KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ for location eval_rank2_stop

Found invariant X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location eval_rank2_.critedge_in

Found invariant 1 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ X₃ ≤ 1+X₅ ∧ 3 ≤ X₂+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location eval_rank2_4

Found invariant 1 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ X₃ ≤ 1+X₅ ∧ 3 ≤ X₂+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location eval_rank2_bb5_in

Found invariant 1 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ X₃ ≤ 1+X₅ ∧ 3 ≤ X₂+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location eval_rank2_3

Found invariant X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location eval_rank2_bb3_in

Found invariant X₃ ≤ 1 ∧ X₃ ≤ X₂ for location eval_rank2_bb6_in

Found invariant X₃ ≤ X₂ for location eval_rank2_bb1_in

Found invariant X₃ ≤ X₂ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2 ≤ X₂ for location eval_rank2_bb2_in

Found invariant 1 ≤ X₅ ∧ 3 ≤ X₃+X₅ ∧ X₃ ≤ 1+X₅ ∧ 3 ≤ X₂+X₅ ∧ 2 ≤ X₀+X₅ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₀ for location eval_rank2_bb4_in

Problem after Preprocessing

Start: eval_rank2_start
Program_Vars: X₀, X₁, X₂, X₃, X₄, X₅
Temp_Vars: nondef.0
Locations: eval_rank2_.critedge_in, eval_rank2_3, eval_rank2_4, eval_rank2_bb0_in, eval_rank2_bb1_in, eval_rank2_bb2_in, eval_rank2_bb3_in, eval_rank2_bb4_in, eval_rank2_bb5_in, eval_rank2_bb6_in, eval_rank2_start, eval_rank2_stop
Transitions:
t₁₃: eval_rank2_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_bb1_in(X₀, X₁, X₂, X₀-1, 1+X₅-X₀, X₅) :|: X₃ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 4 ≤ X₂+X₃ ∧ X₃ ≤ X₂
t₉: eval_rank2_3(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_4(X₀, nondef.0, X₂, X₃, X₄, X₅) :|: X₃ ≤ 1+X₀ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₂+X₃ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂
t₁₁: eval_rank2_4(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ 0 ∧ X₃ ≤ 1+X₀ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₂+X₃ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂
t₁₀: eval_rank2_4(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₂+X₃ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂
t₁: eval_rank2_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_bb1_in(X₀, X₁, X₂, X₂, X₂, X₅)
t₂: eval_rank2_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2 ≤ X₃ ∧ X₃ ≤ X₂
t₃: eval_rank2_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ 1 ∧ X₃ ≤ X₂
t₄: eval_rank2_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_bb3_in(X₃-1, X₁, X₂, X₃, X₄, X₃+X₄-1) :|: 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₃ ≤ X₂
t₆: eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₅ ≤ X₀ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 4 ≤ X₂+X₃ ∧ X₃ ≤ X₂
t₅: eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₅ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 4 ≤ X₂+X₃ ∧ X₃ ≤ X₂
t₇: eval_rank2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ 1+X₀ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₂+X₃ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂
t₁₂: eval_rank2_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅-1) :|: X₃ ≤ 1+X₀ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₂+X₃ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂
t₁₄: eval_rank2_bb6_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_stop(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ 1 ∧ X₃ ≤ X₂
t₀: eval_rank2_start(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_bb0_in(X₀, X₁, X₂, X₃, X₄, X₅)

MPRF for transition t₂: eval_rank2_bb1_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 2 ≤ X₃ ∧ X₃ ≤ X₂ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• eval_rank2_.critedge_in: [X₃-3]
• eval_rank2_3: [X₃-3]
• eval_rank2_4: [X₃-3]
• eval_rank2_bb1_in: [X₃-1]
• eval_rank2_bb2_in: [X₃-3]
• eval_rank2_bb3_in: [X₀-2]
• eval_rank2_bb4_in: [X₃-3]
• eval_rank2_bb5_in: [X₃-3]

MPRF for transition t₄: eval_rank2_bb2_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_bb3_in(X₃-1, X₁, X₂, X₃, X₄, X₃+X₄-1) :|: 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₃ ≤ X₂ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

• eval_rank2_.critedge_in: [X₀-1]
• eval_rank2_3: [X₃-2]
• eval_rank2_4: [X₃-2]
• eval_rank2_bb1_in: [X₃]
• eval_rank2_bb2_in: [X₃-1]
• eval_rank2_bb3_in: [X₀-1]
• eval_rank2_bb4_in: [X₃-2]
• eval_rank2_bb5_in: [X₀-1]

MPRF for transition t₅: eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₀ ≤ X₅ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 4 ≤ X₂+X₃ ∧ X₃ ≤ X₂ of depth 1:

new bound:

2⋅X₂ {O(n)}

MPRF:

• eval_rank2_.critedge_in: [X₅]
• eval_rank2_3: [X₅]
• eval_rank2_4: [X₅]
• eval_rank2_bb1_in: [X₃+X₄]
• eval_rank2_bb2_in: [X₃+X₄]
• eval_rank2_bb3_in: [1+X₅]
• eval_rank2_bb4_in: [X₅]
• eval_rank2_bb5_in: [X₅]

MPRF for transition t₆: eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1+X₅ ≤ X₀ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 4 ≤ X₂+X₃ ∧ X₃ ≤ X₂ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

• eval_rank2_.critedge_in: [X₀-1]
• eval_rank2_3: [X₃-1]
• eval_rank2_4: [X₃-1]
• eval_rank2_bb1_in: [X₃]
• eval_rank2_bb2_in: [X₃]
• eval_rank2_bb3_in: [X₀]
• eval_rank2_bb4_in: [X₀]
• eval_rank2_bb5_in: [X₀]

MPRF for transition t₇: eval_rank2_bb4_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_3(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₃ ≤ 1+X₀ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₂+X₃ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ of depth 1:

new bound:

5⋅X₂+3 {O(n)}

MPRF:

• eval_rank2_.critedge_in: [3⋅X₅-1-X₃]
• eval_rank2_3: [3⋅X₅-2-X₀]
• eval_rank2_4: [3⋅X₅-2-X₀]
• eval_rank2_bb1_in: [2⋅X₃+3⋅X₄-3]
• eval_rank2_bb2_in: [2⋅X₃+3⋅X₄-3]
• eval_rank2_bb3_in: [3⋅X₅-X₃]
• eval_rank2_bb4_in: [3⋅X₅-1-X₀]
• eval_rank2_bb5_in: [X₀+3⋅X₅-2⋅X₃]

MPRF for transition t₉: eval_rank2_3(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_4(X₀, nondef.0, X₂, X₃, X₄, X₅) :|: X₃ ≤ 1+X₀ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₂+X₃ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ of depth 1:

new bound:

2⋅X₂ {O(n)}

MPRF:

• eval_rank2_.critedge_in: [X₅]
• eval_rank2_3: [1+X₅]
• eval_rank2_4: [X₅]
• eval_rank2_bb1_in: [X₃+X₄]
• eval_rank2_bb2_in: [X₃+X₄]
• eval_rank2_bb3_in: [1+X₅]
• eval_rank2_bb4_in: [1+X₅]
• eval_rank2_bb5_in: [X₅]

MPRF for transition t₁₀: eval_rank2_4(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: 1 ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₂+X₃ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ of depth 1:

new bound:

3⋅X₂+3 {O(n)}

MPRF:

• eval_rank2_.critedge_in: [X₂+X₃+X₅-3-X₀]
• eval_rank2_3: [X₂+X₅-2]
• eval_rank2_4: [X₂+X₅-2]
• eval_rank2_bb1_in: [X₂+X₃+X₄-3]
• eval_rank2_bb2_in: [X₂+X₃+X₄-3]
• eval_rank2_bb3_in: [X₂+X₅-2]
• eval_rank2_bb4_in: [X₂+X₅-2]
• eval_rank2_bb5_in: [X₂+X₅-3]

MPRF for transition t₁₁: eval_rank2_4(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅) :|: X₁ ≤ 0 ∧ X₃ ≤ 1+X₀ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₂+X₃ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• eval_rank2_.critedge_in: [X₃-1]
• eval_rank2_3: [1+X₀]
• eval_rank2_4: [1+X₀]
• eval_rank2_bb1_in: [1+X₃]
• eval_rank2_bb2_in: [X₃]
• eval_rank2_bb3_in: [1+X₀]
• eval_rank2_bb4_in: [1+X₀]
• eval_rank2_bb5_in: [1+X₀]

MPRF for transition t₁₂: eval_rank2_bb5_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_bb3_in(X₀, X₁, X₂, X₃, X₄, X₅-1) :|: X₃ ≤ 1+X₀ ∧ X₃ ≤ 1+X₅ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₅ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₅ ∧ 2 ≤ X₁+X₅ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₅ ∧ 3 ≤ X₃+X₅ ∧ 4 ≤ X₂+X₃ ∧ X₀ ≤ X₅ ∧ X₃ ≤ X₂ of depth 1:

new bound:

2⋅X₂ {O(n)}

MPRF:

• eval_rank2_.critedge_in: [X₅]
• eval_rank2_3: [X₅]
• eval_rank2_4: [X₅]
• eval_rank2_bb1_in: [X₃+X₄]
• eval_rank2_bb2_in: [X₃+X₄]
• eval_rank2_bb3_in: [X₅]
• eval_rank2_bb4_in: [X₅]
• eval_rank2_bb5_in: [X₅]

MPRF for transition t₁₃: eval_rank2_.critedge_in(X₀, X₁, X₂, X₃, X₄, X₅) → eval_rank2_bb1_in(X₀, X₁, X₂, X₀-1, 1+X₅-X₀, X₅) :|: X₃ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₀+X₃ ∧ 4 ≤ X₂+X₃ ∧ X₃ ≤ X₂ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

• eval_rank2_.critedge_in: [X₃-1]
• eval_rank2_3: [X₀]
• eval_rank2_4: [X₀]
• eval_rank2_bb1_in: [X₃-1]
• eval_rank2_bb2_in: [X₃-1]
• eval_rank2_bb3_in: [X₀]
• eval_rank2_bb4_in: [X₀]
• eval_rank2_bb5_in: [X₀]

All Bounds

Timebounds

Overall timebound:19⋅X₂+13 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₂ {O(n)}
t₅: 2⋅X₂ {O(n)}
t₆: X₂ {O(n)}
t₇: 5⋅X₂+3 {O(n)}
t₉: 2⋅X₂ {O(n)}
t₁₀: 3⋅X₂+3 {O(n)}
t₁₁: X₂+1 {O(n)}
t₁₂: 2⋅X₂ {O(n)}
t₁₃: X₂+1 {O(n)}
t₁₄: 1 {O(1)}

Costbounds

Overall costbound: 19⋅X₂+13 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₂+1 {O(n)}
t₃: 1 {O(1)}
t₄: X₂ {O(n)}
t₅: 2⋅X₂ {O(n)}
t₆: X₂ {O(n)}
t₇: 5⋅X₂+3 {O(n)}
t₉: 2⋅X₂ {O(n)}
t₁₀: 3⋅X₂+3 {O(n)}
t₁₁: X₂+1 {O(n)}
t₁₂: 2⋅X₂ {O(n)}
t₁₃: X₂+1 {O(n)}
t₁₄: 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)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₂ {O(n)}
t₁, X₄: X₂ {O(n)}
t₁, X₅: X₅ {O(n)}
t₂, X₀: 2⋅X₂+X₀ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₂ {O(n)}
t₂, X₄: 3⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
t₂, X₅: 6⋅X₂⋅X₂+12⋅X₂+X₅ {O(n^2)}
t₃, X₀: 2⋅X₂+X₀ {O(n)}
t₃, X₂: 2⋅X₂ {O(n)}
t₃, X₃: 2⋅X₂ {O(n)}
t₃, X₄: 3⋅X₂⋅X₂+7⋅X₂ {O(n^2)}
t₃, X₅: 6⋅X₂⋅X₂+12⋅X₂+X₅ {O(n^2)}
t₄, X₀: X₂ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₂ {O(n)}
t₄, X₄: 3⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
t₄, X₅: 3⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
t₅, X₀: X₂ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₂ {O(n)}
t₅, X₄: 3⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
t₅, X₅: 3⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
t₆, X₀: X₂ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: 2⋅X₂ {O(n)}
t₆, X₄: 6⋅X₂⋅X₂+12⋅X₂ {O(n^2)}
t₆, X₅: 3⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
t₇, X₀: X₂ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₂ {O(n)}
t₇, X₄: 3⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
t₇, X₅: 3⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
t₉, X₀: X₂ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₂ {O(n)}
t₉, X₄: 3⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
t₉, X₅: 3⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
t₁₀, X₀: X₂ {O(n)}
t₁₀, X₂: X₂ {O(n)}
t₁₀, X₃: X₂ {O(n)}
t₁₀, X₄: 3⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
t₁₀, X₅: 3⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
t₁₁, X₀: X₂ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₂ {O(n)}
t₁₁, X₄: 3⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
t₁₁, X₅: 3⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
t₁₂, X₀: X₂ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₂ {O(n)}
t₁₂, X₄: 3⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
t₁₂, X₅: 3⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
t₁₃, X₀: 2⋅X₂ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₂ {O(n)}
t₁₃, X₄: 3⋅X₂⋅X₂+6⋅X₂ {O(n^2)}
t₁₃, X₅: 6⋅X₂⋅X₂+12⋅X₂ {O(n^2)}
t₁₄, X₀: 2⋅X₂+X₀ {O(n)}
t₁₄, X₂: 2⋅X₂ {O(n)}
t₁₄, X₃: 2⋅X₂ {O(n)}
t₁₄, X₄: 3⋅X₂⋅X₂+7⋅X₂ {O(n^2)}
t₁₄, X₅: 6⋅X₂⋅X₂+12⋅X₂+X₅ {O(n^2)}