KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₀ for location eval_realselect_20

Found invariant 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ X₂ ≤ 1+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 4 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1+X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 2 ≤ X₀ for location eval_realselect_27

Found invariant 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location eval_realselect_bb3_in

Found invariant 1+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂ for location eval_realselect_bb2_in

Found invariant 0 ≤ X₃ ∧ X₂ ≤ 1+X₃ for location eval_realselect_stop

Found invariant 0 ≤ X₃ ∧ X₂ ≤ 1+X₃ for location eval_realselect_bb5_in

Found invariant 0 ≤ X₃ for location eval_realselect_bb1_in

Problem after Preprocessing

Start: eval_realselect_start
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars: nondef_0, nondef_1
Locations: eval_realselect_0, eval_realselect_1, eval_realselect_19, eval_realselect_2, eval_realselect_20, eval_realselect_27, eval_realselect_28, eval_realselect_3, eval_realselect_4, eval_realselect_5, eval_realselect_6, eval_realselect_bb0_in, eval_realselect_bb1_in, eval_realselect_bb2_in, eval_realselect_bb3_in, eval_realselect_bb4_in, eval_realselect_bb5_in, eval_realselect_start, eval_realselect_stop
Transitions:
t₂: eval_realselect_0(X₀, X₁, X₂, X₃, X₄) → eval_realselect_1(X₀, X₁, X₂, X₃, X₄)
t₃: eval_realselect_1(X₀, X₁, X₂, X₃, X₄) → eval_realselect_2(X₀, X₁, X₂, X₃, X₄)
t₁₆: eval_realselect_19(X₀, X₁, X₂, X₃, X₄) → eval_realselect_20(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 1+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃
t₄: eval_realselect_2(X₀, X₁, X₂, X₃, X₄) → eval_realselect_3(X₀, X₁, X₂, X₃, X₄)
t₁₇: eval_realselect_20(X₀, X₁, X₂, X₃, X₄) → eval_realselect_27(X₀, 1+X₃, X₂, X₃, X₄) :|: X₀ ≤ 1+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃
t₁₈: eval_realselect_27(X₀, X₁, X₂, X₃, X₄) → eval_realselect_28(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 1+X₄ ∧ X₁ ≤ 1+X₃ ∧ X₂ ≤ 1+X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₃
t₁₉: eval_realselect_28(X₀, X₁, X₂, X₃, X₄) → eval_realselect_bb1_in(X₀, X₁, X₂, X₁, X₄) :|: X₀ ≤ 1+X₄ ∧ X₁ ≤ 1+X₃ ∧ X₂ ≤ 1+X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₃
t₅: eval_realselect_3(X₀, X₁, X₂, X₃, X₄) → eval_realselect_4(X₀, X₁, X₂, X₃, X₄)
t₆: eval_realselect_4(X₀, X₁, X₂, X₃, X₄) → eval_realselect_5(X₀, X₁, X₂, X₃, X₄)
t₇: eval_realselect_5(X₀, X₁, X₂, X₃, X₄) → eval_realselect_6(X₀, X₁, X₂, X₃, X₄)
t₈: eval_realselect_6(X₀, X₁, X₂, X₃, X₄) → eval_realselect_bb1_in(X₀, X₁, X₂, 0, X₄)
t₁: eval_realselect_bb0_in(X₀, X₁, X₂, X₃, X₄) → eval_realselect_0(X₀, X₁, X₂, X₃, X₄)
t₉: eval_realselect_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_realselect_bb2_in(X₀, X₁, X₂, X₃, X₃) :|: 2+X₃ ≤ X₂ ∧ 0 ≤ X₃
t₁₀: eval_realselect_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_realselect_bb5_in(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1+X₃ ∧ 0 ≤ X₃
t₁₁: eval_realselect_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_realselect_bb3_in(1+X₄, X₁, X₂, X₃, X₄) :|: 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 2 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄
t₁₂: eval_realselect_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_realselect_bb4_in(1+X₄, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1+X₄ ∧ 1+X₄ ≤ X₂ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 2 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄
t₁₃: eval_realselect_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_realselect_bb2_in(X₀, X₁, X₂, X₃, X₀) :|: 1+nondef_0 ≤ nondef_1 ∧ X₀ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 2 ≤ X₂+X₄ ∧ 2+X₄ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄
t₁₄: eval_realselect_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_realselect_bb2_in(X₀, X₁, X₂, X₃, X₀) :|: nondef_1 ≤ nondef_0 ∧ X₀ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 2 ≤ X₂+X₄ ∧ 2+X₄ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄
t₁₅: eval_realselect_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_realselect_19(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 1+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃
t₂₀: eval_realselect_bb5_in(X₀, X₁, X₂, X₃, X₄) → eval_realselect_stop(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1+X₃ ∧ 0 ≤ X₃
t₀: eval_realselect_start(X₀, X₁, X₂, X₃, X₄) → eval_realselect_bb0_in(X₀, X₁, X₂, X₃, X₄)

MPRF for transition t₉: eval_realselect_bb1_in(X₀, X₁, X₂, X₃, X₄) → eval_realselect_bb2_in(X₀, X₁, X₂, X₃, X₃) :|: 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• eval_realselect_19: [X₂-2-X₃]
• eval_realselect_20: [X₀-2-X₃]
• eval_realselect_27: [X₂-2-X₃]
• eval_realselect_28: [X₂+X₃-2⋅X₁]
• eval_realselect_bb1_in: [X₂-1-X₃]
• eval_realselect_bb2_in: [X₂-2-X₃]
• eval_realselect_bb3_in: [X₂-2-X₃]
• eval_realselect_bb4_in: [X₄-1-X₃]

MPRF for transition t₁₂: eval_realselect_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_realselect_bb4_in(1+X₄, X₁, X₂, X₃, X₄) :|: X₂ ≤ 1+X₄ ∧ 1+X₄ ≤ X₂ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 2 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• eval_realselect_19: [X₀-2-X₃]
• eval_realselect_20: [X₄-1-X₃]
• eval_realselect_27: [X₀-2-X₃]
• eval_realselect_28: [X₀-1-X₁]
• eval_realselect_bb1_in: [X₂-1-X₃]
• eval_realselect_bb2_in: [X₂-1-X₃]
• eval_realselect_bb3_in: [X₂-1-X₃]
• eval_realselect_bb4_in: [X₂-2-X₃]

MPRF for transition t₁₅: eval_realselect_bb4_in(X₀, X₁, X₂, X₃, X₄) → eval_realselect_19(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 1+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• eval_realselect_19: [X₄-1-X₃]
• eval_realselect_20: [X₂+X₄-1-X₀-X₃]
• eval_realselect_27: [X₂-2-X₃]
• eval_realselect_28: [X₀-2-X₃]
• eval_realselect_bb1_in: [X₂-1-X₃]
• eval_realselect_bb2_in: [X₂-1-X₃]
• eval_realselect_bb3_in: [X₂-1-X₃]
• eval_realselect_bb4_in: [X₂-1-X₃]

MPRF for transition t₁₆: eval_realselect_19(X₀, X₁, X₂, X₃, X₄) → eval_realselect_20(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 1+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• eval_realselect_19: [1+X₀-X₃]
• eval_realselect_20: [X₀-X₃]
• eval_realselect_27: [2⋅X₂-1-X₃-X₄]
• eval_realselect_28: [2⋅X₀-X₁-X₄]
• eval_realselect_bb1_in: [1+X₂-X₃]
• eval_realselect_bb2_in: [1+X₂-X₃]
• eval_realselect_bb3_in: [1+X₂-X₃]
• eval_realselect_bb4_in: [1+X₂-X₃]

MPRF for transition t₁₇: eval_realselect_20(X₀, X₁, X₂, X₃, X₄) → eval_realselect_27(X₀, 1+X₃, X₂, X₃, X₄) :|: X₀ ≤ 1+X₄ ∧ X₂ ≤ 1+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• eval_realselect_19: [2⋅X₂-X₃-X₄]
• eval_realselect_20: [1+X₀-X₃]
• eval_realselect_27: [X₀-X₃]
• eval_realselect_28: [X₀+X₂-X₁-X₄]
• eval_realselect_bb1_in: [1+X₂-X₃]
• eval_realselect_bb2_in: [1+X₂-X₃]
• eval_realselect_bb3_in: [1+X₂-X₃]
• eval_realselect_bb4_in: [X₀+X₂-X₃-X₄]

MPRF for transition t₁₈: eval_realselect_27(X₀, X₁, X₂, X₃, X₄) → eval_realselect_28(X₀, X₁, X₂, X₃, X₄) :|: X₀ ≤ 1+X₄ ∧ X₁ ≤ 1+X₃ ∧ X₂ ≤ 1+X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• eval_realselect_19: [X₀-1-X₃]
• eval_realselect_20: [1+2⋅X₄-X₀-X₃]
• eval_realselect_27: [1+X₄-X₁]
• eval_realselect_28: [X₄-X₁]
• eval_realselect_bb1_in: [X₂-1-X₃]
• eval_realselect_bb2_in: [X₂-1-X₃]
• eval_realselect_bb3_in: [X₂-1-X₃]
• eval_realselect_bb4_in: [X₀-1-X₃]

MPRF for transition t₁₉: eval_realselect_28(X₀, X₁, X₂, X₃, X₄) → eval_realselect_bb1_in(X₀, X₁, X₂, X₁, X₄) :|: X₀ ≤ 1+X₄ ∧ X₁ ≤ 1+X₃ ∧ X₂ ≤ 1+X₄ ∧ 1+X₁ ≤ X₀ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₁ ∧ 1+X₁ ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₃ ∧ 2+X₃ ≤ X₀ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₀+X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₁ ≤ X₄ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• eval_realselect_19: [X₀-1-X₃]
• eval_realselect_20: [X₄-X₃]
• eval_realselect_27: [X₄-X₃]
• eval_realselect_28: [X₄-X₃]
• eval_realselect_bb1_in: [X₂-1-X₃]
• eval_realselect_bb2_in: [X₂-1-X₃]
• eval_realselect_bb3_in: [X₂-1-X₃]
• eval_realselect_bb4_in: [X₂-1-X₃]

MPRF for transition t₁₁: eval_realselect_bb2_in(X₀, X₁, X₂, X₃, X₄) → eval_realselect_bb3_in(1+X₄, X₁, X₂, X₃, X₄) :|: 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₂ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 2 ≤ X₂+X₄ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₂⋅X₂+2⋅X₂ {O(n^2)}

MPRF:

• eval_realselect_19: [X₂-X₄]
• eval_realselect_20: [X₂-X₄]
• eval_realselect_27: [X₂-X₄]
• eval_realselect_28: [X₂-X₄]
• eval_realselect_bb1_in: [X₂]
• eval_realselect_bb2_in: [X₂-X₄]
• eval_realselect_bb3_in: [X₂-1-X₄]
• eval_realselect_bb4_in: [X₂-X₄]

MPRF for transition t₁₃: eval_realselect_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_realselect_bb2_in(X₀, X₁, X₂, X₃, X₀) :|: 1+nondef_0 ≤ nondef_1 ∧ X₀ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 2 ≤ X₂+X₄ ∧ 2+X₄ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₂⋅X₂+2⋅X₂ {O(n^2)}

MPRF:

• eval_realselect_19: [0]
• eval_realselect_20: [0]
• eval_realselect_27: [0]
• eval_realselect_28: [0]
• eval_realselect_bb1_in: [X₂]
• eval_realselect_bb2_in: [X₂-1-X₄]
• eval_realselect_bb3_in: [X₂-1-X₄]
• eval_realselect_bb4_in: [0]

MPRF for transition t₁₄: eval_realselect_bb3_in(X₀, X₁, X₂, X₃, X₄) → eval_realselect_bb2_in(X₀, X₁, X₂, X₃, X₀) :|: nondef_1 ≤ nondef_0 ∧ X₀ ≤ 1+X₄ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀+X₄ ∧ 1+X₄ ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₂ ∧ 2 ≤ X₂+X₃ ∧ 2+X₃ ≤ X₂ ∧ 2 ≤ X₂+X₄ ∧ 2+X₄ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₄ of depth 1:

new bound:

X₂⋅X₂+2⋅X₂ {O(n^2)}

MPRF:

• eval_realselect_19: [X₂-1-X₄]
• eval_realselect_20: [X₂-1-X₄]
• eval_realselect_27: [X₂-1-X₄]
• eval_realselect_28: [X₂-1-X₄]
• eval_realselect_bb1_in: [X₂]
• eval_realselect_bb2_in: [X₂-1-X₄]
• eval_realselect_bb3_in: [X₂-1-X₄]
• eval_realselect_bb4_in: [X₂-1-X₄]

Cut unsatisfiable transition [t₁₂: eval_realselect_bb2_in→eval_realselect_bb4_in; t₁₀₇: eval_realselect_bb2_in→eval_realselect_bb4_in]

Found invariant 1+X₄ ≤ X₂ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₀ ≤ X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location eval_realselect_bb2_in_v1

Found invariant X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 2+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location eval_realselect_bb3_in_v1

Found invariant 2+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₀ ≤ 1+X₄ ∧ 3+X₃ ≤ X₂ ∧ 2+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₀+X₃ ∧ 3 ≤ X₂ ∧ 5 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 2 ≤ X₀ for location eval_realselect_bb3_in_v2

Found invariant X₄ ≤ X₃ ∧ 2+X₄ ≤ X₂ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₂+X₄ ∧ 2+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂ for location eval_realselect_bb2_in

Found invariant 0 ≤ X₃ ∧ X₂ ≤ 1+X₃ for location eval_realselect_stop

Found invariant 0 ≤ X₃ ∧ X₂ ≤ 1+X₃ for location eval_realselect_bb5_in

Found invariant 0 ≤ X₃ for location eval_realselect_bb1_in

All Bounds

Timebounds

Overall timebound:3⋅X₂⋅X₂+13⋅X₂+18 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₂+1 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₂⋅X₂+2⋅X₂ {O(n^2)}
t₁₂: X₂+1 {O(n)}
t₁₃: X₂⋅X₂+2⋅X₂ {O(n^2)}
t₁₄: X₂⋅X₂+2⋅X₂ {O(n^2)}
t₁₅: X₂+1 {O(n)}
t₁₆: X₂+1 {O(n)}
t₁₇: X₂+1 {O(n)}
t₁₈: X₂+1 {O(n)}
t₁₉: X₂+1 {O(n)}
t₂₀: 1 {O(1)}

Costbounds

Overall costbound: 3⋅X₂⋅X₂+13⋅X₂+18 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₂+1 {O(n)}
t₁₀: 1 {O(1)}
t₁₁: X₂⋅X₂+2⋅X₂ {O(n^2)}
t₁₂: X₂+1 {O(n)}
t₁₃: X₂⋅X₂+2⋅X₂ {O(n^2)}
t₁₄: X₂⋅X₂+2⋅X₂ {O(n^2)}
t₁₅: X₂+1 {O(n)}
t₁₆: X₂+1 {O(n)}
t₁₇: X₂+1 {O(n)}
t₁₈: X₂+1 {O(n)}
t₁₉: X₂+1 {O(n)}
t₂₀: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₀, X₄: X₄ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: 0 {O(1)}
t₈, X₄: X₄ {O(n)}
t₉, X₀: 2⋅X₂⋅X₂+6⋅X₂+X₀+4 {O(n^2)}
t₉, X₁: X₁+X₂+1 {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₂+1 {O(n)}
t₉, X₄: X₂+1 {O(n)}
t₁₀, X₀: 2⋅X₂⋅X₂+6⋅X₂+X₀+4 {O(n^2)}
t₁₀, X₁: X₁+X₂+1 {O(n)}
t₁₀, X₂: 2⋅X₂ {O(n)}
t₁₀, X₃: X₂+1 {O(n)}
t₁₀, X₄: 2⋅X₂⋅X₂+6⋅X₂+X₄+2 {O(n^2)}
t₁₁, X₀: X₂⋅X₂+3⋅X₂+1 {O(n^2)}
t₁₁, X₁: X₁+X₂+1 {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₂+1 {O(n)}
t₁₁, X₄: 2⋅X₂⋅X₂+7⋅X₂+3 {O(n^2)}
t₁₂, X₀: 2⋅X₂⋅X₂+6⋅X₂+4 {O(n^2)}
t₁₂, X₁: 2⋅X₁+2⋅X₂+2 {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₂+1 {O(n)}
t₁₂, X₄: 2⋅X₂⋅X₂+6⋅X₂+2 {O(n^2)}
t₁₃, X₀: X₂⋅X₂+3⋅X₂+1 {O(n^2)}
t₁₃, X₁: X₁+X₂+1 {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₂+1 {O(n)}
t₁₃, X₄: X₂⋅X₂+3⋅X₂+1 {O(n^2)}
t₁₄, X₀: X₂⋅X₂+3⋅X₂+1 {O(n^2)}
t₁₄, X₁: X₁+X₂+1 {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₂+1 {O(n)}
t₁₄, X₄: X₂⋅X₂+3⋅X₂+1 {O(n^2)}
t₁₅, X₀: 2⋅X₂⋅X₂+6⋅X₂+4 {O(n^2)}
t₁₅, X₁: 2⋅X₁+2⋅X₂+2 {O(n)}
t₁₅, X₂: X₂ {O(n)}
t₁₅, X₃: X₂+1 {O(n)}
t₁₅, X₄: 2⋅X₂⋅X₂+6⋅X₂+2 {O(n^2)}
t₁₆, X₀: 2⋅X₂⋅X₂+6⋅X₂+4 {O(n^2)}
t₁₆, X₁: 2⋅X₁+2⋅X₂+2 {O(n)}
t₁₆, X₂: X₂ {O(n)}
t₁₆, X₃: X₂+1 {O(n)}
t₁₆, X₄: 2⋅X₂⋅X₂+6⋅X₂+2 {O(n^2)}
t₁₇, X₀: 2⋅X₂⋅X₂+6⋅X₂+4 {O(n^2)}
t₁₇, X₁: X₂+1 {O(n)}
t₁₇, X₂: X₂ {O(n)}
t₁₇, X₃: X₂+1 {O(n)}
t₁₇, X₄: 2⋅X₂⋅X₂+6⋅X₂+2 {O(n^2)}
t₁₈, X₀: 2⋅X₂⋅X₂+6⋅X₂+4 {O(n^2)}
t₁₈, X₁: X₂+1 {O(n)}
t₁₈, X₂: X₂ {O(n)}
t₁₈, X₃: X₂+1 {O(n)}
t₁₈, X₄: 2⋅X₂⋅X₂+6⋅X₂+2 {O(n^2)}
t₁₉, X₀: 2⋅X₂⋅X₂+6⋅X₂+4 {O(n^2)}
t₁₉, X₁: X₂+1 {O(n)}
t₁₉, X₂: X₂ {O(n)}
t₁₉, X₃: X₂+1 {O(n)}
t₁₉, X₄: 2⋅X₂⋅X₂+6⋅X₂+2 {O(n^2)}
t₂₀, X₀: 2⋅X₂⋅X₂+6⋅X₂+X₀+4 {O(n^2)}
t₂₀, X₁: X₁+X₂+1 {O(n)}
t₂₀, X₂: 2⋅X₂ {O(n)}
t₂₀, X₃: X₂+1 {O(n)}
t₂₀, X₄: 2⋅X₂⋅X₂+6⋅X₂+X₄+2 {O(n^2)}