KoAT2 Proof Output

Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_start, eval_foo_stop
Transitions:
t₁: eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(0, 3, X₂, X₃, X₄)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb2_in(X₀, X₁, X₁, X₃, X₄) :|: X₀ ≤ 9
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄) :|: 10 ≤ X₀
t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 11
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄) :|: 12 ≤ X₂
t₆: eval_foo_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb2_in(X₀, X₁, 1+X₂, X₃, X₄)
t₇: eval_foo_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb1_in(1+X₀, X₂, X₂, X₃, X₄)
t₈: eval_foo_bb5_in(X₀, X₁, X₂, X₃, X₄) → eval_foo_stop(X₀, X₁, X₂, X₃, X₄)
t₀: eval_foo_start(X₀, X₁, X₂, X₃, X₄) → eval_foo_bb0_in(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Eliminate variables [X₃; X₄] that do not contribute to the problem

Found invariant 3 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ 10 ≤ X₀ for location eval_foo_bb5_in

Found invariant 3 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_foo_bb2_in

Found invariant 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_foo_bb1_in

Found invariant 3 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ 10 ≤ X₀ for location eval_foo_stop

Found invariant X₂ ≤ 11 ∧ X₂ ≤ 8+X₁ ∧ X₁+X₂ ≤ 22 ∧ X₂ ≤ 11+X₀ ∧ 3 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ X₁ ≤ 11 ∧ X₁ ≤ 11+X₀ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_foo_bb3_in

Found invariant 12 ≤ X₂ ∧ 15 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₀ for location eval_foo_bb4_in

Problem after Preprocessing

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂
Temp_Vars:
Locations: eval_foo_bb0_in, eval_foo_bb1_in, eval_foo_bb2_in, eval_foo_bb3_in, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_start, eval_foo_stop
Transitions:
t₁₇: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb1_in(0, 3, X₂)
t₁₈: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₁) :|: X₀ ≤ 9 ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁ ∧ 0 ≤ X₀
t₁₉: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb5_in(X₀, X₁, X₂) :|: 10 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁ ∧ 0 ≤ X₀
t₂₀: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₂ ≤ 11 ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
t₂₁: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb4_in(X₀, X₁, X₂) :|: 12 ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
t₂₂: eval_foo_bb3_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, 1+X₂) :|: X₁+X₂ ≤ 22 ∧ X₁ ≤ 11+X₀ ∧ X₂ ≤ 11+X₀ ∧ X₁ ≤ 11 ∧ X₂ ≤ 11 ∧ X₂ ≤ 8+X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
t₂₃: eval_foo_bb4_in(X₀, X₁, X₂) → eval_foo_bb1_in(1+X₀, X₂, X₂) :|: 3 ≤ X₀+X₁ ∧ 3 ≤ X₁ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
t₂₄: eval_foo_bb5_in(X₀, X₁, X₂) → eval_foo_stop(X₀, X₁, X₂) :|: 3 ≤ X₁ ∧ 10 ≤ X₀ ∧ 13 ≤ X₀+X₁
t₂₅: eval_foo_start(X₀, X₁, X₂) → eval_foo_bb0_in(X₀, X₁, X₂)

MPRF for transition t₁₈: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, X₁) :|: X₀ ≤ 9 ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

10 {O(1)}

MPRF:

• eval_foo_bb1_in: [10-X₀]
• eval_foo_bb2_in: [9-X₀]
• eval_foo_bb3_in: [9-X₀]
• eval_foo_bb4_in: [9-X₀]

MPRF for transition t₂₀: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₂ ≤ 11 ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:

new bound:

15 {O(1)}

MPRF:

• eval_foo_bb1_in: [12-X₁]
• eval_foo_bb2_in: [12-X₂]
• eval_foo_bb3_in: [11-X₂]
• eval_foo_bb4_in: [12-X₂]

MPRF for transition t₂₂: eval_foo_bb3_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, X₁, 1+X₂) :|: X₁+X₂ ≤ 22 ∧ X₁ ≤ 11+X₀ ∧ X₂ ≤ 11+X₀ ∧ X₁ ≤ 11 ∧ X₂ ≤ 11 ∧ X₂ ≤ 8+X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ of depth 1:

new bound:

23 {O(1)}

MPRF:

• eval_foo_bb1_in: [20-X₁]
• eval_foo_bb2_in: [20-X₂]
• eval_foo_bb3_in: [20-X₂]
• eval_foo_bb4_in: [20-X₂]

TWN: t₂₃: eval_foo_bb4_in→eval_foo_bb1_in

cycle: [t₂₃: eval_foo_bb4_in→eval_foo_bb1_in; t₁₈: eval_foo_bb1_in→eval_foo_bb2_in; t₂₁: eval_foo_bb2_in→eval_foo_bb4_in]
loop: (X₀ ≤ 9 ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁ ∧ 0 ≤ X₀ ∧ 12 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁ ∧ 3 ≤ X₁ ∧ 3 ≤ X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ 0 ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁ ∧ 12 ≤ X₀+X₁ ∧ 12 ≤ X₁ ∧ 15 ≤ 2⋅X₁ ∧ 0 ≤ X₀ ∧ 0 ≤ 0,(X₀,X₁) -> (1+X₀,X₁))
order: [X₁; X₀]
closed-form:

X₁: X₁
X₀: X₀ + [[n != 0]]⋅n^1

Termination: true
Formula:

0 ≤ 0 ∧ X₀ ≤ 9 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁ ∧ 9 ≤ X₀ ∧ 12 ≤ X₀+X₁ ∧ 12 ≤ X₁ ∧ 15 ≤ 2⋅X₁ ∧ 0 ≤ X₀
∨ 0 ≤ 0 ∧ X₀ ≤ 8 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁ ∧ 12 ≤ X₀+X₁ ∧ 12 ≤ X₁ ∧ 15 ≤ 2⋅X₁ ∧ 0 ≤ X₀
∨ 0 ≤ 0 ∧ 1 ≤ 0 ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁ ∧ 12 ≤ X₀+X₁ ∧ 12 ≤ X₁ ∧ 15 ≤ 2⋅X₁ ∧ 0 ≤ X₀

Stabilization-Threshold for: X₀ ≤ 9

alphas_abs: 10+X₀
M: 0
N: 1
Bound: 2⋅X₀+22 {O(n)}

loop: (12 ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 3 ≤ X₂ ∧ 6 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₁ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ X₁+X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂ ∧ X₀ ≤ 8 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 0 ≤ 1+X₀,(X₀,X₁,X₂) -> (1+X₀,X₂,X₂))
order: [X₂; X₁; X₀]
closed-form:

X₂: X₂
X₁: [[n == 0]]⋅X₁ + [[n != 0]]⋅X₂
X₀: X₀ + [[n != 0]]⋅n^1

Termination: true
Formula:

0 ≤ 0 ∧ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 8 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 8 ≤ X₀ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 8 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₀ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 8 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 8 ≤ X₀ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₀ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 7 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 7 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 7 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ 2⋅X₂ ≤ 15 ∧ X₂ ≤ 3 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ 2⋅X₂ ≤ 15 ∧ X₂ ≤ 3 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ 2⋅X₂ ≤ 15 ∧ X₂ ≤ 3 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ 2⋅X₂ ≤ 15 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ X₀ ≤ 8 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 8 ≤ X₀ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ X₀ ≤ 8 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₀ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ X₀ ≤ 8 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 8 ≤ X₀ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ X₀ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₀ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ X₀ ≤ 7 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ X₀ ≤ 7 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ X₀ ≤ 7 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ X₀ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ X₂ ≤ 3 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ X₂ ≤ 3 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ X₂ ≤ 3 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 0 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 8 ∧ X₀+X₂ ≤ 3 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 8 ≤ X₀ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 8 ∧ X₀+X₂ ≤ 3 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₀ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 8 ∧ X₀+X₂ ≤ 3 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 8 ≤ X₀ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 8 ∧ X₀+X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₀ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 8 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₂ ∧ 8 ≤ X₀ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 8 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₀ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 8 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 8 ≤ X₀ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₀ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 7 ∧ X₀+X₂ ≤ 3 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 7 ∧ X₀+X₂ ≤ 3 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 7 ∧ X₀+X₂ ≤ 3 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 7 ∧ X₀+X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 7 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 7 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 7 ≤ 2⋅X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 7 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀+X₂ ≤ 3 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀+X₂ ≤ 3 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀+X₂ ≤ 3 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₀+X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 7 ≤ 2⋅X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 2⋅X₂ ≤ 15 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 15 ≤ 2⋅X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀ ≤ 8 ∧ X₀+X₂ ≤ 3 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 8 ≤ X₀ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀ ≤ 8 ∧ X₀+X₂ ≤ 3 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₀ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀ ≤ 8 ∧ X₀+X₂ ≤ 3 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 8 ≤ X₀ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀ ≤ 8 ∧ X₀+X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₀ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀ ≤ 8 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₂ ∧ 8 ≤ X₀ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀ ≤ 8 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₀ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀ ≤ 8 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 8 ≤ X₀ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀ ≤ 8 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₀ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀ ≤ 7 ∧ X₀+X₂ ≤ 3 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀ ≤ 7 ∧ X₀+X₂ ≤ 3 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀ ≤ 7 ∧ X₀+X₂ ≤ 3 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀ ≤ 7 ∧ X₀+X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀ ≤ 7 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀ ≤ 7 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀ ≤ 7 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀ ≤ 7 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀+X₂ ≤ 3 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀+X₂ ≤ 3 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀+X₂ ≤ 3 ∧ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₀+X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ X₂ ≤ 3 ∧ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂
∨ 0 ≤ 1 ∧ 0 ≤ 1+X₀ ∧ 1 ≤ 0 ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ 4 ≤ X₂ ∧ 7 ≤ 2⋅X₂ ∧ 8 ≤ X₂ ∧ 12 ≤ X₀+X₂ ∧ 12 ≤ X₂ ∧ 0 ≤ X₀ ∧ X₁ ≤ X₂

Stabilization-Threshold for: X₀ ≤ 8

alphas_abs: 9+X₀
M: 0
N: 1
Bound: 2⋅X₀+20 {O(n)}

Stabilization-Threshold for: 3 ≤ X₀+X₁

alphas_abs: 2+X₀+X₂
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₂+6 {O(n)}

TWN - Lifting for [18: eval_foo_bb1_in->eval_foo_bb2_in; 21: eval_foo_bb2_in->eval_foo_bb4_in; 23: eval_foo_bb4_in->eval_foo_bb1_in] of 2⋅X₀+24 {O(n)}

relevant size-bounds w.r.t. t₁₇: eval_foo_bb0_in→eval_foo_bb1_in:
X₀: 0 {O(1)}
Runtime-bound of t₁₇: 1 {O(1)}
Results in: 24 {O(1)}

TWN - Lifting for [18: eval_foo_bb1_in->eval_foo_bb2_in; 21: eval_foo_bb2_in->eval_foo_bb4_in; 23: eval_foo_bb4_in->eval_foo_bb1_in] of 2⋅X₂+4⋅X₀+31 {O(n)}

relevant size-bounds w.r.t. t₂₂: eval_foo_bb3_in→eval_foo_bb2_in:
X₀: 9 {O(1)}
X₂: 12 {O(1)}
Runtime-bound of t₂₂: 23 {O(1)}
Results in: 2093 {O(1)}

All Bounds

Timebounds

Overall timebound:4286 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 10 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 15 {O(1)}
t₂₁: 2117 {O(1)}
t₂₂: 23 {O(1)}
t₂₃: 2117 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}

Costbounds

Overall costbound: 4286 {O(1)}
t₁₇: 1 {O(1)}
t₁₈: 10 {O(1)}
t₁₉: 1 {O(1)}
t₂₀: 15 {O(1)}
t₂₁: 2117 {O(1)}
t₂₂: 23 {O(1)}
t₂₃: 2117 {O(1)}
t₂₄: 1 {O(1)}
t₂₅: 1 {O(1)}

Sizebounds

t₁₇, X₀: 0 {O(1)}
t₁₇, X₁: 3 {O(1)}
t₁₇, X₂: X₂ {O(n)}
t₁₈, X₀: 9 {O(1)}
t₁₈, X₁: 18 {O(1)}
t₁₈, X₂: 15 {O(1)}
t₁₉, X₀: 19 {O(1)}
t₁₉, X₁: 15 {O(1)}
t₁₉, X₂: 15 {O(1)}
t₂₀, X₀: 9 {O(1)}
t₂₀, X₁: 11 {O(1)}
t₂₀, X₂: 11 {O(1)}
t₂₁, X₀: 18 {O(1)}
t₂₁, X₁: 29 {O(1)}
t₂₁, X₂: 15 {O(1)}
t₂₂, X₀: 9 {O(1)}
t₂₂, X₁: 11 {O(1)}
t₂₂, X₂: 12 {O(1)}
t₂₃, X₀: 19 {O(1)}
t₂₃, X₁: 15 {O(1)}
t₂₃, X₂: 15 {O(1)}
t₂₄, X₀: 19 {O(1)}
t₂₄, X₁: 15 {O(1)}
t₂₄, X₂: 15 {O(1)}
t₂₅, X₀: X₀ {O(n)}
t₂₅, X₁: X₁ {O(n)}
t₂₅, X₂: X₂ {O(n)}