KoAT2 Proof Output

Initial Problem

Start: start0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: lbl151, lbl171, start, start0, stop
Transitions:
t₉: lbl151(X₀, X₁, X₂, X₃) → lbl151(X₀, 7+X₁, X₂, 1+X₃) :|: 140⋅X₀+28⋅X₂+56⋅X₃ ≤ 5719+23⋅X₁ ∧ 35⋅X₀+7⋅X₂+14⋅X₃ ≤ 1561+2⋅X₁ ∧ 5⋅X₀+X₂+2⋅X₃ ≤ 203+X₁ ∧ X₀ ≤ 29 ∧ X₁ ≤ 5+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 6 ≤ X₁ ∧ 7+5⋅X₀+X₂ ≤ X₁+5⋅X₃ ∧ 7+5⋅X₀+X₂ ≤ 6⋅X₃ ∧ 161+140⋅X₀+28⋅X₂ ≤ 23⋅X₁+140⋅X₃ ∧ 7⋅X₀+X₁ ≤ X₂+7⋅X₃
t₁₀: lbl151(X₀, X₁, X₂, X₃) → lbl151(X₀, 2+X₁, X₂, 1+X₃) :|: 140⋅X₀+28⋅X₂+56⋅X₃ ≤ 5719+23⋅X₁ ∧ 35⋅X₀+7⋅X₂+14⋅X₃ ≤ 1561+2⋅X₁ ∧ 5⋅X₀+X₂+2⋅X₃ ≤ 203+X₁ ∧ X₀ ≤ 29 ∧ X₁ ≤ 5 ∧ X₁ ≤ 5+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 7+5⋅X₀+X₂ ≤ X₁+5⋅X₃ ∧ 7+5⋅X₀+X₂ ≤ 6⋅X₃ ∧ 161+140⋅X₀+28⋅X₂ ≤ 23⋅X₁+140⋅X₃ ∧ 7⋅X₀+X₁ ≤ X₂+7⋅X₃
t₈: lbl151(X₀, X₁, X₂, X₃) → lbl171(X₀, X₁-10, X₂, 2+X₃) :|: 140⋅X₀+28⋅X₂+56⋅X₃ ≤ 5719+23⋅X₁ ∧ 35⋅X₀+7⋅X₂+14⋅X₃ ≤ 1561+2⋅X₁ ∧ 5⋅X₀+X₂+2⋅X₃ ≤ 203+X₁ ∧ X₀ ≤ 29 ∧ X₁ ≤ 5+X₃ ∧ 1+X₀ ≤ X₃ ∧ 7+5⋅X₀+X₂ ≤ X₁+5⋅X₃ ∧ 7+5⋅X₀+X₂ ≤ 6⋅X₃ ∧ 161+140⋅X₀+28⋅X₂ ≤ 23⋅X₁+140⋅X₃ ∧ 7⋅X₀+X₁ ≤ X₂+7⋅X₃ ∧ X₃ ≤ X₁
t₆: lbl171(X₀, X₁, X₂, X₃) → lbl151(X₀, 7+X₁, X₂, 1+X₃) :|: 35⋅X₀+7⋅X₂+19⋅X₃ ≤ 1674+7⋅X₁ ∧ X₀ ≤ 29 ∧ X₃ ≤ 29 ∧ X₃ ≤ 12+X₁ ∧ 1+X₁ ≤ X₃ ∧ 6 ≤ X₁ ∧ 24+7⋅X₀+X₁ ≤ X₂+7⋅X₃ ∧ 5⋅X₀+X₂ ≤ X₁+5⋅X₃
t₇: lbl171(X₀, X₁, X₂, X₃) → lbl151(X₀, 2+X₁, X₂, 1+X₃) :|: 35⋅X₀+7⋅X₂+19⋅X₃ ≤ 1674+7⋅X₁ ∧ X₀ ≤ 29 ∧ X₃ ≤ 29 ∧ X₃ ≤ 12+X₁ ∧ X₁ ≤ 5 ∧ 1+X₁ ≤ X₃ ∧ 24+7⋅X₀+X₁ ≤ X₂+7⋅X₃ ∧ 5⋅X₀+X₂ ≤ X₁+5⋅X₃
t₅: lbl171(X₀, X₁, X₂, X₃) → lbl171(X₀, X₁-10, X₂, 2+X₃) :|: 35⋅X₀+7⋅X₂+19⋅X₃ ≤ 1674+7⋅X₁ ∧ X₀ ≤ 29 ∧ X₃ ≤ 29 ∧ X₃ ≤ 12+X₁ ∧ 24+7⋅X₀+X₁ ≤ X₂+7⋅X₃ ∧ 5⋅X₀+X₂ ≤ X₁+5⋅X₃ ∧ X₃ ≤ X₁
t₄: lbl171(X₀, X₁, X₂, X₃) → stop(X₀, X₁, X₂, X₃) :|: 35⋅X₀+7⋅X₂+19⋅X₃ ≤ 1674+7⋅X₁ ∧ X₀ ≤ 29 ∧ X₃ ≤ 12+X₁ ∧ 24+7⋅X₀+X₁ ≤ X₂+7⋅X₃ ∧ 30 ≤ X₃ ∧ 5⋅X₀+X₂ ≤ X₁+5⋅X₃
t₂: start(X₀, X₁, X₂, X₃) → lbl151(X₀, 7+X₁, X₂, 1+X₃) :|: X₀ ≤ 29 ∧ 1+X₂ ≤ X₀ ∧ 6 ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₃: start(X₀, X₁, X₂, X₃) → lbl151(X₀, 2+X₁, X₂, 1+X₃) :|: X₀ ≤ 29 ∧ X₂ ≤ 5 ∧ 1+X₂ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₁: start(X₀, X₁, X₂, X₃) → lbl171(X₀, X₁-10, X₂, 2+X₃) :|: X₀ ≤ 29 ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₀: start(X₀, X₁, X₂, X₃) → stop(X₀, X₁, X₂, X₃) :|: 30 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₁₁: start0(X₀, X₁, X₂, X₃) → start(X₀, X₂, X₂, X₀)

Preprocessing

Found invariant X₁ ≤ 5+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₀ ≤ 29 for location lbl151

Found invariant 30 ≤ X₃ ∧ X₀ ≤ X₃ for location stop

Found invariant X₃ ≤ 12+X₁ ∧ 2+X₀ ≤ X₃ ∧ X₀ ≤ 10+X₁ ∧ X₀ ≤ 29 for location lbl171

Found invariant X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂ for location start

Problem after Preprocessing

Start: start0
Program_Vars: X₀, X₁, X₂, X₃
Temp_Vars:
Locations: lbl151, lbl171, start, start0, stop
Transitions:
t₉: lbl151(X₀, X₁, X₂, X₃) → lbl151(X₀, 7+X₁, X₂, 1+X₃) :|: 140⋅X₀+28⋅X₂+56⋅X₃ ≤ 5719+23⋅X₁ ∧ 35⋅X₀+7⋅X₂+14⋅X₃ ≤ 1561+2⋅X₁ ∧ 5⋅X₀+X₂+2⋅X₃ ≤ 203+X₁ ∧ X₀ ≤ 29 ∧ X₁ ≤ 5+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 6 ≤ X₁ ∧ 7+5⋅X₀+X₂ ≤ X₁+5⋅X₃ ∧ 7+5⋅X₀+X₂ ≤ 6⋅X₃ ∧ 161+140⋅X₀+28⋅X₂ ≤ 23⋅X₁+140⋅X₃ ∧ 7⋅X₀+X₁ ≤ X₂+7⋅X₃
t₁₀: lbl151(X₀, X₁, X₂, X₃) → lbl151(X₀, 2+X₁, X₂, 1+X₃) :|: 140⋅X₀+28⋅X₂+56⋅X₃ ≤ 5719+23⋅X₁ ∧ 35⋅X₀+7⋅X₂+14⋅X₃ ≤ 1561+2⋅X₁ ∧ 5⋅X₀+X₂+2⋅X₃ ≤ 203+X₁ ∧ X₀ ≤ 29 ∧ X₁ ≤ 5 ∧ X₁ ≤ 5+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 7+5⋅X₀+X₂ ≤ X₁+5⋅X₃ ∧ 7+5⋅X₀+X₂ ≤ 6⋅X₃ ∧ 161+140⋅X₀+28⋅X₂ ≤ 23⋅X₁+140⋅X₃ ∧ 7⋅X₀+X₁ ≤ X₂+7⋅X₃
t₈: lbl151(X₀, X₁, X₂, X₃) → lbl171(X₀, X₁-10, X₂, 2+X₃) :|: 140⋅X₀+28⋅X₂+56⋅X₃ ≤ 5719+23⋅X₁ ∧ 35⋅X₀+7⋅X₂+14⋅X₃ ≤ 1561+2⋅X₁ ∧ 5⋅X₀+X₂+2⋅X₃ ≤ 203+X₁ ∧ X₀ ≤ 29 ∧ X₁ ≤ 5+X₃ ∧ 1+X₀ ≤ X₃ ∧ 7+5⋅X₀+X₂ ≤ X₁+5⋅X₃ ∧ 7+5⋅X₀+X₂ ≤ 6⋅X₃ ∧ 161+140⋅X₀+28⋅X₂ ≤ 23⋅X₁+140⋅X₃ ∧ 7⋅X₀+X₁ ≤ X₂+7⋅X₃ ∧ X₃ ≤ X₁
t₆: lbl171(X₀, X₁, X₂, X₃) → lbl151(X₀, 7+X₁, X₂, 1+X₃) :|: 35⋅X₀+7⋅X₂+19⋅X₃ ≤ 1674+7⋅X₁ ∧ X₀ ≤ 29 ∧ X₃ ≤ 29 ∧ X₃ ≤ 12+X₁ ∧ 1+X₁ ≤ X₃ ∧ 6 ≤ X₁ ∧ 24+7⋅X₀+X₁ ≤ X₂+7⋅X₃ ∧ 5⋅X₀+X₂ ≤ X₁+5⋅X₃ ∧ X₀ ≤ 10+X₁ ∧ 2+X₀ ≤ X₃
t₇: lbl171(X₀, X₁, X₂, X₃) → lbl151(X₀, 2+X₁, X₂, 1+X₃) :|: 35⋅X₀+7⋅X₂+19⋅X₃ ≤ 1674+7⋅X₁ ∧ X₀ ≤ 29 ∧ X₃ ≤ 29 ∧ X₃ ≤ 12+X₁ ∧ X₁ ≤ 5 ∧ 1+X₁ ≤ X₃ ∧ 24+7⋅X₀+X₁ ≤ X₂+7⋅X₃ ∧ 5⋅X₀+X₂ ≤ X₁+5⋅X₃ ∧ X₀ ≤ 10+X₁ ∧ 2+X₀ ≤ X₃
t₅: lbl171(X₀, X₁, X₂, X₃) → lbl171(X₀, X₁-10, X₂, 2+X₃) :|: 35⋅X₀+7⋅X₂+19⋅X₃ ≤ 1674+7⋅X₁ ∧ X₀ ≤ 29 ∧ X₃ ≤ 29 ∧ X₃ ≤ 12+X₁ ∧ 24+7⋅X₀+X₁ ≤ X₂+7⋅X₃ ∧ 5⋅X₀+X₂ ≤ X₁+5⋅X₃ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 10+X₁ ∧ 2+X₀ ≤ X₃
t₄: lbl171(X₀, X₁, X₂, X₃) → stop(X₀, X₁, X₂, X₃) :|: 35⋅X₀+7⋅X₂+19⋅X₃ ≤ 1674+7⋅X₁ ∧ X₀ ≤ 29 ∧ X₃ ≤ 12+X₁ ∧ 24+7⋅X₀+X₁ ≤ X₂+7⋅X₃ ∧ 30 ≤ X₃ ∧ 5⋅X₀+X₂ ≤ X₁+5⋅X₃ ∧ X₀ ≤ 10+X₁ ∧ 2+X₀ ≤ X₃
t₂: start(X₀, X₁, X₂, X₃) → lbl151(X₀, 7+X₁, X₂, 1+X₃) :|: X₀ ≤ 29 ∧ 1+X₂ ≤ X₀ ∧ 6 ≤ X₂ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₃: start(X₀, X₁, X₂, X₃) → lbl151(X₀, 2+X₁, X₂, 1+X₃) :|: X₀ ≤ 29 ∧ X₂ ≤ 5 ∧ 1+X₂ ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₁: start(X₀, X₁, X₂, X₃) → lbl171(X₀, X₁-10, X₂, 2+X₃) :|: X₀ ≤ 29 ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₀: start(X₀, X₁, X₂, X₃) → stop(X₀, X₁, X₂, X₃) :|: 30 ≤ X₀ ∧ X₃ ≤ X₀ ∧ X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₁ ≤ X₂
t₁₁: start0(X₀, X₁, X₂, X₃) → start(X₀, X₂, X₂, X₀)

MPRF for transition t₅: lbl171(X₀, X₁, X₂, X₃) → lbl171(X₀, X₁-10, X₂, 2+X₃) :|: 35⋅X₀+7⋅X₂+19⋅X₃ ≤ 1674+7⋅X₁ ∧ X₀ ≤ 29 ∧ X₃ ≤ 29 ∧ X₃ ≤ 12+X₁ ∧ 24+7⋅X₀+X₁ ≤ X₂+7⋅X₃ ∧ 5⋅X₀+X₂ ≤ X₁+5⋅X₃ ∧ X₃ ≤ X₁ ∧ X₀ ≤ 10+X₁ ∧ 2+X₀ ≤ X₃ of depth 1:

new bound:

34⋅X₂+94⋅X₀+3715 {O(n)}

MPRF:

• lbl151: [583+5⋅X₁-35⋅X₃]
• lbl171: [871+29⋅X₁-59⋅X₃]

MPRF for transition t₆: lbl171(X₀, X₁, X₂, X₃) → lbl151(X₀, 7+X₁, X₂, 1+X₃) :|: 35⋅X₀+7⋅X₂+19⋅X₃ ≤ 1674+7⋅X₁ ∧ X₀ ≤ 29 ∧ X₃ ≤ 29 ∧ X₃ ≤ 12+X₁ ∧ 1+X₁ ≤ X₃ ∧ 6 ≤ X₁ ∧ 24+7⋅X₀+X₁ ≤ X₂+7⋅X₃ ∧ 5⋅X₀+X₂ ≤ X₁+5⋅X₃ ∧ X₀ ≤ 10+X₁ ∧ 2+X₀ ≤ X₃ of depth 1:

new bound:

13⋅X₀+X₂+791 {O(n)}

MPRF:

• lbl151: [175+X₁-7⋅X₃]
• lbl171: [175-6⋅X₃]

MPRF for transition t₇: lbl171(X₀, X₁, X₂, X₃) → lbl151(X₀, 2+X₁, X₂, 1+X₃) :|: 35⋅X₀+7⋅X₂+19⋅X₃ ≤ 1674+7⋅X₁ ∧ X₀ ≤ 29 ∧ X₃ ≤ 29 ∧ X₃ ≤ 12+X₁ ∧ X₁ ≤ 5 ∧ 1+X₁ ≤ X₃ ∧ 24+7⋅X₀+X₁ ≤ X₂+7⋅X₃ ∧ 5⋅X₀+X₂ ≤ X₁+5⋅X₃ ∧ X₀ ≤ 10+X₁ ∧ 2+X₀ ≤ X₃ of depth 1:

new bound:

2⋅X₀+119 {O(n)}

MPRF:

• lbl151: [28-X₃]
• lbl171: [30-X₃]

MPRF for transition t₈: lbl151(X₀, X₁, X₂, X₃) → lbl171(X₀, X₁-10, X₂, 2+X₃) :|: 140⋅X₀+28⋅X₂+56⋅X₃ ≤ 5719+23⋅X₁ ∧ 35⋅X₀+7⋅X₂+14⋅X₃ ≤ 1561+2⋅X₁ ∧ 5⋅X₀+X₂+2⋅X₃ ≤ 203+X₁ ∧ X₀ ≤ 29 ∧ X₁ ≤ 5+X₃ ∧ 1+X₀ ≤ X₃ ∧ 7+5⋅X₀+X₂ ≤ X₁+5⋅X₃ ∧ 7+5⋅X₀+X₂ ≤ 6⋅X₃ ∧ 161+140⋅X₀+28⋅X₂ ≤ 23⋅X₁+140⋅X₃ ∧ 7⋅X₀+X₁ ≤ X₂+7⋅X₃ ∧ X₃ ≤ X₁ of depth 1:

new bound:

18⋅X₂+98⋅X₀+6453 {O(n)}

MPRF:

• lbl151: [1562+2⋅X₁-35⋅X₀-7⋅X₂-14⋅X₃]
• lbl171: [1562+2⋅X₁-35⋅X₀-7⋅X₂-14⋅X₃]

MPRF for transition t₉: lbl151(X₀, X₁, X₂, X₃) → lbl151(X₀, 7+X₁, X₂, 1+X₃) :|: 140⋅X₀+28⋅X₂+56⋅X₃ ≤ 5719+23⋅X₁ ∧ 35⋅X₀+7⋅X₂+14⋅X₃ ≤ 1561+2⋅X₁ ∧ 5⋅X₀+X₂+2⋅X₃ ≤ 203+X₁ ∧ X₀ ≤ 29 ∧ X₁ ≤ 5+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 6 ≤ X₁ ∧ 7+5⋅X₀+X₂ ≤ X₁+5⋅X₃ ∧ 7+5⋅X₀+X₂ ≤ 6⋅X₃ ∧ 161+140⋅X₀+28⋅X₂ ≤ 23⋅X₁+140⋅X₃ ∧ 7⋅X₀+X₁ ≤ X₂+7⋅X₃ of depth 1:

new bound:

12⋅X₀+2⋅X₂+814 {O(n)}

MPRF:

• lbl151: [203-5⋅X₀-X₂-X₃]
• lbl171: [202-5⋅X₀-X₂-X₃]

MPRF for transition t₁₀: lbl151(X₀, X₁, X₂, X₃) → lbl151(X₀, 2+X₁, X₂, 1+X₃) :|: 140⋅X₀+28⋅X₂+56⋅X₃ ≤ 5719+23⋅X₁ ∧ 35⋅X₀+7⋅X₂+14⋅X₃ ≤ 1561+2⋅X₁ ∧ 5⋅X₀+X₂+2⋅X₃ ≤ 203+X₁ ∧ X₀ ≤ 29 ∧ X₁ ≤ 5 ∧ X₁ ≤ 5+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₁ ≤ X₃ ∧ 7+5⋅X₀+X₂ ≤ X₁+5⋅X₃ ∧ 7+5⋅X₀+X₂ ≤ 6⋅X₃ ∧ 161+140⋅X₀+28⋅X₂ ≤ 23⋅X₁+140⋅X₃ ∧ 7⋅X₀+X₁ ≤ X₂+7⋅X₃ of depth 1:

new bound:

56⋅X₀+6⋅X₂+3383 {O(n)}

MPRF:

• lbl151: [828-27⋅X₀-3⋅X₂-X₃]
• lbl171: [827-27⋅X₀-3⋅X₂-X₃]

All Bounds

Timebounds

Overall timebound:275⋅X₀+61⋅X₂+15281 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 34⋅X₂+94⋅X₀+3715 {O(n)}
t₆: 13⋅X₀+X₂+791 {O(n)}
t₇: 2⋅X₀+119 {O(n)}
t₈: 18⋅X₂+98⋅X₀+6453 {O(n)}
t₉: 12⋅X₀+2⋅X₂+814 {O(n)}
t₁₀: 56⋅X₀+6⋅X₂+3383 {O(n)}
t₁₁: 1 {O(1)}

Costbounds

Overall costbound: 275⋅X₀+61⋅X₂+15281 {O(n)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₃: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 34⋅X₂+94⋅X₀+3715 {O(n)}
t₆: 13⋅X₀+X₂+791 {O(n)}
t₇: 2⋅X₀+119 {O(n)}
t₈: 18⋅X₂+98⋅X₀+6453 {O(n)}
t₉: 12⋅X₀+2⋅X₂+814 {O(n)}
t₁₀: 56⋅X₀+6⋅X₂+3383 {O(n)}
t₁₁: 1 {O(1)}

Sizebounds

t₀, X₀: X₀ {O(n)}
t₀, X₁: X₂ {O(n)}
t₀, X₂: X₂ {O(n)}
t₀, X₃: X₀ {O(n)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₂+10 {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₀+2 {O(n)}
t₂, X₀: 29 {O(1)}
t₂, X₁: 35 {O(1)}
t₂, X₂: 28 {O(1)}
t₂, X₃: 30 {O(1)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₂+2 {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₀+1 {O(n)}
t₄, X₀: 5⋅X₀+29 {O(n)}
t₄, X₁: 3060⋅X₀+891⋅X₂+151644 {O(n)}
t₄, X₂: 5⋅X₂+28 {O(n)}
t₄, X₃: 180⋅X₂+647⋅X₀+32151 {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: 341⋅X₂+940⋅X₀+37160 {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: 189⋅X₀+68⋅X₂+7432 {O(n)}
t₆, X₀: 3⋅X₀+29 {O(n)}
t₆, X₁: 35 {O(1)}
t₆, X₂: 3⋅X₂+28 {O(n)}
t₆, X₃: 30 {O(1)}
t₇, X₀: 3⋅X₀+29 {O(n)}
t₇, X₁: 2120⋅X₀+549⋅X₂+114474 {O(n)}
t₇, X₂: 3⋅X₂+28 {O(n)}
t₇, X₃: 112⋅X₂+457⋅X₀+24717 {O(n)}
t₈, X₀: 3⋅X₀+29 {O(n)}
t₈, X₁: 2120⋅X₀+549⋅X₂+114474 {O(n)}
t₈, X₂: 3⋅X₂+28 {O(n)}
t₈, X₃: 112⋅X₂+457⋅X₀+24717 {O(n)}
t₉, X₀: 3⋅X₀+29 {O(n)}
t₉, X₁: 2120⋅X₀+549⋅X₂+114474 {O(n)}
t₉, X₂: 3⋅X₂+28 {O(n)}
t₉, X₃: 112⋅X₂+457⋅X₀+24717 {O(n)}
t₁₀, X₀: 3⋅X₀+29 {O(n)}
t₁₀, X₁: 2120⋅X₀+549⋅X₂+114474 {O(n)}
t₁₀, X₂: 3⋅X₂+28 {O(n)}
t₁₀, X₃: 112⋅X₂+457⋅X₀+24717 {O(n)}
t₁₁, X₀: X₀ {O(n)}
t₁₁, X₁: X₂ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₀ {O(n)}