅X₀⋅X₀+10⋅X₀+8 {O(n^2)}

2⋅X₀⋅X₀+10⋅X₀+8 {O(n^2)}

Analysing control-flow refined program

Cut unsatisfiable transition t₈: l6→l5

Found invariant 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l6___2

Found invariant X₂ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location l6

Found invariant X₂ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location n_l7___3

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l5

Found invariant X₁ ≤ X₀ ∧ 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₀+X₁ ∧ 0 ≤ X₀ for location l1

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location l4

Found invariant 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 3 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 3 ≤ X₀ for location n_l7___1

knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₉₄: l6(X₀, X₁, X₂) → n_l7___3(X₀, X₁, X₂) :|: X₂ < X₁ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ X₂ < X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀

knowledge_propagation leads to new time bound X₀+1 {O(n)} for transition t₉₆: n_l7___3(X₀, X₁, X₂) → n_l6___2(X₀, X₁, 2⋅X₂) :|: 2 ≤ X₁ ∧ X₂ < X₁ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ 1 ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀

MPRF for transition t₉₃: n_l6___2(X₀, X₁, X₂) → n_l7___1(X₀, X₁, X₂) :|: 2 ≤ X₁ ∧ 1 ≤ X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₂ ∧ 2+X₂ ≤ 2⋅X₁ ∧ X₁ ≤ X₀ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ X₂ < X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

2⋅X₀⋅X₀+4⋅X₀ {O(n^2)}

MPRF:

l1 [2⋅X₀ ]
l4 [2⋅X₀ ]
l5 [0 ]
l6 [2⋅X₀ ]
n_l7___1 [2⋅X₁-2⋅X₂-1 ]
n_l7___3 [2⋅X₀ ]
n_l6___2 [2⋅X₁-X₂-1 ]

MPRF for transition t₁₀₀: n_l6___2(X₀, X₁, X₂) → l5(X₀, X₁, X₂) :|: X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

l4 [X₁-1 ]
l1 [X₁-1 ]
l6 [X₁-X₂ ]
l5 [X₁-2 ]
n_l7___1 [X₁-1 ]
n_l7___3 [X₁-X₂ ]
n_l6___2 [X₁-1 ]

MPRF for transition t₉₅: n_l7___1(X₀, X₁, X₂) → n_l6___2(X₀, X₁, 2⋅X₂) :|: X₁ ≤ X₀ ∧ X₂ < X₁ ∧ 2 ≤ X₂ ∧ X₁ ≤ X₀ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 5 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 3 ≤ X₁ ∧ 6 ≤ X₀+X₁ ∧ 3 ≤ X₀ of depth 1:

new bound:

X₀⋅X₀+2⋅X₀ {O(n^2)}

MPRF:

l1 [X₀ ]
l4 [X₀ ]
l5 [X₀ ]
l6 [X₀ ]
n_l7___1 [X₀-X₂ ]
n_l7___3 [X₀ ]
n_l6___2 [X₀-X₂ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:4⋅X₀⋅X₀+25⋅X₀+26 {O(n^2)}
t₀: 1 {O(1)}
t₃: X₀+1 {O(n)}
t₄: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: X₀+1 {O(n)}
t₆: X₀+1 {O(n)}
t₁₀: X₀+1 {O(n)}
t₇: 2⋅X₀⋅X₀+10⋅X₀+8 {O(n^2)}
t₈: X₀+1 {O(n)}
t₉: 2⋅X₀⋅X₀+10⋅X₀+8 {O(n^2)}

Costbounds

Overall costbound: 4⋅X₀⋅X₀+25⋅X₀+26 {O(n^2)}
t₀: 1 {O(1)}
t₃: X₀+1 {O(n)}
t₄: 1 {O(1)}
t₁₁: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₅: X₀+1 {O(n)}
t₆: X₀+1 {O(n)}
t₁₀: X₀+1 {O(n)}
t₇: 2⋅X₀⋅X₀+10⋅X₀+8 {O(n^2)}
t₈: X₀+1 {O(n)}
t₉: 2⋅X₀⋅X₀+10⋅X₀+8 {O(n^2)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₀+2 {O(n)}
t₃, X₂: 2^(2⋅X₀⋅X₀+10⋅X₀+8)+X₂ {O(EXP)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: 1 {O(1)}
t₄, X₂: 2^(2⋅X₀⋅X₀+10⋅X₀+8)+X₂ {O(EXP)}
t₁₁, X₀: 2⋅X₀ {O(n)}
t₁₁, X₁: X₁+1 {O(n)}
t₁₁, X₂: 2^(2⋅X₀⋅X₀+10⋅X₀+8)+2⋅X₂ {O(EXP)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₀ {O(n)}
t₁, X₂: X₂ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₀+2 {O(n)}
t₅, X₂: 1 {O(1)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: 1 {O(1)}
t₆, X₂: 2^(2⋅X₀⋅X₀+10⋅X₀+8)+X₂ {O(EXP)}
t₁₀, X₀: X₀ {O(n)}
t₁₀, X₁: X₀+2 {O(n)}
t₁₀, X₂: 2^(2⋅X₀⋅X₀+10⋅X₀+8)+X₂ {O(EXP)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₀+2 {O(n)}
t₇, X₂: 2^(2⋅X₀⋅X₀+10⋅X₀+8) {O(EXP)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₀+2 {O(n)}
t₈, X₂: 2^(2⋅X₀⋅X₀+10⋅X₀+8) {O(EXP)}
t₉, X₀: X₀ {O(n)}
t₉, X₁: X₀+2 {O(n)}
t₉, X₂: 2^(2⋅X₀⋅X₀+10⋅X₀+8) {O(EXP)}