Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀+1, X₁, X₂, X₃, X₄) :|: X₀+1 ≤ X₂
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₀+1, X₄) :|: X₂ ≤ X₀
t₁₃: l2(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄)
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l4(1, X₁, X₂, X₃, X₄)
t₂: l4(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, 1, X₃, X₄) :|: X₀ ≤ X₁
t₃: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₁+1 ≤ X₀
t₈: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₃
t₉: l5(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₃+1 ≤ X₄
t₁₀: l6(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄+1)
t₁₁: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃+1, X₄)
t₆: l8(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, 1) :|: X₃ ≤ X₁
t₇: l8(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: X₁+1 ≤ X₃
t₁₂: l9(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂+1, X₃, X₄)

Preprocessing

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l2

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 l6

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 l7

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 l5

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 l8

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 l1

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l10

Found invariant 1 ≤ X₀ for location l4

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 l9

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l10, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₅: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀+1, X₁, X₂, X₃, X₄) :|: X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₄: l1(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₀+1, X₄) :|: X₂ ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀
t₁₃: l2(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: 1+X₁ ≤ X₀ ∧ 1 ≤ X₀
t₁: l3(X₀, X₁, X₂, X₃, X₄) → l4(1, X₁, X₂, X₃, X₄)
t₂: l4(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, 1, X₃, X₄) :|: X₀ ≤ X₁ ∧ 1 ≤ X₀
t₃: l4(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄) :|: X₁+1 ≤ X₀ ∧ 1 ≤ X₀
t₈: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₃ ∧ 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
t₉: l5(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₃+1 ≤ X₄ ∧ 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
t₁₀: l6(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄+1) :|: 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
t₁₁: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃+1, X₄) :|: 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
t₆: l8(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, 1) :|: X₃ ≤ X₁ ∧ 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
t₇: l8(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: X₁+1 ≤ X₃ ∧ 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
t₁₂: l9(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂+1, X₃, X₄) :|: 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

MPRF for transition t₅: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀+1, X₁, X₂, X₃, X₄) :|: X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₁+1 {O(n)}

MPRF:

l4 [2⋅X₁-X₀ ]
l6 [2⋅X₁-X₀ ]
l7 [2⋅X₁-X₀ ]
l5 [2⋅X₁-X₀ ]
l8 [2⋅X₁-X₀ ]
l9 [2⋅X₁-X₀ ]
l1 [2⋅X₁-X₀ ]

MPRF for transition t₂: l4(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, 1, X₃, X₄) :|: X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+2 {O(n)}

MPRF:

l4 [X₁+1-X₀ ]
l6 [X₁-X₀ ]
l7 [X₁-X₀ ]
l5 [X₁-X₀ ]
l8 [X₁-X₀ ]
l9 [X₁-X₀ ]
l1 [X₁-X₀ ]

MPRF for transition t₄: l1(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₀+1, X₄) :|: X₂ ≤ X₀ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁⋅X₁+4⋅X₁+4 {O(n^2)}

MPRF:

l4 [X₁-X₀ ]
l6 [X₁-X₂ ]
l7 [X₁-X₂ ]
l5 [X₁-X₂ ]
l8 [X₁-X₂ ]
l9 [X₁-X₂ ]
l1 [X₁+1-X₂ ]

MPRF for transition t₇: l8(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄) :|: X₁+1 ≤ X₃ ∧ 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 of depth 1:

new bound:

3⋅X₁⋅X₁+10⋅X₁+8 {O(n^2)}

MPRF:

l4 [X₁ ]
l6 [X₀+X₁+1-X₂ ]
l7 [X₀+X₁+2⋅X₄-X₂-2⋅X₃-1 ]
l5 [X₀+X₁+1-X₂ ]
l8 [X₀+X₁+1-X₂ ]
l9 [X₀+X₃-X₂-1 ]
l1 [X₀+X₁+1-X₂ ]

MPRF for transition t₁₂: l9(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂+1, X₃, X₄) :|: 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 of depth 1:

new bound:

4⋅X₁⋅X₁+13⋅X₁+10 {O(n^2)}

MPRF:

l4 [X₀-2 ]
l6 [2⋅X₀-X₂ ]
l7 [2⋅X₀-X₂ ]
l5 [2⋅X₀-X₂ ]
l8 [2⋅X₀-X₂ ]
l9 [2⋅X₀-X₂ ]
l1 [2⋅X₀-X₂ ]

MPRF for transition t₉: l5(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: X₃+1 ≤ X₄ ∧ 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 of depth 1:

new bound:

12⋅X₁⋅X₁⋅X₁+47⋅X₁⋅X₁+57⋅X₁+21 {O(n^3)}

MPRF:

l4 [X₁-X₀ ]
l1 [X₁-X₀ ]
l6 [X₁+1-X₃ ]
l7 [X₁-X₃ ]
l5 [X₁+1-X₃ ]
l8 [X₁+1-X₃ ]
l9 [X₁-X₃ ]

MPRF for transition t₁₁: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃+1, X₄) :|: 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 of depth 1:

new bound:

16⋅X₁⋅X₁⋅X₁+60⋅X₁⋅X₁+68⋅X₁+21 {O(n^3)}

MPRF:

l4 [2⋅X₁-X₀ ]
l1 [2⋅X₁-X₀ ]
l6 [2⋅X₁-X₃ ]
l7 [2⋅X₁-X₃ ]
l5 [2⋅X₁-X₃ ]
l8 [2⋅X₁-X₃ ]
l9 [2⋅X₁-X₃ ]

MPRF for transition t₆: l8(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, 1) :|: X₃ ≤ X₁ ∧ 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 of depth 1:

new bound:

12⋅X₁⋅X₁⋅X₁+51⋅X₁⋅X₁+70⋅X₁+32 {O(n^3)}

MPRF:

l4 [X₁+1-X₀ ]
l1 [X₁+1-X₀ ]
l6 [X₁+1-X₃ ]
l7 [X₁+1-X₃ ]
l5 [X₁+1-X₃ ]
l8 [X₁+2-X₃ ]
l9 [X₁-X₃ ]

MPRF for transition t₈: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₃ ∧ 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 of depth 1:

new bound:

12⋅X₁⋅X₁⋅X₁⋅X₁+87⋅X₁⋅X₁⋅X₁+223⋅X₁⋅X₁+242⋅X₁+96 {O(n^4)}

MPRF:

l4 [0 ]
l6 [X₁+1-X₄ ]
l5 [X₁+2-X₄ ]
l7 [X₁+2-X₄ ]
l8 [0 ]
l9 [0 ]
l1 [0 ]

MPRF for transition t₁₀: l6(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄+1) :|: 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 of depth 1:

new bound:

192⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+1536⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+5044⋅X₁⋅X₁⋅X₁⋅X₁+8732⋅X₁⋅X₁⋅X₁+8439⋅X₁⋅X₁+4334⋅X₁+928 {O(n^6)}

MPRF:

l4 [0 ]
l6 [X₃+1-X₄ ]
l5 [X₃+1-X₄ ]
l7 [X₃+1-X₄ ]
l8 [0 ]
l9 [0 ]
l1 [0 ]

knowledge_propagation leads to new time bound 12⋅X₁⋅X₁⋅X₁⋅X₁+87⋅X₁⋅X₁⋅X₁+223⋅X₁⋅X₁+242⋅X₁+96 {O(n^4)} for transition t₁₀: l6(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄+1) :|: 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

Analysing control-flow refined program

Cut unsatisfiable transition t₅: l1→l4

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 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 n_l6___9

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l2

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 n_l8___1

Found invariant X₄ ≤ 1+X₁ ∧ 4 ≤ X₄ ∧ 7 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 6 ≤ X₂+X₄ ∧ 2+X₂ ≤ X₄ ∧ 7 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 6 ≤ X₀+X₄ ∧ 2+X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 6 ≤ X₁+X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ for location n_l8___3

Found invariant X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 3 ≤ X₄ ∧ 6 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 5 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 5 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ 2+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₁ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___4

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 n_l8___6

Found invariant X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₀ ∧ 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 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l1___2

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 n_l5___10

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 n_l5___8

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 n_l8___14

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 n_l5___13

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 n_l6___11

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 l1

Found invariant 1+X₁ ≤ X₀ ∧ 1 ≤ X₀ for location l10

Found invariant 1 ≤ X₀ for location l4

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 n_l7___7

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 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ for location n_l9___12

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 n_l9___5

knowledge_propagation leads to new time bound X₁+2 {O(n)} for transition t₁₁₅: l1(X₀, X₁, X₂, X₃, X₄) → n_l8___14(X₀, X₁, X₂, X₀+1, X₄) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ 1 ∧ 1 ≤ X₂ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ 1 ∧ X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₁+2 {O(n)} for transition t₁₂₆: n_l8___14(X₀, X₁, X₂, X₃, X₄) → n_l5___13(X₀, X₁, X₂, X₃, 1) :|: 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 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

knowledge_propagation leads to new time bound X₁+2 {O(n)} for transition t₁₂₇: n_l8___14(X₀, X₁, X₂, X₃, X₄) → n_l9___12(X₀, X₁, X₂, X₁+1, X₄) :|: 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁+1 ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 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

MPRF for transition t₁₁₆: n_l1___2(X₀, X₁, X₂, X₃, X₄) → n_l8___1(X₀, X₁, X₂, X₀+1, X₄) :|: 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₀ ∧ 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 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁⋅X₁+4⋅X₁+4 {O(n^2)}

MPRF:

l1 [0 ]
l4 [0 ]
n_l6___11 [0 ]
n_l5___10 [0 ]
n_l6___9 [0 ]
n_l5___8 [0 ]
n_l7___7 [0 ]
n_l8___1 [X₀+1-X₂ ]
n_l8___14 [0 ]
n_l8___3 [0 ]
n_l5___13 [0 ]
n_l8___6 [0 ]
n_l9___12 [X₁+1-X₂ ]
n_l1___2 [X₃+1-X₂ ]
n_l9___5 [0 ]
n_l1___4 [0 ]

MPRF for transition t₁₄₆: n_l1___2(X₀, X₁, X₂, X₃, X₄) → l4(X₀+1, X₁, X₂, X₃, X₄) :|: X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₃ ≤ 1+X₁ ∧ X₃ ≤ 1+X₀ ∧ 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 ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+2 {O(n)}

MPRF:

l1 [X₁+1-X₀ ]
l4 [X₁+1-X₀ ]
n_l6___11 [X₁+1-X₀ ]
n_l5___10 [X₁+1-X₀ ]
n_l6___9 [X₁+1-X₀ ]
n_l5___8 [X₁+1-X₀ ]
n_l7___7 [X₁+1-X₀ ]
n_l8___1 [X₃-X₀ ]
n_l8___14 [X₁+X₂-X₀ ]
n_l8___3 [X₁+2-X₃ ]
n_l5___13 [X₁+X₄-X₀ ]
n_l8___6 [X₁+1-X₀ ]
n_l9___12 [X₃-X₁ ]
n_l1___2 [1 ]
n_l9___5 [X₁+1-X₀ ]
n_l1___4 [X₁+1-X₀ ]

MPRF for transition t₁₁₇: n_l1___4(X₀, X₁, X₂, X₃, X₄) → n_l8___3(X₀, X₁, X₂, X₀+1, X₄) :|: 1+X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 2 ≤ X₂ ∧ X₂ ≤ 1+X₀ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 3 ≤ X₄ ∧ 6 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 5 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 5 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ 2+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₁ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁⋅X₁+3⋅X₁+2 {O(n^2)}

MPRF:

l1 [1-X₂ ]
l4 [0 ]
n_l6___11 [X₁-X₂ ]
n_l5___10 [X₁-X₂ ]
n_l6___9 [X₁-X₂ ]
n_l5___8 [X₁-X₂ ]
n_l7___7 [X₁-X₂ ]
n_l8___1 [0 ]
n_l8___14 [1-X₂ ]
n_l8___3 [X₁-X₂ ]
n_l5___13 [X₁-X₂ ]
n_l8___6 [X₁-X₂ ]
n_l9___12 [X₁-X₀ ]
n_l1___2 [0 ]
n_l9___5 [X₁-X₂ ]
n_l1___4 [X₁+1-X₂ ]

MPRF for transition t₁₄₇: n_l1___4(X₀, X₁, X₂, X₃, X₄) → l4(X₀+1, X₁, X₂, X₃, X₄) :|: X₀+1 ≤ X₂ ∧ X₂ ≤ 1+X₁ ∧ X₂ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 3 ≤ X₄ ∧ 6 ≤ X₃+X₄ ∧ X₃ ≤ X₄ ∧ 5 ≤ X₂+X₄ ∧ 1+X₂ ≤ X₄ ∧ 5 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 4 ≤ X₀+X₄ ∧ 2+X₀ ≤ X₄ ∧ X₃ ≤ 1+X₁ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 5 ≤ X₁+X₃ ∧ 1+X₁ ≤ X₃ ∧ 4 ≤ X₀+X₃ ∧ 2+X₀ ≤ X₃ ∧ X₂ ≤ X₁ ∧ X₂ ≤ 1+X₀ ∧ 2 ≤ X₂ ∧ 4 ≤ X₁+X₂ ∧ 3 ≤ X₀+X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁+1 {O(n)}

MPRF:

l1 [X₁-X₀ ]
l4 [X₁-X₀ ]
n_l6___11 [X₁-X₀ ]
n_l5___10 [X₁-X₀ ]
n_l6___9 [X₁-X₀ ]
n_l5___8 [X₁-X₀ ]
n_l7___7 [X₁-X₀ ]
n_l8___1 [-1 ]
n_l8___14 [X₁-X₀ ]
n_l8___3 [X₁-X₀ ]
n_l5___13 [X₁-X₀ ]
n_l8___6 [X₁-X₀ ]
n_l9___12 [X₁-X₀-1 ]
n_l1___2 [X₁-X₃ ]
n_l9___5 [X₁-X₀ ]
n_l1___4 [X₁-X₀ ]

MPRF for transition t₁₂₅: n_l8___1(X₀, X₁, X₂, X₃, X₄) → n_l9___12(X₀, X₁, X₂, X₁+1, X₄) :|: 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁+1 ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 1+X₀ ≤ X₃ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1+X₁ ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁+1 ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 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 of depth 1:

new bound:

X₁⋅X₁+3⋅X₁+2 {O(n^2)}

MPRF:

l1 [0 ]
l4 [0 ]
n_l6___11 [0 ]
n_l5___10 [0 ]
n_l6___9 [0 ]
n_l5___8 [0 ]
n_l7___7 [0 ]
n_l8___1 [X₀+1-X₂ ]
n_l8___14 [0 ]
n_l8___3 [0 ]
n_l5___13 [0 ]
n_l8___6 [0 ]
n_l9___12 [X₁-X₂ ]
n_l1___2 [X₁+1-X₂ ]
n_l9___5 [0 ]
n_l1___4 [0 ]

MPRF for transition t₁₂₈: n_l8___3(X₀, X₁, X₂, X₃, X₄) → n_l5___13(X₀, X₁, X₂, X₃, 1) :|: X₃ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ X₃ ≤ X₁ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ X₄ ≤ 1+X₁ ∧ 4 ≤ X₄ ∧ 7 ≤ X₃+X₄ ∧ 1+X₃ ≤ X₄ ∧ 6 ≤ X₂+X₄ ∧ 2+X₂ ≤ X₄ ∧ 7 ≤ X₁+X₄ ∧ 1+X₁ ≤ X₄ ∧ 6 ≤ X₀+X₄ ∧ 2+X₀ ≤ X₄ ∧ X₃ ≤ X₁ ∧ X₃ ≤ 1+X₀ ∧ 3 ≤ X₃ ∧ 5 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 6 ≤ X₁+X₃ ∧ 5 ≤ X₀+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 2 ≤ X₂ ∧ 5 ≤ X₁+X₂ ∧ 4 ≤ X₀+X₂ ∧ 3 ≤ X₁ ∧ 5 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 2 ≤ X₀ of depth 1:

new bound:

X₁⋅X₁+3⋅X₁+2 {O(n^2)}

MPRF:

l1 [0 ]
l4 [0 ]
n_l6___11 [X₁-X₂ ]
n_l5___10 [X₁-X₂ ]
n_l6___9 [X₁-X₂ ]
n_l5___8 [X₁-X₂ ]
n_l7___7 [X₁-X₂ ]
n_l8___1 [0 ]
n_l8___14 [0 ]
n_l8___3 [X₁+1-X₂ ]
n_l5___13 [X₁-X₂ ]
n_l8___6 [X₁-X₂ ]
n_l9___12 [0 ]
n_l1___2 [0 ]
n_l9___5 [X₁-X₂ ]
n_l1___4 [X₁+1-X₂ ]

MPRF for transition t₁₃₀: n_l8___6(X₀, X₁, X₂, X₃, X₄) → n_l9___5(X₀, X₁, X₂, X₁+1, X₄) :|: 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ 2+X₀ ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁+1 ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 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 of depth 1:

new bound:

X₁⋅X₁+5⋅X₁+6 {O(n^2)}

MPRF:

l1 [0 ]
l4 [0 ]
n_l6___11 [X₁+2⋅X₄-X₂ ]
n_l5___10 [X₁+2-X₂ ]
n_l6___9 [X₁+2-X₂ ]
n_l5___8 [X₁+2-X₂ ]
n_l7___7 [X₁+2-X₂ ]
n_l8___1 [0 ]
n_l8___14 [0 ]
n_l8___3 [X₁+2⋅X₃-2⋅X₀-X₂ ]
n_l5___13 [X₁+2-X₂ ]
n_l8___6 [X₁+2-X₂ ]
n_l9___12 [0 ]
n_l1___2 [0 ]
n_l9___5 [X₁+1-X₂ ]
n_l1___4 [X₁+2-X₂ ]

MPRF for transition t₁₃₁: n_l9___12(X₀, X₁, X₂, X₃, X₄) → n_l1___2(X₀, X₁, X₂+1, X₁+1, X₄) :|: X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₁ ≤ X₀ ∧ X₀+1 ≤ X₃ ∧ X₃ ≤ 1+X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁+1 ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 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 ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₁ ≤ X₀ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ X₀ ≤ X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₁⋅X₁+9⋅X₁+8 {O(n^2)}

MPRF:

l1 [X₁ ]
l4 [X₁ ]
n_l6___11 [X₁ ]
n_l5___10 [X₁ ]
n_l6___9 [X₁ ]
n_l5___8 [X₁ ]
n_l7___7 [X₁ ]
n_l8___1 [2⋅X₁+1-X₂ ]
n_l8___14 [X₁ ]
n_l8___3 [X₁ ]
n_l5___13 [X₁ ]
n_l8___6 [X₁ ]
n_l9___12 [2⋅X₃-X₂-1 ]
n_l1___2 [2⋅X₁+1-X₂ ]
n_l9___5 [X₁ ]
n_l1___4 [X₁ ]

MPRF for transition t₁₃₂: n_l9___5(X₀, X₁, X₂, X₃, X₄) → n_l1___4(X₀, X₁, X₂+1, X₁+1, X₄) :|: 1+X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₁+1 ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ X₁+1 ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁+1 ≤ X₃ ∧ X₃ ≤ 1+X₁ ∧ 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 of depth 1:

new bound:

4⋅X₁⋅X₁+11⋅X₁+4 {O(n^2)}

MPRF:

l1 [X₁ ]
l4 [X₁ ]
n_l6___11 [4⋅X₁-2⋅X₂ ]
n_l5___10 [4⋅X₁-2⋅X₂ ]
n_l6___9 [4⋅X₁-2⋅X₂ ]
n_l5___8 [4⋅X₁-2⋅X₂ ]
n_l7___7 [4⋅X₁-2⋅X₂ ]
n_l8___1 [2⋅X₁-X₀ ]
n_l8___14 [X₁+1-X₂ ]
n_l8___3 [4⋅X₁-2⋅X₂ ]
n_l5___13 [4⋅X₁-2⋅X₂ ]
n_l8___6 [4⋅X₁-2⋅X₂ ]
n_l9___12 [2⋅X₁-X₀ ]
n_l1___2 [X₁ ]
n_l9___5 [4⋅X₁-2⋅X₂ ]
n_l1___4 [4⋅X₁-2⋅X₂ ]

MPRF for transition t₁₁₈: n_l5___10(X₀, X₁, X₂, X₃, X₄) → n_l6___9(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₄ ∧ X₄ ≤ 1+X₃ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 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 of depth 1:

new bound:

4⋅X₁⋅X₁⋅X₁+11⋅X₁⋅X₁+5⋅X₁ {O(n^3)}

MPRF:

l1 [X₁ ]
n_l1___4 [X₁ ]
l4 [X₁ ]
n_l6___11 [X₁+1-X₃ ]
n_l5___10 [X₁+1-X₃ ]
n_l6___9 [X₁-X₃ ]
n_l5___8 [X₁-X₃ ]
n_l7___7 [X₁-X₃ ]
n_l8___1 [X₀ ]
n_l8___14 [X₁ ]
n_l8___3 [X₁ ]
n_l5___13 [X₁+X₄-X₃ ]
n_l8___6 [X₁+1-X₄ ]
n_l9___5 [X₁-X₄ ]
n_l9___12 [X₀ ]
n_l1___2 [X₁ ]

MPRF for transition t₁₁₉: n_l5___13(X₀, X₁, X₂, X₃, X₄) → n_l6___11(X₀, X₁, X₂, X₃, X₄) :|: X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₄ ∧ X₄ ≤ X₃ ∧ X₄ ≤ 1 ∧ 1 ≤ X₄ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 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 of depth 1:

new bound:

4⋅X₁⋅X₁⋅X₁+11⋅X₁⋅X₁+5⋅X₁ {O(n^3)}

MPRF:

l1 [X₁ ]
n_l1___4 [X₁ ]
l4 [X₁ ]
n_l6___11 [X₁-X₃ ]
n_l5___10 [X₁-X₃ ]
n_l6___9 [X₁-X₃ ]
n_l5___8 [X₁-X₃ ]
n_l7___7 [X₁-X₃ ]
n_l8___1 [X₁ ]
n_l8___14 [X₁ ]
n_l8___3 [X₁ ]
n_l5___13 [X₁+1-X₃ ]
n_l8___6 [X₁+1-X₄ ]
n_l9___5 [X₁-X₄ ]
n_l9___12 [X₁ ]
n_l1___2 [X₀ ]

MPRF for transition t₁₂₁: n_l5___8(X₀, X₁, X₂, X₃, X₄) → n_l7___7(X₀, X₁, X₂, X₃, X₃+1) :|: 1 ≤ X₄ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₄ ∧ X₄ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₃+1 ≤ X₄ ∧ X₄ ≤ 1+X₃ ∧ 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 of depth 1:

new bound:

4⋅X₁⋅X₁⋅X₁+11⋅X₁⋅X₁+5⋅X₁ {O(n^3)}

MPRF:

l1 [X₁ ]
n_l1___4 [X₁ ]
l4 [X₁ ]
n_l6___11 [X₁+1-X₃ ]
n_l5___10 [X₁+1-X₃ ]
n_l6___9 [X₁+1-X₃ ]
n_l5___8 [X₁+1-X₃ ]
n_l7___7 [X₁-X₃ ]
n_l8___1 [X₀ ]
n_l8___14 [X₁ ]
n_l8___3 [X₁ ]
n_l5___13 [X₁+1-X₃ ]
n_l8___6 [X₁+1-X₄ ]
n_l9___5 [X₁-X₄ ]
n_l9___12 [X₀ ]
n_l1___2 [X₀ ]

MPRF for transition t₁₂₂: n_l6___11(X₀, X₁, X₂, X₃, X₄) → n_l5___10(X₀, X₁, X₂, X₃, X₄+1) :|: X₃ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₄ ≤ 1 ∧ 1 ≤ X₄ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 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 of depth 1:

new bound:

4⋅X₁⋅X₁⋅X₁+11⋅X₁⋅X₁+5⋅X₁ {O(n^3)}

MPRF:

l1 [X₁ ]
n_l1___4 [X₁ ]
l4 [X₁ ]
n_l6___11 [X₁+1-X₃ ]
n_l5___10 [X₁-X₃ ]
n_l6___9 [X₁-X₃ ]
n_l5___8 [X₁-X₃ ]
n_l7___7 [X₁-X₃ ]
n_l8___1 [X₀ ]
n_l8___14 [X₁ ]
n_l8___3 [X₁ ]
n_l5___13 [X₁+1-X₃ ]
n_l8___6 [X₁+1-X₃ ]
n_l9___5 [X₁-X₄ ]
n_l9___12 [X₀ ]
n_l1___2 [X₀ ]

MPRF for transition t₁₂₄: n_l7___7(X₀, X₁, X₂, X₃, X₄) → n_l8___6(X₀, X₁, X₂, X₃+1, X₃+1) :|: X₃ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₃+1 ≤ X₄ ∧ X₄ ≤ 1+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₃+1 ≤ X₄ ∧ X₄ ≤ 1+X₃ ∧ 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 of depth 1:

new bound:

16⋅X₁⋅X₁⋅X₁⋅X₁+108⋅X₁⋅X₁⋅X₁+228⋅X₁⋅X₁+166⋅X₁+37 {O(n^4)}

MPRF:

l1 [3⋅X₁-X₀ ]
n_l1___4 [3⋅X₁+X₂-2⋅X₀ ]
l4 [3⋅X₁-X₀ ]
n_l6___11 [3⋅X₁+2⋅X₂-2⋅X₀-X₃ ]
n_l5___10 [3⋅X₁+2⋅X₂-2⋅X₀-X₃ ]
n_l6___9 [3⋅X₁+2⋅X₂-2⋅X₀-X₃ ]
n_l5___8 [3⋅X₁+2⋅X₂-2⋅X₀-X₃ ]
n_l7___7 [3⋅X₁+2⋅X₂-2⋅X₀-X₃ ]
n_l8___1 [2⋅X₃-3 ]
n_l8___14 [X₀+3⋅X₁+1-2⋅X₃ ]
n_l8___3 [3⋅X₁+X₂-2⋅X₀ ]
n_l5___13 [3⋅X₁+2⋅X₂-2⋅X₀-X₃ ]
n_l8___6 [3⋅X₁+2⋅X₂-2⋅X₀-X₃ ]
n_l9___5 [3⋅X₁+2⋅X₂-2⋅X₀-X₄ ]
n_l9___12 [X₀+X₁-1 ]
n_l1___2 [3⋅X₁-X₃ ]

MPRF for transition t₁₂₉: n_l8___6(X₀, X₁, X₂, X₃, X₄) → n_l5___13(X₀, X₁, X₂, X₃, 1) :|: 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₀ ≤ X₁ ∧ X₃ ≤ X₄ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₂ ∧ X₂ ≤ X₀ ∧ 2+X₀ ≤ X₄ ∧ X₄ ≤ 1+X₁ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 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 of depth 1:

new bound:

4⋅X₁⋅X₁⋅X₁+11⋅X₁⋅X₁+5⋅X₁ {O(n^3)}

MPRF:

l1 [X₁ ]
n_l1___4 [X₁ ]
l4 [X₁ ]
n_l6___11 [X₁-X₃ ]
n_l5___10 [X₁-X₃ ]
n_l6___9 [X₁-X₃ ]
n_l5___8 [X₁-X₃ ]
n_l7___7 [X₁-X₃ ]
n_l8___1 [X₁ ]
n_l8___14 [X₁ ]
n_l8___3 [X₁ ]
n_l5___13 [X₁-X₃ ]
n_l8___6 [X₁+1-X₃ ]
n_l9___5 [X₁-X₄ ]
n_l9___12 [X₁ ]
n_l1___2 [X₀ ]

knowledge_propagation leads to new time bound 4⋅X₁⋅X₁⋅X₁+11⋅X₁⋅X₁+5⋅X₁ {O(n^3)} for transition t₁₂₄: n_l7___7(X₀, X₁, X₂, X₃, X₄) → n_l8___6(X₀, X₁, X₂, X₃+1, X₃+1) :|: X₃ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ 1 ≤ X₂ ∧ X₃+1 ≤ X₄ ∧ X₄ ≤ 1+X₃ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₃+1 ≤ X₄ ∧ X₄ ≤ 1+X₃ ∧ 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

MPRF for transition t₁₂₀: n_l5___8(X₀, X₁, X₂, X₃, X₄) → n_l6___9(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ 1+X₀ ≤ X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₄ ∧ X₄ ≤ 1+X₃ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ 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 of depth 1:

new bound:

16⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+88⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+177⋅X₁⋅X₁⋅X₁⋅X₁+194⋅X₁⋅X₁⋅X₁+155⋅X₁⋅X₁+50⋅X₁ {O(n^6)}

MPRF:

l1 [X₁ ]
n_l1___4 [X₁ ]
l4 [X₁ ]
n_l6___11 [X₁+X₃-X₀-X₄ ]
n_l5___10 [2⋅X₃-X₀-X₄ ]
n_l6___9 [2⋅X₃-X₀-X₄-1 ]
n_l5___8 [2⋅X₃-X₀-X₄ ]
n_l7___7 [X₃-X₀-X₂ ]
n_l8___1 [X₀ ]
n_l8___14 [X₁ ]
n_l8___3 [X₁+X₃-X₀-1 ]
n_l5___13 [X₁+X₃-X₀-X₄ ]
n_l8___6 [X₃-X₀-2⋅X₂ ]
n_l9___5 [X₄-X₀-2⋅X₂ ]
n_l9___12 [X₀ ]
n_l1___2 [X₁ ]

MPRF for transition t₁₂₃: n_l6___9(X₀, X₁, X₂, X₃, X₄) → n_l5___8(X₀, X₁, X₂, X₃, X₄+1) :|: X₄ ≤ X₃ ∧ 2 ≤ X₄ ∧ 1 ≤ X₂ ∧ 1+X₀ ≤ X₃ ∧ X₂ ≤ X₀ ∧ X₃ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₄ ≤ X₃ ∧ 1 ≤ X₄ ∧ 1 ≤ X₂ ∧ X₃ ≤ X₁ ∧ 1+X₀ ≤ X₃ ∧ X₄ ≤ X₃ ∧ X₄ ≤ X₁ ∧ 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 of depth 1:

new bound:

16⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+88⋅X₁⋅X₁⋅X₁⋅X₁⋅X₁+177⋅X₁⋅X₁⋅X₁⋅X₁+198⋅X₁⋅X₁⋅X₁+166⋅X₁⋅X₁+55⋅X₁ {O(n^6)}

MPRF:

l1 [X₁ ]
n_l1___4 [X₁ ]
l4 [X₁ ]
n_l6___11 [X₁+X₃-X₀-X₄-1 ]
n_l5___10 [X₁+X₃-X₀-X₄ ]
n_l6___9 [X₁+X₃-X₀-X₄ ]
n_l5___8 [X₁+X₃-X₀-X₄ ]
n_l7___7 [X₁-X₀-1 ]
n_l8___1 [X₃-1 ]
n_l8___14 [X₁+X₃-X₀-1 ]
n_l8___3 [X₁ ]
n_l5___13 [X₁+X₃-X₀-X₄-1 ]
n_l8___6 [X₁-X₀-1 ]
n_l9___5 [X₁-X₀-1 ]
n_l9___12 [X₁ ]
n_l1___2 [2⋅X₁-X₀ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:24⋅X₁⋅X₁⋅X₁⋅X₁+214⋅X₁⋅X₁⋅X₁+612⋅X₁⋅X₁+709⋅X₁+295 {O(n^4)}
t₀: 1 {O(1)}
t₄: X₁⋅X₁+4⋅X₁+4 {O(n^2)}
t₅: 2⋅X₁+1 {O(n)}
t₁₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+2 {O(n)}
t₃: 1 {O(1)}
t₈: 12⋅X₁⋅X₁⋅X₁⋅X₁+87⋅X₁⋅X₁⋅X₁+223⋅X₁⋅X₁+242⋅X₁+96 {O(n^4)}
t₉: 12⋅X₁⋅X₁⋅X₁+47⋅X₁⋅X₁+57⋅X₁+21 {O(n^3)}
t₁₀: 12⋅X₁⋅X₁⋅X₁⋅X₁+87⋅X₁⋅X₁⋅X₁+223⋅X₁⋅X₁+242⋅X₁+96 {O(n^4)}
t₁₁: 16⋅X₁⋅X₁⋅X₁+60⋅X₁⋅X₁+68⋅X₁+21 {O(n^3)}
t₆: 12⋅X₁⋅X₁⋅X₁+51⋅X₁⋅X₁+70⋅X₁+32 {O(n^3)}
t₇: 3⋅X₁⋅X₁+10⋅X₁+8 {O(n^2)}
t₁₂: 4⋅X₁⋅X₁+13⋅X₁+10 {O(n^2)}

Costbounds

Overall costbound: 24⋅X₁⋅X₁⋅X₁⋅X₁+214⋅X₁⋅X₁⋅X₁+612⋅X₁⋅X₁+709⋅X₁+295 {O(n^4)}
t₀: 1 {O(1)}
t₄: X₁⋅X₁+4⋅X₁+4 {O(n^2)}
t₅: 2⋅X₁+1 {O(n)}
t₁₃: 1 {O(1)}
t₁: 1 {O(1)}
t₂: X₁+2 {O(n)}
t₃: 1 {O(1)}
t₈: 12⋅X₁⋅X₁⋅X₁⋅X₁+87⋅X₁⋅X₁⋅X₁+223⋅X₁⋅X₁+242⋅X₁+96 {O(n^4)}
t₉: 12⋅X₁⋅X₁⋅X₁+47⋅X₁⋅X₁+57⋅X₁+21 {O(n^3)}
t₁₀: 12⋅X₁⋅X₁⋅X₁⋅X₁+87⋅X₁⋅X₁⋅X₁+223⋅X₁⋅X₁+242⋅X₁+96 {O(n^4)}
t₁₁: 16⋅X₁⋅X₁⋅X₁+60⋅X₁⋅X₁+68⋅X₁+21 {O(n^3)}
t₆: 12⋅X₁⋅X₁⋅X₁+51⋅X₁⋅X₁+70⋅X₁+32 {O(n^3)}
t₇: 3⋅X₁⋅X₁+10⋅X₁+8 {O(n^2)}
t₁₂: 4⋅X₁⋅X₁+13⋅X₁+10 {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)}
t₄, X₀: 2⋅X₁+2 {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: 4⋅X₁⋅X₁+13⋅X₁+11 {O(n^2)}
t₄, X₃: 4⋅X₁+6 {O(n)}
t₄, X₄: 12⋅X₁⋅X₁⋅X₁⋅X₁+87⋅X₁⋅X₁⋅X₁+223⋅X₁⋅X₁+242⋅X₁+X₄+97 {O(n^4)}
t₅, X₀: 2⋅X₁+2 {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: 4⋅X₁⋅X₁+13⋅X₁+11 {O(n^2)}
t₅, X₃: 16⋅X₁⋅X₁⋅X₁+60⋅X₁⋅X₁+76⋅X₁+33 {O(n^3)}
t₅, X₄: 12⋅X₁⋅X₁⋅X₁⋅X₁+87⋅X₁⋅X₁⋅X₁+223⋅X₁⋅X₁+242⋅X₁+X₄+97 {O(n^4)}
t₁₃, X₀: 2⋅X₁+3 {O(n)}
t₁₃, X₁: 2⋅X₁ {O(n)}
t₁₃, X₂: 4⋅X₁⋅X₁+13⋅X₁+X₂+11 {O(n^2)}
t₁₃, X₃: 16⋅X₁⋅X₁⋅X₁+60⋅X₁⋅X₁+76⋅X₁+X₃+33 {O(n^3)}
t₁₃, X₄: 12⋅X₁⋅X₁⋅X₁⋅X₁+87⋅X₁⋅X₁⋅X₁+223⋅X₁⋅X₁+2⋅X₄+242⋅X₁+97 {O(n^4)}
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: 2⋅X₁+2 {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: 1 {O(1)}
t₂, X₃: 16⋅X₁⋅X₁⋅X₁+60⋅X₁⋅X₁+76⋅X₁+X₃+33 {O(n^3)}
t₂, X₄: 12⋅X₁⋅X₁⋅X₁⋅X₁+87⋅X₁⋅X₁⋅X₁+223⋅X₁⋅X₁+242⋅X₁+X₄+97 {O(n^4)}
t₃, X₀: 2⋅X₁+3 {O(n)}
t₃, X₁: 2⋅X₁ {O(n)}
t₃, X₂: 4⋅X₁⋅X₁+13⋅X₁+X₂+11 {O(n^2)}
t₃, X₃: 16⋅X₁⋅X₁⋅X₁+60⋅X₁⋅X₁+76⋅X₁+X₃+33 {O(n^3)}
t₃, X₄: 12⋅X₁⋅X₁⋅X₁⋅X₁+87⋅X₁⋅X₁⋅X₁+223⋅X₁⋅X₁+2⋅X₄+242⋅X₁+97 {O(n^4)}
t₈, X₀: 2⋅X₁+2 {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: 4⋅X₁⋅X₁+13⋅X₁+11 {O(n^2)}
t₈, X₃: 16⋅X₁⋅X₁⋅X₁+60⋅X₁⋅X₁+72⋅X₁+27 {O(n^3)}
t₈, X₄: 12⋅X₁⋅X₁⋅X₁⋅X₁+87⋅X₁⋅X₁⋅X₁+223⋅X₁⋅X₁+242⋅X₁+97 {O(n^4)}
t₉, X₀: 2⋅X₁+2 {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: 4⋅X₁⋅X₁+13⋅X₁+11 {O(n^2)}
t₉, X₃: 16⋅X₁⋅X₁⋅X₁+60⋅X₁⋅X₁+72⋅X₁+27 {O(n^3)}
t₉, X₄: 12⋅X₁⋅X₁⋅X₁⋅X₁+87⋅X₁⋅X₁⋅X₁+223⋅X₁⋅X₁+242⋅X₁+97 {O(n^4)}
t₁₀, X₀: 2⋅X₁+2 {O(n)}
t₁₀, X₁: X₁ {O(n)}
t₁₀, X₂: 4⋅X₁⋅X₁+13⋅X₁+11 {O(n^2)}
t₁₀, X₃: 16⋅X₁⋅X₁⋅X₁+60⋅X₁⋅X₁+72⋅X₁+27 {O(n^3)}
t₁₀, X₄: 12⋅X₁⋅X₁⋅X₁⋅X₁+87⋅X₁⋅X₁⋅X₁+223⋅X₁⋅X₁+242⋅X₁+97 {O(n^4)}
t₁₁, X₀: 2⋅X₁+2 {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: 4⋅X₁⋅X₁+13⋅X₁+11 {O(n^2)}
t₁₁, X₃: 16⋅X₁⋅X₁⋅X₁+60⋅X₁⋅X₁+72⋅X₁+27 {O(n^3)}
t₁₁, X₄: 12⋅X₁⋅X₁⋅X₁⋅X₁+87⋅X₁⋅X₁⋅X₁+223⋅X₁⋅X₁+242⋅X₁+97 {O(n^4)}
t₆, X₀: 2⋅X₁+2 {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: 4⋅X₁⋅X₁+13⋅X₁+11 {O(n^2)}
t₆, X₃: 16⋅X₁⋅X₁⋅X₁+60⋅X₁⋅X₁+72⋅X₁+27 {O(n^3)}
t₆, X₄: 1 {O(1)}
t₇, X₀: 2⋅X₁+2 {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: 4⋅X₁⋅X₁+13⋅X₁+11 {O(n^2)}
t₇, X₃: 16⋅X₁⋅X₁⋅X₁+60⋅X₁⋅X₁+76⋅X₁+33 {O(n^3)}
t₇, X₄: 12⋅X₁⋅X₁⋅X₁⋅X₁+87⋅X₁⋅X₁⋅X₁+223⋅X₁⋅X₁+242⋅X₁+X₄+97 {O(n^4)}
t₁₂, X₀: 2⋅X₁+2 {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: 4⋅X₁⋅X₁+13⋅X₁+11 {O(n^2)}
t₁₂, X₃: 16⋅X₁⋅X₁⋅X₁+60⋅X₁⋅X₁+76⋅X₁+33 {O(n^3)}
t₁₂, X₄: 12⋅X₁⋅X₁⋅X₁⋅X₁+87⋅X₁⋅X₁⋅X₁+223⋅X₁⋅X₁+242⋅X₁+X₄+97 {O(n^4)}