KoAT2 Proof Output

Initial Problem

Preprocessing

Found invariant X₄ ≤ 1+X₃ ∧ X₄ ≤ 1+X₁ ∧ 3 ≤ X₄ ∧ 5 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 2+X₂ ≤ X₄ ∧ 5 ≤ X₁+X₄ ∧ 4 ≤ X₀+X₄ ∧ 2+X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location evalfbb5in

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location evalfreturnin

Found invariant 1 ≤ X₀ for location evalfbb10in

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location evalfbb3in

Found invariant X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location evalfbb6in

Found invariant X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location evalfbb7in

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location evalfstop

Found invariant X₄ ≤ 1+X₃ ∧ X₄ ≤ 1+X₁ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location evalfbb4in

Found invariant X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location evalfbb8in

Problem after Preprocessing

Start: evalfstart
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: evalfbb10in, evalfbb3in, evalfbb4in, evalfbb5in, evalfbb6in, evalfbb7in, evalfbb8in, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
t₂: evalfbb10in(X₀, X₁, X₂, X₃, X₄) → evalfbb8in(X₀, X₁, 1, X₃, X₄) :|: X₀ ≤ X₁ ∧ 1 ≤ X₀
t₃: evalfbb10in(X₀, X₁, X₂, X₃, X₄) → evalfreturnin(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₀
t₁₀: evalfbb3in(X₀, X₁, X₂, X₃, X₄) → evalfbb4in(X₀, X₁, X₂, X₃, 1+X₄) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₃+X₄ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₃
t₈: evalfbb4in(X₀, X₁, X₂, X₃, X₄) → evalfbb3in(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ X₄ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₃+X₄ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁
t₉: evalfbb4in(X₀, X₁, X₂, X₃, X₄) → evalfbb5in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ X₄ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₃+X₄ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁
t₁₁: evalfbb5in(X₀, X₁, X₂, X₃, X₄) → evalfbb6in(X₀, X₁, X₂, 1+X₃, X₄) :|: X₄ ≤ 1+X₁ ∧ X₄ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₃ ≤ X₄ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₄ ∧ 2 ≤ X₁ ∧ 2+X₂ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₂+X₄ ∧ 5 ≤ X₁+X₄ ∧ 5 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁
t₆: evalfbb6in(X₀, X₁, X₂, X₃, X₄) → evalfbb4in(X₀, X₁, X₂, X₃, 1) :|: X₃ ≤ X₁ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁
t₇: evalfbb6in(X₀, X₁, X₂, X₃, X₄) → evalfbb7in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁
t₁₂: evalfbb7in(X₀, X₁, X₂, X₃, X₄) → evalfbb8in(X₀, X₁, 1+X₂, X₃, X₄) :|: X₃ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁
t₅: evalfbb8in(X₀, X₁, X₂, X₃, X₄) → evalfbb10in(1+X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ X₀ ≤ X₁
t₄: evalfbb8in(X₀, X₁, X₂, X₃, X₄) → evalfbb6in(X₀, X₁, X₂, 1+X₀, X₄) :|: X₂ ≤ X₀ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ X₀ ≤ X₁
t₁: evalfentryin(X₀, X₁, X₂, X₃, X₄) → evalfbb10in(1, X₁, X₂, X₃, X₄)
t₁₃: evalfreturnin(X₀, X₁, X₂, X₃, X₄) → evalfstop(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₀ ∧ 1+X₁ ≤ X₀
t₀: evalfstart(X₀, X₁, X₂, X₃, X₄) → evalfentryin(X₀, X₁, X₂, X₃, X₄)

MPRF for transition t₂: evalfbb10in(X₀, X₁, X₂, X₃, X₄) → evalfbb8in(X₀, X₁, 1, X₃, X₄) :|: X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+2 {O(n)}

MPRF:

• evalfbb10in: [1+X₁-X₀]
• evalfbb3in: [X₁-X₀]
• evalfbb4in: [X₁-X₀]
• evalfbb5in: [X₁-X₀]
• evalfbb6in: [X₁-X₀]
• evalfbb7in: [X₃-1-X₀]
• evalfbb8in: [X₁-X₀]

MPRF for transition t₅: evalfbb8in(X₀, X₁, X₂, X₃, X₄) → evalfbb10in(1+X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₁+2 {O(n)}

MPRF:

• evalfbb10in: [1+X₁-X₀]
• evalfbb3in: [1+X₁-X₀]
• evalfbb4in: [1+X₁-X₀]
• evalfbb5in: [1+X₁-X₀]
• evalfbb6in: [1+X₁-X₀]
• evalfbb7in: [X₃-X₀]
• evalfbb8in: [1+X₁-X₀]

MPRF for transition t₄: evalfbb8in(X₀, X₁, X₂, X₃, X₄) → evalfbb6in(X₀, X₁, X₂, 1+X₀, X₄) :|: X₂ ≤ X₀ ∧ X₂ ≤ 1+X₀ ∧ X₂ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ X₀ ≤ X₁ of depth 1:

new bound:

X₁⋅X₁+3⋅X₁ {O(n^2)}

MPRF:

• evalfbb10in: [X₁]
• evalfbb3in: [X₁-X₂]
• evalfbb4in: [X₁-X₂]
• evalfbb5in: [X₁-X₂]
• evalfbb6in: [X₁-X₂]
• evalfbb7in: [X₁-X₂]
• evalfbb8in: [1+X₁-X₂]

MPRF for transition t₇: evalfbb6in(X₀, X₁, X₂, X₃, X₄) → evalfbb7in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₁⋅X₁+5⋅X₁+7 {O(n^2)}

MPRF:

• evalfbb10in: [X₀]
• evalfbb3in: [1+X₀-X₂]
• evalfbb4in: [1+X₀-X₂]
• evalfbb5in: [1+X₀-X₂]
• evalfbb6in: [1+X₀-X₂]
• evalfbb7in: [X₀-X₂]
• evalfbb8in: [1+X₀-X₂]

MPRF for transition t₁₂: evalfbb7in(X₀, X₁, X₂, X₃, X₄) → evalfbb8in(X₀, X₁, 1+X₂, X₃, X₄) :|: X₃ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ of depth 1:

new bound:

X₁⋅X₁+5⋅X₁+7 {O(n^2)}

MPRF:

• evalfbb10in: [X₀]
• evalfbb3in: [1+X₀-X₂]
• evalfbb4in: [1+X₀-X₂]
• evalfbb5in: [1+X₀-X₂]
• evalfbb6in: [1+X₀-X₂]
• evalfbb7in: [1+X₀-X₂]
• evalfbb8in: [1+X₀-X₂]

MPRF for transition t₆: evalfbb6in(X₀, X₁, X₂, X₃, X₄) → evalfbb4in(X₀, X₁, X₂, X₃, 1) :|: X₃ ≤ X₁ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₂+X₃ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₁ of depth 1:

new bound:

2⋅X₁⋅X₁⋅X₁+13⋅X₁⋅X₁+30⋅X₁+22 {O(n^3)}

MPRF:

• evalfbb10in: [X₁-X₀]
• evalfbb3in: [X₁-X₃]
• evalfbb4in: [X₁-X₃]
• evalfbb5in: [X₁-X₃]
• evalfbb6in: [1+X₁-X₃]
• evalfbb7in: [X₁-X₃]
• evalfbb8in: [X₁-X₀]

MPRF for transition t₉: evalfbb4in(X₀, X₁, X₂, X₃, X₄) → evalfbb5in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ X₄ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₃+X₄ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ of depth 1:

new bound:

X₁⋅X₁⋅X₁+5⋅X₁⋅X₁+8⋅X₁ {O(n^3)}

MPRF:

• evalfbb10in: [X₁]
• evalfbb3in: [1+X₁-X₃]
• evalfbb4in: [1+X₁-X₃]
• evalfbb5in: [X₁-X₃]
• evalfbb6in: [1+X₁-X₃]
• evalfbb7in: [X₁-X₃]
• evalfbb8in: [X₁]

MPRF for transition t₁₁: evalfbb5in(X₀, X₁, X₂, X₃, X₄) → evalfbb6in(X₀, X₁, X₂, 1+X₃, X₄) :|: X₄ ≤ 1+X₁ ∧ X₄ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₃ ≤ X₄ ∧ 2 ≤ X₀+X₂ ∧ 2+X₀ ≤ X₄ ∧ 2 ≤ X₁ ∧ 2+X₂ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₂+X₄ ∧ 5 ≤ X₁+X₄ ∧ 5 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ of depth 1:

new bound:

3⋅X₁⋅X₁⋅X₁+18⋅X₁⋅X₁+38⋅X₁+22 {O(n^3)}

MPRF:

• evalfbb10in: [2⋅X₁-X₀]
• evalfbb3in: [2⋅X₁-1-X₃]
• evalfbb4in: [2⋅X₁-1-X₃]
• evalfbb5in: [2⋅X₁-X₄]
• evalfbb6in: [2⋅X₁-1-X₃]
• evalfbb7in: [2⋅X₁-1-X₃]
• evalfbb8in: [2⋅X₁-X₀]

MPRF for transition t₈: evalfbb4in(X₀, X₁, X₂, X₃, X₄) → evalfbb3in(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ X₄ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₃+X₄ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ of depth 1:

new bound:

9⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+108⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+561⋅X₁⋅X₁⋅X₁⋅X₁+1581⋅X₁⋅X₁⋅X₁+2512⋅X₁⋅X₁+2082⋅X₁+682 {O(n^6)}

MPRF:

• evalfbb10in: [2⋅X₁]
• evalfbb3in: [X₃-X₄]
• evalfbb4in: [1+X₃-X₄]
• evalfbb5in: [X₃-X₄]
• evalfbb6in: [X₁+X₃-1]
• evalfbb7in: [X₁+X₃-1]
• evalfbb8in: [2⋅X₁]

MPRF for transition t₁₀: evalfbb3in(X₀, X₁, X₂, X₃, X₄) → evalfbb4in(X₀, X₁, X₂, X₃, 1+X₄) :|: 1 ≤ X₀ ∧ 1+X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₀+X₁ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₃+X₄ ∧ 4 ≤ X₁+X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₄ ≤ X₁ ∧ X₄ ≤ X₃ of depth 1:

new bound:

9⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+108⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+564⋅X₁⋅X₁⋅X₁⋅X₁+1608⋅X₁⋅X₁⋅X₁+2604⋅X₁⋅X₁+2217⋅X₁+748 {O(n^6)}

MPRF:

• evalfbb10in: [X₁]
• evalfbb3in: [X₁+X₃-X₀-X₄]
• evalfbb4in: [X₁+X₃-X₀-X₄]
• evalfbb5in: [X₁+2⋅X₂+X₃-3⋅X₀-X₄]
• evalfbb6in: [X₁+X₃-1-X₀]
• evalfbb7in: [X₃-1]
• evalfbb8in: [X₁]

Cut unsatisfiable transition [t₅: evalfbb8in→evalfbb10in; t₇₆: evalfbb8in→evalfbb10in]

Found invariant X₄ ≤ 1+X₃ ∧ X₄ ≤ 1+X₁ ∧ 3 ≤ X₄ ∧ 5 ≤ X₃+X₄ ∧ 4 ≤ X₂+X₄ ∧ 5 ≤ X₁+X₄ ∧ 4 ≤ X₀+X₄ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location evalfbb4in_v3

Found invariant X₄ ≤ 2 ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₂ ∧ X₄ ≤ X₁ ∧ X₄ ≤ 1+X₀ ∧ 2 ≤ X₄ ∧ 4 ≤ X₃+X₄ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location evalfbb3in_v2

Found invariant X₃ ≤ 1+X₁ ∧ 2 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location evalfbb8in_v1

Found invariant X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₀ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location evalfbb7in_v3

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 3 ≤ X₄ ∧ 6 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 2+X₂ ≤ X₄ ∧ 5 ≤ X₁+X₄ ∧ 4 ≤ X₀+X₄ ∧ 2+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₁ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location evalfbb6in_v2

Found invariant X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location evalfbb7in_v1

Found invariant X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location evalfbb8in

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 3 ≤ X₄ ∧ 6 ≤ X₃+X₄ ∧ 4 ≤ X₂+X₄ ∧ 6 ≤ X₁+X₄ ∧ 4 ≤ X₀+X₄ ∧ X₃ ≤ X₁ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 6 ≤ X₁+X₃ ∧ 4 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location evalfbb3in_v3

Found invariant X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₀ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 4 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 2 ≤ X₀ for location evalfbb6in_v3

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location evalfreturnin

Found invariant 1 ≤ X₀ for location evalfbb10in

Found invariant X₄ ≤ 1 ∧ 1+X₄ ≤ X₃ ∧ X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ X₄ ≤ X₀ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ X₃ ≤ X₁ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location evalfbb3in_v1

Found invariant X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₀ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location evalfbb6in_v1

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location evalfstop

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 3 ≤ X₄ ∧ 6 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 2+X₂ ≤ X₄ ∧ 5 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ 2+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₁ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location evalfbb7in_v2

All Bounds

Timebounds

Overall timebound:18⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+216⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+1125⋅X₁⋅X₁⋅X₁⋅X₁+3195⋅X₁⋅X₁⋅X₁+5155⋅X₁⋅X₁+4390⋅X₁+1496 {O(n^6)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+2 {O(n)}
t₃: 1 {O(1)}
t₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₅: X₁+2 {O(n)}
t₆: 2⋅X₁⋅X₁⋅X₁+13⋅X₁⋅X₁+30⋅X₁+22 {O(n^3)}
t₇: X₁⋅X₁+5⋅X₁+7 {O(n^2)}
t₈: 9⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+108⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+561⋅X₁⋅X₁⋅X₁⋅X₁+1581⋅X₁⋅X₁⋅X₁+2512⋅X₁⋅X₁+2082⋅X₁+682 {O(n^6)}
t₉: X₁⋅X₁⋅X₁+5⋅X₁⋅X₁+8⋅X₁ {O(n^3)}
t₁₀: 9⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+108⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+564⋅X₁⋅X₁⋅X₁⋅X₁+1608⋅X₁⋅X₁⋅X₁+2604⋅X₁⋅X₁+2217⋅X₁+748 {O(n^6)}
t₁₁: 3⋅X₁⋅X₁⋅X₁+18⋅X₁⋅X₁+38⋅X₁+22 {O(n^3)}
t₁₂: X₁⋅X₁+5⋅X₁+7 {O(n^2)}
t₁₃: 1 {O(1)}

Costbounds

Overall costbound: 18⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+216⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+1125⋅X₁⋅X₁⋅X₁⋅X₁+3195⋅X₁⋅X₁⋅X₁+5155⋅X₁⋅X₁+4390⋅X₁+1496 {O(n^6)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+2 {O(n)}
t₃: 1 {O(1)}
t₄: X₁⋅X₁+3⋅X₁ {O(n^2)}
t₅: X₁+2 {O(n)}
t₆: 2⋅X₁⋅X₁⋅X₁+13⋅X₁⋅X₁+30⋅X₁+22 {O(n^3)}
t₇: X₁⋅X₁+5⋅X₁+7 {O(n^2)}
t₈: 9⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+108⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+561⋅X₁⋅X₁⋅X₁⋅X₁+1581⋅X₁⋅X₁⋅X₁+2512⋅X₁⋅X₁+2082⋅X₁+682 {O(n^6)}
t₉: X₁⋅X₁⋅X₁+5⋅X₁⋅X₁+8⋅X₁ {O(n^3)}
t₁₀: 9⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+108⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+564⋅X₁⋅X₁⋅X₁⋅X₁+1608⋅X₁⋅X₁⋅X₁+2604⋅X₁⋅X₁+2217⋅X₁+748 {O(n^6)}
t₁₁: 3⋅X₁⋅X₁⋅X₁+18⋅X₁⋅X₁+38⋅X₁+22 {O(n^3)}
t₁₂: X₁⋅X₁+5⋅X₁+7 {O(n^2)}
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)}
t₀, X₄: X₄ {O(n)}
t₁, X₀: 1 {O(1)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₁+3 {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 1 {O(1)}
t₂, X₃: 3⋅X₁⋅X₁⋅X₁+18⋅X₁⋅X₁+42⋅X₁+X₃+38 {O(n^3)}
t₂, X₄: 9⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+108⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+564⋅X₁⋅X₁⋅X₁⋅X₁+1608⋅X₁⋅X₁⋅X₁+2604⋅X₁⋅X₁+2217⋅X₁+X₄+749 {O(n^6)}
t₃, X₀: X₁+4 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: X₁⋅X₁+5⋅X₁+X₂+8 {O(n^2)}
t₃, X₃: 3⋅X₁⋅X₁⋅X₁+18⋅X₁⋅X₁+42⋅X₁+X₃+38 {O(n^3)}
t₃, X₄: 9⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+108⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+564⋅X₁⋅X₁⋅X₁⋅X₁+1608⋅X₁⋅X₁⋅X₁+2604⋅X₁⋅X₁+2⋅X₄+2217⋅X₁+749 {O(n^6)}
t₄, X₀: X₁+3 {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₁⋅X₁+5⋅X₁+8 {O(n^2)}
t₄, X₃: 2⋅X₁+8 {O(n)}
t₄, X₄: 9⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+108⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+564⋅X₁⋅X₁⋅X₁⋅X₁+1608⋅X₁⋅X₁⋅X₁+2604⋅X₁⋅X₁+2217⋅X₁+X₄+749 {O(n^6)}
t₅, X₀: X₁+3 {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₁⋅X₁+5⋅X₁+8 {O(n^2)}
t₅, X₃: 3⋅X₁⋅X₁⋅X₁+18⋅X₁⋅X₁+42⋅X₁+38 {O(n^3)}
t₅, X₄: 9⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+108⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+564⋅X₁⋅X₁⋅X₁⋅X₁+1608⋅X₁⋅X₁⋅X₁+2604⋅X₁⋅X₁+2217⋅X₁+X₄+749 {O(n^6)}
t₆, X₀: X₁+3 {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₁⋅X₁+5⋅X₁+8 {O(n^2)}
t₆, X₃: 3⋅X₁⋅X₁⋅X₁+18⋅X₁⋅X₁+40⋅X₁+30 {O(n^3)}
t₆, X₄: 1 {O(1)}
t₇, X₀: X₁+3 {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₁⋅X₁+5⋅X₁+8 {O(n^2)}
t₇, X₃: 3⋅X₁⋅X₁⋅X₁+18⋅X₁⋅X₁+42⋅X₁+38 {O(n^3)}
t₇, X₄: 9⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+108⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+564⋅X₁⋅X₁⋅X₁⋅X₁+1608⋅X₁⋅X₁⋅X₁+2604⋅X₁⋅X₁+2217⋅X₁+X₄+749 {O(n^6)}
t₈, X₀: X₁+3 {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₁⋅X₁+5⋅X₁+8 {O(n^2)}
t₈, X₃: 3⋅X₁⋅X₁⋅X₁+18⋅X₁⋅X₁+40⋅X₁+30 {O(n^3)}
t₈, X₄: 9⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+108⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+564⋅X₁⋅X₁⋅X₁⋅X₁+1608⋅X₁⋅X₁⋅X₁+2604⋅X₁⋅X₁+2217⋅X₁+749 {O(n^6)}
t₉, X₀: X₁+3 {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₁⋅X₁+5⋅X₁+8 {O(n^2)}
t₉, X₃: 3⋅X₁⋅X₁⋅X₁+18⋅X₁⋅X₁+40⋅X₁+30 {O(n^3)}
t₉, X₄: 9⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+108⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+564⋅X₁⋅X₁⋅X₁⋅X₁+1608⋅X₁⋅X₁⋅X₁+2604⋅X₁⋅X₁+2217⋅X₁+749 {O(n^6)}
t₁₀, X₀: X₁+3 {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: X₁⋅X₁+5⋅X₁+8 {O(n^2)}
t₁₀, X₃: 3⋅X₁⋅X₁⋅X₁+18⋅X₁⋅X₁+40⋅X₁+30 {O(n^3)}
t₁₀, X₄: 9⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+108⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+564⋅X₁⋅X₁⋅X₁⋅X₁+1608⋅X₁⋅X₁⋅X₁+2604⋅X₁⋅X₁+2217⋅X₁+749 {O(n^6)}
t₁₁, X₀: X₁+3 {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₁⋅X₁+5⋅X₁+8 {O(n^2)}
t₁₁, X₃: 3⋅X₁⋅X₁⋅X₁+18⋅X₁⋅X₁+40⋅X₁+30 {O(n^3)}
t₁₁, X₄: 9⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+108⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+564⋅X₁⋅X₁⋅X₁⋅X₁+1608⋅X₁⋅X₁⋅X₁+2604⋅X₁⋅X₁+2217⋅X₁+749 {O(n^6)}
t₁₂, X₀: X₁+3 {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₁⋅X₁+5⋅X₁+8 {O(n^2)}
t₁₂, X₃: 3⋅X₁⋅X₁⋅X₁+18⋅X₁⋅X₁+42⋅X₁+38 {O(n^3)}
t₁₂, X₄: 9⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+108⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+564⋅X₁⋅X₁⋅X₁⋅X₁+1608⋅X₁⋅X₁⋅X₁+2604⋅X₁⋅X₁+2217⋅X₁+X₄+749 {O(n^6)}
t₁₃, X₀: X₁+4 {O(n)}
t₁₃, X₁: 2⋅X₁ {O(n)}
t₁₃, X₂: X₁⋅X₁+5⋅X₁+X₂+8 {O(n^2)}
t₁₃, X₃: 3⋅X₁⋅X₁⋅X₁+18⋅X₁⋅X₁+42⋅X₁+X₃+38 {O(n^3)}
t₁₃, X₄: 9⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+108⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+564⋅X₁⋅X₁⋅X₁⋅X₁+1608⋅X₁⋅X₁⋅X₁+2604⋅X₁⋅X₁+2⋅X₄+2217⋅X₁+749 {O(n^6)}