Initial Problem

Start: eval_realselect_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: 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:
t₈: eval_realselect_4(X₀, X₁, X₂, X₃) → eval_realselect_5(X₀, X₁, X₂, X₃)
t₁₀: eval_realselect_5(X₀, X₁, X₂, X₃) → eval_realselect_6(X₀, X₁, X₂, X₃)
t₁₁: eval_realselect_6(X₀, X₁, X₂, X₃) → eval_realselect_bb2_in(X₀, X₁, X₂, X₀)
t₁: eval_realselect_bb0_in(X₀, X₁, X₂, X₃) → eval_realselect_bb1_in(X₀, X₁, 0, X₃)
t₂: eval_realselect_bb1_in(X₀, X₁, X₂, X₃) → eval_realselect_bb2_in(X₀, X₁, X₂, X₂) :|: 2+X₂ ≤ X₁
t₃: eval_realselect_bb1_in(X₀, X₁, X₂, X₃) → eval_realselect_bb5_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1+X₂
t₄: eval_realselect_bb2_in(X₀, X₁, X₂, X₃) → eval_realselect_bb3_in(1+X₃, X₁, X₂, X₃) :|: 2+X₃ ≤ X₁
t₅: eval_realselect_bb2_in(X₀, X₁, X₂, X₃) → eval_realselect_bb4_in(1+X₃, X₁, X₂, X₃) :|: X₁ ≤ 1+X₃
t₆: eval_realselect_bb3_in(X₀, X₁, X₂, X₃) → eval_realselect_4(X₀, X₁, X₂, X₃)
t₁₂: eval_realselect_bb4_in(X₀, X₁, X₂, X₃) → eval_realselect_bb1_in(X₀, X₁, 1+X₂, X₃)
t₁₃: eval_realselect_bb5_in(X₀, X₁, X₂, X₃) → eval_realselect_stop(X₀, X₁, X₂, X₃)
t₀: eval_realselect_start(X₀, X₁, X₂, X₃) → eval_realselect_bb0_in(X₀, X₁, X₂, X₃)

Preprocessing

Found invariant 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location eval_realselect_bb2_in

Found invariant 0 ≤ X₂ ∧ X₁ ≤ 1+X₂ for location eval_realselect_stop

Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location eval_realselect_6

Found invariant 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location eval_realselect_bb4_in

Found invariant 0 ≤ X₂ ∧ X₁ ≤ 1+X₂ for location eval_realselect_bb5_in

Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location eval_realselect_5

Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location eval_realselect_4

Found invariant 0 ≤ X₂ for location eval_realselect_bb1_in

Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location eval_realselect_bb3_in

Problem after Preprocessing

Start: eval_realselect_start
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: 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:
t₈: eval_realselect_4(X₀, X₁, X₂, X₃) → eval_realselect_5(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 2+X₃ ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃
t₁₀: eval_realselect_5(X₀, X₁, X₂, X₃) → eval_realselect_6(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 2+X₃ ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃
t₁₁: eval_realselect_6(X₀, X₁, X₂, X₃) → eval_realselect_bb2_in(X₀, X₁, X₂, X₀) :|: X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 2+X₃ ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃
t₁: eval_realselect_bb0_in(X₀, X₁, X₂, X₃) → eval_realselect_bb1_in(X₀, X₁, 0, X₃)
t₂: eval_realselect_bb1_in(X₀, X₁, X₂, X₃) → eval_realselect_bb2_in(X₀, X₁, X₂, X₂) :|: 2+X₂ ≤ X₁ ∧ 0 ≤ X₂
t₃: eval_realselect_bb1_in(X₀, X₁, X₂, X₃) → eval_realselect_bb5_in(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1+X₂ ∧ 0 ≤ X₂
t₄: eval_realselect_bb2_in(X₀, X₁, X₂, X₃) → eval_realselect_bb3_in(1+X₃, X₁, X₂, X₃) :|: 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃
t₅: eval_realselect_bb2_in(X₀, X₁, X₂, X₃) → eval_realselect_bb4_in(1+X₃, X₁, X₂, X₃) :|: X₁ ≤ 1+X₃ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃
t₆: eval_realselect_bb3_in(X₀, X₁, X₂, X₃) → eval_realselect_4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 2+X₃ ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃
t₁₂: eval_realselect_bb4_in(X₀, X₁, X₂, X₃) → eval_realselect_bb1_in(X₀, X₁, 1+X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ 2+X₂ ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₂
t₁₃: eval_realselect_bb5_in(X₀, X₁, X₂, X₃) → eval_realselect_stop(X₀, X₁, X₂, X₃) :|: X₁ ≤ 1+X₂ ∧ 0 ≤ X₂
t₀: eval_realselect_start(X₀, X₁, X₂, X₃) → eval_realselect_bb0_in(X₀, X₁, X₂, X₃)

MPRF for transition t₂: eval_realselect_bb1_in(X₀, X₁, X₂, X₃) → eval_realselect_bb2_in(X₀, X₁, X₂, X₂) :|: 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₁+1 {O(n)}

• eval_realselect_4: [X₁-2-X₂]
• eval_realselect_5: [X₁-2-X₂]
• eval_realselect_6: [X₁-2-X₂]
• eval_realselect_bb1_in: [X₁-1-X₂]
• eval_realselect_bb2_in: [X₁-2-X₂]
• eval_realselect_bb3_in: [X₁-2-X₂]
• eval_realselect_bb4_in: [X₃-1-X₂]

MPRF for transition t₅: eval_realselect_bb2_in(X₀, X₁, X₂, X₃) → eval_realselect_bb4_in(1+X₃, X₁, X₂, X₃) :|: X₁ ≤ 1+X₃ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₁+1 {O(n)}

• eval_realselect_4: [1+X₁-X₂]
• eval_realselect_5: [1+X₁-X₂]
• eval_realselect_6: [X₀+X₁-X₂-X₃]
• eval_realselect_bb1_in: [1+X₁-X₂]
• eval_realselect_bb2_in: [1+X₁-X₂]
• eval_realselect_bb3_in: [1+X₁-X₂]
• eval_realselect_bb4_in: [X₁-X₂]

MPRF for transition t₁₂: eval_realselect_bb4_in(X₀, X₁, X₂, X₃) → eval_realselect_bb1_in(X₀, X₁, 1+X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ X₁ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀ ∧ 2 ≤ X₀+X₂ ∧ 2+X₂ ≤ X₀ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₁ ∧ X₁ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₁+1 {O(n)}

• eval_realselect_4: [X₁-1-X₂]
• eval_realselect_5: [X₁-1-X₂]
• eval_realselect_6: [X₁-1-X₂]
• eval_realselect_bb1_in: [X₁-1-X₂]
• eval_realselect_bb2_in: [X₁-1-X₂]
• eval_realselect_bb3_in: [X₁-1-X₂]
• eval_realselect_bb4_in: [X₀-1-X₂]

MPRF for transition t₄: eval_realselect_bb2_in(X₀, X₁, X₂, X₃) → eval_realselect_bb3_in(1+X₃, X₁, X₂, X₃) :|: 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

2⋅X₁⋅X₁+4⋅X₁+1 {O(n^2)}

• eval_realselect_4: [X₁-1-X₃]
• eval_realselect_5: [X₁-1-X₃]
• eval_realselect_6: [X₁-X₀]
• eval_realselect_bb1_in: [X₁-X₂]
• eval_realselect_bb2_in: [X₁-X₃]
• eval_realselect_bb3_in: [X₁-1-X₃]
• eval_realselect_bb4_in: [0]

MPRF for transition t₆: eval_realselect_bb3_in(X₀, X₁, X₂, X₃) → eval_realselect_4(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 2+X₃ ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₁⋅X₁+3⋅X₁+2 {O(n^2)}

• eval_realselect_4: [X₁-X₃]
• eval_realselect_5: [X₁-X₃]
• eval_realselect_6: [X₁-X₃]
• eval_realselect_bb1_in: [1+X₁]
• eval_realselect_bb2_in: [1+X₁-X₃]
• eval_realselect_bb3_in: [1+X₁-X₃]
• eval_realselect_bb4_in: [1+X₁-X₃]

MPRF for transition t₈: eval_realselect_4(X₀, X₁, X₂, X₃) → eval_realselect_5(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 2+X₃ ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

2⋅X₁⋅X₁+4⋅X₁+1 {O(n^2)}

• eval_realselect_4: [X₁-1-X₃]
• eval_realselect_5: [X₁-2-X₃]
• eval_realselect_6: [X₁-2-X₃]
• eval_realselect_bb1_in: [X₁-X₂]
• eval_realselect_bb2_in: [X₁-1-X₃]
• eval_realselect_bb3_in: [X₁-1-X₃]
• eval_realselect_bb4_in: [X₁-1-X₃]

MPRF for transition t₁₀: eval_realselect_5(X₀, X₁, X₂, X₃) → eval_realselect_6(X₀, X₁, X₂, X₃) :|: X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 2+X₃ ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₁⋅X₁+4⋅X₁+4 {O(n^2)}

• eval_realselect_4: [2+X₁-X₃]
• eval_realselect_5: [2+X₁-X₃]
• eval_realselect_6: [1+X₁-X₃]
• eval_realselect_bb1_in: [2+X₁]
• eval_realselect_bb2_in: [2+X₁-X₃]
• eval_realselect_bb3_in: [2+X₁-X₃]
• eval_realselect_bb4_in: [X₁-X₃]

MPRF for transition t₁₁: eval_realselect_6(X₀, X₁, X₂, X₃) → eval_realselect_bb2_in(X₀, X₁, X₂, X₀) :|: X₀ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₂ ∧ 1+X₂ ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 2 ≤ X₁+X₃ ∧ 2+X₃ ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₁⋅X₁+2⋅X₁ {O(n^2)}

• eval_realselect_4: [X₁-X₀]
• eval_realselect_5: [X₁-1-X₃]
• eval_realselect_6: [X₁-X₀]
• eval_realselect_bb1_in: [X₁]
• eval_realselect_bb2_in: [X₁-1-X₃]
• eval_realselect_bb3_in: [X₁-1-X₃]
• eval_realselect_bb4_in: [X₁-1-X₃]

Cut unsatisfiable transition [t₅: eval_realselect_bb2_in→eval_realselect_bb4_in; t₆₄: eval_realselect_bb2_in→eval_realselect_bb4_in]

Found invariant X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁ for location eval_realselect_bb2_in

Found invariant 0 ≤ X₂ ∧ X₁ ≤ 1+X₂ for location eval_realselect_stop

Found invariant X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location eval_realselect_4_v1

Found invariant 1+X₃ ≤ X₁ ∧ X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location eval_realselect_bb2_in_v1

Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location eval_realselect_4_v2

Found invariant 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ X₁ ≤ 1+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location eval_realselect_bb4_in

Found invariant 0 ≤ X₂ ∧ X₁ ≤ 1+X₂ for location eval_realselect_bb5_in

Found invariant X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location eval_realselect_5_v1

Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location eval_realselect_5_v2

Found invariant X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location eval_realselect_bb3_in_v1

Found invariant X₃ ≤ X₂ ∧ 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 2+X₂ ≤ X₁ ∧ 1+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₀+X₂ ∧ X₀ ≤ 1+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location eval_realselect_6_v1

Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location eval_realselect_bb3_in_v2

Found invariant 0 ≤ X₂ for location eval_realselect_bb1_in

Found invariant 2+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 3+X₂ ≤ X₁ ∧ 2+X₂ ≤ X₀ ∧ 0 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location eval_realselect_6_v2

All Bounds

Timebounds

Overall timebound:7⋅X₁⋅X₁+20⋅X₁+15 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+1 {O(n)}
t₃: 1 {O(1)}
t₄: 2⋅X₁⋅X₁+4⋅X₁+1 {O(n^2)}
t₅: X₁+1 {O(n)}
t₆: X₁⋅X₁+3⋅X₁+2 {O(n^2)}
t₈: 2⋅X₁⋅X₁+4⋅X₁+1 {O(n^2)}
t₁₀: X₁⋅X₁+4⋅X₁+4 {O(n^2)}
t₁₁: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₁₂: X₁+1 {O(n)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 7⋅X₁⋅X₁+20⋅X₁+15 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+1 {O(n)}
t₃: 1 {O(1)}
t₄: 2⋅X₁⋅X₁+4⋅X₁+1 {O(n^2)}
t₅: X₁+1 {O(n)}
t₆: X₁⋅X₁+3⋅X₁+2 {O(n^2)}
t₈: 2⋅X₁⋅X₁+4⋅X₁+1 {O(n^2)}
t₁₀: X₁⋅X₁+4⋅X₁+4 {O(n^2)}
t₁₁: X₁⋅X₁+2⋅X₁ {O(n^2)}
t₁₂: X₁+1 {O(n)}
t₁₃: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₁ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₃ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: 0 {O(1)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: 2⋅X₁⋅X₁+5⋅X₁+X₀+3 {O(n^2)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₁+1 {O(n)}
t₂, X₃: X₁+1 {O(n)}
t₃, X₀: 2⋅X₁⋅X₁+5⋅X₁+X₀+3 {O(n^2)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: X₁+1 {O(n)}
t₃, X₃: 2⋅X₁⋅X₁+5⋅X₁+X₃+2 {O(n^2)}
t₄, X₀: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₁+1 {O(n)}
t₄, X₃: 3⋅X₁+3 {O(n)}
t₅, X₀: 2⋅X₁⋅X₁+5⋅X₁+3 {O(n^2)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₁+1 {O(n)}
t₅, X₃: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
t₆, X₀: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₁+1 {O(n)}
t₆, X₃: 3⋅X₁+3 {O(n)}
t₈, X₀: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₁+1 {O(n)}
t₈, X₃: 3⋅X₁+3 {O(n)}
t₁₀, X₀: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₁+1 {O(n)}
t₁₀, X₃: 3⋅X₁+3 {O(n)}
t₁₁, X₀: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₁+1 {O(n)}
t₁₁, X₃: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
t₁₂, X₀: 2⋅X₁⋅X₁+5⋅X₁+3 {O(n^2)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₁+1 {O(n)}
t₁₂, X₃: 2⋅X₁⋅X₁+5⋅X₁+2 {O(n^2)}
t₁₃, X₀: 2⋅X₁⋅X₁+5⋅X₁+X₀+3 {O(n^2)}
t₁₃, X₁: 2⋅X₁ {O(n)}
t₁₃, X₂: X₁+1 {O(n)}
t₁₃, X₃: 2⋅X₁⋅X₁+5⋅X₁+X₃+2 {O(n^2)}