Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₁₁: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₃+1, X₁, X₂, X₃, 0)
t₁₅: l11(X₀, X₁, X₂, X₃, X₄) → l14(X₀, X₁, X₂, X₃, X₄)
t₁₂: l12(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: X₄ < X₁
t₁₃: l12(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₀, X₄) :|: X₁ ≤ X₄
t₁₄: l13(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄+1)
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄)
t₆: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₇: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
t₈: l8(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, 0, X₄)
t₉: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₂
t₁₀: l9(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₃

Preprocessing

Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l11

Found invariant 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l12

Found invariant 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location l13

Found invariant 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location l10

Found invariant 0 ≤ X₃ for location l9

Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l14

Problem after Preprocessing

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l2, l3, l4, l5, l6, l7, l8, l9
Transitions:
t₀: l0(X₀, X₁, X₂, X₃, X₄) → l2(X₀, X₁, X₂, X₃, X₄)
t₃: l1(X₀, X₁, X₂, X₃, X₄) → l4(X₀, X₁, X₂, X₃, X₄)
t₁₁: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₃+1, X₁, X₂, X₃, 0) :|: 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂
t₁₅: l11(X₀, X₁, X₂, X₃, X₄) → l14(X₀, X₁, X₂, X₃, X₄) :|: 0 ≤ X₃ ∧ X₂ ≤ X₃
t₁₂: l12(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: X₄ < X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₁₃: l12(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₀, X₄) :|: X₁ ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀
t₁₄: l13(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄+1) :|: 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀
t₁: l2(X₀, X₁, X₂, X₃, X₄) → l3(X₀, X₁, X₂, X₃, X₄)
t₂: l3(X₀, X₁, X₂, X₃, X₄) → l1(X₀, X₁, X₂, X₃, X₄)
t₄: l4(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₁, X₂, X₃, X₄)
t₅: l5(X₀, X₁, X₂, X₃, X₄) → l6(X₀, X₁, X₂, X₃, X₄)
t₆: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₇: l7(X₀, X₁, X₂, X₃, X₄) → l8(X₀, X₁, X₂, X₃, X₄)
t₈: l8(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, 0, X₄)
t₉: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₂ ∧ 0 ≤ X₃
t₁₀: l9(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₂ ≤ X₃ ∧ 0 ≤ X₃

MPRF for transition t₁₁: l10(X₀, X₁, X₂, X₃, X₄) → l12(X₃+1, X₁, X₂, X₃, 0) :|: 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

l13 [X₂-X₃-1 ]
l12 [X₂-X₃-1 ]
l9 [X₂-X₃ ]
l10 [X₂-X₃ ]

MPRF for transition t₁₃: l12(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₀, X₄) :|: X₁ ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂+1 {O(n)}

MPRF:

l13 [X₀+X₂-2⋅X₃ ]
l12 [X₂+1-X₃ ]
l9 [X₂+1-X₃ ]
l10 [X₂+1-X₃ ]

MPRF for transition t₉: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄) :|: X₃ < X₂ ∧ 0 ≤ X₃ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

l13 [X₂-X₀ ]
l12 [X₂-X₀ ]
l9 [X₂-X₃ ]
l10 [X₂-X₃-1 ]

MPRF for transition t₁₂: l12(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: X₄ < X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁⋅X₂ {O(n^2)}

MPRF:

l10 [X₁ ]
l9 [X₁-X₄ ]
l13 [X₁-X₄-1 ]
l12 [X₁-X₄ ]

MPRF for transition t₁₄: l13(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂, X₃, X₄+1) :|: 1+X₄ ≤ X₁ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁⋅X₂ {O(n^2)}

MPRF:

l10 [X₁ ]
l9 [X₁-X₄ ]
l13 [X₁-X₄ ]
l12 [X₁-X₄ ]

Analysing control-flow refined program

Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l11

Found invariant X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l13___3

Found invariant 1+X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l13___1

Found invariant X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ for location n_l12___2

Found invariant X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ for location l12

Found invariant 1+X₃ ≤ X₂ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₂ for location l10

Found invariant 0 ≤ X₃ for location l9

Found invariant 0 ≤ X₃ ∧ X₂ ≤ X₃ for location l14

knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₉₆: l12(X₀, X₁, X₂, X₃, X₄) → n_l13___3(X₀, X₁, X₂, X₀-1, X₄) :|: X₀ ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ X₄ ≤ 0 ∧ 0 ≤ X₄ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1+X₃ ≤ X₂ ∧ X₄ < X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀

knowledge_propagation leads to new time bound X₂ {O(n)} for transition t₉₈: n_l13___3(X₀, X₁, X₂, X₃, X₄) → n_l12___2(X₀, X₁, X₂, X₀-1, X₄+1) :|: 1+X₃ ≤ X₂ ∧ 0 < X₁ ∧ 0 ≤ X₃ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ X₄ ≤ 0 ∧ 0 ≤ X₄ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ X₄ ≤ 0 ∧ X₄ ≤ X₃ ∧ 1+X₄ ≤ X₂ ∧ 1+X₄ ≤ X₁ ∧ 1+X₄ ≤ X₀ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₁+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀

MPRF for transition t₉₅: n_l12___2(X₀, X₁, X₂, X₃, X₄) → n_l13___1(X₀, X₁, X₂, X₀-1, X₄) :|: X₀ ≤ X₂ ∧ 0 ≤ X₄ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ X₀ ≤ 1+X₃ ∧ 1+X₃ ≤ X₀ ∧ 1 ≤ X₀ ∧ 1 ≤ X₄ ∧ X₄ ≤ X₁ ∧ X₀ ≤ X₂ ∧ X₄ < X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₁⋅X₂+2⋅X₂ {O(n^2)}

MPRF:

l12 [0 ]
n_l13___3 [0 ]
l10 [0 ]
l9 [0 ]
n_l13___1 [X₁-X₄ ]
n_l12___2 [X₁+1-X₄ ]

MPRF for transition t₁₀₂: n_l12___2(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₀, X₄) :|: X₁ ≤ X₄ ∧ 0 ≤ X₄ ∧ 0 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₀ ∧ X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 1 ≤ X₁ ∧ 2 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

X₂ {O(n)}

MPRF:

l12 [X₂-X₃ ]
l10 [X₂-X₃ ]
l9 [X₂-X₃ ]
n_l13___1 [X₂+1-X₀ ]
n_l13___3 [X₂-X₃ ]
n_l12___2 [X₂+1-X₀ ]

MPRF for transition t₉₇: n_l13___1(X₀, X₁, X₂, X₃, X₄) → n_l12___2(X₀, X₁, X₂, X₀-1, X₄+1) :|: X₀ ≤ X₂ ∧ X₄ < X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₀ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₀ ∧ 0 ≤ X₄ ∧ X₀ ≤ X₂ ∧ X₀ ≤ X₃+1 ∧ 1+X₃ ≤ X₀ ∧ 1+X₄ ≤ X₁ ∧ 1 ≤ X₄ ∧ 1 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 3 ≤ X₁+X₄ ∧ 2 ≤ X₀+X₄ ∧ 1+X₃ ≤ X₂ ∧ 1+X₃ ≤ X₀ ∧ 0 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₀+X₃ ∧ X₀ ≤ 1+X₃ ∧ 1 ≤ X₂ ∧ 3 ≤ X₁+X₂ ∧ 2 ≤ X₀+X₂ ∧ X₀ ≤ X₂ ∧ 2 ≤ X₁ ∧ 3 ≤ X₀+X₁ ∧ 1 ≤ X₀ of depth 1:

new bound:

2⋅X₁⋅X₂+3⋅X₂+X₁ {O(n^2)}

MPRF:

l12 [X₁-2⋅X₀ ]
n_l13___3 [X₁-2⋅X₂ ]
l10 [X₁-2⋅X₃ ]
l9 [X₁-2⋅X₃ ]
n_l13___1 [2⋅X₁-X₄-2 ]
n_l12___2 [2⋅X₁-X₄-2 ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:2⋅X₁⋅X₂+3⋅X₂+12 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₁: X₂ {O(n)}
t₁₅: 1 {O(1)}
t₁₂: X₁⋅X₂ {O(n^2)}
t₁₃: X₂+1 {O(n)}
t₁₄: X₁⋅X₂ {O(n^2)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₂ {O(n)}
t₁₀: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₁⋅X₂+3⋅X₂+12 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₁₁: X₂ {O(n)}
t₁₅: 1 {O(1)}
t₁₂: X₁⋅X₂ {O(n^2)}
t₁₃: X₂+1 {O(n)}
t₁₄: X₁⋅X₂ {O(n^2)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}
t₇: 1 {O(1)}
t₈: 1 {O(1)}
t₉: X₂ {O(n)}
t₁₀: 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)}
t₃, X₀: X₀ {O(n)}
t₃, X₁: X₁ {O(n)}
t₃, X₂: X₂ {O(n)}
t₃, X₃: X₃ {O(n)}
t₃, X₄: X₄ {O(n)}
t₁₁, X₀: X₂ {O(n)}
t₁₁, X₁: X₁ {O(n)}
t₁₁, X₂: X₂ {O(n)}
t₁₁, X₃: X₂ {O(n)}
t₁₁, X₄: 0 {O(1)}
t₁₅, X₀: 2⋅X₂+X₀ {O(n)}
t₁₅, X₁: 2⋅X₁ {O(n)}
t₁₅, X₂: 2⋅X₂ {O(n)}
t₁₅, X₃: X₂ {O(n)}
t₁₅, X₄: X₁⋅X₂+X₄ {O(n^2)}
t₁₂, X₀: X₂ {O(n)}
t₁₂, X₁: X₁ {O(n)}
t₁₂, X₂: X₂ {O(n)}
t₁₂, X₃: X₂ {O(n)}
t₁₂, X₄: X₁⋅X₂ {O(n^2)}
t₁₃, X₀: 2⋅X₂ {O(n)}
t₁₃, X₁: X₁ {O(n)}
t₁₃, X₂: X₂ {O(n)}
t₁₃, X₃: X₂ {O(n)}
t₁₃, X₄: X₁⋅X₂ {O(n^2)}
t₁₄, X₀: X₂ {O(n)}
t₁₄, X₁: X₁ {O(n)}
t₁₄, X₂: X₂ {O(n)}
t₁₄, X₃: X₂ {O(n)}
t₁₄, X₄: X₁⋅X₂ {O(n^2)}
t₁, X₀: X₀ {O(n)}
t₁, X₁: X₁ {O(n)}
t₁, X₂: X₂ {O(n)}
t₁, X₃: X₃ {O(n)}
t₁, X₄: X₄ {O(n)}
t₂, X₀: X₀ {O(n)}
t₂, X₁: X₁ {O(n)}
t₂, X₂: X₂ {O(n)}
t₂, X₃: X₃ {O(n)}
t₂, X₄: X₄ {O(n)}
t₄, X₀: X₀ {O(n)}
t₄, X₁: X₁ {O(n)}
t₄, X₂: X₂ {O(n)}
t₄, X₃: X₃ {O(n)}
t₄, X₄: X₄ {O(n)}
t₅, X₀: X₀ {O(n)}
t₅, X₁: X₁ {O(n)}
t₅, X₂: X₂ {O(n)}
t₅, X₃: X₃ {O(n)}
t₅, X₄: X₄ {O(n)}
t₆, X₀: X₀ {O(n)}
t₆, X₁: X₁ {O(n)}
t₆, X₂: X₂ {O(n)}
t₆, X₃: X₃ {O(n)}
t₆, X₄: X₄ {O(n)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₁ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₈, X₀: X₀ {O(n)}
t₈, X₁: X₁ {O(n)}
t₈, X₂: X₂ {O(n)}
t₈, X₃: 0 {O(1)}
t₈, X₄: X₄ {O(n)}
t₉, X₀: 2⋅X₂+X₀ {O(n)}
t₉, X₁: X₁ {O(n)}
t₉, X₂: X₂ {O(n)}
t₉, X₃: X₂ {O(n)}
t₉, X₄: X₁⋅X₂+X₄ {O(n^2)}
t₁₀, X₀: 2⋅X₂+X₀ {O(n)}
t₁₀, X₁: 2⋅X₁ {O(n)}
t₁₀, X₂: 2⋅X₂ {O(n)}
t₁₀, X₃: X₂ {O(n)}
t₁₀, X₄: X₁⋅X₂+X₄ {O(n^2)}