KoAT2 Proof Output

Initial Problem

Start: f0
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆
Temp_Vars: R, S
Locations: f0, f11, f14, f33, f36, f58
Transitions:
t₉: f0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → f11(0, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, 0, X₁₅, X₁₆)
t₀: f11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → f14(X₀, 0, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: X₀ ≤ 9
t₈: f11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → f33(X₀, X₁, 0, X₃, 0, 0, 0, 0, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, 1000) :|: 10 ≤ X₀
t₇: f14(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → f11(1+X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: 10 ≤ X₁
t₆: f14(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → f14(X₀, 1+X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, S, S, X₁₆) :|: X₁ ≤ 9
t₁: f33(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → f36(X₀, X₁, X₂, 0, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: X₂ ≤ 9
t₅: f33(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → f58(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₄, X₅, X₆, X₇, 1500, S, X₁₄, X₁₅, X₁₆) :|: 10 ≤ X₂
t₄: f36(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → f33(X₀, X₁, 1+X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: 10 ≤ X₃
t₂: f36(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → f36(X₀, X₁, X₂, 1+X₃, S+X₄, 1+X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: X₃ ≤ 9 ∧ 1+R ≤ 0
t₃: f36(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) → f36(X₀, X₁, X₂, 1+X₃, X₄, X₅, S+X₆, 1+X₇, X₈, X₉, X₁₀, X₁₁, X₁₂, X₁₃, X₁₄, X₁₅, X₁₆) :|: X₃ ≤ 9

Preprocessing

Eliminate variables [S; X₄; X₅; X₆; X₇; X₈; X₉; X₁₀; X₁₁; X₁₂; X₁₃; X₁₄; X₁₅; X₁₆] that do not contribute to the problem

Found invariant X₃ ≤ 10 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ for location f36

Found invariant X₁ ≤ 10 ∧ X₁ ≤ 10+X₀ ∧ 0 ≤ X₁ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location f14

Found invariant 10 ≤ X₂ ∧ 20 ≤ X₀+X₂ ∧ 10 ≤ X₀ for location f58

Found invariant 0 ≤ X₀ for location f11

Found invariant 0 ≤ X₂ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ for location f33

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: R
Locations: f0, f11, f14, f33, f36, f58
Transitions:
t₂₁: f0(X₀, X₁, X₂, X₃) → f11(0, X₁, X₂, X₃)
t₂₂: f11(X₀, X₁, X₂, X₃) → f14(X₀, 0, X₂, X₃) :|: X₀ ≤ 9 ∧ 0 ≤ X₀
t₂₃: f11(X₀, X₁, X₂, X₃) → f33(X₀, X₁, 0, X₃) :|: 10 ≤ X₀ ∧ 0 ≤ X₀
t₂₄: f14(X₀, X₁, X₂, X₃) → f11(1+X₀, X₁, X₂, X₃) :|: 10 ≤ X₁ ∧ X₁ ≤ 10+X₀ ∧ X₁ ≤ 10 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₅: f14(X₀, X₁, X₂, X₃) → f14(X₀, 1+X₁, X₂, X₃) :|: X₁ ≤ 9 ∧ X₁ ≤ 10+X₀ ∧ X₁ ≤ 10 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
t₂₆: f33(X₀, X₁, X₂, X₃) → f36(X₀, X₁, X₂, 0) :|: X₂ ≤ 9 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂
t₂₇: f33(X₀, X₁, X₂, X₃) → f58(X₀, X₁, X₂, X₃) :|: 10 ≤ X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂
t₂₈: f36(X₀, X₁, X₂, X₃) → f33(X₀, X₁, 1+X₂, X₃) :|: 10 ≤ X₃ ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₂₉: f36(X₀, X₁, X₂, X₃) → f36(X₀, X₁, X₂, 1+X₃) :|: X₃ ≤ 9 ∧ 1+R ≤ 0 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
t₃₀: f36(X₀, X₁, X₂, X₃) → f36(X₀, X₁, X₂, 1+X₃) :|: X₃ ≤ 9 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃

MPRF for transition t₂₂: f11(X₀, X₁, X₂, X₃) → f14(X₀, 0, X₂, X₃) :|: X₀ ≤ 9 ∧ 0 ≤ X₀ of depth 1:

new bound:

10 {O(1)}

MPRF:

• f11: [10-X₀]
• f14: [9-X₀]

TWN: t₂₅: f14→f14

cycle: [t₂₅: f14→f14]
original loop: (X₁ ≤ 9 ∧ X₁ ≤ 10+X₀ ∧ X₁ ≤ 10 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁,(X₀,X₁) -> (X₀,1+X₁))
transformed loop: (X₁ ≤ 9 ∧ X₁ ≤ 10+X₀ ∧ X₁ ≤ 10 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁,(X₀,X₁) -> (X₀,1+X₁))
loop: (X₁ ≤ 9 ∧ X₁ ≤ 10+X₀ ∧ X₁ ≤ 10 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁,(X₀,X₁) -> (X₀,1+X₁))
order: [X₁; X₀]
closed-form:

X₁: X₁ + [[n != 0]]⋅n^1
X₀: X₀

Termination: true
Formula:

X₁ ≤ 10+X₀ ∧ X₁ ≤ 10 ∧ X₁ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₁ ∧ 10+X₀ ≤ X₁ ∧ 10 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 10+X₀ ∧ X₁ ≤ 10 ∧ X₁ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10+X₀ ≤ X₁ ∧ 10 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 10+X₀ ∧ X₁ ≤ 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10+X₀ ≤ X₁ ∧ 10 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 10+X₀ ∧ X₁ ≤ 9 ∧ X₁ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 10+X₀ ∧ X₁ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₁ ∧ 10+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 10+X₀ ∧ X₁ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 10+X₀ ∧ X₁ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 10+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10+X₀ ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 10 ∧ X₁ ≤ 9+X₀ ∧ X₁ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₁ ∧ 10 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 10 ∧ X₁ ≤ 9+X₀ ∧ X₁ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 10 ∧ X₁ ≤ 9+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 10 ∧ X₁ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₁ ∧ 10 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 10 ∧ X₁ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 9+X₀ ∧ X₁ ≤ 9 ∧ X₁ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 9+X₀ ∧ X₁ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 9+X₀ ∧ X₁ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 9+X₀ ∧ X₁ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 9+X₀ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 9 ∧ X₁ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ X₁ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁
∨ 1 ≤ 0 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁

Stabilization-Threshold for: X₁ ≤ 10

alphas_abs: 11+X₁
M: 0
N: 1
Bound: 2⋅X₁+24 {O(n)}

Stabilization-Threshold for: X₁ ≤ 10+X₀

alphas_abs: 11+X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+24 {O(n)}

Stabilization-Threshold for: X₁ ≤ 9

alphas_abs: 10+X₁
M: 0
N: 1
Bound: 2⋅X₁+22 {O(n)}

TWN - Lifting for [25: f14->f14] of 2⋅X₀+6⋅X₁+72 {O(n)}

relevant size-bounds w.r.t. t₂₂: f11→f14:
X₀: 9 {O(1)}
X₁: 0 {O(1)}
Runtime-bound of t₂₂: 10 {O(1)}
Results in: 900 {O(1)}

knowledge_propagation leads to new time bound 900 {O(1)} for transition t₂₄: f14(X₀, X₁, X₂, X₃) → f11(1+X₀, X₁, X₂, X₃) :|: 10 ≤ X₁ ∧ X₁ ≤ 10+X₀ ∧ X₁ ≤ 10 ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₁ ∧ 0 ≤ X₁

MPRF for transition t₂₆: f33(X₀, X₁, X₂, X₃) → f36(X₀, X₁, X₂, 0) :|: X₂ ≤ 9 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

10 {O(1)}

MPRF:

• f33: [10-X₂]
• f36: [9-X₂]

TWN: t₂₉: f36→f36

cycle: [t₂₉: f36→f36; t₃₀: f36→f36]
original loop: (X₃ ≤ 9 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ ∨ X₃ ≤ 9 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃,(X₀,X₂,X₃) -> (X₀,X₂,1+X₃))
transformed loop: (X₃ ≤ 9 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ ∨ X₃ ≤ 9 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃,(X₀,X₂,X₃) -> (X₀,X₂,1+X₃))
loop: (X₃ ≤ 9 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ ∨ X₃ ≤ 9 ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃,(X₀,X₂,X₃) -> (X₀,X₂,1+X₃))
order: [X₃; X₂; X₀]
closed-form:

X₃: X₃ + [[n != 0]]⋅n^1
X₂: X₂
X₀: X₀

Termination: true
Formula:

X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 9 ≤ X₃ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 10 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₃ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 10 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₃ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 10 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 10 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 10 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 10 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 10 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 10 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 10 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 9 ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 9 ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 9 ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 9 ≤ X₃ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₃ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₃ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10+X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10+X₂ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ X₃ ≤ 9+X₂ ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 9 ≤ X₃ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ X₃ ≤ 9+X₂ ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₃ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ X₃ ≤ 9+X₂ ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₃ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ X₃ ≤ 9+X₂ ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ X₃ ≤ 9+X₂ ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ X₃ ≤ 9+X₂ ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ X₃ ≤ 9+X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ X₃ ≤ 9+X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ X₃ ≤ 9+X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 9 ≤ X₃ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₃ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₃ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10 ≤ X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 10 ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9+X₂ ∧ X₃ ≤ 9 ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9+X₂ ∧ X₃ ≤ 9 ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9+X₂ ∧ X₃ ≤ 9 ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9+X₂ ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 9 ≤ X₃ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9+X₂ ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9+X₂ ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₃ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9+X₂ ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₃ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9+X₂ ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9+X₂ ∧ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9+X₂ ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9+X₂ ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9+X₂ ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9+X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9+X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9+X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9 ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9 ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9 ∧ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 9 ≤ X₃ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₃ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₃ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ X₃ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 1+X₃ ≤ X₀ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃
∨ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃

Stabilization-Threshold for: X₃ ≤ X₀

alphas_abs: 1+X₀+X₃
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₃+4 {O(n)}

Stabilization-Threshold for: X₃ ≤ 10

alphas_abs: 11+X₃
M: 0
N: 1
Bound: 2⋅X₃+24 {O(n)}

Stabilization-Threshold for: X₃ ≤ 10+X₂

alphas_abs: 11+X₂+X₃
M: 0
N: 1
Bound: 2⋅X₂+2⋅X₃+24 {O(n)}

Stabilization-Threshold for: X₃ ≤ 9

alphas_abs: 10+X₃
M: 0
N: 1
Bound: 2⋅X₃+22 {O(n)}

TWN - Lifting for [29: f36->f36; 30: f36->f36] of 2⋅X₀+2⋅X₂+8⋅X₃+76 {O(n)}

relevant size-bounds w.r.t. t₂₆: f33→f36:
X₀: 10 {O(1)}
X₂: 9 {O(1)}
X₃: 0 {O(1)}
Runtime-bound of t₂₆: 10 {O(1)}
Results in: 1140 {O(1)}

TWN: t₂₆: f33→f36

cycle: [t₂₆: f33→f36; t₂₈: f36→f33]
original loop: (X₂ ≤ 9 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₂ ∧ 0 ≤ 1 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ 0,(X₀,X₂) -> (X₀,1+X₂))
transformed loop: (X₂ ≤ 9 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₂ ∧ 0 ≤ 1 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ 0,(X₀,X₂) -> (X₀,1+X₂))
loop: (X₂ ≤ 9 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ 1 ≤ 0 ∧ 0 ≤ 10+X₂ ∧ 0 ≤ 1 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 0 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ 0,(X₀,X₂) -> (X₀,1+X₂))
order: [X₂; X₀]
closed-form:

X₂: X₂ + [[n != 0]]⋅n^1
X₀: X₀

Termination: true
Formula:

0 ≤ 0 ∧ 0 ≤ 10+X₂ ∧ X₂ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 9 ≤ X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₂
∨ 0 ≤ 0 ∧ 0 ≤ 10+X₂ ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₂
∨ 0 ≤ 0 ∧ 0 ≤ 10+X₂ ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ 0 ≤ X₂

Stabilization-Threshold for: X₂ ≤ 9

alphas_abs: 10+X₂
M: 0
N: 1
Bound: 2⋅X₂+22 {O(n)}

original loop: (10 ≤ X₃ ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ ∧ X₂ ≤ 8 ∧ 10 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 0 ≤ 1+X₂,(X₀,X₂,X₃) -> (X₀,1+X₂,0))
transformed loop: (10 ≤ X₃ ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ ∧ X₂ ≤ 8 ∧ 10 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 0 ≤ 1+X₂,(X₀,X₂,X₃) -> (X₀,1+X₂,0))
loop: (10 ≤ X₃ ∧ X₃ ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10 ≤ X₀+X₃ ∧ X₃ ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₃ ∧ X₂ ≤ 8 ∧ 10 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 0 ≤ 1+X₂,(X₀,X₂,X₃) -> (X₀,1+X₂,0))
order: [X₃; X₂; X₀]
closed-form:

X₃: [[n == 0]]⋅X₃
X₂: X₂ + [[n != 0]]⋅n^1
X₀: X₀

Termination: true
Formula:

0 ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 0 ∧ X₃ ≤ 10 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₀ ≤ 10 ∧ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ 0 ≤ 10+X₂ ∧ X₃ ≤ 10 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 10+X₂ ≤ 0 ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 8 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ X₂ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₀ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 1 ≤ X₂ ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
∨ X₃ ≤ 10 ∧ 0 ≤ 9+X₂ ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₂ ∧ 1 ≤ 0 ∧ 9 ≤ X₀+X₂ ∧ 10 ≤ X₀ ∧ 10 ≤ X₀+X₂ ∧ 11 ≤ X₀ ∧ 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ 0 ≤ X₃

Stabilization-Threshold for: X₂ ≤ 8

alphas_abs: 9+X₂
M: 0
N: 1
Bound: 2⋅X₂+20 {O(n)}

Stabilization-Threshold for: 0 ≤ X₂+X₃

alphas_abs: 1+X₂
M: 0
N: 1
Bound: 2⋅X₂+4 {O(n)}

Stabilization-Threshold for: X₃ ≤ 10+X₂

alphas_abs: 11+X₂
M: 0
N: 1
Bound: 2⋅X₂+24 {O(n)}

X₃: [[n == 0]]⋅X₃
X₂: X₂ + [[n != 0]]⋅n^1
X₀: X₀

Termination: true
Formula:

Stabilization-Threshold for: X₂ ≤ 8

alphas_abs: 9+X₂
M: 0
N: 1
Bound: 2⋅X₂+20 {O(n)}

Stabilization-Threshold for: 0 ≤ X₂+X₃

alphas_abs: 1+X₂
M: 0
N: 1
Bound: 2⋅X₂+4 {O(n)}

Stabilization-Threshold for: X₃ ≤ 10+X₂

alphas_abs: 11+X₂
M: 0
N: 1
Bound: 2⋅X₂+24 {O(n)}

TWN - Lifting for [26: f33->f36; 28: f36->f33] of 2⋅X₂+24 {O(n)}

relevant size-bounds w.r.t. t₂₃: f11→f33:
X₂: 0 {O(1)}
Runtime-bound of t₂₃: 1 {O(1)}
Results in: 24 {O(1)}

TWN - Lifting for [26: f33->f36; 28: f36->f33] of 6⋅X₂+53 {O(n)}

relevant size-bounds w.r.t. t₂₉: f36→f36:
X₂: 9 {O(1)}
Runtime-bound of t₂₉: 1140 {O(1)}
Results in: 121980 {O(1)}

TWN - Lifting for [26: f33->f36; 28: f36->f33] of 6⋅X₂+53 {O(n)}

relevant size-bounds w.r.t. t₃₀: f36→f36:
X₂: 9 {O(1)}
Runtime-bound of t₃₀: 1140 {O(1)}
Results in: 121980 {O(1)}

All Bounds

Timebounds

Overall timebound:248087 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 10 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 900 {O(1)}
t₂₅: 900 {O(1)}
t₂₆: 10 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 243984 {O(1)}
t₂₉: 1140 {O(1)}
t₃₀: 1140 {O(1)}

Costbounds

Overall costbound: 248087 {O(1)}
t₂₁: 1 {O(1)}
t₂₂: 10 {O(1)}
t₂₃: 1 {O(1)}
t₂₄: 900 {O(1)}
t₂₅: 900 {O(1)}
t₂₆: 10 {O(1)}
t₂₇: 1 {O(1)}
t₂₈: 243984 {O(1)}
t₂₉: 1140 {O(1)}
t₃₀: 1140 {O(1)}

Sizebounds

t₂₁, X₀: 0 {O(1)}
t₂₁, X₁: X₁ {O(n)}
t₂₁, X₂: X₂ {O(n)}
t₂₁, X₃: X₃ {O(n)}
t₂₂, X₀: 9 {O(1)}
t₂₂, X₁: 0 {O(1)}
t₂₂, X₂: X₂ {O(n)}
t₂₂, X₃: X₃ {O(n)}
t₂₃, X₀: 10 {O(1)}
t₂₃, X₁: 10 {O(1)}
t₂₃, X₂: 0 {O(1)}
t₂₃, X₃: X₃ {O(n)}
t₂₄, X₀: 10 {O(1)}
t₂₄, X₁: 10 {O(1)}
t₂₄, X₂: X₂ {O(n)}
t₂₄, X₃: X₃ {O(n)}
t₂₅, X₀: 9 {O(1)}
t₂₅, X₁: 10 {O(1)}
t₂₅, X₂: X₂ {O(n)}
t₂₅, X₃: X₃ {O(n)}
t₂₆, X₀: 10 {O(1)}
t₂₆, X₁: 10 {O(1)}
t₂₆, X₂: 9 {O(1)}
t₂₆, X₃: 0 {O(1)}
t₂₇, X₀: 10 {O(1)}
t₂₇, X₁: 10 {O(1)}
t₂₇, X₂: 20 {O(1)}
t₂₇, X₃: 10 {O(1)}
t₂₈, X₀: 10 {O(1)}
t₂₈, X₁: 10 {O(1)}
t₂₈, X₂: 20 {O(1)}
t₂₈, X₃: 10 {O(1)}
t₂₉, X₀: 10 {O(1)}
t₂₉, X₁: 10 {O(1)}
t₂₉, X₂: 9 {O(1)}
t₂₉, X₃: 10 {O(1)}
t₃₀, X₀: 10 {O(1)}
t₃₀, X₁: 10 {O(1)}
t₃₀, X₂: 9 {O(1)}
t₃₀, X₃: 10 {O(1)}