KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₀ for location evalfreturnin

Found invariant 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalfbb1in

Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalfbb2in

Found invariant 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalfbbin

Found invariant 1+X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 2+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalfbb3in

Found invariant 0 ≤ X₀ for location evalfbb6in

Found invariant X₁ ≤ X₀ ∧ 0 ≤ X₀ for location evalfstop

Found invariant X₃ ≤ X₁ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 0 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location evalfbb4in

Problem after Preprocessing

Start: evalfstart
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars: E
Locations: evalfbb1in, evalfbb2in, evalfbb3in, evalfbb4in, evalfbb6in, evalfbbin, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
t₁₀: evalfbb1in(X₀, X₁, X₂, X₃) → evalfbb2in(X₀, X₁, 1+X₂, 1+X₃) :|: 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₂
t₆: evalfbb2in(X₀, X₁, X₂, X₃) → evalfbb3in(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂
t₅: evalfbb2in(X₀, X₁, X₂, X₃) → evalfbb4in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂
t₇: evalfbb3in(X₀, X₁, X₂, X₃) → evalfbb1in(X₀, X₁, X₂, X₃) :|: 1+E ≤ 0 ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₂
t₈: evalfbb3in(X₀, X₁, X₂, X₃) → evalfbb1in(X₀, X₁, X₂, X₃) :|: 1 ≤ E ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₂
t₉: evalfbb3in(X₀, X₁, X₂, X₃) → evalfbb4in(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₂
t₁₁: evalfbb4in(X₀, X₁, X₂, X₃) → evalfbb6in(X₃-1, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂
t₁₂: evalfbb4in(X₀, X₁, X₂, X₃) → evalfbb6in(X₃, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂
t₂: evalfbb6in(X₀, X₁, X₂, X₃) → evalfbbin(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₃: evalfbb6in(X₀, X₁, X₂, X₃) → evalfreturnin(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₀ ∧ 0 ≤ X₀
t₄: evalfbbin(X₀, X₁, X₂, X₃) → evalfbb2in(X₀, X₁, 0, 1+X₀) :|: 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀
t₁: evalfentryin(X₀, X₁, X₂, X₃) → evalfbb6in(0, X₁, X₂, X₃)
t₁₃: evalfreturnin(X₀, X₁, X₂, X₃) → evalfstop(X₀, X₁, X₂, X₃) :|: 0 ≤ X₀ ∧ X₁ ≤ X₀
t₀: evalfstart(X₀, X₁, X₂, X₃) → evalfentryin(X₀, X₁, X₂, X₃)

MPRF for transition t₂: evalfbb6in(X₀, X₁, X₂, X₃) → evalfbbin(X₀, X₁, X₂, X₃) :|: 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

• evalfbb1in: [X₁+X₂-X₃]
• evalfbb2in: [X₁+X₂-X₃]
• evalfbb3in: [X₁+X₂-X₃]
• evalfbb4in: [X₁+X₂-X₃]
• evalfbb6in: [X₁-X₀]
• evalfbbin: [X₁-1-X₀]

MPRF for transition t₄: evalfbbin(X₀, X₁, X₂, X₃) → evalfbb2in(X₀, X₁, 0, 1+X₀) :|: 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

• evalfbb1in: [X₁+X₂-X₃]
• evalfbb2in: [X₁+X₂-X₃]
• evalfbb3in: [X₁+X₂-X₃]
• evalfbb4in: [X₁+X₂-X₃]
• evalfbb6in: [X₁-X₀]
• evalfbbin: [X₁-X₀]

MPRF for transition t₅: evalfbb2in(X₀, X₁, X₂, X₃) → evalfbb4in(X₀, X₁, X₂, X₃) :|: X₁ ≤ X₃ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

• evalfbb1in: [1+X₁+X₂-X₃]
• evalfbb2in: [1+X₁+X₂-X₃]
• evalfbb3in: [1+X₁+X₂-X₃]
• evalfbb4in: [X₁+X₂-X₃]
• evalfbb6in: [X₁-X₀]
• evalfbbin: [X₁-X₀]

MPRF for transition t₆: evalfbb2in(X₀, X₁, X₂, X₃) → evalfbb3in(X₀, X₁, X₂, X₃) :|: 1+X₃ ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

2⋅X₁+1 {O(n)}

MPRF:

• evalfbb1in: [2⋅X₁+X₂-2⋅X₃]
• evalfbb2in: [1+2⋅X₁+X₂-2⋅X₃]
• evalfbb3in: [2⋅X₁+X₂-2⋅X₃]
• evalfbb4in: [2⋅X₁+X₂-2⋅X₃]
• evalfbb6in: [2⋅X₁-1-2⋅X₀]
• evalfbbin: [2⋅X₁-1-2⋅X₀]

MPRF for transition t₇: evalfbb3in(X₀, X₁, X₂, X₃) → evalfbb1in(X₀, X₁, X₂, X₃) :|: 1+E ≤ 0 ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

• evalfbb1in: [X₁-1-X₃]
• evalfbb2in: [X₁-X₃]
• evalfbb3in: [X₁-X₃]
• evalfbb4in: [X₁-X₃]
• evalfbb6in: [X₁-1-X₀]
• evalfbbin: [X₁-1-X₀]

MPRF for transition t₈: evalfbb3in(X₀, X₁, X₂, X₃) → evalfbb1in(X₀, X₁, X₂, X₃) :|: 1 ≤ E ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

2⋅X₁+1 {O(n)}

MPRF:

• evalfbb1in: [2⋅X₁-1-X₃]
• evalfbb2in: [2⋅X₁-X₃]
• evalfbb3in: [2⋅X₁-X₃]
• evalfbb4in: [2⋅X₁-X₃]
• evalfbb6in: [2⋅X₁-1-X₀]
• evalfbbin: [2⋅X₁-1-X₀]

MPRF for transition t₉: evalfbb3in(X₀, X₁, X₂, X₃) → evalfbb4in(X₀, X₁, X₂, X₃) :|: 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

• evalfbb1in: [X₁+X₂-X₃]
• evalfbb2in: [X₁+X₂-X₃]
• evalfbb3in: [X₁+X₂-X₃]
• evalfbb4in: [X₁+X₂-1-X₃]
• evalfbb6in: [X₁-1-X₀]
• evalfbbin: [X₁-1-X₀]

MPRF for transition t₁₀: evalfbb1in(X₀, X₁, X₂, X₃) → evalfbb2in(X₀, X₁, 1+X₂, 1+X₃) :|: 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₃ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2+X₀ ≤ X₁ ∧ 2 ≤ X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₂ ≤ X₁ ∧ 3 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ 0 ≤ X₂ of depth 1:

new bound:

3⋅X₁+2 {O(n)}

MPRF:

• evalfbb1in: [3⋅X₁-1-X₃]
• evalfbb2in: [3⋅X₁-1-X₃]
• evalfbb3in: [3⋅X₁-1-X₃]
• evalfbb4in: [3⋅X₁-1-X₃]
• evalfbb6in: [3⋅X₁-2-X₀]
• evalfbbin: [3⋅X₁-2-X₀]

MPRF for transition t₁₁: evalfbb4in(X₀, X₁, X₂, X₃) → evalfbb6in(X₃-1, X₁, X₂, X₃) :|: 1 ≤ X₂ ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

• evalfbb1in: [2+X₁+X₂-X₃]
• evalfbb2in: [2+X₁+X₂-X₃]
• evalfbb3in: [2+X₁+X₂-X₃]
• evalfbb4in: [2+X₁+X₂-X₃]
• evalfbb6in: [1+X₁-X₀]
• evalfbbin: [1+X₁-X₀]

MPRF for transition t₁₂: evalfbb4in(X₀, X₁, X₂, X₃) → evalfbb6in(X₃, X₁, X₂, X₃) :|: X₂ ≤ 0 ∧ 1 ≤ X₀+X₁ ∧ 1 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁+X₂ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 0 ≤ X₀ ∧ 0 ≤ X₀+X₂ ∧ X₃ ≤ X₁ ∧ 0 ≤ X₂ of depth 1:

new bound:

X₁ {O(n)}

MPRF:

• evalfbb1in: [X₁-X₀]
• evalfbb2in: [X₁-X₀]
• evalfbb3in: [X₁-X₀]
• evalfbb4in: [1+X₁-X₃]
• evalfbb6in: [X₁-X₀]
• evalfbbin: [X₁-X₀]

All Bounds

Timebounds

Overall timebound:14⋅X₁+11 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁ {O(n)}
t₃: 1 {O(1)}
t₄: X₁ {O(n)}
t₅: X₁ {O(n)}
t₆: 2⋅X₁+1 {O(n)}
t₇: X₁+1 {O(n)}
t₈: 2⋅X₁+1 {O(n)}
t₉: X₁+1 {O(n)}
t₁₀: 3⋅X₁+2 {O(n)}
t₁₁: X₁+1 {O(n)}
t₁₂: X₁ {O(n)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 14⋅X₁+11 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁ {O(n)}
t₃: 1 {O(1)}
t₄: X₁ {O(n)}
t₅: X₁ {O(n)}
t₆: 2⋅X₁+1 {O(n)}
t₇: X₁+1 {O(n)}
t₈: 2⋅X₁+1 {O(n)}
t₉: X₁+1 {O(n)}
t₁₀: 3⋅X₁+2 {O(n)}
t₁₁: X₁+1 {O(n)}
t₁₂: X₁ {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: 0 {O(1)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₂, X₀: 4⋅X₁+2 {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 6⋅X₁+X₂+4 {O(n)}
t₂, X₃: 16⋅X₁+X₃+8 {O(n)}
t₃, X₀: 4⋅X₁+2 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: 8⋅X₁+X₃+4 {O(n)}
t₄, X₀: 4⋅X₁+2 {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: 0 {O(1)}
t₄, X₃: 4⋅X₁+2 {O(n)}
t₅, X₀: 8⋅X₁+4 {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: 3⋅X₁+2 {O(n)}
t₅, X₃: 4⋅X₁+2 {O(n)}
t₆, X₀: 4⋅X₁+2 {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: 3⋅X₁+2 {O(n)}
t₆, X₃: 4⋅X₁+2 {O(n)}
t₇, X₀: 4⋅X₁+2 {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: 3⋅X₁+2 {O(n)}
t₇, X₃: 4⋅X₁+2 {O(n)}
t₈, X₀: 4⋅X₁+2 {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: 3⋅X₁+2 {O(n)}
t₈, X₃: 4⋅X₁+2 {O(n)}
t₉, X₀: 4⋅X₁+2 {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: 3⋅X₁+2 {O(n)}
t₉, X₃: 4⋅X₁+2 {O(n)}
t₁₀, X₀: 4⋅X₁+2 {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: 3⋅X₁+2 {O(n)}
t₁₀, X₃: 4⋅X₁+2 {O(n)}
t₁₁, X₀: 4⋅X₁+2 {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: 6⋅X₁+4 {O(n)}
t₁₁, X₃: 8⋅X₁+4 {O(n)}
t₁₂, X₀: 4⋅X₁+2 {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: 0 {O(1)}
t₁₂, X₃: 8⋅X₁+4 {O(n)}
t₁₃, X₀: 4⋅X₁+2 {O(n)}
t₁₃, X₁: 2⋅X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: 8⋅X₁+X₃+4 {O(n)}