KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location f14

Found invariant X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location f6

Found invariant X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location f4

Found invariant X₃ ≤ 1+X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location f7

Problem after Preprocessing

Start: f0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: f0, f14, f4, f6, f7
Transitions:
t₂: f0(X₀, X₁, X₂, X₃) → f4(X₀, X₁, X₂, 1+X₁) :|: 0 ≤ X₁ ∧ X₁ ≤ X₂
t₈: f4(X₀, X₁, X₂, X₃) → f14(X₀, X₁, X₂, X₁) :|: X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₃: f4(X₀, X₁, X₂, X₃) → f6(E, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₄: f4(X₀, X₁, X₂, X₃) → f6(E, X₁, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₇: f6(X₀, X₁, X₂, X₃) → f14(0, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₀: f6(X₀, X₁, X₂, X₃) → f7(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₁: f6(X₀, X₁, X₂, X₃) → f7(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₅: f7(X₀, X₁, X₂, X₃) → f4(X₀, X₁, X₂, 1+X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₆: f7(X₀, X₁, X₂, X₃) → f4(X₀, X₁, X₂, 0) :|: 1+X₂ ≤ X₃ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂

Cut unreachable locations [f6] from the program graph

Cut unsatisfiable transition [t₈: f4→f14; t₅₅: f4→f6_v2; t₅₆: f4→f14]

Cut unreachable locations [f4_v1; f6_v2; f7_v1; f7_v2] from the program graph

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location f7_v7

Found invariant X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location f6_v1

Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location f7_v9

Found invariant X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location f7_v5

Found invariant X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 3+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location f7_v6

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location f6_v4

Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2 ≤ X₁ for location f6_v5

Found invariant X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₀+X₂ ∧ 0 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location f7_v3

Found invariant X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location f4

Found invariant X₃ ≤ 1+X₂ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1+X₀ ≤ X₂ ∧ 0 ≤ X₁ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location f7_v4

Found invariant 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₁+X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 3+X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location f7_v10

Found invariant X₃ ≤ 0 ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₀+X₃ ≤ 0 ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2+X₀ ≤ X₁ ∧ 1+X₀ ≤ 0 for location f7_v8

Found invariant X₃ ≤ 0 ∧ X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location f4_v2

Found invariant X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ for location f6_v3

Found invariant X₃ ≤ 1+X₂ ∧ 0 ≤ X₃ ∧ 0 ≤ X₂+X₃ ∧ 0 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₁ for location f14

Found invariant X₃ ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 1 ≤ X₁ for location f4_v4

Found invariant X₃ ≤ 1+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 0 ≤ X₁ for location f4_v3

Analysing control-flow refined program

MPRF for transition t₆₉: f4_v3(X₀, X₁, X₂, X₃) → f6_v3(E, X₁, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

2⋅X₁+2⋅X₂+8 {O(n)}

MPRF:

• f4_v3: [2+X₂-X₃]
• f6_v3: [1+X₂-X₃]
• f7_v5: [1+X₂-X₃]
• f7_v6: [1+X₂-X₃]

MPRF for transition t₇₀: f6_v3(X₀, X₁, X₂, X₃) → f7_v5(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

2⋅X₁+2⋅X₂+8 {O(n)}

MPRF:

• f4_v3: [2+X₂-X₃]
• f6_v3: [2+X₂-X₃]
• f7_v5: [1+X₂-X₃]
• f7_v6: [1+X₂-X₃]

MPRF for transition t₇₁: f6_v3(X₀, X₁, X₂, X₃) → f7_v6(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

2⋅X₁+2⋅X₂+8 {O(n)}

MPRF:

• f4_v3: [2+X₂-X₃]
• f6_v3: [2+X₂-X₃]
• f7_v5: [1+X₂-X₃]
• f7_v6: [1+X₂-X₃]

MPRF for transition t₇₄: f7_v6(X₀, X₁, X₂, X₃) → f4_v3(X₀, X₁, X₂, 1+X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 1+X₀ ≤ 0 ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3+X₀ ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

2⋅X₁+2⋅X₂+8 {O(n)}

MPRF:

• f4_v3: [2+X₂-X₃]
• f6_v3: [2+X₂-X₃]
• f7_v5: [1+X₂-X₃]
• f7_v6: [2+X₂-X₃]

MPRF for transition t₇₆: f7_v5(X₀, X₁, X₂, X₃) → f4_v3(X₀, X₁, X₂, 1+X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

2⋅X₁+2⋅X₂+6 {O(n)}

MPRF:

• f4_v3: [1+X₂-X₃]
• f6_v3: [1+X₂-X₃]
• f7_v5: [1+X₂-X₃]
• f7_v6: [X₂-X₃]

MPRF for transition t₈₃: f4_v4(X₀, X₁, X₂, X₃) → f6_v5(E, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

12⋅X₂+4 {O(n)}

MPRF:

• f4_v4: [1+X₂-X₃]
• f6_v5: [X₂-X₃]
• f7_v10: [X₂-X₃]
• f7_v9: [X₂-X₃]

MPRF for transition t₈₅: f6_v5(X₀, X₁, X₂, X₃) → f7_v9(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

12⋅X₁+2 {O(n)}

MPRF:

• f4_v4: [X₁-X₃]
• f6_v5: [X₁-X₃]
• f7_v10: [X₁-X₃]
• f7_v9: [X₁-1-X₃]

MPRF for transition t₈₆: f6_v5(X₀, X₁, X₂, X₃) → f7_v10(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

12⋅X₂+2 {O(n)}

MPRF:

• f4_v4: [X₂-X₃]
• f6_v5: [X₂-X₃]
• f7_v10: [X₂-1-X₃]
• f7_v9: [X₂-X₃]

MPRF for transition t₈₈: f7_v10(X₀, X₁, X₂, X₃) → f4_v4(X₀, X₁, X₂, 1+X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 1+X₀ ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂ ∧ 3+X₀ ≤ X₁ ∧ 3+X₀ ≤ X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

12⋅X₂+4 {O(n)}

MPRF:

• f4_v4: [1+X₂-X₃]
• f6_v5: [1+X₂-X₃]
• f7_v10: [1+X₂-X₃]
• f7_v9: [X₂-X₃]

MPRF for transition t₈₉: f7_v9(X₀, X₁, X₂, X₃) → f4_v4(X₀, X₁, X₂, 1+X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

12⋅X₂+4 {O(n)}

MPRF:

• f4_v4: [1+X₂-X₃]
• f6_v5: [1+X₂-X₃]
• f7_v10: [X₂-X₃]
• f7_v9: [1+X₂-X₃]

CFR: Improvement to new bound with the following program:

method: PartialEvaluation new bound:

O(n)

cfr-program:

Start: f0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: f0, f14, f4, f4_v2, f4_v3, f4_v4, f6_v1, f6_v3, f6_v4, f6_v5, f7_v10, f7_v3, f7_v4, f7_v5, f7_v6, f7_v7, f7_v8, f7_v9
Transitions:
t₂: f0(X₀, X₁, X₂, X₃) → f4(X₀, X₁, X₂, 1+X₁) :|: 0 ≤ X₁ ∧ X₁ ≤ X₂
t₅₄: f4(X₀, X₁, X₂, X₃) → f6_v1(E, X₁, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₇₈: f4_v2(X₀, X₁, X₂, X₃) → f14(X₀, X₁, X₂, X₁) :|: X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ 0
t₇₇: f4_v2(X₀, X₁, X₂, X₃) → f6_v4(E, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ 0 ≤ X₁+X₃ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₂+X₃ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ 0
t₆₉: f4_v3(X₀, X₁, X₂, X₃) → f6_v3(E, X₁, X₂, X₃) :|: 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ X₁ ≤ X₃ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃
t₈₄: f4_v4(X₀, X₁, X₂, X₃) → f14(X₀, X₁, X₂, X₁) :|: X₃ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃
t₈₃: f4_v4(X₀, X₁, X₂, X₃) → f6_v5(E, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ ∧ X₃ ≤ X₂ ∧ 0 ≤ X₃
t₆₆: f6_v1(X₀, X₁, X₂, X₃) → f14(0, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₆₄: f6_v1(X₀, X₁, X₂, X₃) → f7_v3(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₆₅: f6_v1(X₀, X₁, X₂, X₃) → f7_v4(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ 0 ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₇₂: f6_v3(X₀, X₁, X₂, X₃) → f14(0, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₇₀: f6_v3(X₀, X₁, X₂, X₃) → f7_v5(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₇₁: f6_v3(X₀, X₁, X₂, X₃) → f7_v6(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₈₁: f6_v4(X₀, X₁, X₂, X₃) → f14(0, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ 0
t₇₉: f6_v4(X₀, X₁, X₂, X₃) → f7_v7(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ 0
t₈₀: f6_v4(X₀, X₁, X₂, X₃) → f7_v8(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ 0
t₈₇: f6_v5(X₀, X₁, X₂, X₃) → f14(0, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₀ ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₈₆: f6_v5(X₀, X₁, X₂, X₃) → f7_v10(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ 0 ∧ X₃ ≤ 1+X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₈₅: f6_v5(X₀, X₁, X₂, X₃) → f7_v9(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀ ∧ X₃ ≤ 1+X₂ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₈₈: f7_v10(X₀, X₁, X₂, X₃) → f4_v4(X₀, X₁, X₂, 1+X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 1+X₀ ≤ 0 ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂ ∧ 3+X₀ ≤ X₁ ∧ 3+X₀ ≤ X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₉₁: f7_v3(X₀, X₁, X₂, X₃) → f4_v2(X₀, X₁, X₂, 0) :|: 1+X₂ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₉₂: f7_v3(X₀, X₁, X₂, X₃) → f4_v3(X₀, X₁, X₂, 1+X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₂ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₆₇: f7_v4(X₀, X₁, X₂, X₃) → f4_v2(X₀, X₁, X₂, 0) :|: 1+X₂ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₂ ∧ 1+X₀ ≤ 0 ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₆₈: f7_v4(X₀, X₁, X₂, X₃) → f4_v3(X₀, X₁, X₂, 1+X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₂ ∧ 1+X₀ ≤ 0 ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₃ ∧ 2+X₀ ≤ X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₇₅: f7_v5(X₀, X₁, X₂, X₃) → f4_v2(X₀, X₁, X₂, 0) :|: 1+X₂ ≤ X₃ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₇₆: f7_v5(X₀, X₁, X₂, X₃) → f4_v3(X₀, X₁, X₂, 1+X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₇₃: f7_v6(X₀, X₁, X₂, X₃) → f4_v2(X₀, X₁, X₂, 0) :|: 1+X₂ ≤ X₃ ∧ X₃ ≤ 1+X₂ ∧ 1+X₀ ≤ 0 ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3+X₀ ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₇₄: f7_v6(X₀, X₁, X₂, X₃) → f4_v3(X₀, X₁, X₂, 1+X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 1+X₀ ≤ 0 ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₁ ≤ X₂ ∧ 1 ≤ X₂ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 2 ≤ X₃ ∧ 3+X₀ ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂
t₉₀: f7_v7(X₀, X₁, X₂, X₃) → f4_v4(X₀, X₁, X₂, 1+X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₀+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ 0
t₈₂: f7_v8(X₀, X₁, X₂, X₃) → f4_v4(X₀, X₁, X₂, 1+X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 1+X₀ ≤ 0 ∧ 1+X₀ ≤ X₃ ∧ 1+X₀+X₃ ≤ 0 ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₃ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₂+X₃ ∧ 1+X₃ ≤ X₂ ∧ 2+X₀ ≤ X₁ ∧ 2+X₀ ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂ ∧ 0 ≤ X₃ ∧ X₃ ≤ 0
t₈₉: f7_v9(X₀, X₁, X₂, X₃) → f4_v4(X₀, X₁, X₂, 1+X₃) :|: X₃ ≤ X₂ ∧ X₃ ≤ 1+X₂ ∧ 1 ≤ X₀ ∧ 1+X₃ ≤ X₁ ∧ 1+X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ 4 ≤ X₁+X₂ ∧ 0 ≤ X₁ ∧ 0 ≤ X₁+X₂ ∧ X₁ ≤ X₂ ∧ 0 ≤ X₂

All Bounds

Timebounds

Overall timebound:22⋅X₁+58⋅X₂+75 {O(n)}
t₂: 1 {O(1)}
t₅₄: 1 {O(1)}
t₆₄: 1 {O(1)}
t₆₅: 1 {O(1)}
t₆₆: 1 {O(1)}
t₆₇: 1 {O(1)}
t₆₈: 1 {O(1)}
t₆₉: 2⋅X₁+2⋅X₂+8 {O(n)}
t₇₀: 2⋅X₁+2⋅X₂+8 {O(n)}
t₇₁: 2⋅X₁+2⋅X₂+8 {O(n)}
t₇₂: 1 {O(1)}
t₇₃: 1 {O(1)}
t₇₄: 2⋅X₁+2⋅X₂+8 {O(n)}
t₇₅: 1 {O(1)}
t₇₆: 2⋅X₁+2⋅X₂+6 {O(n)}
t₇₇: 1 {O(1)}
t₇₈: 1 {O(1)}
t₇₉: 1 {O(1)}
t₈₀: 1 {O(1)}
t₈₁: 1 {O(1)}
t₈₂: 1 {O(1)}
t₈₃: 12⋅X₂+4 {O(n)}
t₈₄: 1 {O(1)}
t₈₅: 12⋅X₁+2 {O(n)}
t₈₆: 12⋅X₂+2 {O(n)}
t₈₇: 1 {O(1)}
t₈₈: 12⋅X₂+4 {O(n)}
t₈₉: 12⋅X₂+4 {O(n)}
t₉₀: 1 {O(1)}
t₉₁: 1 {O(1)}
t₉₂: 1 {O(1)}

Costbounds

Overall costbound: 22⋅X₁+58⋅X₂+75 {O(n)}
t₂: 1 {O(1)}
t₅₄: 1 {O(1)}
t₆₄: 1 {O(1)}
t₆₅: 1 {O(1)}
t₆₆: 1 {O(1)}
t₆₇: 1 {O(1)}
t₆₈: 1 {O(1)}
t₆₉: 2⋅X₁+2⋅X₂+8 {O(n)}
t₇₀: 2⋅X₁+2⋅X₂+8 {O(n)}
t₇₁: 2⋅X₁+2⋅X₂+8 {O(n)}
t₇₂: 1 {O(1)}
t₇₃: 1 {O(1)}
t₇₄: 2⋅X₁+2⋅X₂+8 {O(n)}
t₇₅: 1 {O(1)}
t₇₆: 2⋅X₁+2⋅X₂+6 {O(n)}
t₇₇: 1 {O(1)}
t₇₈: 1 {O(1)}
t₇₉: 1 {O(1)}
t₈₀: 1 {O(1)}
t₈₁: 1 {O(1)}
t₈₂: 1 {O(1)}
t₈₃: 12⋅X₂+4 {O(n)}
t₈₄: 1 {O(1)}
t₈₅: 12⋅X₁+2 {O(n)}
t₈₆: 12⋅X₂+2 {O(n)}
t₈₇: 1 {O(1)}
t₈₈: 12⋅X₂+4 {O(n)}
t₈₉: 12⋅X₂+4 {O(n)}
t₉₀: 1 {O(1)}
t₉₁: 1 {O(1)}
t₉₂: 1 {O(1)}

Sizebounds

t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₁+1 {O(n)}
t₅₄, X₁: X₁ {O(n)}
t₅₄, X₂: X₂ {O(n)}
t₅₄, X₃: X₁+1 {O(n)}
t₆₄, X₁: X₁ {O(n)}
t₆₄, X₂: X₂ {O(n)}
t₆₄, X₃: X₁+1 {O(n)}
t₆₅, X₁: X₁ {O(n)}
t₆₅, X₂: X₂ {O(n)}
t₆₅, X₃: X₁+1 {O(n)}
t₆₆, X₀: 0 {O(1)}
t₆₆, X₁: X₁ {O(n)}
t₆₆, X₂: X₂ {O(n)}
t₆₆, X₃: X₁+1 {O(n)}
t₆₇, X₁: X₁ {O(n)}
t₆₇, X₂: X₂ {O(n)}
t₆₇, X₃: 0 {O(1)}
t₆₈, X₁: X₁ {O(n)}
t₆₈, X₂: X₂ {O(n)}
t₆₈, X₃: X₁+2 {O(n)}
t₆₉, X₁: 2⋅X₁ {O(n)}
t₆₉, X₂: 2⋅X₂ {O(n)}
t₆₉, X₃: 4⋅X₂+6⋅X₁+18 {O(n)}
t₇₀, X₁: 2⋅X₁ {O(n)}
t₇₀, X₂: 2⋅X₂ {O(n)}
t₇₀, X₃: 4⋅X₂+6⋅X₁+18 {O(n)}
t₇₁, X₁: 2⋅X₁ {O(n)}
t₇₁, X₂: 2⋅X₂ {O(n)}
t₇₁, X₃: 4⋅X₂+6⋅X₁+18 {O(n)}
t₇₂, X₀: 0 {O(1)}
t₇₂, X₁: 2⋅X₁ {O(n)}
t₇₂, X₂: 2⋅X₂ {O(n)}
t₇₂, X₃: 4⋅X₂+6⋅X₁+18 {O(n)}
t₇₃, X₁: 2⋅X₁ {O(n)}
t₇₃, X₂: 2⋅X₂ {O(n)}
t₇₃, X₃: 0 {O(1)}
t₇₄, X₁: 2⋅X₁ {O(n)}
t₇₄, X₂: 2⋅X₂ {O(n)}
t₇₄, X₃: 4⋅X₂+6⋅X₁+18 {O(n)}
t₇₅, X₁: 2⋅X₁ {O(n)}
t₇₅, X₂: 2⋅X₂ {O(n)}
t₇₅, X₃: 0 {O(1)}
t₇₆, X₁: 2⋅X₁ {O(n)}
t₇₆, X₂: 2⋅X₂ {O(n)}
t₇₆, X₃: 4⋅X₂+6⋅X₁+18 {O(n)}
t₇₇, X₁: 6⋅X₁ {O(n)}
t₇₇, X₂: 6⋅X₂ {O(n)}
t₇₇, X₃: 0 {O(1)}
t₇₈, X₁: 0 {O(1)}
t₇₈, X₂: 6⋅X₂ {O(n)}
t₇₈, X₃: 0 {O(1)}
t₇₉, X₁: 6⋅X₁ {O(n)}
t₇₉, X₂: 6⋅X₂ {O(n)}
t₇₉, X₃: 0 {O(1)}
t₈₀, X₁: 6⋅X₁ {O(n)}
t₈₀, X₂: 6⋅X₂ {O(n)}
t₈₀, X₃: 0 {O(1)}
t₈₁, X₀: 0 {O(1)}
t₈₁, X₁: 6⋅X₁ {O(n)}
t₈₁, X₂: 6⋅X₂ {O(n)}
t₈₁, X₃: 0 {O(1)}
t₈₂, X₁: 6⋅X₁ {O(n)}
t₈₂, X₂: 6⋅X₂ {O(n)}
t₈₂, X₃: 1 {O(1)}
t₈₃, X₁: 12⋅X₁ {O(n)}
t₈₃, X₂: 12⋅X₂ {O(n)}
t₈₃, X₃: 24⋅X₂+10 {O(n)}
t₈₄, X₁: 36⋅X₁ {O(n)}
t₈₄, X₂: 36⋅X₂ {O(n)}
t₈₄, X₃: 36⋅X₁ {O(n)}
t₈₅, X₁: 12⋅X₁ {O(n)}
t₈₅, X₂: 12⋅X₂ {O(n)}
t₈₅, X₃: 24⋅X₂+10 {O(n)}
t₈₆, X₁: 12⋅X₁ {O(n)}
t₈₆, X₂: 12⋅X₂ {O(n)}
t₈₆, X₃: 24⋅X₂+10 {O(n)}
t₈₇, X₀: 0 {O(1)}
t₈₇, X₁: 12⋅X₁ {O(n)}
t₈₇, X₂: 12⋅X₂ {O(n)}
t₈₇, X₃: 24⋅X₂+10 {O(n)}
t₈₈, X₁: 12⋅X₁ {O(n)}
t₈₈, X₂: 12⋅X₂ {O(n)}
t₈₈, X₃: 24⋅X₂+10 {O(n)}
t₈₉, X₁: 12⋅X₁ {O(n)}
t₈₉, X₂: 12⋅X₂ {O(n)}
t₈₉, X₃: 24⋅X₂+10 {O(n)}
t₉₀, X₁: 6⋅X₁ {O(n)}
t₉₀, X₂: 6⋅X₂ {O(n)}
t₉₀, X₃: 1 {O(1)}
t₉₁, X₁: X₁ {O(n)}
t₉₁, X₂: X₂ {O(n)}
t₉₁, X₃: 0 {O(1)}
t₉₂, X₁: X₁ {O(n)}
t₉₂, X₂: X₂ {O(n)}
t₉₂, X₃: X₁+2 {O(n)}