KoAT2 Proof Output

Initial Problem

Start: eval_foo_start
Program_Vars: X₀, X₁, X₂, X₃
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) → eval_foo_bb1_in(X₂, X₁, X₂, X₃)
t₂: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, 0, X₂, X₃) :|: X₀ ≤ 4
t₃: eval_foo_bb1_in(X₀, X₁, X₂, X₃) → eval_foo_bb5_in(X₀, X₁, X₂, X₃) :|: 5 ≤ X₀
t₄: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb3_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ 9 ∧ 3 ≤ X₀
t₅: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb4_in(X₀, X₁, X₂, X₃) :|: X₀ ≤ 2
t₆: eval_foo_bb2_in(X₀, X₁, X₂, X₃) → eval_foo_bb4_in(X₀, X₁, X₂, X₃) :|: 10 ≤ X₁
t₇: eval_foo_bb3_in(X₀, X₁, X₂, X₃) → eval_foo_bb2_in(X₀, 1+X₁, X₂, X₃)
t₈: eval_foo_bb4_in(X₀, X₁, X₂, X₃) → eval_foo_bb1_in(1+X₀, X₁, X₂, X₃)
t₉: eval_foo_bb5_in(X₀, X₁, X₂, X₃) → eval_foo_stop(X₀, X₁, X₂, X₃)
t₀: eval_foo_start(X₀, X₁, X₂, X₃) → eval_foo_bb0_in(X₀, X₁, X₂, X₃)

Preprocessing

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

Found invariant X₂ ≤ X₀ ∧ 5 ≤ X₀ for location eval_foo_bb5_in

Found invariant X₂ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ 0 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 for location eval_foo_bb2_in

Found invariant X₂ ≤ X₀ for location eval_foo_bb1_in

Found invariant X₂ ≤ X₀ ∧ 5 ≤ X₀ for location eval_foo_stop

Found invariant X₂ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₁+X₂ ≤ 13 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 9 ∧ X₁ ≤ 6+X₀ ∧ X₀+X₁ ≤ 13 ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 ∧ 3 ≤ X₀ for location eval_foo_bb3_in

Found invariant X₂ ≤ 4 ∧ X₂ ≤ 2+X₁ ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ 0 ≤ X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 4 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:
t₁₉: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb1_in(X₂, X₁, X₂)
t₂₀: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, 0, X₂) :|: X₀ ≤ 4 ∧ X₂ ≤ X₀
t₂₁: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb5_in(X₀, X₁, X₂) :|: 5 ≤ X₀ ∧ X₂ ≤ X₀
t₂₂: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb3_in(X₀, X₁, X₂) :|: X₁ ≤ 9 ∧ 3 ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
t₂₃: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb4_in(X₀, X₁, X₂) :|: X₀ ≤ 2 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
t₂₄: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb4_in(X₀, X₁, X₂) :|: 10 ≤ X₁ ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
t₂₅: eval_foo_bb3_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, 1+X₁, X₂) :|: X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 13 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
t₂₆: eval_foo_bb4_in(X₀, X₁, X₂) → eval_foo_bb1_in(1+X₀, X₁, X₂) :|: X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₂ ≤ 4 ∧ X₀ ≤ 2+X₁ ∧ X₂ ≤ 2+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
t₂₇: eval_foo_bb5_in(X₀, X₁, X₂) → eval_foo_stop(X₀, X₁, X₂) :|: 5 ≤ X₀ ∧ X₂ ≤ X₀
t₂₈: eval_foo_start(X₀, X₁, X₂) → eval_foo_bb0_in(X₀, X₁, X₂)

MPRF for transition t₂₀: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, 0, X₂) :|: X₀ ≤ 4 ∧ X₂ ≤ X₀ of depth 1:

new bound:

X₂+5 {O(n)}

MPRF:

• eval_foo_bb1_in: [5-X₀]
• eval_foo_bb2_in: [4-X₀]
• eval_foo_bb3_in: [4-X₀]
• eval_foo_bb4_in: [4-X₀]

MPRF for transition t₂₃: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb4_in(X₀, X₁, X₂) :|: X₀ ≤ 2 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₂+5 {O(n)}

MPRF:

• eval_foo_bb1_in: [5-X₀]
• eval_foo_bb2_in: [5-X₀]
• eval_foo_bb3_in: [5-X₀]
• eval_foo_bb4_in: [4-X₀]

MPRF for transition t₂₄: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb4_in(X₀, X₁, X₂) :|: 10 ≤ X₁ ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₂+5 {O(n)}

MPRF:

• eval_foo_bb1_in: [5-X₀]
• eval_foo_bb2_in: [5-X₀]
• eval_foo_bb3_in: [5-X₀]
• eval_foo_bb4_in: [4-X₀]

MPRF for transition t₂₆: eval_foo_bb4_in(X₀, X₁, X₂) → eval_foo_bb1_in(1+X₀, X₁, X₂) :|: X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₂ ≤ 4 ∧ X₀ ≤ 2+X₁ ∧ X₂ ≤ 2+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₂+5 {O(n)}

MPRF:

• eval_foo_bb1_in: [5-X₀]
• eval_foo_bb2_in: [5-X₀]
• eval_foo_bb3_in: [5-X₀]
• eval_foo_bb4_in: [5-X₀]

TWN: t₂₅: eval_foo_bb3_in→eval_foo_bb2_in

cycle: [t₂₅: eval_foo_bb3_in→eval_foo_bb2_in; t₂₂: eval_foo_bb2_in→eval_foo_bb3_in]
loop: (X₁ ≤ 9 ∧ 3 ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 13 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁,(X₀,X₁,X₂) -> (X₀,1+X₁,X₂))
order: [X₂; X₁; X₀]
closed-form:

X₂: X₂
X₁: X₁ + [[n != 0]]⋅n^1
X₀: X₀

Termination: true
Formula:

X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 13 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 9 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 13 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 9 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 13 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 9 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 13 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 13 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₀+X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 13 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₀+X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 13 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 13 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₀+X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 13 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₀+X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 12 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 9 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 12 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 9 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 12 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 9 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 9 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 9 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 9 ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 13 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 13 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 13 ∧ X₀+X₁ ≤ 12 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 9 ≤ X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 13 ∧ X₀+X₁ ≤ 12 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 9 ≤ X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 13 ∧ X₀+X₁ ≤ 12 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 9 ≤ X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 13 ∧ X₀+X₁ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 13 ∧ X₀+X₁ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 13 ∧ X₀+X₁ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 13 ∧ X₀+X₁ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 13 ∧ X₀+X₁ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 13 ∧ X₀+X₁ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 13 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 9 ≤ X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 13 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 9 ≤ X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 13 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 9 ≤ X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 13 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 13 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 13 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 13 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 13 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 13 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 13 ≤ X₁+X₂ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 12 ∧ X₁+X₂ ≤ 12 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 9 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 12 ∧ X₁+X₂ ≤ 12 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 9 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 12 ∧ X₁+X₂ ≤ 12 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 9 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 12 ∧ X₁+X₂ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 12 ∧ X₁+X₂ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 12 ∧ X₁+X₂ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 12 ∧ X₁+X₂ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 12 ∧ X₁+X₂ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 12 ∧ X₁+X₂ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 12 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 9 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 12 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 9 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 12 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 9 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₁ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 12 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 9 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 12 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 9 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 12 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 9 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁+X₂ ≤ 12 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ 9 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 9 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 9 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₂ ≤ 8 ∧ X₁ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 6+X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₂ ≤ 8 ∧ X₁ ≤ 5+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 0 ≤ 1 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
∨ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ 1 ≤ 0 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁

Stabilization-Threshold for: X₁ ≤ 6+X₀

alphas_abs: 7+X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+16 {O(n)}

Stabilization-Threshold for: X₁ ≤ 9

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

Stabilization-Threshold for: X₁+X₂ ≤ 13

alphas_abs: 14+X₁+X₂
M: 0
N: 1
Bound: 2⋅X₁+2⋅X₂+30 {O(n)}

Stabilization-Threshold for: X₀+X₁ ≤ 13

alphas_abs: 14+X₀+X₁
M: 0
N: 1
Bound: 2⋅X₀+2⋅X₁+30 {O(n)}

TWN - Lifting for [22: eval_foo_bb2_in->eval_foo_bb3_in; 25: eval_foo_bb3_in->eval_foo_bb2_in] of 2⋅X₂+4⋅X₀+8⋅X₁+100 {O(n)}

relevant size-bounds w.r.t. t₂₀: eval_foo_bb1_in→eval_foo_bb2_in:
X₀: 2⋅X₂+16 {O(n)}
X₁: 0 {O(1)}
X₂: X₂ {O(n)}
Runtime-bound of t₂₀: X₂+5 {O(n)}
Results in: 10⋅X₂⋅X₂+214⋅X₂+820 {O(n^2)}

Cut unsatisfiable transition [t₂₄: eval_foo_bb2_in→eval_foo_bb4_in; t₅₃: eval_foo_bb2_in→eval_foo_bb4_in]

Found invariant X₂ ≤ 4 ∧ X₂ ≤ 3+X₁ ∧ X₁+X₂ ≤ 13 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 9 ∧ X₁ ≤ 6+X₀ ∧ X₀+X₁ ≤ 13 ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 4 ∧ 3 ≤ X₀ for location eval_foo_bb3_in_v2

Found invariant X₂ ≤ X₀ ∧ 5 ≤ X₀ for location eval_foo_bb5_in

Found invariant X₂ ≤ X₀ ∧ 5 ≤ X₀ for location eval_foo_stop

Found invariant X₂ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₁+X₂ ≤ 4 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 0 ∧ X₀+X₁ ≤ 4 ∧ 0 ≤ X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 for location eval_foo_bb2_in

Found invariant X₂ ≤ X₀ for location eval_foo_bb1_in

Found invariant X₂ ≤ 4 ∧ X₂ ≤ 3+X₁ ∧ X₁+X₂ ≤ 14 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 10 ∧ X₁ ≤ 7+X₀ ∧ X₀+X₁ ≤ 14 ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ 3+X₁ ∧ X₀ ≤ 4 ∧ 3 ≤ X₀ for location eval_foo_bb2_in_v1

Found invariant X₂ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₁+X₂ ≤ 4 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 0 ∧ 3+X₁ ≤ X₀ ∧ X₀+X₁ ≤ 4 ∧ 0 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ X₀ ≤ 4+X₁ ∧ X₀ ≤ 4 ∧ 3 ≤ X₀ for location eval_foo_bb3_in_v1

Found invariant X₂ ≤ 4 ∧ X₂ ≤ 2+X₁ ∧ X₁+X₂ ≤ 14 ∧ X₂ ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 10 ∧ X₀+X₁ ≤ 14 ∧ 0 ≤ X₁ ∧ X₀ ≤ 2+X₁ ∧ X₀ ≤ 4 for location eval_foo_bb4_in

Analysing control-flow refined program

knowledge_propagation leads to new time bound X₂+5 {O(n)} for transition t₅₄: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb4_in(X₀, X₁, X₂) :|: X₀ ≤ 2 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₀+X₁ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₁+X₂ ≤ 4 ∧ X₂ ≤ 4 ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0

knowledge_propagation leads to new time bound X₂+5 {O(n)} for transition t₅₅: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb3_in_v1(X₀, X₁, X₂) :|: X₁ ≤ 9 ∧ 3 ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₀+X₁ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₁+X₂ ≤ 4 ∧ X₂ ≤ 4 ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0

knowledge_propagation leads to new time bound X₂+5 {O(n)} for transition t₅₆: eval_foo_bb3_in_v1(X₀, X₁, X₂) → eval_foo_bb2_in_v1(X₀, 1+X₁, X₂) :|: X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 13 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₀+X₁ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₁+X₂ ≤ 4 ∧ X₂ ≤ 4 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 3+X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0

MPRF for transition t₅₇: eval_foo_bb2_in_v1(X₀, X₁, X₂) → eval_foo_bb4_in(X₀, X₁, X₂) :|: 10 ≤ X₁ ∧ X₀+X₁ ≤ 14 ∧ X₁+X₂ ≤ 14 ∧ X₁ ≤ 10 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 7+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ X₀ ≤ 3+X₁ ∧ X₂ ≤ 3+X₁ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

X₂+14 {O(n)}

MPRF:

• eval_foo_bb1_in: [14-X₀]
• eval_foo_bb2_in: [14-X₀]
• eval_foo_bb2_in_v1: [14-X₀]
• eval_foo_bb3_in_v1: [14-X₀]
• eval_foo_bb3_in_v2: [14-X₀]
• eval_foo_bb4_in: [13-X₀]

MPRF for transition t₅₈: eval_foo_bb2_in_v1(X₀, X₁, X₂) → eval_foo_bb3_in_v2(X₀, X₁, X₂) :|: X₁ ≤ 9 ∧ 3 ≤ X₀ ∧ X₀+X₁ ≤ 14 ∧ X₁+X₂ ≤ 14 ∧ X₁ ≤ 10 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 7+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ X₀ ≤ 3+X₁ ∧ X₂ ≤ 3+X₁ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

9⋅X₂+45 {O(n)}

MPRF:

• eval_foo_bb1_in: [45-9⋅X₀]
• eval_foo_bb2_in: [45-9⋅X₀]
• eval_foo_bb2_in_v1: [46-9⋅X₀-X₁]
• eval_foo_bb3_in_v1: [45-9⋅X₀]
• eval_foo_bb3_in_v2: [45-9⋅X₀-X₁]
• eval_foo_bb4_in: [36-9⋅X₀]

MPRF for transition t₅₉: eval_foo_bb3_in_v2(X₀, X₁, X₂) → eval_foo_bb2_in_v1(X₀, 1+X₁, X₂) :|: X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 13 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ X₀ ≤ 3+X₁ ∧ X₂ ≤ 3+X₁ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ of depth 1:

new bound:

9⋅X₂+45 {O(n)}

MPRF:

• eval_foo_bb1_in: [45-9⋅X₀]
• eval_foo_bb2_in: [45-9⋅X₀]
• eval_foo_bb2_in_v1: [46-9⋅X₀-X₁]
• eval_foo_bb3_in_v1: [45-9⋅X₀]
• eval_foo_bb3_in_v2: [46-9⋅X₀-X₁]
• eval_foo_bb4_in: [36-9⋅X₀]

CFR: Improvement to new bound with the following program:

method: PartialEvaluation new bound:

O(n)

cfr-program:

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_bb2_in_v1, eval_foo_bb3_in_v1, eval_foo_bb3_in_v2, eval_foo_bb4_in, eval_foo_bb5_in, eval_foo_start, eval_foo_stop
Transitions:
t₁₉: eval_foo_bb0_in(X₀, X₁, X₂) → eval_foo_bb1_in(X₂, X₁, X₂)
t₂₀: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb2_in(X₀, 0, X₂) :|: X₀ ≤ 4 ∧ X₂ ≤ X₀
t₂₁: eval_foo_bb1_in(X₀, X₁, X₂) → eval_foo_bb5_in(X₀, X₁, X₂) :|: 5 ≤ X₀ ∧ X₂ ≤ X₀
t₅₅: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb3_in_v1(X₀, X₁, X₂) :|: X₁ ≤ 9 ∧ 3 ≤ X₀ ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₀+X₁ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₁+X₂ ≤ 4 ∧ X₂ ≤ 4 ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
t₂₃: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb4_in(X₀, X₁, X₂) :|: X₀ ≤ 2 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₀+X₁ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₁+X₂ ≤ 4 ∧ X₂ ≤ 4 ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
t₅₄: eval_foo_bb2_in(X₀, X₁, X₂) → eval_foo_bb4_in(X₀, X₁, X₂) :|: X₀ ≤ 2 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₀+X₁ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₁+X₂ ≤ 4 ∧ X₂ ≤ 4 ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
t₅₈: eval_foo_bb2_in_v1(X₀, X₁, X₂) → eval_foo_bb3_in_v2(X₀, X₁, X₂) :|: X₁ ≤ 9 ∧ 3 ≤ X₀ ∧ X₀+X₁ ≤ 14 ∧ X₁+X₂ ≤ 14 ∧ X₁ ≤ 10 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 7+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ X₀ ≤ 3+X₁ ∧ X₂ ≤ 3+X₁ ∧ 1 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
t₅₇: eval_foo_bb2_in_v1(X₀, X₁, X₂) → eval_foo_bb4_in(X₀, X₁, X₂) :|: 10 ≤ X₁ ∧ X₀+X₁ ≤ 14 ∧ X₁+X₂ ≤ 14 ∧ X₁ ≤ 10 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 7+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ X₀ ≤ 3+X₁ ∧ X₂ ≤ 3+X₁ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀ ∧ 4 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
t₅₆: eval_foo_bb3_in_v1(X₀, X₁, X₂) → eval_foo_bb2_in_v1(X₀, 1+X₁, X₂) :|: X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 13 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₀+X₁ ≤ 4 ∧ X₂ ≤ 4+X₁ ∧ X₁+X₂ ≤ 4 ∧ X₂ ≤ 4 ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 3+X₁ ≤ X₀ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁ ∧ X₁ ≤ 0
t₅₉: eval_foo_bb3_in_v2(X₀, X₁, X₂) → eval_foo_bb2_in_v1(X₀, 1+X₁, X₂) :|: X₀+X₁ ≤ 13 ∧ X₁+X₂ ≤ 13 ∧ X₁ ≤ 9 ∧ X₀+X₂ ≤ 8 ∧ X₁ ≤ 6+X₀ ∧ X₀ ≤ 4 ∧ X₀ ≤ 4+X₁ ∧ X₂ ≤ 4+X₁ ∧ X₂ ≤ 4 ∧ X₀ ≤ 3+X₁ ∧ X₂ ≤ 3+X₁ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀ ∧ 3 ≤ X₀+X₁ ∧ 4 ≤ X₀+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
t₂₆: eval_foo_bb4_in(X₀, X₁, X₂) → eval_foo_bb1_in(1+X₀, X₁, X₂) :|: X₀+X₁ ≤ 14 ∧ X₁+X₂ ≤ 14 ∧ X₁ ≤ 10 ∧ X₀+X₂ ≤ 8 ∧ X₀ ≤ 4 ∧ X₂ ≤ 4 ∧ X₀ ≤ 2+X₁ ∧ X₂ ≤ 2+X₁ ∧ X₂ ≤ X₀ ∧ 0 ≤ X₁
t₂₇: eval_foo_bb5_in(X₀, X₁, X₂) → eval_foo_stop(X₀, X₁, X₂) :|: 5 ≤ X₀ ∧ X₂ ≤ X₀
t₂₈: eval_foo_start(X₀, X₁, X₂) → eval_foo_bb0_in(X₀, X₁, X₂)

All Bounds

Timebounds

Overall timebound:25⋅X₂+138 {O(n)}
t₁₉: 1 {O(1)}
t₂₀: X₂+5 {O(n)}
t₂₁: 1 {O(1)}
t₂₃: X₂+5 {O(n)}
t₂₆: X₂+5 {O(n)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₅₄: X₂+5 {O(n)}
t₅₅: X₂+5 {O(n)}
t₅₆: X₂+5 {O(n)}
t₅₇: X₂+14 {O(n)}
t₅₈: 9⋅X₂+45 {O(n)}
t₅₉: 9⋅X₂+45 {O(n)}

Costbounds

Overall costbound: 25⋅X₂+138 {O(n)}
t₁₉: 1 {O(1)}
t₂₀: X₂+5 {O(n)}
t₂₁: 1 {O(1)}
t₂₃: X₂+5 {O(n)}
t₂₆: X₂+5 {O(n)}
t₂₇: 1 {O(1)}
t₂₈: 1 {O(1)}
t₅₄: X₂+5 {O(n)}
t₅₅: X₂+5 {O(n)}
t₅₆: X₂+5 {O(n)}
t₅₇: X₂+14 {O(n)}
t₅₈: 9⋅X₂+45 {O(n)}
t₅₉: 9⋅X₂+45 {O(n)}

Sizebounds

t₁₉, X₀: X₂ {O(n)}
t₁₉, X₁: X₁ {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₂₀, X₀: 2⋅X₂+9 {O(n)}
t₂₀, X₁: 0 {O(1)}
t₂₀, X₂: X₂ {O(n)}
t₂₁, X₀: 3⋅X₂+9 {O(n)}
t₂₁, X₁: X₁+10 {O(n)}
t₂₁, X₂: 2⋅X₂ {O(n)}
t₂₃, X₀: 2⋅X₂+9 {O(n)}
t₂₃, X₁: 0 {O(1)}
t₂₃, X₂: X₂ {O(n)}
t₂₆, X₀: 2⋅X₂+9 {O(n)}
t₂₆, X₁: 10 {O(1)}
t₂₆, X₂: X₂ {O(n)}
t₂₇, X₀: 3⋅X₂+9 {O(n)}
t₂₇, X₁: X₁+10 {O(n)}
t₂₇, X₂: 2⋅X₂ {O(n)}
t₂₈, X₀: X₀ {O(n)}
t₂₈, X₁: X₁ {O(n)}
t₂₈, X₂: X₂ {O(n)}
t₅₄, X₀: 2⋅X₂+9 {O(n)}
t₅₄, X₁: 0 {O(1)}
t₅₄, X₂: X₂ {O(n)}
t₅₅, X₀: 4 {O(1)}
t₅₅, X₁: 0 {O(1)}
t₅₅, X₂: X₂ {O(n)}
t₅₆, X₀: 4 {O(1)}
t₅₆, X₁: 1 {O(1)}
t₅₆, X₂: X₂ {O(n)}
t₅₇, X₀: 4 {O(1)}
t₅₇, X₁: 10 {O(1)}
t₅₇, X₂: X₂ {O(n)}
t₅₈, X₀: 4 {O(1)}
t₅₈, X₁: 9 {O(1)}
t₅₈, X₂: X₂ {O(n)}
t₅₉, X₀: 4 {O(1)}
t₅₉, X₁: 10 {O(1)}
t₅₉, X₂: X₂ {O(n)}