KoAT2 Proof Output

Initial Problem

Preprocessing

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

Found invariant X₁ ≤ 0 for location evalfreturnin

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

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

Found invariant 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalfbb7in

Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ for location evalfbb9in

Found invariant X₁ ≤ 0 for location evalfstop

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

Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ 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, evalfbb9in, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
t₂: evalfbb10in(X₀, X₁, X₂, X₃, X₄) → evalfbb8in(X₀, X₁, 1, X₃, X₄) :|: 1 ≤ X₁
t₃: evalfbb10in(X₀, X₁, X₂, X₃, X₄) → evalfreturnin(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 0
t₁₀: evalfbb3in(X₀, X₁, X₂, X₃, X₄) → evalfbb4in(X₀, X₁, X₂, X₃, 1+X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₃
t₈: evalfbb4in(X₀, X₁, X₂, X₃, X₄) → evalfbb3in(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₃ ∧ X₄ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₃
t₉: evalfbb4in(X₀, X₁, X₂, X₃, X₄) → evalfbb5in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ X₄ ∧ X₄ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₃
t₁₁: evalfbb5in(X₀, X₁, X₂, X₃, X₄) → evalfbb6in(X₀, X₁, X₂, 1+X₃, X₄) :|: X₄ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₃
t₆: evalfbb6in(X₀, X₁, X₂, X₃, X₄) → evalfbb4in(X₀, X₁, X₂, X₃, 1) :|: X₃ ≤ X₁+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₃
t₇: evalfbb6in(X₀, X₁, X₂, X₃, X₄) → evalfbb7in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁+X₂ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₃
t₁₂: evalfbb7in(X₀, X₁, X₂, X₃, X₄) → evalfbb8in(X₀, X₁, 1+X₂, X₃, X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₃ ∧ 2+X₂ ≤ X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₀
t₄: evalfbb8in(X₀, X₁, X₂, X₃, X₄) → evalfbb6in(X₀, X₁, X₂, X₁, X₄) :|: X₂ ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂
t₅: evalfbb8in(X₀, X₁, X₂, X₃, X₄) → evalfbb9in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂
t₁₃: evalfbb9in(X₀, X₁, X₂, X₃, X₄) → evalfbb10in(X₀, X₁-1, X₂, X₃, X₄) :|: 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂
t₁: evalfentryin(X₀, X₁, X₂, X₃, X₄) → evalfbb10in(X₁, X₀, X₂, X₃, X₄)
t₁₄: evalfreturnin(X₀, X₁, X₂, X₃, X₄) → evalfstop(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 0
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) :|: 1 ≤ X₁ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

• evalfbb10in: [X₁]
• evalfbb3in: [X₁-1]
• evalfbb4in: [X₁-1]
• evalfbb5in: [X₁-1]
• evalfbb6in: [X₁-1]
• evalfbb7in: [X₁-1]
• evalfbb8in: [X₁-1]
• evalfbb9in: [X₁-1]

MPRF for transition t₅: evalfbb8in(X₀, X₁, X₂, X₃, X₄) → evalfbb9in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

• evalfbb10in: [1+X₁]
• evalfbb3in: [1+X₁]
• evalfbb4in: [1+X₁]
• evalfbb5in: [X₁+X₄-X₃]
• evalfbb6in: [1+X₁]
• evalfbb7in: [1+X₁]
• evalfbb8in: [1+X₁]
• evalfbb9in: [X₁]

MPRF for transition t₁₃: evalfbb9in(X₀, X₁, X₂, X₃, X₄) → evalfbb10in(X₀, X₁-1, X₂, X₃, X₄) :|: 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ of depth 1:

new bound:

X₀ {O(n)}

MPRF:

• evalfbb10in: [X₁]
• evalfbb3in: [X₁]
• evalfbb4in: [X₁]
• evalfbb5in: [X₁]
• evalfbb6in: [X₁]
• evalfbb7in: [X₁]
• evalfbb8in: [X₁]
• evalfbb9in: [X₁]

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

new bound:

X₀⋅X₁+X₁ {O(n^2)}

MPRF:

• evalfbb10in: [X₀]
• evalfbb3in: [X₀-X₂]
• evalfbb4in: [X₀-X₂]
• evalfbb5in: [X₀-X₂]
• evalfbb6in: [X₀-X₂]
• evalfbb7in: [X₀-X₂]
• evalfbb8in: [1+X₀-X₂]
• evalfbb9in: [X₀-X₂]

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

new bound:

X₀⋅X₁+X₁ {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]
• evalfbb9in: [X₀-X₂]

MPRF for transition t₁₂: evalfbb7in(X₀, X₁, X₂, X₃, X₄) → evalfbb8in(X₀, X₁, 1+X₂, X₃, X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₃ ∧ 2+X₂ ≤ X₃ ∧ 3 ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₂+X₃ ∧ X₂ ≤ X₀ of depth 1:

new bound:

2⋅X₀⋅X₁+2⋅X₁ {O(n^2)}

MPRF:

• evalfbb10in: [2⋅X₀]
• evalfbb3in: [2⋅X₀-X₂]
• evalfbb4in: [2⋅X₀-X₂]
• evalfbb5in: [2⋅X₀-X₂]
• evalfbb6in: [2⋅X₀-X₂]
• evalfbb7in: [2⋅X₀-X₂]
• evalfbb8in: [2⋅X₀-X₂]
• evalfbb9in: [2⋅X₀-X₂]

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

new bound:

4⋅X₀⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₁⋅X₁+4⋅X₁⋅X₁+6⋅X₀⋅X₁+4⋅X₁+X₀+2 {O(n^4)}

MPRF:

• evalfbb10in: [2+X₁]
• evalfbb3in: [X₁+X₂-X₃]
• evalfbb4in: [X₁+X₂-X₃]
• evalfbb5in: [X₁+X₂-X₃]
• evalfbb6in: [1+X₁+X₂-X₃]
• evalfbb7in: [X₁+X₂-X₃]
• evalfbb8in: [1+X₁+X₂]
• evalfbb9in: [X₁+X₂]

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

new bound:

4⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+6⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₁⋅X₁⋅X₁+14⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀⋅X₁+4⋅X₁⋅X₁⋅X₁+7⋅X₀⋅X₁+8⋅X₁⋅X₁+7⋅X₁+X₀+2 {O(n^5)}

MPRF:

• evalfbb10in: [X₀]
• evalfbb3in: [1+X₀]
• evalfbb4in: [1+X₀]
• evalfbb5in: [X₀]
• evalfbb6in: [X₀]
• evalfbb7in: [X₀]
• evalfbb8in: [X₀]
• evalfbb9in: [X₀]

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

new bound:

4⋅X₀⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₁⋅X₁+4⋅X₁⋅X₁+6⋅X₀⋅X₁+4⋅X₁+X₀+2 {O(n^4)}

MPRF:

• evalfbb10in: [0]
• evalfbb3in: [1]
• evalfbb4in: [1]
• evalfbb5in: [1]
• evalfbb6in: [0]
• evalfbb7in: [0]
• evalfbb8in: [0]
• evalfbb9in: [0]

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

new bound:

32⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+128⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+32⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+160⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+192⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+128⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+288⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+84⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+18⋅X₀⋅X₀⋅X₀⋅X₁+208⋅X₀⋅X₀⋅X₁⋅X₁+224⋅X₀⋅X₁⋅X₁⋅X₁+32⋅X₁⋅X₁⋅X₁⋅X₁+196⋅X₀⋅X₁⋅X₁+64⋅X₁⋅X₁⋅X₁+70⋅X₀⋅X₀⋅X₁+64⋅X₁⋅X₁+7⋅X₀⋅X₀+84⋅X₀⋅X₁+19⋅X₀+32⋅X₁+8 {O(n^8)}

MPRF:

• evalfbb10in: [X₁]
• evalfbb3in: [2⋅X₃-X₁-X₄]
• evalfbb4in: [1+2⋅X₃-X₁-X₄]
• evalfbb5in: [2⋅X₃-X₁-X₄]
• evalfbb6in: [2⋅X₃-X₁]
• evalfbb7in: [X₁]
• evalfbb8in: [X₁]
• evalfbb9in: [X₁]

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

new bound:

16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+64⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+4⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+80⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+96⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+148⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+40⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+64⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+102⋅X₀⋅X₀⋅X₁⋅X₁+120⋅X₀⋅X₁⋅X₁⋅X₁+16⋅X₁⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₁+102⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₀⋅X₁+36⋅X₁⋅X₁⋅X₁+3⋅X₀⋅X₀+36⋅X₁⋅X₁+41⋅X₀⋅X₁+19⋅X₁+9⋅X₀+4 {O(n^8)}

MPRF:

• evalfbb10in: [X₀+X₁]
• evalfbb3in: [1+2⋅X₃-X₁-X₄]
• evalfbb4in: [1+2⋅X₃-X₁-X₄]
• evalfbb5in: [2⋅X₃-X₁-X₄]
• evalfbb6in: [X₀+X₃]
• evalfbb7in: [X₀+X₃]
• evalfbb8in: [X₀+X₁]
• evalfbb9in: [X₀+X₁]

Found invariant X₁ ≤ 0 for location evalfreturnin

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

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

Found invariant X₄ ≤ 1+X₃ ∧ 2 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₀+X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ X₁ ≤ X₃ ∧ 2 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalfbb4in_v2

Found invariant X₄ ≤ X₃ ∧ 3 ≤ X₄ ∧ 6 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 5 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalfbb8in_v1

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

Found invariant X₄ ≤ X₃ ∧ 3 ≤ X₄ ∧ 6 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 4 ≤ X₂+X₄ ∧ 2+X₂ ≤ X₄ ∧ 4 ≤ X₁+X₄ ∧ 2+X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ 3 ≤ X₃ ∧ 4 ≤ X₂+X₃ ∧ 2+X₂ ≤ X₃ ∧ 4 ≤ X₁+X₃ ∧ 2+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location evalfbb7in_v1

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

Found invariant 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ for location evalfbb9in

Found invariant X₁ ≤ 0 for location evalfstop

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

Analysing control-flow refined program

knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₈₁: evalfbb8in(X₀, X₁, X₂, X₃, X₄) → evalfbb9in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₂ ≤ X₁

knowledge_propagation leads to new time bound X₀ {O(n)} for transition t₈₂: evalfbb8in(X₀, X₁, X₂, X₃, X₄) → evalfbb6in_v1(X₀, X₁, X₂, X₁, X₄) :|: X₂ ≤ X₀ ∧ X₂ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₂ ≤ X₁

MPRF for transition t₈₃: evalfbb6in_v1(X₀, X₁, X₂, X₃, X₄) → evalfbb4in_v1(X₀, X₁, X₂, X₃, 1) :|: X₃ ≤ X₁+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃ of depth 1:

new bound:

X₀⋅X₁+2⋅X₀ {O(n^2)}

MPRF:

• evalfbb10in: [0]
• evalfbb3in_v1: [X₀-X₂]
• evalfbb3in_v2: [X₀-X₂]
• evalfbb4in_v1: [X₀-X₂]
• evalfbb4in_v2: [X₀-X₂]
• evalfbb5in_v1: [X₀-X₂]
• evalfbb6in_v1: [1+X₀-X₂]
• evalfbb6in_v2: [X₀-X₂]
• evalfbb7in_v1: [X₀-X₂]
• evalfbb8in: [0]
• evalfbb8in_v1: [1+X₀-X₂]
• evalfbb9in: [0]

MPRF for transition t₉₀: evalfbb6in_v2(X₀, X₁, X₂, X₃, X₄) → evalfbb7in_v1(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁+X₂ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ of depth 1:

new bound:

X₀⋅X₁+2⋅X₀ {O(n^2)}

MPRF:

• evalfbb10in: [0]
• evalfbb3in_v1: [1+X₀-X₂]
• evalfbb3in_v2: [1+X₀-X₂]
• evalfbb4in_v1: [1+X₀-X₂]
• evalfbb4in_v2: [1+X₀-X₂]
• evalfbb5in_v1: [1+X₀-X₂]
• evalfbb6in_v1: [1+X₀-X₂]
• evalfbb6in_v2: [1+X₀-X₂]
• evalfbb7in_v1: [X₀-X₂]
• evalfbb8in: [0]
• evalfbb8in_v1: [1+X₀-X₂]
• evalfbb9in: [0]

MPRF for transition t₉₂: evalfbb7in_v1(X₀, X₁, X₂, X₃, X₄) → evalfbb8in_v1(X₀, X₁, 1+X₂, X₃, X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₃ ∧ 2+X₁ ≤ X₄ ∧ 2+X₂ ≤ X₃ ∧ 2+X₂ ≤ X₄ ∧ 3 ≤ X₃ ∧ 3 ≤ X₄ ∧ 4 ≤ X₀+X₃ ∧ 4 ≤ X₀+X₄ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₁+X₄ ∧ 4 ≤ X₂+X₃ ∧ 4 ≤ X₂+X₄ ∧ 6 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ of depth 1:

new bound:

X₀⋅X₁+2⋅X₀ {O(n^2)}

MPRF:

• evalfbb10in: [0]
• evalfbb3in_v1: [1+X₀-X₂]
• evalfbb3in_v2: [1+X₀-X₂]
• evalfbb4in_v1: [1+X₀-X₂]
• evalfbb4in_v2: [1+X₀-X₂]
• evalfbb5in_v1: [1+X₀-X₂]
• evalfbb6in_v1: [1+X₀-X₂]
• evalfbb6in_v2: [1+X₀-X₂]
• evalfbb7in_v1: [1+X₀-X₂]
• evalfbb8in: [0]
• evalfbb8in_v1: [1+X₀-X₂]
• evalfbb9in: [0]

MPRF for transition t₉₃: evalfbb8in_v1(X₀, X₁, X₂, X₃, X₄) → evalfbb9in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₃ ∧ 2+X₁ ≤ X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₃ ∧ 3 ≤ X₄ ∧ 4 ≤ X₀+X₃ ∧ 4 ≤ X₀+X₄ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₁+X₄ ∧ 5 ≤ X₂+X₃ ∧ 5 ≤ X₂+X₄ ∧ 6 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ of depth 1:

new bound:

X₀+1 {O(n)}

MPRF:

• evalfbb10in: [1+X₁]
• evalfbb3in_v1: [1+X₁]
• evalfbb3in_v2: [1+X₁]
• evalfbb4in_v1: [1+X₁]
• evalfbb4in_v2: [1+X₁]
• evalfbb5in_v1: [1+X₁]
• evalfbb6in_v1: [1+X₁]
• evalfbb6in_v2: [1+X₁]
• evalfbb7in_v1: [1+X₁]
• evalfbb8in: [X₁+X₂]
• evalfbb8in_v1: [1+X₁]
• evalfbb9in: [X₁]

MPRF for transition t₉₄: evalfbb8in_v1(X₀, X₁, X₂, X₃, X₄) → evalfbb6in_v1(X₀, X₁, X₂, X₁, X₄) :|: X₂ ≤ X₀ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₃ ∧ 2+X₁ ≤ X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₃ ∧ 3 ≤ X₄ ∧ 4 ≤ X₀+X₃ ∧ 4 ≤ X₀+X₄ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₁+X₄ ∧ 5 ≤ X₂+X₃ ∧ 5 ≤ X₂+X₄ ∧ 6 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ of depth 1:

new bound:

X₀⋅X₁+X₀ {O(n^2)}

MPRF:

• evalfbb10in: [0]
• evalfbb3in_v1: [X₀-X₂]
• evalfbb3in_v2: [X₀-X₂]
• evalfbb4in_v1: [X₀-X₂]
• evalfbb4in_v2: [X₀-X₂]
• evalfbb5in_v1: [X₀-X₂]
• evalfbb6in_v1: [X₀-X₂]
• evalfbb6in_v2: [X₀-X₂]
• evalfbb7in_v1: [X₀-X₂]
• evalfbb8in: [0]
• evalfbb8in_v1: [1+X₀-X₂]
• evalfbb9in: [0]

MPRF for transition t₈₄: evalfbb4in_v1(X₀, X₁, X₂, X₃, X₄) → evalfbb3in_v1(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₃ ∧ X₄ ≤ 1+X₃ ∧ X₄ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁+X₂ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₂ of depth 1:

new bound:

2⋅X₀⋅X₀⋅X₁+X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+3⋅X₀⋅X₁+2⋅X₀+2⋅X₁+2 {O(n^3)}

MPRF:

• evalfbb10in: [1+X₀]
• evalfbb3in_v1: [X₀+X₁-X₃]
• evalfbb3in_v2: [X₀+X₁-X₃]
• evalfbb4in_v1: [1+X₀+X₁-X₃]
• evalfbb4in_v2: [X₀+X₁-X₃]
• evalfbb5in_v1: [1+X₀+X₁-X₄]
• evalfbb6in_v1: [1+X₀+X₁-X₃]
• evalfbb6in_v2: [1+X₀+X₁-X₄]
• evalfbb7in_v1: [X₀+X₁-X₄]
• evalfbb8in: [1+X₀]
• evalfbb8in_v1: [X₀+X₁-X₄]
• evalfbb9in: [1+X₀]

MPRF for transition t₈₅: evalfbb3in_v1(X₀, X₁, X₂, X₃, X₄) → evalfbb4in_v2(X₀, X₁, X₂, X₃, 1+X₄) :|: X₄ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁+X₂ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₃ of depth 1:

new bound:

X₀⋅X₀⋅X₁⋅X₁+5⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁+4⋅X₀⋅X₀+4⋅X₀+4 {O(n^4)}

MPRF:

• evalfbb10in: [2]
• evalfbb3in_v1: [1+X₁+X₂-X₃]
• evalfbb3in_v2: [X₁+X₂-X₃]
• evalfbb4in_v1: [1+X₁+X₂-X₃]
• evalfbb4in_v2: [X₁+X₂-X₃]
• evalfbb5in_v1: [1+X₁+X₂-X₄]
• evalfbb6in_v1: [1+X₁+X₂-X₃]
• evalfbb6in_v2: [1+X₁+X₂+X₃-2⋅X₄]
• evalfbb7in_v1: [1+X₁+X₂-X₄]
• evalfbb8in: [2]
• evalfbb8in_v1: [X₁+X₂-X₄]
• evalfbb9in: [2]

MPRF for transition t₈₆: evalfbb4in_v2(X₀, X₁, X₂, X₃, X₄) → evalfbb5in_v1(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ X₄ ∧ X₄ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁+X₂ ∧ X₁ ≤ X₃ of depth 1:

new bound:

X₀⋅X₀⋅X₁+X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₁+5⋅X₀+3 {O(n^3)}

MPRF:

• evalfbb10in: [2+X₀+X₁]
• evalfbb3in_v1: [3+X₀+X₁-X₃]
• evalfbb3in_v2: [3+X₀+X₁-X₃]
• evalfbb4in_v1: [3+X₀+X₁-X₃]
• evalfbb4in_v2: [3+X₀+X₁-X₃]
• evalfbb5in_v1: [3+X₀+X₁-X₄]
• evalfbb6in_v1: [2+X₀+X₁]
• evalfbb6in_v2: [3+X₀+X₁-X₄]
• evalfbb7in_v1: [X₀+X₁-X₄]
• evalfbb8in: [2+X₀+X₁]
• evalfbb8in_v1: [X₀+X₁-X₄]
• evalfbb9in: [1+X₀+X₁]

MPRF for transition t₈₉: evalfbb5in_v1(X₀, X₁, X₂, X₃, X₄) → evalfbb6in_v2(X₀, X₁, X₂, 1+X₃, X₄) :|: X₄ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁+X₂ ∧ X₁ ≤ X₃ of depth 1:

new bound:

2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+4⋅X₁ {O(n^3)}

MPRF:

• evalfbb10in: [2⋅X₀]
• evalfbb3in_v1: [2⋅X₀+X₁-X₃]
• evalfbb3in_v2: [2⋅X₀+X₁-X₃]
• evalfbb4in_v1: [2⋅X₀+X₁-X₃]
• evalfbb4in_v2: [2⋅X₀+X₁-X₃]
• evalfbb5in_v1: [2⋅X₀+X₁-X₃]
• evalfbb6in_v1: [2⋅X₀+X₁-X₃]
• evalfbb6in_v2: [2⋅X₀+X₁-X₃]
• evalfbb7in_v1: [2⋅X₀+X₁-X₃]
• evalfbb8in: [2⋅X₀]
• evalfbb8in_v1: [2⋅X₀+X₁-X₃]
• evalfbb9in: [2⋅X₀]

MPRF for transition t₉₁: evalfbb6in_v2(X₀, X₁, X₂, X₃, X₄) → evalfbb4in_v1(X₀, X₁, X₂, X₃, 1) :|: X₃ ≤ X₁+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄ of depth 1:

new bound:

X₀⋅X₀⋅X₁⋅X₁+4⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁+4⋅X₀⋅X₀+4⋅X₀+2 {O(n^4)}

MPRF:

• evalfbb10in: [1]
• evalfbb3in_v1: [X₁+X₂-X₃]
• evalfbb3in_v2: [X₁+X₂-X₃]
• evalfbb4in_v1: [X₁+X₂-X₃]
• evalfbb4in_v2: [X₁+X₂-X₃]
• evalfbb5in_v1: [X₁+X₂-X₃]
• evalfbb6in_v1: [X₂]
• evalfbb6in_v2: [1+X₁+X₂+X₄-2⋅X₃]
• evalfbb7in_v1: [X₁+X₂+X₄-2⋅X₃]
• evalfbb8in: [1]
• evalfbb8in_v1: [X₁+X₂+X₄-1-2⋅X₃]
• evalfbb9in: [X₂]

knowledge_propagation leads to new time bound 2⋅X₀⋅X₀⋅X₁+X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+3⋅X₀⋅X₁+2⋅X₀+2⋅X₁+2 {O(n^3)} for transition t₈₅: evalfbb3in_v1(X₀, X₁, X₂, X₃, X₄) → evalfbb4in_v2(X₀, X₁, X₂, X₃, 1+X₄) :|: X₄ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁+X₂ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₃

knowledge_propagation leads to new time bound 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+4⋅X₁ {O(n^3)} for transition t₉₁: evalfbb6in_v2(X₀, X₁, X₂, X₃, X₄) → evalfbb4in_v1(X₀, X₁, X₂, X₃, 1) :|: X₃ ≤ X₁+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄

MPRF for transition t₈₇: evalfbb4in_v2(X₀, X₁, X₂, X₃, X₄) → evalfbb3in_v2(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₃ ∧ X₄ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁+X₂ ∧ X₁ ≤ X₃ of depth 1:

new bound:

4⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+4⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+24⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+16⋅X₀⋅X₁⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁+4⋅X₀⋅X₀⋅X₀⋅X₀+27⋅X₀⋅X₀⋅X₁+34⋅X₀⋅X₁⋅X₁+4⋅X₀⋅X₀⋅X₀+12⋅X₀⋅X₁+16⋅X₁⋅X₁+4⋅X₀⋅X₀+2⋅X₀+4⋅X₁ {O(n^6)}

MPRF:

• evalfbb10in: [X₁]
• evalfbb3in_v1: [X₃-X₄]
• evalfbb3in_v2: [X₃-X₄]
• evalfbb4in_v1: [X₃-X₄]
• evalfbb4in_v2: [1+X₃-X₄]
• evalfbb5in_v1: [1+X₃-X₄]
• evalfbb6in_v1: [X₁]
• evalfbb6in_v2: [0]
• evalfbb7in_v1: [0]
• evalfbb8in: [X₁]
• evalfbb8in_v1: [0]
• evalfbb9in: [X₁]

MPRF for transition t₈₈: evalfbb3in_v2(X₀, X₁, X₂, X₃, X₄) → evalfbb4in_v2(X₀, X₁, X₂, X₃, 1+X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁+X₂ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₃ of depth 1:

new bound:

16⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+52⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₁⋅X₁⋅X₁+56⋅X₀⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀+94⋅X₀⋅X₀⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀+78⋅X₀⋅X₁⋅X₁+88⋅X₀⋅X₀⋅X₁+20⋅X₀⋅X₀+32⋅X₁⋅X₁+54⋅X₀⋅X₁+12⋅X₁+14⋅X₀ {O(n^6)}

MPRF:

• evalfbb10in: [6⋅X₁]
• evalfbb3in_v1: [2⋅X₁+2⋅X₂+2⋅X₃-X₄]
• evalfbb3in_v2: [2⋅X₁+2⋅X₂+2⋅X₃-2-X₄]
• evalfbb4in_v1: [2⋅X₁+2⋅X₂+2⋅X₃-X₄]
• evalfbb4in_v2: [2⋅X₁+2⋅X₂+2⋅X₃-2-X₄]
• evalfbb5in_v1: [2⋅X₁+2⋅X₂+2⋅X₃-2-X₄]
• evalfbb6in_v1: [2⋅X₁+2⋅X₂+2⋅X₃]
• evalfbb6in_v2: [2⋅X₁+2⋅X₂+2⋅X₃-4-X₄]
• evalfbb7in_v1: [3⋅X₁+3⋅X₂+X₃-3-X₄]
• evalfbb8in: [6⋅X₁]
• evalfbb8in_v1: [3⋅X₁+3⋅X₂+X₃-6-X₄]
• evalfbb9in: [6⋅X₁]

CFR: Improvement to new bound with the following program:

method: PartialEvaluation new bound:

O(n^6)

cfr-program:

Start: evalfstart
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: evalfbb10in, evalfbb3in_v1, evalfbb3in_v2, evalfbb4in_v1, evalfbb4in_v2, evalfbb5in_v1, evalfbb6in_v1, evalfbb6in_v2, evalfbb7in_v1, evalfbb8in, evalfbb8in_v1, evalfbb9in, evalfentryin, evalfreturnin, evalfstart, evalfstop
Transitions:
t₂: evalfbb10in(X₀, X₁, X₂, X₃, X₄) → evalfbb8in(X₀, X₁, 1, X₃, X₄) :|: 1 ≤ X₁
t₃: evalfbb10in(X₀, X₁, X₂, X₃, X₄) → evalfreturnin(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 0
t₈₅: evalfbb3in_v1(X₀, X₁, X₂, X₃, X₄) → evalfbb4in_v2(X₀, X₁, X₂, X₃, 1+X₄) :|: X₄ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁+X₂ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₂ ∧ X₄ ≤ X₃
t₈₈: evalfbb3in_v2(X₀, X₁, X₂, X₃, X₄) → evalfbb4in_v2(X₀, X₁, X₂, X₃, 1+X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁+X₂ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₃
t₈₄: evalfbb4in_v1(X₀, X₁, X₂, X₃, X₄) → evalfbb3in_v1(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₃ ∧ X₄ ≤ 1+X₃ ∧ X₄ ≤ 1 ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₀ ∧ X₃ ≤ X₁+X₂ ∧ X₄ ≤ X₁ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₂
t₈₇: evalfbb4in_v2(X₀, X₁, X₂, X₃, X₄) → evalfbb3in_v2(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₃ ∧ X₄ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁+X₂ ∧ X₁ ≤ X₃
t₈₆: evalfbb4in_v2(X₀, X₁, X₂, X₃, X₄) → evalfbb5in_v1(X₀, X₁, X₂, X₃, X₄) :|: 1+X₃ ≤ X₄ ∧ X₄ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1 ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₀+X₄ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁+X₂ ∧ X₁ ≤ X₃
t₈₉: evalfbb5in_v1(X₀, X₁, X₂, X₃, X₄) → evalfbb6in_v2(X₀, X₁, X₂, 1+X₃, X₄) :|: X₄ ≤ 1+X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 1+X₃ ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₄ ∧ 3 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁+X₂ ∧ X₁ ≤ X₃
t₈₃: evalfbb6in_v1(X₀, X₁, X₂, X₃, X₄) → evalfbb4in_v1(X₀, X₁, X₂, X₃, 1) :|: X₃ ≤ X₁+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₁ ≤ X₃
t₉₁: evalfbb6in_v2(X₀, X₁, X₂, X₃, X₄) → evalfbb4in_v1(X₀, X₁, X₂, X₃, 1) :|: X₃ ≤ X₁+X₂ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄
t₉₀: evalfbb6in_v2(X₀, X₁, X₂, X₃, X₄) → evalfbb7in_v1(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁+X₂ ≤ X₃ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ 1+X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₀+X₃ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₁+X₃ ∧ 2 ≤ X₂+X₃ ∧ 2 ≤ X₃ ∧ 2 ≤ X₄ ∧ 3 ≤ X₀+X₃ ∧ 3 ≤ X₀+X₄ ∧ 3 ≤ X₁+X₃ ∧ 3 ≤ X₁+X₄ ∧ 3 ≤ X₂+X₃ ∧ 3 ≤ X₂+X₄ ∧ 4 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₁ ≤ X₃ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄
t₉₂: evalfbb7in_v1(X₀, X₁, X₂, X₃, X₄) → evalfbb8in_v1(X₀, X₁, 1+X₂, X₃, X₄) :|: 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1+X₁+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₀+X₂ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₃ ∧ 2+X₁ ≤ X₄ ∧ 2+X₂ ≤ X₃ ∧ 2+X₂ ≤ X₄ ∧ 3 ≤ X₃ ∧ 3 ≤ X₄ ∧ 4 ≤ X₀+X₃ ∧ 4 ≤ X₀+X₄ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₁+X₄ ∧ 4 ≤ X₂+X₃ ∧ 4 ≤ X₂+X₄ ∧ 6 ≤ X₃+X₄ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄
t₈₂: evalfbb8in(X₀, X₁, X₂, X₃, X₄) → evalfbb6in_v1(X₀, X₁, X₂, X₁, X₄) :|: X₂ ≤ X₀ ∧ X₂ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₂ ≤ X₁
t₅: evalfbb8in(X₀, X₁, X₂, X₃, X₄) → evalfbb9in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₂ ≤ X₁
t₈₁: evalfbb8in(X₀, X₁, X₂, X₃, X₄) → evalfbb9in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ 1 ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ X₂ ≤ X₁
t₉₄: evalfbb8in_v1(X₀, X₁, X₂, X₃, X₄) → evalfbb6in_v1(X₀, X₁, X₂, X₁, X₄) :|: X₂ ≤ X₀ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₃ ∧ 2+X₁ ≤ X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₃ ∧ 3 ≤ X₄ ∧ 4 ≤ X₀+X₃ ∧ 4 ≤ X₀+X₄ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₁+X₄ ∧ 5 ≤ X₂+X₃ ∧ 5 ≤ X₂+X₄ ∧ 6 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄
t₉₃: evalfbb8in_v1(X₀, X₁, X₂, X₃, X₄) → evalfbb9in(X₀, X₁, X₂, X₃, X₄) :|: 1+X₀ ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₀+X₁ ∧ 2 ≤ X₁+X₂ ∧ 2+X₁ ≤ X₃ ∧ 2+X₁ ≤ X₄ ∧ 2 ≤ X₂ ∧ 3 ≤ X₀+X₂ ∧ 3 ≤ X₁+X₂ ∧ 3 ≤ X₃ ∧ 3 ≤ X₄ ∧ 4 ≤ X₀+X₃ ∧ 4 ≤ X₀+X₄ ∧ 4 ≤ X₁+X₃ ∧ 4 ≤ X₁+X₄ ∧ 5 ≤ X₂+X₃ ∧ 5 ≤ X₂+X₄ ∧ 6 ≤ X₃+X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₄
t₁₃: evalfbb9in(X₀, X₁, X₂, X₃, X₄) → evalfbb10in(X₀, X₁-1, X₂, X₃, X₄) :|: 1+X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂
t₁: evalfentryin(X₀, X₁, X₂, X₃, X₄) → evalfbb10in(X₁, X₀, X₂, X₃, X₄)
t₁₄: evalfreturnin(X₀, X₁, X₂, X₃, X₄) → evalfstop(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ 0
t₀: evalfstart(X₀, X₁, X₂, X₃, X₄) → evalfentryin(X₀, X₁, X₂, X₃, X₄)

All Bounds

Timebounds

Overall timebound:12⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+12⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+24⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+24⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+52⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+76⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+12⋅X₀⋅X₀⋅X₀⋅X₀+130⋅X₀⋅X₀⋅X₁⋅X₁+48⋅X₀⋅X₁⋅X₁⋅X₁+76⋅X₀⋅X₀⋅X₀⋅X₁+119⋅X₀⋅X₁⋅X₁+124⋅X₀⋅X₀⋅X₁+24⋅X₀⋅X₀⋅X₀+34⋅X₀⋅X₀+48⋅X₁⋅X₁+88⋅X₀⋅X₁+30⋅X₁+38⋅X₀+13 {O(n^6)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀ {O(n)}
t₃: 1 {O(1)}
t₅: X₀+1 {O(n)}
t₁₃: X₀ {O(n)}
t₁₄: 1 {O(1)}
t₈₁: X₀ {O(n)}
t₈₂: X₀ {O(n)}
t₈₃: X₀⋅X₁+2⋅X₀ {O(n^2)}
t₈₄: 2⋅X₀⋅X₀⋅X₁+X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+3⋅X₀⋅X₁+2⋅X₀+2⋅X₁+2 {O(n^3)}
t₈₅: 2⋅X₀⋅X₀⋅X₁+X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+3⋅X₀⋅X₁+2⋅X₀+2⋅X₁+2 {O(n^3)}
t₈₆: X₀⋅X₀⋅X₁+X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₁+5⋅X₀+3 {O(n^3)}
t₈₇: 4⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+4⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+24⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+16⋅X₀⋅X₁⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁+4⋅X₀⋅X₀⋅X₀⋅X₀+27⋅X₀⋅X₀⋅X₁+34⋅X₀⋅X₁⋅X₁+4⋅X₀⋅X₀⋅X₀+12⋅X₀⋅X₁+16⋅X₁⋅X₁+4⋅X₀⋅X₀+2⋅X₀+4⋅X₁ {O(n^6)}
t₈₈: 16⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+52⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₁⋅X₁⋅X₁+56⋅X₀⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀+94⋅X₀⋅X₀⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀+78⋅X₀⋅X₁⋅X₁+88⋅X₀⋅X₀⋅X₁+20⋅X₀⋅X₀+32⋅X₁⋅X₁+54⋅X₀⋅X₁+12⋅X₁+14⋅X₀ {O(n^6)}
t₈₉: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+4⋅X₁ {O(n^3)}
t₉₀: X₀⋅X₁+2⋅X₀ {O(n^2)}
t₉₁: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+4⋅X₁ {O(n^3)}
t₉₂: X₀⋅X₁+2⋅X₀ {O(n^2)}
t₉₃: X₀+1 {O(n)}
t₉₄: X₀⋅X₁+X₀ {O(n^2)}

Costbounds

Overall costbound: 12⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+12⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+24⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+24⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+52⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+76⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+12⋅X₀⋅X₀⋅X₀⋅X₀+130⋅X₀⋅X₀⋅X₁⋅X₁+48⋅X₀⋅X₁⋅X₁⋅X₁+76⋅X₀⋅X₀⋅X₀⋅X₁+119⋅X₀⋅X₁⋅X₁+124⋅X₀⋅X₀⋅X₁+24⋅X₀⋅X₀⋅X₀+34⋅X₀⋅X₀+48⋅X₁⋅X₁+88⋅X₀⋅X₁+30⋅X₁+38⋅X₀+13 {O(n^6)}
t₀: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₀ {O(n)}
t₃: 1 {O(1)}
t₅: X₀+1 {O(n)}
t₁₃: X₀ {O(n)}
t₁₄: 1 {O(1)}
t₈₁: X₀ {O(n)}
t₈₂: X₀ {O(n)}
t₈₃: X₀⋅X₁+2⋅X₀ {O(n^2)}
t₈₄: 2⋅X₀⋅X₀⋅X₁+X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+3⋅X₀⋅X₁+2⋅X₀+2⋅X₁+2 {O(n^3)}
t₈₅: 2⋅X₀⋅X₀⋅X₁+X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+3⋅X₀⋅X₁+2⋅X₀+2⋅X₁+2 {O(n^3)}
t₈₆: X₀⋅X₀⋅X₁+X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₁+5⋅X₀+3 {O(n^3)}
t₈₇: 4⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+4⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+24⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+16⋅X₀⋅X₁⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁+4⋅X₀⋅X₀⋅X₀⋅X₀+27⋅X₀⋅X₀⋅X₁+34⋅X₀⋅X₁⋅X₁+4⋅X₀⋅X₀⋅X₀+12⋅X₀⋅X₁+16⋅X₁⋅X₁+4⋅X₀⋅X₀+2⋅X₀+4⋅X₁ {O(n^6)}
t₈₈: 16⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+52⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₁⋅X₁⋅X₁+56⋅X₀⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀+94⋅X₀⋅X₀⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀+78⋅X₀⋅X₁⋅X₁+88⋅X₀⋅X₀⋅X₁+20⋅X₀⋅X₀+32⋅X₁⋅X₁+54⋅X₀⋅X₁+12⋅X₁+14⋅X₀ {O(n^6)}
t₈₉: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+4⋅X₁ {O(n^3)}
t₉₀: X₀⋅X₁+2⋅X₀ {O(n^2)}
t₉₁: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+4⋅X₁ {O(n^3)}
t₉₂: X₀⋅X₁+2⋅X₀ {O(n^2)}
t₉₃: X₀+1 {O(n)}
t₉₄: X₀⋅X₁+X₀ {O(n^2)}

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: X₁ {O(n)}
t₁, X₁: X₀ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₁ {O(n)}
t₂, X₁: X₀ {O(n)}
t₂, X₂: 1 {O(1)}
t₂, X₃: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₀+4⋅X₁+X₃ {O(n^3)}
t₂, X₄: 16⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+52⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₁⋅X₁⋅X₁+56⋅X₀⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀+94⋅X₀⋅X₀⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀+78⋅X₀⋅X₁⋅X₁+88⋅X₀⋅X₀⋅X₁+20⋅X₀⋅X₀+32⋅X₁⋅X₁+54⋅X₀⋅X₁+12⋅X₁+14⋅X₀+X₄+4 {O(n^6)}
t₃, X₀: 2⋅X₁ {O(n)}
t₃, X₁: 2⋅X₀ {O(n)}
t₃, X₂: X₀⋅X₁+2⋅X₀+X₂+3 {O(n^2)}
t₃, X₃: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₀+2⋅X₃+4⋅X₁ {O(n^3)}
t₃, X₄: 16⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+52⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₁⋅X₁⋅X₁+56⋅X₀⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀+94⋅X₀⋅X₀⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀+78⋅X₀⋅X₁⋅X₁+88⋅X₀⋅X₀⋅X₁+20⋅X₀⋅X₀+32⋅X₁⋅X₁+54⋅X₀⋅X₁+12⋅X₁+14⋅X₀+2⋅X₄+4 {O(n^6)}
t₅, X₀: X₁ {O(n)}
t₅, X₁: X₀ {O(n)}
t₅, X₂: 1 {O(1)}
t₅, X₃: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₀+4⋅X₁+X₃ {O(n^3)}
t₅, X₄: 16⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+52⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₁⋅X₁⋅X₁+56⋅X₀⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀+94⋅X₀⋅X₀⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀+78⋅X₀⋅X₁⋅X₁+88⋅X₀⋅X₀⋅X₁+20⋅X₀⋅X₀+32⋅X₁⋅X₁+54⋅X₀⋅X₁+12⋅X₁+14⋅X₀+X₄+4 {O(n^6)}
t₁₃, X₀: X₁ {O(n)}
t₁₃, X₁: X₀ {O(n)}
t₁₃, X₂: X₀⋅X₁+2⋅X₀+3 {O(n^2)}
t₁₃, X₃: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₀+4⋅X₁+X₃ {O(n^3)}
t₁₃, X₄: 16⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+52⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₁⋅X₁⋅X₁+56⋅X₀⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀+94⋅X₀⋅X₀⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀+78⋅X₀⋅X₁⋅X₁+88⋅X₀⋅X₀⋅X₁+20⋅X₀⋅X₀+32⋅X₁⋅X₁+54⋅X₀⋅X₁+12⋅X₁+14⋅X₀+X₄+4 {O(n^6)}
t₁₄, X₀: 2⋅X₁ {O(n)}
t₁₄, X₁: 2⋅X₀ {O(n)}
t₁₄, X₂: X₀⋅X₁+2⋅X₀+X₂+3 {O(n^2)}
t₁₄, X₃: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₀+2⋅X₃+4⋅X₁ {O(n^3)}
t₁₄, X₄: 16⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+52⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₁⋅X₁⋅X₁+56⋅X₀⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀+94⋅X₀⋅X₀⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀+78⋅X₀⋅X₁⋅X₁+88⋅X₀⋅X₀⋅X₁+20⋅X₀⋅X₀+32⋅X₁⋅X₁+54⋅X₀⋅X₁+12⋅X₁+14⋅X₀+2⋅X₄+4 {O(n^6)}
t₈₁, X₀: X₁ {O(n)}
t₈₁, X₁: X₀ {O(n)}
t₈₁, X₂: 1 {O(1)}
t₈₁, X₃: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₀+4⋅X₁+X₃ {O(n^3)}
t₈₁, X₄: 16⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+52⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₁⋅X₁⋅X₁+56⋅X₀⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀+94⋅X₀⋅X₀⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀+78⋅X₀⋅X₁⋅X₁+88⋅X₀⋅X₀⋅X₁+20⋅X₀⋅X₀+32⋅X₁⋅X₁+54⋅X₀⋅X₁+12⋅X₁+14⋅X₀+X₄+4 {O(n^6)}
t₈₂, X₀: X₁ {O(n)}
t₈₂, X₁: X₀ {O(n)}
t₈₂, X₂: 1 {O(1)}
t₈₂, X₃: X₀ {O(n)}
t₈₂, X₄: 16⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+52⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₁⋅X₁⋅X₁+56⋅X₀⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀+94⋅X₀⋅X₀⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀+78⋅X₀⋅X₁⋅X₁+88⋅X₀⋅X₀⋅X₁+20⋅X₀⋅X₀+32⋅X₁⋅X₁+54⋅X₀⋅X₁+12⋅X₁+14⋅X₀+X₄+4 {O(n^6)}
t₈₃, X₀: X₁ {O(n)}
t₈₃, X₁: X₀ {O(n)}
t₈₃, X₂: X₀⋅X₁+2⋅X₀+1 {O(n^2)}
t₈₃, X₃: 2⋅X₀ {O(n)}
t₈₃, X₄: 1 {O(1)}
t₈₄, X₀: X₁ {O(n)}
t₈₄, X₁: X₀ {O(n)}
t₈₄, X₂: X₀⋅X₁+2⋅X₀+1 {O(n^2)}
t₈₄, X₃: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₀+4⋅X₁ {O(n^3)}
t₈₄, X₄: 1 {O(1)}
t₈₅, X₀: X₁ {O(n)}
t₈₅, X₁: X₀ {O(n)}
t₈₅, X₂: X₀⋅X₁+2⋅X₀+1 {O(n^2)}
t₈₅, X₃: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₀+4⋅X₁ {O(n^3)}
t₈₅, X₄: 2 {O(1)}
t₈₆, X₀: X₁ {O(n)}
t₈₆, X₁: X₀ {O(n)}
t₈₆, X₂: X₀⋅X₁+2⋅X₀+1 {O(n^2)}
t₈₆, X₃: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₀+4⋅X₁ {O(n^3)}
t₈₆, X₄: 16⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+52⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₁⋅X₁⋅X₁+56⋅X₀⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀+94⋅X₀⋅X₀⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀+78⋅X₀⋅X₁⋅X₁+88⋅X₀⋅X₀⋅X₁+20⋅X₀⋅X₀+32⋅X₁⋅X₁+54⋅X₀⋅X₁+12⋅X₁+14⋅X₀+4 {O(n^6)}
t₈₇, X₀: X₁ {O(n)}
t₈₇, X₁: X₀ {O(n)}
t₈₇, X₂: X₀⋅X₁+2⋅X₀+1 {O(n^2)}
t₈₇, X₃: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₀+4⋅X₁ {O(n^3)}
t₈₇, X₄: 16⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+52⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₁⋅X₁⋅X₁+56⋅X₀⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀+94⋅X₀⋅X₀⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀+78⋅X₀⋅X₁⋅X₁+88⋅X₀⋅X₀⋅X₁+20⋅X₀⋅X₀+32⋅X₁⋅X₁+54⋅X₀⋅X₁+12⋅X₁+14⋅X₀+2 {O(n^6)}
t₈₈, X₀: X₁ {O(n)}
t₈₈, X₁: X₀ {O(n)}
t₈₈, X₂: X₀⋅X₁+2⋅X₀+1 {O(n^2)}
t₈₈, X₃: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₀+4⋅X₁ {O(n^3)}
t₈₈, X₄: 16⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+52⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₁⋅X₁⋅X₁+56⋅X₀⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀+94⋅X₀⋅X₀⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀+78⋅X₀⋅X₁⋅X₁+88⋅X₀⋅X₀⋅X₁+20⋅X₀⋅X₀+32⋅X₁⋅X₁+54⋅X₀⋅X₁+12⋅X₁+14⋅X₀+2 {O(n^6)}
t₈₉, X₀: X₁ {O(n)}
t₈₉, X₁: X₀ {O(n)}
t₈₉, X₂: X₀⋅X₁+2⋅X₀+1 {O(n^2)}
t₈₉, X₃: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₀+4⋅X₁ {O(n^3)}
t₈₉, X₄: 16⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+52⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₁⋅X₁⋅X₁+56⋅X₀⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀+94⋅X₀⋅X₀⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀+78⋅X₀⋅X₁⋅X₁+88⋅X₀⋅X₀⋅X₁+20⋅X₀⋅X₀+32⋅X₁⋅X₁+54⋅X₀⋅X₁+12⋅X₁+14⋅X₀+4 {O(n^6)}
t₉₀, X₀: X₁ {O(n)}
t₉₀, X₁: X₀ {O(n)}
t₉₀, X₂: X₀⋅X₁+2⋅X₀+1 {O(n^2)}
t₉₀, X₃: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₀+4⋅X₁ {O(n^3)}
t₉₀, X₄: 16⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+52⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₁⋅X₁⋅X₁+56⋅X₀⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀+94⋅X₀⋅X₀⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀+78⋅X₀⋅X₁⋅X₁+88⋅X₀⋅X₀⋅X₁+20⋅X₀⋅X₀+32⋅X₁⋅X₁+54⋅X₀⋅X₁+12⋅X₁+14⋅X₀+4 {O(n^6)}
t₉₁, X₀: X₁ {O(n)}
t₉₁, X₁: X₀ {O(n)}
t₉₁, X₂: X₀⋅X₁+2⋅X₀+1 {O(n^2)}
t₉₁, X₃: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₀+4⋅X₁ {O(n^3)}
t₉₁, X₄: 1 {O(1)}
t₉₂, X₀: X₁ {O(n)}
t₉₂, X₁: X₀ {O(n)}
t₉₂, X₂: X₀⋅X₁+2⋅X₀+1 {O(n^2)}
t₉₂, X₃: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₀+4⋅X₁ {O(n^3)}
t₉₂, X₄: 16⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+52⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₁⋅X₁⋅X₁+56⋅X₀⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀+94⋅X₀⋅X₀⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀+78⋅X₀⋅X₁⋅X₁+88⋅X₀⋅X₀⋅X₁+20⋅X₀⋅X₀+32⋅X₁⋅X₁+54⋅X₀⋅X₁+12⋅X₁+14⋅X₀+4 {O(n^6)}
t₉₃, X₀: X₁ {O(n)}
t₉₃, X₁: X₀ {O(n)}
t₉₃, X₂: X₀⋅X₁+2⋅X₀+1 {O(n^2)}
t₉₃, X₃: 2⋅X₀⋅X₀⋅X₁+2⋅X₀⋅X₁⋅X₁+2⋅X₀⋅X₀+4⋅X₀⋅X₁+2⋅X₀+4⋅X₁ {O(n^3)}
t₉₃, X₄: 16⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+52⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₁⋅X₁⋅X₁+56⋅X₀⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀+94⋅X₀⋅X₀⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀+78⋅X₀⋅X₁⋅X₁+88⋅X₀⋅X₀⋅X₁+20⋅X₀⋅X₀+32⋅X₁⋅X₁+54⋅X₀⋅X₁+12⋅X₁+14⋅X₀+4 {O(n^6)}
t₉₄, X₀: X₁ {O(n)}
t₉₄, X₁: X₀ {O(n)}
t₉₄, X₂: X₀⋅X₁+2⋅X₀+1 {O(n^2)}
t₉₄, X₃: X₀ {O(n)}
t₉₄, X₄: 16⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+8⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁⋅X₁+16⋅X₀⋅X₀⋅X₀⋅X₀⋅X₁+36⋅X₀⋅X₀⋅X₁⋅X₁⋅X₁+52⋅X₀⋅X₀⋅X₀⋅X₁⋅X₁+32⋅X₀⋅X₁⋅X₁⋅X₁+56⋅X₀⋅X₀⋅X₀⋅X₁+8⋅X₀⋅X₀⋅X₀⋅X₀+94⋅X₀⋅X₀⋅X₁⋅X₁+20⋅X₀⋅X₀⋅X₀+78⋅X₀⋅X₁⋅X₁+88⋅X₀⋅X₀⋅X₁+20⋅X₀⋅X₀+32⋅X₁⋅X₁+54⋅X₀⋅X₁+12⋅X₁+14⋅X₀+4 {O(n^6)}