KoAT2 Proof Output

Initial Problem

Start: eval_speedNestedMultiple_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈
Temp_Vars: nondef_0
Locations: eval_speedNestedMultiple_0, eval_speedNestedMultiple_1, eval_speedNestedMultiple_11, eval_speedNestedMultiple_12, eval_speedNestedMultiple_2, eval_speedNestedMultiple_3, eval_speedNestedMultiple_4, eval_speedNestedMultiple_5, eval_speedNestedMultiple_6, eval_speedNestedMultiple_7, eval_speedNestedMultiple__critedge_in, eval_speedNestedMultiple_bb0_in, eval_speedNestedMultiple_bb1_in, eval_speedNestedMultiple_bb2_in, eval_speedNestedMultiple_bb3_in, eval_speedNestedMultiple_bb4_in, eval_speedNestedMultiple_bb5_in, eval_speedNestedMultiple_start, eval_speedNestedMultiple_stop
Transitions:
t₂: eval_speedNestedMultiple_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₃: eval_speedNestedMultiple_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₈: eval_speedNestedMultiple_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₉: eval_speedNestedMultiple_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb1_in(X₄, X₂, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₄: eval_speedNestedMultiple_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₅: eval_speedNestedMultiple_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₆: eval_speedNestedMultiple_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₇: eval_speedNestedMultiple_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb1_in(X₇, X₈, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₃: eval_speedNestedMultiple_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_7(X₀, X₁, X₂, nondef_0, X₄, X₅, X₆, X₇, X₈)
t₁₅: eval_speedNestedMultiple_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₃ ≤ 0
t₁₄: eval_speedNestedMultiple_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1 ≤ X₃
t₁₇: eval_speedNestedMultiple__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_11(X₀, X₁, X₂, X₃, 1+X₀, X₅, X₆, X₇, X₈)
t₁: eval_speedNestedMultiple_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₈: eval_speedNestedMultiple_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb2_in(X₀, X₁, X₁, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₀ ≤ X₆
t₉: eval_speedNestedMultiple_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₆ ≤ X₀
t₁₁: eval_speedNestedMultiple_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₅ ≤ X₂
t₁₀: eval_speedNestedMultiple_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₂ ≤ X₅
t₁₂: eval_speedNestedMultiple_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₆: eval_speedNestedMultiple_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb2_in(X₀, X₁, 1+X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₂₀: eval_speedNestedMultiple_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₀: eval_speedNestedMultiple_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)

Preprocessing

Found invariant 1+X₈ ≤ X₅ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ 1+X₀ ≤ X₆ ∧ 1+X₂ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₁ ≤ X₂ for location eval_speedNestedMultiple_bb3_in

Found invariant 1+X₈ ≤ X₅ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ 1+X₀ ≤ X₆ ∧ 1+X₂ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₁ ≤ X₂ for location eval_speedNestedMultiple_6

Found invariant X₈ ≤ X₁ ∧ X₇ ≤ X₀ ∧ X₆ ≤ X₀ for location eval_speedNestedMultiple_bb5_in

Found invariant X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ 1+X₇ ≤ X₆ ∧ 1+X₇ ≤ X₄ ∧ X₇ ≤ X₀ ∧ X₄ ≤ X₆ ∧ 1+X₀ ≤ X₆ ∧ X₄ ≤ 1+X₀ ∧ 1+X₀ ≤ X₄ ∧ X₁ ≤ X₂ for location eval_speedNestedMultiple_11

Found invariant X₈ ≤ X₁ ∧ X₇ ≤ X₀ for location eval_speedNestedMultiple_bb1_in

Found invariant X₈ ≤ X₁ ∧ X₇ ≤ X₀ ∧ X₆ ≤ X₀ for location eval_speedNestedMultiple_stop

Found invariant X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ 1+X₀ ≤ X₆ ∧ X₁ ≤ X₂ for location eval_speedNestedMultiple__critedge_in

Found invariant 1+X₈ ≤ X₅ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ 1+X₀ ≤ X₆ ∧ 1+X₂ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₃ ∧ X₁ ≤ X₂ for location eval_speedNestedMultiple_bb4_in

Found invariant 1+X₈ ≤ X₅ ∧ X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ 1+X₀ ≤ X₆ ∧ 1+X₂ ≤ X₅ ∧ 1+X₁ ≤ X₅ ∧ X₁ ≤ X₂ for location eval_speedNestedMultiple_7

Found invariant X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ 1+X₀ ≤ X₆ ∧ X₁ ≤ X₂ for location eval_speedNestedMultiple_bb2_in

Found invariant X₈ ≤ X₂ ∧ X₈ ≤ X₁ ∧ 1+X₇ ≤ X₆ ∧ 1+X₇ ≤ X₄ ∧ X₇ ≤ X₀ ∧ X₄ ≤ X₆ ∧ 1+X₀ ≤ X₆ ∧ X₄ ≤ 1+X₀ ∧ 1+X₀ ≤ X₄ ∧ X₁ ≤ X₂ for location eval_speedNestedMultiple_12

Problem after Preprocessing

Start: eval_speedNestedMultiple_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈
Temp_Vars: nondef_0
Locations: eval_speedNestedMultiple_0, eval_speedNestedMultiple_1, eval_speedNestedMultiple_11, eval_speedNestedMultiple_12, eval_speedNestedMultiple_2, eval_speedNestedMultiple_3, eval_speedNestedMultiple_4, eval_speedNestedMultiple_5, eval_speedNestedMultiple_6, eval_speedNestedMultiple_7, eval_speedNestedMultiple__critedge_in, eval_speedNestedMultiple_bb0_in, eval_speedNestedMultiple_bb1_in, eval_speedNestedMultiple_bb2_in, eval_speedNestedMultiple_bb3_in, eval_speedNestedMultiple_bb4_in, eval_speedNestedMultiple_bb5_in, eval_speedNestedMultiple_start, eval_speedNestedMultiple_stop
Transitions:
t₂: eval_speedNestedMultiple_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₃: eval_speedNestedMultiple_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₈: eval_speedNestedMultiple_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₄ ≤ 1+X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₆ ∧ 1+X₇ ≤ X₄ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂ ∧ X₄ ≤ X₆
t₁₉: eval_speedNestedMultiple_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb1_in(X₄, X₂, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₄ ≤ 1+X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₆ ∧ 1+X₇ ≤ X₄ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂ ∧ X₄ ≤ X₆
t₄: eval_speedNestedMultiple_2(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₅: eval_speedNestedMultiple_3(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₆: eval_speedNestedMultiple_4(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₇: eval_speedNestedMultiple_5(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb1_in(X₇, X₈, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₁₃: eval_speedNestedMultiple_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_7(X₀, X₁, X₂, nondef_0, X₄, X₅, X₆, X₇, X₈) :|: 1+X₀ ≤ X₆ ∧ 1+X₁ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₈ ≤ X₅ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂
t₁₅: eval_speedNestedMultiple_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₃ ≤ 0 ∧ 1+X₀ ≤ X₆ ∧ 1+X₁ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₈ ≤ X₅ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂
t₁₄: eval_speedNestedMultiple_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1 ≤ X₃ ∧ 1+X₀ ≤ X₆ ∧ 1+X₁ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₈ ≤ X₅ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂
t₁₇: eval_speedNestedMultiple__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_11(X₀, X₁, X₂, X₃, 1+X₀, X₅, X₆, X₇, X₈) :|: 1+X₀ ≤ X₆ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂
t₁: eval_speedNestedMultiple_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)
t₈: eval_speedNestedMultiple_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb2_in(X₀, X₁, X₁, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₀ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁
t₉: eval_speedNestedMultiple_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₆ ≤ X₀ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁
t₁₁: eval_speedNestedMultiple_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₅ ≤ X₂ ∧ 1+X₀ ≤ X₆ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂
t₁₀: eval_speedNestedMultiple_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₂ ≤ X₅ ∧ 1+X₀ ≤ X₆ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂
t₁₂: eval_speedNestedMultiple_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₀ ≤ X₆ ∧ 1+X₁ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₈ ≤ X₅ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂
t₁₆: eval_speedNestedMultiple_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb2_in(X₀, X₁, 1+X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₀ ≤ X₆ ∧ 1+X₁ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1+X₈ ≤ X₅ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂
t₂₀: eval_speedNestedMultiple_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₆ ≤ X₀ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁
t₀: eval_speedNestedMultiple_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈)

MPRF for transition t₈: eval_speedNestedMultiple_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb2_in(X₀, X₁, X₁, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₀ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ of depth 1:

new bound:

X₆+X₇ {O(n)}

MPRF:

• eval_speedNestedMultiple_11: [X₆-1-X₀]
• eval_speedNestedMultiple_12: [X₆-X₄]
• eval_speedNestedMultiple_6: [X₆-1-X₀]
• eval_speedNestedMultiple_7: [X₆-1-X₀]
• eval_speedNestedMultiple__critedge_in: [X₆-1-X₀]
• eval_speedNestedMultiple_bb1_in: [X₆-X₀]
• eval_speedNestedMultiple_bb2_in: [X₆-1-X₀]
• eval_speedNestedMultiple_bb3_in: [X₆-1-X₀]
• eval_speedNestedMultiple_bb4_in: [X₆-1-X₀]

MPRF for transition t₁₀: eval_speedNestedMultiple_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₂ ≤ X₅ ∧ 1+X₀ ≤ X₆ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂ of depth 1:

new bound:

X₅+X₆+X₇+X₈ {O(n)}

MPRF:

• eval_speedNestedMultiple_11: [X₅+X₆-1-X₀-X₂]
• eval_speedNestedMultiple_12: [X₅+X₆-1-X₀-X₂]
• eval_speedNestedMultiple_6: [X₅+X₆-1-X₀-X₂]
• eval_speedNestedMultiple_7: [X₅+X₆-1-X₀-X₂]
• eval_speedNestedMultiple__critedge_in: [X₅+X₆-1-X₀-X₂]
• eval_speedNestedMultiple_bb1_in: [X₅+X₆-X₀-X₁]
• eval_speedNestedMultiple_bb2_in: [X₅+X₆-X₀-X₂]
• eval_speedNestedMultiple_bb3_in: [X₅+X₆-1-X₀-X₂]
• eval_speedNestedMultiple_bb4_in: [X₅+X₆-1-X₀-X₂]

MPRF for transition t₁₁: eval_speedNestedMultiple_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₅ ≤ X₂ ∧ 1+X₀ ≤ X₆ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂ of depth 1:

new bound:

X₆+X₇ {O(n)}

MPRF:

• eval_speedNestedMultiple_11: [X₆-1-X₀]
• eval_speedNestedMultiple_12: [X₆-X₄]
• eval_speedNestedMultiple_6: [X₆-X₀]
• eval_speedNestedMultiple_7: [X₆-X₀]
• eval_speedNestedMultiple__critedge_in: [X₆-1-X₀]
• eval_speedNestedMultiple_bb1_in: [X₆-X₀]
• eval_speedNestedMultiple_bb2_in: [X₆-X₀]
• eval_speedNestedMultiple_bb3_in: [X₆-X₀]
• eval_speedNestedMultiple_bb4_in: [X₆-X₀]

MPRF for transition t₁₂: eval_speedNestedMultiple_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₀ ≤ X₆ ∧ 1+X₁ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₈ ≤ X₅ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂ of depth 1:

new bound:

X₅+X₆+X₇+X₈+1 {O(n)}

MPRF:

• eval_speedNestedMultiple_11: [1+X₅+X₆-X₂-X₄]
• eval_speedNestedMultiple_12: [1+X₅+X₆-X₂-X₄]
• eval_speedNestedMultiple_6: [X₅+X₆-X₀-X₂]
• eval_speedNestedMultiple_7: [X₅+X₆-X₀-X₂]
• eval_speedNestedMultiple__critedge_in: [X₅+X₆-X₀-X₂]
• eval_speedNestedMultiple_bb1_in: [1+X₅+X₆-X₀-X₁]
• eval_speedNestedMultiple_bb2_in: [1+X₅+X₆-X₀-X₂]
• eval_speedNestedMultiple_bb3_in: [1+X₅+X₆-X₀-X₂]
• eval_speedNestedMultiple_bb4_in: [X₅+X₆-X₀-X₂]

MPRF for transition t₁₃: eval_speedNestedMultiple_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_7(X₀, X₁, X₂, nondef_0, X₄, X₅, X₆, X₇, X₈) :|: 1+X₀ ≤ X₆ ∧ 1+X₁ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₈ ≤ X₅ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂ of depth 1:

new bound:

X₅+X₆+X₇+X₈+1 {O(n)}

MPRF:

• eval_speedNestedMultiple_11: [1+X₅+X₆-X₂-X₄]
• eval_speedNestedMultiple_12: [1+X₅+X₆-X₂-X₄]
• eval_speedNestedMultiple_6: [1+X₅+X₆-X₀-X₂]
• eval_speedNestedMultiple_7: [X₅+X₆-X₀-X₂]
• eval_speedNestedMultiple__critedge_in: [X₅+X₆-X₀-X₂]
• eval_speedNestedMultiple_bb1_in: [1+X₅+X₆-X₀-X₁]
• eval_speedNestedMultiple_bb2_in: [1+X₅+X₆-X₀-X₂]
• eval_speedNestedMultiple_bb3_in: [1+X₅+X₆-X₀-X₂]
• eval_speedNestedMultiple_bb4_in: [X₅+X₆-X₀-X₂]

MPRF for transition t₁₄: eval_speedNestedMultiple_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1 ≤ X₃ ∧ 1+X₀ ≤ X₆ ∧ 1+X₁ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₈ ≤ X₅ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂ of depth 1:

new bound:

X₅+X₈+1 {O(n)}

MPRF:

• eval_speedNestedMultiple_11: [1+X₅-X₂]
• eval_speedNestedMultiple_12: [1+X₅-X₂]
• eval_speedNestedMultiple_6: [1+X₅-X₂]
• eval_speedNestedMultiple_7: [1+X₅-X₂]
• eval_speedNestedMultiple__critedge_in: [1+X₅-X₂]
• eval_speedNestedMultiple_bb1_in: [1+X₅-X₁]
• eval_speedNestedMultiple_bb2_in: [1+X₅-X₂]
• eval_speedNestedMultiple_bb3_in: [1+X₅-X₂]
• eval_speedNestedMultiple_bb4_in: [X₅-X₂]

MPRF for transition t₁₅: eval_speedNestedMultiple_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₃ ≤ 0 ∧ 1+X₀ ≤ X₆ ∧ 1+X₁ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ 1+X₈ ≤ X₅ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂ of depth 1:

new bound:

X₆+X₇+1 {O(n)}

MPRF:

• eval_speedNestedMultiple_11: [X₆-X₀]
• eval_speedNestedMultiple_12: [1+X₆-X₄]
• eval_speedNestedMultiple_6: [1+X₆-X₀]
• eval_speedNestedMultiple_7: [1+X₆-X₀]
• eval_speedNestedMultiple__critedge_in: [X₆-X₀]
• eval_speedNestedMultiple_bb1_in: [1+X₆-X₀]
• eval_speedNestedMultiple_bb2_in: [1+X₆-X₀]
• eval_speedNestedMultiple_bb3_in: [1+X₆-X₀]
• eval_speedNestedMultiple_bb4_in: [1+X₆-X₀]

MPRF for transition t₁₆: eval_speedNestedMultiple_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb2_in(X₀, X₁, 1+X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: 1+X₀ ≤ X₆ ∧ 1+X₁ ≤ X₅ ∧ 1+X₂ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1+X₈ ≤ X₅ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂ of depth 1:

new bound:

X₅+X₈ {O(n)}

MPRF:

• eval_speedNestedMultiple_11: [X₅-X₂]
• eval_speedNestedMultiple_12: [X₅-X₂]
• eval_speedNestedMultiple_6: [X₅-X₂]
• eval_speedNestedMultiple_7: [X₅-X₂]
• eval_speedNestedMultiple__critedge_in: [X₅-X₂]
• eval_speedNestedMultiple_bb1_in: [X₅-X₁]
• eval_speedNestedMultiple_bb2_in: [X₅-X₂]
• eval_speedNestedMultiple_bb3_in: [X₅-X₂]
• eval_speedNestedMultiple_bb4_in: [X₅-X₂]

MPRF for transition t₁₇: eval_speedNestedMultiple__critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_11(X₀, X₁, X₂, X₃, 1+X₀, X₅, X₆, X₇, X₈) :|: 1+X₀ ≤ X₆ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂ of depth 1:

new bound:

X₆+X₇ {O(n)}

MPRF:

• eval_speedNestedMultiple_11: [X₆-X₄]
• eval_speedNestedMultiple_12: [X₆-X₄]
• eval_speedNestedMultiple_6: [X₆-X₀]
• eval_speedNestedMultiple_7: [X₆-X₀]
• eval_speedNestedMultiple__critedge_in: [X₆-X₀]
• eval_speedNestedMultiple_bb1_in: [X₆-X₀]
• eval_speedNestedMultiple_bb2_in: [X₆-X₀]
• eval_speedNestedMultiple_bb3_in: [X₆-X₀]
• eval_speedNestedMultiple_bb4_in: [X₆-X₀]

MPRF for transition t₁₈: eval_speedNestedMultiple_11(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₄ ≤ 1+X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₆ ∧ 1+X₇ ≤ X₄ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂ ∧ X₄ ≤ X₆ of depth 1:

new bound:

X₆+X₇+1 {O(n)}

MPRF:

• eval_speedNestedMultiple_11: [2+X₆-X₄]
• eval_speedNestedMultiple_12: [X₆-X₀]
• eval_speedNestedMultiple_6: [1+X₆-X₀]
• eval_speedNestedMultiple_7: [1+X₆-X₀]
• eval_speedNestedMultiple__critedge_in: [1+X₆-X₀]
• eval_speedNestedMultiple_bb1_in: [1+X₆-X₀]
• eval_speedNestedMultiple_bb2_in: [1+X₆-X₀]
• eval_speedNestedMultiple_bb3_in: [1+X₆-X₀]
• eval_speedNestedMultiple_bb4_in: [1+X₆-X₀]

MPRF for transition t₁₉: eval_speedNestedMultiple_12(X₀, X₁, X₂, X₃, X₄, X₅, X₆, X₇, X₈) → eval_speedNestedMultiple_bb1_in(X₄, X₂, X₂, X₃, X₄, X₅, X₆, X₇, X₈) :|: X₄ ≤ 1+X₀ ∧ 1+X₀ ≤ X₄ ∧ 1+X₀ ≤ X₆ ∧ 1+X₇ ≤ X₄ ∧ 1+X₇ ≤ X₆ ∧ X₇ ≤ X₀ ∧ X₈ ≤ X₁ ∧ X₁ ≤ X₂ ∧ X₈ ≤ X₂ ∧ X₄ ≤ X₆ of depth 1:

new bound:

X₆+X₇ {O(n)}

MPRF:

• eval_speedNestedMultiple_11: [X₆-X₀]
• eval_speedNestedMultiple_12: [X₆-X₀]
• eval_speedNestedMultiple_6: [X₆-X₀]
• eval_speedNestedMultiple_7: [X₆-X₀]
• eval_speedNestedMultiple__critedge_in: [X₆-X₀]
• eval_speedNestedMultiple_bb1_in: [X₆-X₀]
• eval_speedNestedMultiple_bb2_in: [X₆-X₀]
• eval_speedNestedMultiple_bb3_in: [X₆-X₀]
• eval_speedNestedMultiple_bb4_in: [X₆-X₀]

All Bounds

Timebounds

Overall timebound:5⋅X₅+5⋅X₈+9⋅X₆+9⋅X₇+15 {O(n)}
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: X₆+X₇ {O(n)}
t₉: 1 {O(1)}
t₁₀: X₅+X₆+X₇+X₈ {O(n)}
t₁₁: X₆+X₇ {O(n)}
t₁₂: X₅+X₆+X₇+X₈+1 {O(n)}
t₁₃: X₅+X₆+X₇+X₈+1 {O(n)}
t₁₄: X₅+X₈+1 {O(n)}
t₁₅: X₆+X₇+1 {O(n)}
t₁₆: X₅+X₈ {O(n)}
t₁₇: X₆+X₇ {O(n)}
t₁₈: X₆+X₇+1 {O(n)}
t₁₉: X₆+X₇ {O(n)}
t₂₀: 1 {O(1)}

Costbounds

Overall costbound: 5⋅X₅+5⋅X₈+9⋅X₆+9⋅X₇+15 {O(n)}
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: X₆+X₇ {O(n)}
t₉: 1 {O(1)}
t₁₀: X₅+X₆+X₇+X₈ {O(n)}
t₁₁: X₆+X₇ {O(n)}
t₁₂: X₅+X₆+X₇+X₈+1 {O(n)}
t₁₃: X₅+X₆+X₇+X₈+1 {O(n)}
t₁₄: X₅+X₈+1 {O(n)}
t₁₅: X₆+X₇+1 {O(n)}
t₁₆: X₅+X₈ {O(n)}
t₁₇: X₆+X₇ {O(n)}
t₁₈: X₆+X₇+1 {O(n)}
t₁₉: X₆+X₇ {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)}
t₀, X₅: X₅ {O(n)}
t₀, X₆: X₆ {O(n)}
t₀, X₇: X₇ {O(n)}
t₀, X₈: X₈ {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)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₁, X₇: X₇ {O(n)}
t₁, X₈: X₈ {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)}
t₂, X₅: X₅ {O(n)}
t₂, X₆: X₆ {O(n)}
t₂, X₇: X₇ {O(n)}
t₂, X₈: X₈ {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)}
t₃, X₅: X₅ {O(n)}
t₃, X₆: X₆ {O(n)}
t₃, X₇: X₇ {O(n)}
t₃, X₈: X₈ {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)}
t₄, X₅: X₅ {O(n)}
t₄, X₆: X₆ {O(n)}
t₄, X₇: X₇ {O(n)}
t₄, X₈: X₈ {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)}
t₅, X₅: X₅ {O(n)}
t₅, X₆: X₆ {O(n)}
t₅, X₇: X₇ {O(n)}
t₅, X₈: X₈ {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)}
t₆, X₅: X₅ {O(n)}
t₆, X₆: X₆ {O(n)}
t₆, X₇: X₇ {O(n)}
t₆, X₈: X₈ {O(n)}
t₇, X₀: X₇ {O(n)}
t₇, X₁: X₈ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₇, X₅: X₅ {O(n)}
t₇, X₆: X₆ {O(n)}
t₇, X₇: X₇ {O(n)}
t₇, X₈: X₈ {O(n)}
t₈, X₀: 2⋅X₇+X₆ {O(n)}
t₈, X₁: 3⋅X₈+X₅ {O(n)}
t₈, X₂: 2⋅X₈+X₅ {O(n)}
t₈, X₄: 2⋅X₆+4⋅X₇+X₄+2 {O(n)}
t₈, X₅: X₅ {O(n)}
t₈, X₆: X₆ {O(n)}
t₈, X₇: X₇ {O(n)}
t₈, X₈: X₈ {O(n)}
t₉, X₀: 3⋅X₇+X₆ {O(n)}
t₉, X₁: 3⋅X₈+X₅ {O(n)}
t₉, X₂: 2⋅X₈+X₂+X₅ {O(n)}
t₉, X₄: 2⋅X₆+4⋅X₇+X₄+2 {O(n)}
t₉, X₅: 2⋅X₅ {O(n)}
t₉, X₆: 2⋅X₆ {O(n)}
t₉, X₇: 2⋅X₇ {O(n)}
t₉, X₈: 2⋅X₈ {O(n)}
t₁₀, X₀: 2⋅X₇+X₆ {O(n)}
t₁₀, X₁: 3⋅X₈+X₅ {O(n)}
t₁₀, X₂: 2⋅X₈+X₅ {O(n)}
t₁₀, X₄: 2⋅X₆+4⋅X₇+X₄+2 {O(n)}
t₁₀, X₅: X₅ {O(n)}
t₁₀, X₆: X₆ {O(n)}
t₁₀, X₇: X₇ {O(n)}
t₁₀, X₈: X₈ {O(n)}
t₁₁, X₀: 2⋅X₇+X₆ {O(n)}
t₁₁, X₁: 2⋅X₅+6⋅X₈ {O(n)}
t₁₁, X₂: 2⋅X₈+X₅ {O(n)}
t₁₁, X₄: 2⋅X₄+4⋅X₆+8⋅X₇+4 {O(n)}
t₁₁, X₅: X₅ {O(n)}
t₁₁, X₆: X₆ {O(n)}
t₁₁, X₇: X₇ {O(n)}
t₁₁, X₈: X₈ {O(n)}
t₁₂, X₀: 2⋅X₇+X₆ {O(n)}
t₁₂, X₁: 3⋅X₈+X₅ {O(n)}
t₁₂, X₂: 2⋅X₈+X₅ {O(n)}
t₁₂, X₄: 2⋅X₆+4⋅X₇+X₄+2 {O(n)}
t₁₂, X₅: X₅ {O(n)}
t₁₂, X₆: X₆ {O(n)}
t₁₂, X₇: X₇ {O(n)}
t₁₂, X₈: X₈ {O(n)}
t₁₃, X₀: 2⋅X₇+X₆ {O(n)}
t₁₃, X₁: 3⋅X₈+X₅ {O(n)}
t₁₃, X₂: 2⋅X₈+X₅ {O(n)}
t₁₃, X₄: 2⋅X₆+4⋅X₇+X₄+2 {O(n)}
t₁₃, X₅: X₅ {O(n)}
t₁₃, X₆: X₆ {O(n)}
t₁₃, X₇: X₇ {O(n)}
t₁₃, X₈: X₈ {O(n)}
t₁₄, X₀: 2⋅X₇+X₆ {O(n)}
t₁₄, X₁: 3⋅X₈+X₅ {O(n)}
t₁₄, X₂: 2⋅X₈+X₅ {O(n)}
t₁₄, X₄: 2⋅X₆+4⋅X₇+X₄+2 {O(n)}
t₁₄, X₅: X₅ {O(n)}
t₁₄, X₆: X₆ {O(n)}
t₁₄, X₇: X₇ {O(n)}
t₁₄, X₈: X₈ {O(n)}
t₁₅, X₀: 2⋅X₇+X₆ {O(n)}
t₁₅, X₁: 3⋅X₈+X₅ {O(n)}
t₁₅, X₂: 2⋅X₈+X₅ {O(n)}
t₁₅, X₄: 2⋅X₆+4⋅X₇+X₄+2 {O(n)}
t₁₅, X₅: X₅ {O(n)}
t₁₅, X₆: X₆ {O(n)}
t₁₅, X₇: X₇ {O(n)}
t₁₅, X₈: X₈ {O(n)}
t₁₆, X₀: 2⋅X₇+X₆ {O(n)}
t₁₆, X₁: 3⋅X₈+X₅ {O(n)}
t₁₆, X₂: 2⋅X₈+X₅ {O(n)}
t₁₆, X₄: 2⋅X₆+4⋅X₇+X₄+2 {O(n)}
t₁₆, X₅: X₅ {O(n)}
t₁₆, X₆: X₆ {O(n)}
t₁₆, X₇: X₇ {O(n)}
t₁₆, X₈: X₈ {O(n)}
t₁₇, X₀: 2⋅X₇+X₆ {O(n)}
t₁₇, X₁: 3⋅X₅+9⋅X₈ {O(n)}
t₁₇, X₂: 2⋅X₈+X₅ {O(n)}
t₁₇, X₄: 2⋅X₆+4⋅X₇+2 {O(n)}
t₁₇, X₅: X₅ {O(n)}
t₁₇, X₆: X₆ {O(n)}
t₁₇, X₇: X₇ {O(n)}
t₁₇, X₈: X₈ {O(n)}
t₁₈, X₀: 2⋅X₇+X₆ {O(n)}
t₁₈, X₁: 3⋅X₅+9⋅X₈ {O(n)}
t₁₈, X₂: 2⋅X₈+X₅ {O(n)}
t₁₈, X₄: 2⋅X₆+4⋅X₇+2 {O(n)}
t₁₈, X₅: X₅ {O(n)}
t₁₈, X₆: X₆ {O(n)}
t₁₈, X₇: X₇ {O(n)}
t₁₈, X₈: X₈ {O(n)}
t₁₉, X₀: 2⋅X₇+X₆ {O(n)}
t₁₉, X₁: 2⋅X₈+X₅ {O(n)}
t₁₉, X₂: 2⋅X₈+X₅ {O(n)}
t₁₉, X₄: 2⋅X₆+4⋅X₇+2 {O(n)}
t₁₉, X₅: X₅ {O(n)}
t₁₉, X₆: X₆ {O(n)}
t₁₉, X₇: X₇ {O(n)}
t₁₉, X₈: X₈ {O(n)}
t₂₀, X₀: 3⋅X₇+X₆ {O(n)}
t₂₀, X₁: 3⋅X₈+X₅ {O(n)}
t₂₀, X₂: 2⋅X₈+X₂+X₅ {O(n)}
t₂₀, X₄: 2⋅X₆+4⋅X₇+X₄+2 {O(n)}
t₂₀, X₅: 2⋅X₅ {O(n)}
t₂₀, X₆: 2⋅X₆ {O(n)}
t₂₀, X₇: 2⋅X₇ {O(n)}
t₂₀, X₈: 2⋅X₈ {O(n)}