KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₃ ≤ X₄ for location eval_asctoeg_bb1_in

Found invariant X₆ ≤ X₅ ∧ X₆ ≤ X₄ ∧ X₆ ≤ 1+X₁ ∧ 2 ≤ X₆ ∧ 4 ≤ X₅+X₆ ∧ 4 ≤ X₄+X₆ ∧ 3 ≤ X₁+X₆ ∧ 1+X₁ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₄ ∧ X₃ ≤ X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₁ for location eval_asctoeg_6

Found invariant 1+X₅ ≤ X₄ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₃ for location eval_asctoeg_1

Found invariant X₆ ≤ X₅ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ 1 ≤ X₄+X₆ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₄ ∧ X₃ ≤ X₄ for location eval_asctoeg_.critedge_in

Found invariant X₆ ≤ X₅ ∧ X₆ ≤ X₄ ∧ X₆ ≤ 1+X₁ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ 1 ≤ X₄+X₆ ∧ 0 ≤ 1+X₁+X₆ ∧ 1+X₁ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 0 ≤ 1+X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 0 ≤ 1+X₁ for location eval_asctoeg_.critedge1_in

Found invariant X₃ ≤ X₄ ∧ X₃ ≤ 0 for location eval_asctoeg_bb6_in

Found invariant X₃ ≤ X₄ ∧ X₃ ≤ 0 for location eval_asctoeg_stop

Found invariant X₅ ≤ X₄ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₃ for location eval_asctoeg_bb2_in

Found invariant 1+X₅ ≤ X₄ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₃ for location eval_asctoeg_bb4_in

Found invariant 1+X₅ ≤ X₄ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₃ for location eval_asctoeg_bb3_in

Found invariant 1+X₅ ≤ X₄ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₃ for location eval_asctoeg_0

Problem after Preprocessing

Start: eval_asctoeg_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅, X₆
Temp_Vars: nondef.0, nondef.1
Locations: eval_asctoeg_.critedge1_in, eval_asctoeg_.critedge_in, eval_asctoeg_0, eval_asctoeg_1, eval_asctoeg_6, eval_asctoeg_7, eval_asctoeg_bb0_in, eval_asctoeg_bb1_in, eval_asctoeg_bb2_in, eval_asctoeg_bb3_in, eval_asctoeg_bb4_in, eval_asctoeg_bb5_in, eval_asctoeg_bb6_in, eval_asctoeg_start, eval_asctoeg_stop
Transitions:
t₂₁: eval_asctoeg_.critedge1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_bb1_in(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆) :|: 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₁+X₅ ∧ 0 ≤ 1+X₁+X₆ ∧ X₆ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₄+X₆ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆
t₁₄: eval_asctoeg_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_.critedge1_in(X₀, X₆-1, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ 1 ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₄+X₆ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆
t₁₃: eval_asctoeg_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_bb5_in(X₀, X₆-1, X₂, X₃, X₄, X₅, X₆) :|: 2 ≤ X₆ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₄+X₆ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆
t₈: eval_asctoeg_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_1(nondef.0, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅
t₁₁: eval_asctoeg_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₅) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅
t₉: eval_asctoeg_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₀ ≤ 0 ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅
t₁₀: eval_asctoeg_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅
t₁₇: eval_asctoeg_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_7(X₀, X₁, nondef.1, X₃, X₄, X₅, X₆) :|: X₆ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 2 ≤ X₆ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₁+X₆ ∧ 4 ≤ X₄+X₅ ∧ 4 ≤ X₄+X₆ ∧ 4 ≤ X₅+X₆ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₅
t₂₀: eval_asctoeg_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_.critedge1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ X₆ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 2 ≤ X₆ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₁+X₆ ∧ 4 ≤ X₄+X₅ ∧ 4 ≤ X₄+X₆ ∧ 4 ≤ X₅+X₆ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₅
t₁₈: eval_asctoeg_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₁) :|: 1+X₂ ≤ 0 ∧ X₆ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 2 ≤ X₆ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₁+X₆ ∧ 4 ≤ X₄+X₅ ∧ 4 ≤ X₄+X₆ ∧ 4 ≤ X₅+X₆ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₅
t₁₉: eval_asctoeg_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₁) :|: 1 ≤ X₂ ∧ X₆ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 2 ≤ X₆ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₁+X₆ ∧ 4 ≤ X₄+X₅ ∧ 4 ≤ X₄+X₆ ∧ 4 ≤ X₅+X₆ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₅
t₁: eval_asctoeg_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_bb1_in(X₀, X₁, X₂, X₄, X₄, X₅, X₆)
t₂: eval_asctoeg_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_bb2_in(X₀, X₁, X₂, X₃, X₄, 0, X₆) :|: 1 ≤ X₃ ∧ X₃ ≤ X₄
t₃: eval_asctoeg_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 0 ∧ X₃ ≤ X₄
t₅: eval_asctoeg_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₅) :|: X₄ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₅
t₄: eval_asctoeg_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₅ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₅
t₆: eval_asctoeg_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅
t₁₂: eval_asctoeg_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_bb2_in(X₀, X₁, X₂, X₃, X₄, 1+X₅, X₆) :|: 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅
t₁₅: eval_asctoeg_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 2 ≤ X₆ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₁+X₆ ∧ 4 ≤ X₄+X₅ ∧ 4 ≤ X₄+X₆ ∧ 4 ≤ X₅+X₆ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₅
t₂₂: eval_asctoeg_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_stop(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₃ ≤ 0 ∧ X₃ ≤ X₄
t₀: eval_asctoeg_start(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆)

MPRF for transition t₂: eval_asctoeg_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_bb2_in(X₀, X₁, X₂, X₃, X₄, 0, X₆) :|: 1 ≤ X₃ ∧ X₃ ≤ X₄ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_asctoeg_.critedge1_in: [X₃-1]
• eval_asctoeg_.critedge_in: [X₃-1]
• eval_asctoeg_0: [X₃-1]
• eval_asctoeg_1: [X₃-1]
• eval_asctoeg_6: [X₃-1]
• eval_asctoeg_7: [X₃-1]
• eval_asctoeg_bb1_in: [X₃]
• eval_asctoeg_bb2_in: [X₃-1]
• eval_asctoeg_bb3_in: [X₃-1]
• eval_asctoeg_bb4_in: [X₃-1]
• eval_asctoeg_bb5_in: [X₃-1]

MPRF for transition t₅: eval_asctoeg_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₅) :|: X₄ ≤ X₅ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_asctoeg_.critedge1_in: [X₁+X₃-X₆]
• eval_asctoeg_.critedge_in: [X₃-1]
• eval_asctoeg_0: [X₃]
• eval_asctoeg_1: [X₃]
• eval_asctoeg_6: [X₃-1]
• eval_asctoeg_7: [X₃-1]
• eval_asctoeg_bb1_in: [X₃]
• eval_asctoeg_bb2_in: [X₃]
• eval_asctoeg_bb3_in: [X₃]
• eval_asctoeg_bb4_in: [X₃]
• eval_asctoeg_bb5_in: [X₃-1]

MPRF for transition t₁₁: eval_asctoeg_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₅) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

• eval_asctoeg_.critedge1_in: [X₃-1]
• eval_asctoeg_.critedge_in: [X₃-1]
• eval_asctoeg_0: [X₃]
• eval_asctoeg_1: [X₃]
• eval_asctoeg_6: [X₃-1]
• eval_asctoeg_7: [X₃-1]
• eval_asctoeg_bb1_in: [X₃]
• eval_asctoeg_bb2_in: [X₃]
• eval_asctoeg_bb3_in: [X₃]
• eval_asctoeg_bb4_in: [X₃]
• eval_asctoeg_bb5_in: [X₃-1]

MPRF for transition t₄: eval_asctoeg_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₅ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₅ of depth 1:

new bound:

2⋅X₄⋅X₄+X₄ {O(n^2)}

MPRF:

• eval_asctoeg_.critedge1_in: [X₄]
• eval_asctoeg_.critedge_in: [X₄]
• eval_asctoeg_0: [X₄-1-X₅]
• eval_asctoeg_1: [X₄-1-X₅]
• eval_asctoeg_6: [X₄]
• eval_asctoeg_7: [X₄]
• eval_asctoeg_bb1_in: [X₄]
• eval_asctoeg_bb2_in: [X₄-X₅]
• eval_asctoeg_bb3_in: [X₄-1-X₅]
• eval_asctoeg_bb4_in: [X₄-1-X₅]
• eval_asctoeg_bb5_in: [X₄]

MPRF for transition t₆: eval_asctoeg_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅ of depth 1:

new bound:

4⋅X₄⋅X₄+X₄+1 {O(n^2)}

MPRF:

• eval_asctoeg_.critedge1_in: [2⋅X₄]
• eval_asctoeg_.critedge_in: [2⋅X₄]
• eval_asctoeg_0: [X₄-X₅]
• eval_asctoeg_1: [X₄-X₅]
• eval_asctoeg_6: [2⋅X₄]
• eval_asctoeg_7: [2⋅X₄]
• eval_asctoeg_bb1_in: [1+X₄]
• eval_asctoeg_bb2_in: [1+X₄-X₅]
• eval_asctoeg_bb3_in: [1+X₄-X₅]
• eval_asctoeg_bb4_in: [X₄-X₅]
• eval_asctoeg_bb5_in: [2⋅X₄]

MPRF for transition t₈: eval_asctoeg_0(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_1(nondef.0, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅ of depth 1:

new bound:

6⋅X₄⋅X₄+3⋅X₄+2 {O(n^2)}

MPRF:

• eval_asctoeg_.critedge1_in: [3⋅X₄]
• eval_asctoeg_.critedge_in: [3⋅X₄]
• eval_asctoeg_0: [2⋅X₃+X₄-2-X₅]
• eval_asctoeg_1: [2⋅X₃+X₄-3-X₅]
• eval_asctoeg_6: [3⋅X₄]
• eval_asctoeg_7: [3⋅X₄]
• eval_asctoeg_bb1_in: [2⋅X₃+X₄-2]
• eval_asctoeg_bb2_in: [2⋅X₃+X₄-2-X₅]
• eval_asctoeg_bb3_in: [2⋅X₃+X₄-2-X₅]
• eval_asctoeg_bb4_in: [2⋅X₃+X₄-3-X₅]
• eval_asctoeg_bb5_in: [3⋅X₄]

MPRF for transition t₉: eval_asctoeg_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1+X₀ ≤ 0 ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅ of depth 1:

new bound:

6⋅X₄⋅X₄+3⋅X₄ {O(n^2)}

MPRF:

• eval_asctoeg_.critedge1_in: [3⋅X₄]
• eval_asctoeg_.critedge_in: [3⋅X₄]
• eval_asctoeg_0: [2⋅X₃+X₄-X₅]
• eval_asctoeg_1: [2⋅X₃+X₄-X₅]
• eval_asctoeg_6: [3⋅X₄]
• eval_asctoeg_7: [3⋅X₄]
• eval_asctoeg_bb1_in: [2⋅X₃+X₄]
• eval_asctoeg_bb2_in: [2⋅X₃+X₄-X₅]
• eval_asctoeg_bb3_in: [2⋅X₃+X₄-X₅]
• eval_asctoeg_bb4_in: [2⋅X₃+X₄-1-X₅]
• eval_asctoeg_bb5_in: [3⋅X₄]

MPRF for transition t₁₀: eval_asctoeg_1(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 1 ≤ X₀ ∧ 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅ of depth 1:

new bound:

6⋅X₄⋅X₄+X₄+2 {O(n^2)}

MPRF:

• eval_asctoeg_.critedge1_in: [3⋅X₄]
• eval_asctoeg_.critedge_in: [3⋅X₄]
• eval_asctoeg_0: [2+X₄-X₅]
• eval_asctoeg_1: [2+X₄-X₅]
• eval_asctoeg_6: [3⋅X₄]
• eval_asctoeg_7: [3⋅X₄]
• eval_asctoeg_bb1_in: [2+X₄]
• eval_asctoeg_bb2_in: [2+X₄-X₅]
• eval_asctoeg_bb3_in: [2+X₄-X₅]
• eval_asctoeg_bb4_in: [1+X₄-X₅]
• eval_asctoeg_bb5_in: [3⋅X₄]

MPRF for transition t₁₂: eval_asctoeg_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_bb2_in(X₀, X₁, X₂, X₃, X₄, 1+X₅, X₆) :|: 1 ≤ X₃ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1+X₅ ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₅ of depth 1:

new bound:

2⋅X₄⋅X₄+X₄ {O(n^2)}

MPRF:

• eval_asctoeg_.critedge1_in: [X₄]
• eval_asctoeg_.critedge_in: [X₄]
• eval_asctoeg_0: [X₄-X₅]
• eval_asctoeg_1: [X₄-X₅]
• eval_asctoeg_6: [X₄]
• eval_asctoeg_7: [X₄]
• eval_asctoeg_bb1_in: [X₄]
• eval_asctoeg_bb2_in: [X₄-X₅]
• eval_asctoeg_bb3_in: [X₄-X₅]
• eval_asctoeg_bb4_in: [X₄-X₅]
• eval_asctoeg_bb5_in: [X₄]

MPRF for transition t₁₃: eval_asctoeg_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_bb5_in(X₀, X₆-1, X₂, X₃, X₄, X₅, X₆) :|: 2 ≤ X₆ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₄+X₆ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆ of depth 1:

new bound:

3⋅X₄⋅X₄ {O(n^2)}

MPRF:

• eval_asctoeg_.critedge1_in: [4⋅X₆-1-X₄]
• eval_asctoeg_.critedge_in: [2⋅X₄+X₆]
• eval_asctoeg_0: [3⋅X₄]
• eval_asctoeg_1: [3⋅X₄]
• eval_asctoeg_6: [2⋅X₄+2⋅X₆-2-X₁]
• eval_asctoeg_7: [2⋅X₄+4⋅X₆-4-3⋅X₁]
• eval_asctoeg_bb1_in: [-1-X₄]
• eval_asctoeg_bb2_in: [3⋅X₄]
• eval_asctoeg_bb3_in: [3⋅X₄]
• eval_asctoeg_bb4_in: [3⋅X₄]
• eval_asctoeg_bb5_in: [2⋅X₄+X₆-1]

MPRF for transition t₁₄: eval_asctoeg_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_.critedge1_in(X₀, X₆-1, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ 1 ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₄+X₆ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆ of depth 1:

new bound:

4⋅X₄+1 {O(n)}

MPRF:

• eval_asctoeg_.critedge1_in: [1-X₄-X₆]
• eval_asctoeg_.critedge_in: [1]
• eval_asctoeg_0: [1-2⋅X₄]
• eval_asctoeg_1: [1-2⋅X₄]
• eval_asctoeg_6: [1]
• eval_asctoeg_7: [1]
• eval_asctoeg_bb1_in: [1-2⋅X₄]
• eval_asctoeg_bb2_in: [1-2⋅X₄]
• eval_asctoeg_bb3_in: [1-2⋅X₄]
• eval_asctoeg_bb4_in: [1-2⋅X₄]
• eval_asctoeg_bb5_in: [1]

MPRF for transition t₁₅: eval_asctoeg_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: X₆ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 2 ≤ X₆ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₁+X₆ ∧ 4 ≤ X₄+X₅ ∧ 4 ≤ X₄+X₆ ∧ 4 ≤ X₅+X₆ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₅ of depth 1:

new bound:

X₄⋅X₄ {O(n^2)}

MPRF:

• eval_asctoeg_.critedge1_in: [X₆-2]
• eval_asctoeg_.critedge_in: [X₆-1]
• eval_asctoeg_0: [X₄]
• eval_asctoeg_1: [X₄]
• eval_asctoeg_6: [X₁-1]
• eval_asctoeg_7: [X₆-2]
• eval_asctoeg_bb1_in: [X₆-2]
• eval_asctoeg_bb2_in: [X₄]
• eval_asctoeg_bb3_in: [X₄]
• eval_asctoeg_bb4_in: [X₄]
• eval_asctoeg_bb5_in: [X₁]

MPRF for transition t₁₇: eval_asctoeg_6(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_7(X₀, X₁, nondef.1, X₃, X₄, X₅, X₆) :|: X₆ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 2 ≤ X₆ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₁+X₆ ∧ 4 ≤ X₄+X₅ ∧ 4 ≤ X₄+X₆ ∧ 4 ≤ X₅+X₆ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₅ of depth 1:

new bound:

X₄⋅X₄ {O(n^2)}

MPRF:

• eval_asctoeg_.critedge1_in: [-1]
• eval_asctoeg_.critedge_in: [X₆-1]
• eval_asctoeg_0: [X₄]
• eval_asctoeg_1: [X₄]
• eval_asctoeg_6: [X₆-1]
• eval_asctoeg_7: [X₁-1]
• eval_asctoeg_bb1_in: [-1]
• eval_asctoeg_bb2_in: [X₄]
• eval_asctoeg_bb3_in: [X₄]
• eval_asctoeg_bb4_in: [X₄]
• eval_asctoeg_bb5_in: [X₆-1]

MPRF for transition t₁₈: eval_asctoeg_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₁) :|: 1+X₂ ≤ 0 ∧ X₆ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 2 ≤ X₆ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₁+X₆ ∧ 4 ≤ X₄+X₅ ∧ 4 ≤ X₄+X₆ ∧ 4 ≤ X₅+X₆ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₅ of depth 1:

new bound:

X₄⋅X₄ {O(n^2)}

MPRF:

• eval_asctoeg_.critedge1_in: [-1]
• eval_asctoeg_.critedge_in: [X₆-1]
• eval_asctoeg_0: [X₄]
• eval_asctoeg_1: [X₄]
• eval_asctoeg_6: [X₆-1]
• eval_asctoeg_7: [X₁]
• eval_asctoeg_bb1_in: [-1]
• eval_asctoeg_bb2_in: [X₄]
• eval_asctoeg_bb3_in: [X₄]
• eval_asctoeg_bb4_in: [X₄]
• eval_asctoeg_bb5_in: [X₆-1]

MPRF for transition t₁₉: eval_asctoeg_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅, X₁) :|: 1 ≤ X₂ ∧ X₆ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 2 ≤ X₆ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₁+X₆ ∧ 4 ≤ X₄+X₅ ∧ 4 ≤ X₄+X₆ ∧ 4 ≤ X₅+X₆ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₅ of depth 1:

new bound:

X₄⋅X₄ {O(n^2)}

MPRF:

• eval_asctoeg_.critedge1_in: [X₆-1]
• eval_asctoeg_.critedge_in: [X₆-1]
• eval_asctoeg_0: [X₄]
• eval_asctoeg_1: [X₄]
• eval_asctoeg_6: [X₆-1]
• eval_asctoeg_7: [X₆-1]
• eval_asctoeg_bb1_in: [-1]
• eval_asctoeg_bb2_in: [X₄]
• eval_asctoeg_bb3_in: [X₄]
• eval_asctoeg_bb4_in: [X₄]
• eval_asctoeg_bb5_in: [X₆-1]

MPRF for transition t₂₀: eval_asctoeg_7(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_.critedge1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) :|: 0 ≤ X₂ ∧ X₂ ≤ 0 ∧ X₆ ≤ 1+X₁ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 2 ≤ X₄ ∧ 2 ≤ X₅ ∧ 2 ≤ X₆ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₁+X₅ ∧ 3 ≤ X₁+X₆ ∧ 4 ≤ X₄+X₅ ∧ 4 ≤ X₄+X₆ ∧ 4 ≤ X₅+X₆ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₄ ∧ X₆ ≤ X₅ of depth 1:

new bound:

6⋅X₄+X₁+2 {O(n)}

MPRF:

• eval_asctoeg_.critedge1_in: [1+X₆-X₁-X₅]
• eval_asctoeg_.critedge_in: [2]
• eval_asctoeg_0: [2-X₁-2⋅X₄]
• eval_asctoeg_1: [2-X₁-2⋅X₄]
• eval_asctoeg_6: [2]
• eval_asctoeg_7: [2]
• eval_asctoeg_bb1_in: [2-X₁-2⋅X₄]
• eval_asctoeg_bb2_in: [2-X₁-2⋅X₄]
• eval_asctoeg_bb3_in: [2-X₁-2⋅X₄]
• eval_asctoeg_bb4_in: [2-X₁-2⋅X₄]
• eval_asctoeg_bb5_in: [2]

MPRF for transition t₂₁: eval_asctoeg_.critedge1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_bb1_in(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆) :|: 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₁+X₅ ∧ 0 ≤ 1+X₁+X₆ ∧ X₆ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₄+X₆ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆ of depth 1:

new bound:

6⋅X₄⋅X₄+3⋅X₄+1 {O(n^2)}

MPRF:

• eval_asctoeg_.critedge1_in: [3⋅X₄]
• eval_asctoeg_.critedge_in: [3⋅X₄]
• eval_asctoeg_0: [1+2⋅X₃+X₄]
• eval_asctoeg_1: [1+2⋅X₃+X₄]
• eval_asctoeg_6: [1+X₁+3⋅X₄-X₆]
• eval_asctoeg_7: [1+X₁+3⋅X₄-X₆]
• eval_asctoeg_bb1_in: [1+2⋅X₃+X₄]
• eval_asctoeg_bb2_in: [1+2⋅X₃+X₄]
• eval_asctoeg_bb3_in: [1+2⋅X₃+X₄]
• eval_asctoeg_bb4_in: [1+2⋅X₃+X₄]
• eval_asctoeg_bb5_in: [3⋅X₄+X₆-1-X₁]

knowledge_propagation leads to new time bound 10⋅X₄+X₁+3 {O(n)} for transition t₂₁: eval_asctoeg_.critedge1_in(X₀, X₁, X₂, X₃, X₄, X₅, X₆) → eval_asctoeg_bb1_in(X₀, X₁, X₂, X₃-1, X₄, X₅, X₆) :|: 0 ≤ 1+X₁ ∧ 0 ≤ 1+X₁+X₅ ∧ 0 ≤ 1+X₁+X₆ ∧ X₆ ≤ 1+X₁ ∧ 1+X₁ ≤ X₄ ∧ 1+X₁ ≤ X₅ ∧ 1+X₁ ≤ X₆ ∧ 1 ≤ X₄ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₄+X₆ ∧ 0 ≤ X₁+X₄ ∧ X₃ ≤ X₄ ∧ X₅ ≤ X₄ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₅ ∧ 0 ≤ X₅+X₆ ∧ X₆ ≤ X₅ ∧ 0 ≤ X₆

Cut unreachable locations [eval_asctoeg_1; eval_asctoeg_7] from the program graph

Cut unsatisfiable transition [t₅: eval_asctoeg_bb2_in→eval_asctoeg_.critedge_in; t₁₃₄: eval_asctoeg_bb2_in→eval_asctoeg_.critedge_in]

Found invariant X₆ ≤ X₅ ∧ X₆ ≤ X₄ ∧ X₆ ≤ 1+X₁ ∧ 2 ≤ X₆ ∧ 4 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 4 ≤ X₄+X₆ ∧ 3 ≤ X₃+X₆ ∧ 3 ≤ X₁+X₆ ∧ 1+X₁ ≤ X₆ ∧ X₅ ≤ X₄ ∧ X₅ ≤ 1+X₁ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ for location eval_asctoeg_bb5_in_v1

Found invariant 1+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₄ ∧ X₆ ≤ 1+X₁ ∧ 2 ≤ X₆ ∧ 5 ≤ X₅+X₆ ∧ 5 ≤ X₄+X₆ ∧ 3 ≤ X₃+X₆ ∧ 3 ≤ X₁+X₆ ∧ 1+X₁ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 3 ≤ X₅ ∧ 6 ≤ X₄+X₅ ∧ 4 ≤ X₃+X₅ ∧ 4 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 3 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₁ for location eval_asctoeg_7_v2

Found invariant X₅ ≤ 0 ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₃ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₃ for location eval_asctoeg_bb3_in_v1

Found invariant 1+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₄ ∧ X₆ ≤ 1+X₁ ∧ 2 ≤ X₆ ∧ 5 ≤ X₅+X₆ ∧ 5 ≤ X₄+X₆ ∧ 3 ≤ X₃+X₆ ∧ 3 ≤ X₂+X₆ ∧ 3 ≤ X₁+X₆ ∧ 1+X₁ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 3 ≤ X₅ ∧ 6 ≤ X₄+X₅ ∧ 4 ≤ X₃+X₅ ∧ 4 ≤ X₂+X₅ ∧ 4 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 3 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 4 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_asctoeg_bb5_in_v3

Found invariant X₆ ≤ X₅ ∧ X₆ ≤ X₄ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ X₅ ≤ X₆ ∧ 1 ≤ X₄+X₆ ∧ 1 ≤ X₃+X₆ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₃ for location eval_asctoeg_.critedge_in

Found invariant X₃ ≤ X₄ ∧ X₃ ≤ 0 for location eval_asctoeg_bb6_in

Found invariant 1+X₅ ≤ X₄ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2+X₀ ≤ X₅ ∧ 2 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 3+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₀ ≤ 0 for location eval_asctoeg_bb4_in_v4

Found invariant 1+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₄ ∧ X₆ ≤ 1+X₁ ∧ 2 ≤ X₆ ∧ 5 ≤ X₅+X₆ ∧ 5 ≤ X₄+X₆ ∧ 3 ≤ X₃+X₆ ∧ 3+X₂ ≤ X₆ ∧ 3 ≤ X₁+X₆ ∧ 1+X₁ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 3 ≤ X₅ ∧ 6 ≤ X₄+X₅ ∧ 4 ≤ X₃+X₅ ∧ 4+X₂ ≤ X₅ ∧ 4 ≤ X₁+X₅ ∧ 2+X₁ ≤ X₅ ∧ 3 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1 ≤ X₁ for location eval_asctoeg_bb5_in_v2

Found invariant X₅ ≤ 0 ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₃ ∧ 1+X₅ ≤ X₀ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₀+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₀ for location eval_asctoeg_bb4_in_v1

Found invariant 1+X₅ ≤ X₄ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 1 ≤ X₀ for location eval_asctoeg_bb4_in_v3

Found invariant X₅ ≤ 0 ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₃ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₃ for location eval_asctoeg_1_v1

Found invariant 1+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₄ ∧ X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 3 ≤ X₄+X₆ ∧ 2 ≤ X₃+X₆ ∧ 2 ≤ X₂+X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ 3 ≤ X₃+X₅ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location eval_asctoeg_.critedge_in_v1

Found invariant X₃ ≤ X₄ for location eval_asctoeg_bb1_in

Found invariant X₅ ≤ 0 ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₃ ∧ 1+X₀+X₅ ≤ 0 ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1+X₀ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 2+X₀ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₀ ≤ 0 for location eval_asctoeg_bb4_in_v2

Found invariant X₆ ≤ X₅ ∧ X₆ ≤ X₄ ∧ X₆ ≤ 1+X₁ ∧ 0 ≤ X₆ ∧ 0 ≤ X₅+X₆ ∧ 1 ≤ X₄+X₆ ∧ 1 ≤ X₃+X₆ ∧ 0 ≤ 1+X₁+X₆ ∧ 1+X₁ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 0 ≤ 1+X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 0 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ 1+X₁ for location eval_asctoeg_.critedge1_in

Found invariant X₅ ≤ 0 ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₃ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₃ for location eval_asctoeg_0_v1

Found invariant 1+X₅ ≤ X₄ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₃ for location eval_asctoeg_1_v2

Found invariant X₃ ≤ X₄ ∧ X₃ ≤ 0 for location eval_asctoeg_stop

Found invariant X₅ ≤ 0 ∧ 1+X₅ ≤ X₄ ∧ 1+X₅ ≤ X₃ ∧ 0 ≤ X₅ ∧ 1 ≤ X₄+X₅ ∧ 1 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₃ for location eval_asctoeg_bb2_in

Found invariant X₅ ≤ X₄ ∧ 1 ≤ X₅ ∧ 2 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₃ for location eval_asctoeg_bb2_in_v1

Found invariant 1+X₅ ≤ X₄ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₃ for location eval_asctoeg_bb3_in_v2

Found invariant 1+X₆ ≤ X₅ ∧ 1+X₆ ≤ X₄ ∧ X₆ ≤ X₁ ∧ 1 ≤ X₆ ∧ 3 ≤ X₅+X₆ ∧ 3 ≤ X₄+X₆ ∧ 2 ≤ X₃+X₆ ∧ 2+X₂ ≤ X₆ ∧ 2 ≤ X₁+X₆ ∧ X₁ ≤ X₆ ∧ X₅ ≤ X₄ ∧ 2 ≤ X₅ ∧ 4 ≤ X₄+X₅ ∧ 3 ≤ X₃+X₅ ∧ 3+X₂ ≤ X₅ ∧ 3 ≤ X₁+X₅ ∧ 1+X₁ ≤ X₅ ∧ 2 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 3+X₂ ≤ X₄ ∧ 3 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1+X₂ ≤ 0 ∧ 2+X₂ ≤ X₁ ∧ 1 ≤ X₁ for location eval_asctoeg_.critedge_in_v2

Found invariant 1+X₅ ≤ X₄ ∧ 1 ≤ X₅ ∧ 3 ≤ X₄+X₅ ∧ 2 ≤ X₃+X₅ ∧ 2 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 1 ≤ X₃ for location eval_asctoeg_0_v2

All Bounds

Timebounds

Overall timebound:33⋅X₄⋅X₄+2⋅X₁+33⋅X₄+15 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₄ {O(n)}
t₃: 1 {O(1)}
t₄: 2⋅X₄⋅X₄+X₄ {O(n^2)}
t₅: X₄ {O(n)}
t₆: 4⋅X₄⋅X₄+X₄+1 {O(n^2)}
t₈: 6⋅X₄⋅X₄+3⋅X₄+2 {O(n^2)}
t₉: 6⋅X₄⋅X₄+3⋅X₄ {O(n^2)}
t₁₀: 6⋅X₄⋅X₄+X₄+2 {O(n^2)}
t₁₁: X₄ {O(n)}
t₁₂: 2⋅X₄⋅X₄+X₄ {O(n^2)}
t₁₃: 3⋅X₄⋅X₄ {O(n^2)}
t₁₄: 4⋅X₄+1 {O(n)}
t₁₅: X₄⋅X₄ {O(n^2)}
t₁₇: X₄⋅X₄ {O(n^2)}
t₁₈: X₄⋅X₄ {O(n^2)}
t₁₉: X₄⋅X₄ {O(n^2)}
t₂₀: 6⋅X₄+X₁+2 {O(n)}
t₂₁: 10⋅X₄+X₁+3 {O(n)}
t₂₂: 1 {O(1)}

Costbounds

Overall costbound: 33⋅X₄⋅X₄+2⋅X₁+33⋅X₄+15 {O(n^2)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₄ {O(n)}
t₃: 1 {O(1)}
t₄: 2⋅X₄⋅X₄+X₄ {O(n^2)}
t₅: X₄ {O(n)}
t₆: 4⋅X₄⋅X₄+X₄+1 {O(n^2)}
t₈: 6⋅X₄⋅X₄+3⋅X₄+2 {O(n^2)}
t₉: 6⋅X₄⋅X₄+3⋅X₄ {O(n^2)}
t₁₀: 6⋅X₄⋅X₄+X₄+2 {O(n^2)}
t₁₁: X₄ {O(n)}
t₁₂: 2⋅X₄⋅X₄+X₄ {O(n^2)}
t₁₃: 3⋅X₄⋅X₄ {O(n^2)}
t₁₄: 4⋅X₄+1 {O(n)}
t₁₅: X₄⋅X₄ {O(n^2)}
t₁₇: X₄⋅X₄ {O(n^2)}
t₁₈: X₄⋅X₄ {O(n^2)}
t₁₉: X₄⋅X₄ {O(n^2)}
t₂₀: 6⋅X₄+X₁+2 {O(n)}
t₂₁: 10⋅X₄+X₁+3 {O(n)}
t₂₂: 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)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₄ {O(n)}
t₁, X₄: X₄ {O(n)}
t₁, X₅: X₅ {O(n)}
t₁, X₆: X₆ {O(n)}
t₂, X₁: 4⋅X₄⋅X₄+2⋅X₄+X₁+1 {O(n^2)}
t₂, X₃: 11⋅X₄+X₁+3 {O(n)}
t₂, X₄: X₄ {O(n)}
t₂, X₅: 0 {O(1)}
t₂, X₆: 12⋅X₄⋅X₄+6⋅X₄+X₆+1 {O(n^2)}
t₃, X₁: 4⋅X₄⋅X₄+2⋅X₄+X₁+1 {O(n^2)}
t₃, X₃: 12⋅X₄+X₁+3 {O(n)}
t₃, X₄: 2⋅X₄ {O(n)}
t₃, X₅: 16⋅X₄⋅X₄+8⋅X₄+X₅ {O(n^2)}
t₃, X₆: 12⋅X₄⋅X₄+6⋅X₄+X₆+1 {O(n^2)}
t₄, X₁: 4⋅X₄⋅X₄+2⋅X₄+X₁+1 {O(n^2)}
t₄, X₃: 11⋅X₄+X₁+3 {O(n)}
t₄, X₄: X₄ {O(n)}
t₄, X₅: 2⋅X₄⋅X₄+X₄ {O(n^2)}
t₄, X₆: 12⋅X₄⋅X₄+6⋅X₄+X₆+1 {O(n^2)}
t₅, X₁: 4⋅X₄⋅X₄+2⋅X₄+X₁+1 {O(n^2)}
t₅, X₃: 11⋅X₄+X₁+3 {O(n)}
t₅, X₄: X₄ {O(n)}
t₅, X₅: 2⋅X₄⋅X₄+X₄ {O(n^2)}
t₅, X₆: 2⋅X₄⋅X₄+X₄ {O(n^2)}
t₆, X₁: 4⋅X₄⋅X₄+2⋅X₄+X₁+1 {O(n^2)}
t₆, X₃: 11⋅X₄+X₁+3 {O(n)}
t₆, X₄: X₄ {O(n)}
t₆, X₅: 2⋅X₄⋅X₄+X₄ {O(n^2)}
t₆, X₆: 12⋅X₄⋅X₄+6⋅X₄+X₆+1 {O(n^2)}
t₈, X₁: 4⋅X₄⋅X₄+2⋅X₄+X₁+1 {O(n^2)}
t₈, X₃: 11⋅X₄+X₁+3 {O(n)}
t₈, X₄: X₄ {O(n)}
t₈, X₅: 2⋅X₄⋅X₄+X₄ {O(n^2)}
t₈, X₆: 12⋅X₄⋅X₄+6⋅X₄+X₆+1 {O(n^2)}
t₉, X₁: 4⋅X₄⋅X₄+2⋅X₄+X₁+1 {O(n^2)}
t₉, X₃: 11⋅X₄+X₁+3 {O(n)}
t₉, X₄: X₄ {O(n)}
t₉, X₅: 2⋅X₄⋅X₄+X₄ {O(n^2)}
t₉, X₆: 12⋅X₄⋅X₄+6⋅X₄+X₆+1 {O(n^2)}
t₁₀, X₁: 4⋅X₄⋅X₄+2⋅X₄+X₁+1 {O(n^2)}
t₁₀, X₃: 11⋅X₄+X₁+3 {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₀, X₅: 2⋅X₄⋅X₄+X₄ {O(n^2)}
t₁₀, X₆: 12⋅X₄⋅X₄+6⋅X₄+X₆+1 {O(n^2)}
t₁₁, X₀: 0 {O(1)}
t₁₁, X₁: 4⋅X₄⋅X₄+2⋅X₄+X₁+1 {O(n^2)}
t₁₁, X₃: 11⋅X₄+X₁+3 {O(n)}
t₁₁, X₄: X₄ {O(n)}
t₁₁, X₅: 2⋅X₄⋅X₄+X₄ {O(n^2)}
t₁₁, X₆: 2⋅X₄⋅X₄+X₄ {O(n^2)}
t₁₂, X₁: 4⋅X₄⋅X₄+2⋅X₄+X₁+1 {O(n^2)}
t₁₂, X₃: 11⋅X₄+X₁+3 {O(n)}
t₁₂, X₄: X₄ {O(n)}
t₁₂, X₅: 2⋅X₄⋅X₄+X₄ {O(n^2)}
t₁₂, X₆: 12⋅X₄⋅X₄+6⋅X₄+X₆+1 {O(n^2)}
t₁₃, X₁: 4⋅X₄⋅X₄+2⋅X₄ {O(n^2)}
t₁₃, X₃: 11⋅X₄+X₁+3 {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₃, X₅: 4⋅X₄⋅X₄+2⋅X₄ {O(n^2)}
t₁₃, X₆: 12⋅X₄⋅X₄+6⋅X₄ {O(n^2)}
t₁₄, X₁: 1 {O(1)}
t₁₄, X₃: 11⋅X₄+X₁+3 {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₄, X₅: 12⋅X₄⋅X₄+6⋅X₄ {O(n^2)}
t₁₄, X₆: 1 {O(1)}
t₁₅, X₁: 4⋅X₄⋅X₄+2⋅X₄ {O(n^2)}
t₁₅, X₃: 11⋅X₄+X₁+3 {O(n)}
t₁₅, X₄: X₄ {O(n)}
t₁₅, X₅: 4⋅X₄⋅X₄+2⋅X₄ {O(n^2)}
t₁₅, X₆: 12⋅X₄⋅X₄+6⋅X₄ {O(n^2)}
t₁₇, X₁: 4⋅X₄⋅X₄+2⋅X₄ {O(n^2)}
t₁₇, X₃: 11⋅X₄+X₁+3 {O(n)}
t₁₇, X₄: X₄ {O(n)}
t₁₇, X₅: 4⋅X₄⋅X₄+2⋅X₄ {O(n^2)}
t₁₇, X₆: 12⋅X₄⋅X₄+6⋅X₄ {O(n^2)}
t₁₈, X₁: 4⋅X₄⋅X₄+2⋅X₄ {O(n^2)}
t₁₈, X₃: 11⋅X₄+X₁+3 {O(n)}
t₁₈, X₄: X₄ {O(n)}
t₁₈, X₅: 4⋅X₄⋅X₄+2⋅X₄ {O(n^2)}
t₁₈, X₆: 4⋅X₄⋅X₄+2⋅X₄ {O(n^2)}
t₁₉, X₁: 4⋅X₄⋅X₄+2⋅X₄ {O(n^2)}
t₁₉, X₃: 11⋅X₄+X₁+3 {O(n)}
t₁₉, X₄: X₄ {O(n)}
t₁₉, X₅: 4⋅X₄⋅X₄+2⋅X₄ {O(n^2)}
t₁₉, X₆: 4⋅X₄⋅X₄+2⋅X₄ {O(n^2)}
t₂₀, X₁: 4⋅X₄⋅X₄+2⋅X₄ {O(n^2)}
t₂₀, X₂: 0 {O(1)}
t₂₀, X₃: 11⋅X₄+X₁+3 {O(n)}
t₂₀, X₄: X₄ {O(n)}
t₂₀, X₅: 4⋅X₄⋅X₄+2⋅X₄ {O(n^2)}
t₂₀, X₆: 12⋅X₄⋅X₄+6⋅X₄ {O(n^2)}
t₂₁, X₁: 4⋅X₄⋅X₄+2⋅X₄+1 {O(n^2)}
t₂₁, X₃: 11⋅X₄+X₁+3 {O(n)}
t₂₁, X₄: X₄ {O(n)}
t₂₁, X₅: 16⋅X₄⋅X₄+8⋅X₄ {O(n^2)}
t₂₁, X₆: 12⋅X₄⋅X₄+6⋅X₄+1 {O(n^2)}
t₂₂, X₁: 4⋅X₄⋅X₄+2⋅X₄+X₁+1 {O(n^2)}
t₂₂, X₃: 12⋅X₄+X₁+3 {O(n)}
t₂₂, X₄: 2⋅X₄ {O(n)}
t₂₂, X₅: 16⋅X₄⋅X₄+8⋅X₄+X₅ {O(n^2)}
t₂₂, X₆: 12⋅X₄⋅X₄+6⋅X₄+X₆+1 {O(n^2)}