Initial Problem

Start: l0
Program_Vars: X₀, X₁, X₂, X₃, X₄
Temp_Vars:
Locations: l0, l1, l10, l11, l12, l13, l14, l15, 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)
t₇: l10(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₄, X₂, X₃, X₄)
t₁₃: l11(X₀, X₁, X₂, X₃, X₄) → l6(X₁-1, X₁, X₂, X₃, X₄)
t₁₁: l12(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₂ < 1
t₁₀: l12(X₀, X₁, X₂, X₃, X₄) → l14(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₂
t₁₆: l13(X₀, X₁, X₂, X₃, X₄) → l15(X₀, X₁, X₂, X₃, X₄)
t₁₂: l14(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂-1, X₃, X₄)
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) → l8(X₀, X₁, X₂, X₃, X₄)
t₈: l5(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₃, X₃, X₄) :|: 1 ≤ X₁
t₉: l5(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: X₁ < 1
t₁₄: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄)
t₁₅: l7(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₀, X₂, X₃, X₄)
t₅: l8(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄)
t₆: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄)

Preprocessing

Found invariant 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁ for location l11

Found invariant 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l6

Found invariant X₁ ≤ X₄ ∧ X₁ ≤ 0 for location l15

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁ for location l12

Found invariant 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l7

Found invariant X₁ ≤ X₄ for location l5

Found invariant X₁ ≤ X₄ ∧ X₁ ≤ 0 for location l13

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ 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, l15, 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)
t₇: l10(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₄, X₂, X₃, X₄)
t₁₃: l11(X₀, X₁, X₂, X₃, X₄) → l6(X₁-1, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁
t₁₁: l12(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₂ < 1 ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁
t₁₀: l12(X₀, X₁, X₂, X₃, X₄) → l14(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁
t₁₆: l13(X₀, X₁, X₂, X₃, X₄) → l15(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₄ ∧ X₁ ≤ 0
t₁₂: l14(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂-1, X₃, X₄) :|: 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁
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) → l8(X₀, X₁, X₂, X₃, X₄)
t₈: l5(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₃, X₃, X₄) :|: 1 ≤ X₁ ∧ X₁ ≤ X₄
t₉: l5(X₀, X₁, X₂, X₃, X₄) → l13(X₀, X₁, X₂, X₃, X₄) :|: X₁ < 1 ∧ X₁ ≤ X₄
t₁₄: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₁₅: l7(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₀, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀
t₅: l8(X₀, X₁, X₂, X₃, X₄) → l9(X₀, X₁, X₂, X₃, X₄)
t₆: l9(X₀, X₁, X₂, X₃, X₄) → l10(X₀, X₁, X₂, X₃, X₄)

MPRF for transition t₁₃: l11(X₀, X₁, X₂, X₃, X₄) → l6(X₁-1, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

l11 [X₁+1 ]
l14 [X₁+1 ]
l12 [X₁+1 ]
l6 [X₀+1 ]
l7 [X₀+1 ]
l5 [X₁+1 ]

MPRF for transition t₁₁: l12(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₂ < 1 ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₄+1 {O(n)}

MPRF:

l11 [X₁ ]
l14 [X₁+1 ]
l12 [X₁+1 ]
l6 [X₀+1 ]
l7 [X₀+1 ]
l5 [X₁+1 ]

MPRF for transition t₈: l5(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₃, X₃, X₄) :|: 1 ≤ X₁ ∧ X₁ ≤ X₄ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l11 [X₁-1 ]
l14 [X₁-1 ]
l12 [X₁-1 ]
l6 [X₁-1 ]
l7 [X₀ ]
l5 [X₁ ]

MPRF for transition t₁₄: l6(X₀, X₁, X₂, X₃, X₄) → l7(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l11 [X₁ ]
l14 [X₁ ]
l12 [X₁ ]
l6 [X₀+1 ]
l7 [X₀ ]
l5 [X₁ ]

MPRF for transition t₁₅: l7(X₀, X₁, X₂, X₃, X₄) → l5(X₀, X₀, X₂, X₃, X₄) :|: 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l11 [X₁ ]
l14 [X₁ ]
l12 [X₁ ]
l6 [X₁ ]
l7 [X₁ ]
l5 [X₁ ]

MPRF for transition t₁₀: l12(X₀, X₁, X₂, X₃, X₄) → l14(X₀, X₁, X₂, X₃, X₄) :|: 1 ≤ X₂ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₃⋅X₄+X₃ {O(n^2)}

MPRF:

l11 [X₂ ]
l14 [X₂-1 ]
l5 [X₃ ]
l12 [X₂ ]
l6 [X₂ ]
l7 [X₂ ]

MPRF for transition t₁₂: l14(X₀, X₁, X₂, X₃, X₄) → l12(X₀, X₁, X₂-1, X₃, X₄) :|: 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₃⋅X₄+X₃ {O(n^2)}

MPRF:

l11 [X₂ ]
l14 [X₂ ]
l5 [X₃ ]
l12 [X₂ ]
l6 [X₂ ]
l7 [X₂ ]

Analysing control-flow refined program

Found invariant 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ 1 ≤ X₁ for location l11

Found invariant 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l6

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location n_l14___3

Found invariant X₁ ≤ X₄ ∧ X₁ ≤ 0 for location l15

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

Found invariant 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁ for location l12

Found invariant 1 ≤ X₄ ∧ 1+X₂ ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₀+X₄ ∧ 1+X₀ ≤ X₄ ∧ X₂ ≤ X₃ ∧ X₂ ≤ 0 ∧ 1+X₂ ≤ X₁ ∧ X₂ ≤ X₀ ∧ X₁ ≤ 1+X₀ ∧ 1 ≤ X₁ ∧ 1 ≤ X₀+X₁ ∧ 1+X₀ ≤ X₁ ∧ 0 ≤ X₀ for location l7

Found invariant X₁ ≤ X₄ for location l5

Found invariant X₁ ≤ X₄ ∧ X₁ ≤ 0 for location l13

Found invariant 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ for location n_l14___1

knowledge_propagation leads to new time bound X₄ {O(n)} for transition t₁₀₃: l12(X₀, X₁, X₂, X₃, X₄) → n_l14___3(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₄ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 ≤ X₁ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₂ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁

knowledge_propagation leads to new time bound X₄ {O(n)} for transition t₁₀₅: n_l14___3(X₀, X₁, X₂, X₃, X₄) → n_l12___2(X₀, X₁, X₂-1, X₃, X₄) :|: X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₃ ≤ X₂ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₃ ≤ X₂ ∧ 1 ≤ X₃ ∧ 2 ≤ X₂+X₃ ∧ X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁

MPRF for transition t₁₀₂: n_l12___2(X₀, X₁, X₂, X₃, X₄) → n_l14___1(X₀, X₁, X₂, X₃, X₄) :|: X₁ ≤ X₄ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₁ ∧ 0 ≤ X₂ ∧ 1+X₂ ≤ X₃ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

2⋅X₃⋅X₄+X₄ {O(n^2)}

MPRF:

n_l14___3 [0 ]
l12 [0 ]
l6 [0 ]
l7 [0 ]
l5 [0 ]
l11 [0 ]
n_l14___1 [X₂ ]
n_l12___2 [X₂+1 ]

MPRF for transition t₁₀₉: n_l12___2(X₀, X₁, X₂, X₃, X₄) → l11(X₀, X₁, X₂, X₃, X₄) :|: X₂ < 1 ∧ 1 ≤ X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ X₂ ≤ X₃ ∧ 1 ≤ X₁ ∧ 1 ≤ X₄ ∧ 2 ≤ X₃+X₄ ∧ 1 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₃ ∧ 1 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 2 ≤ X₁+X₃ ∧ 0 ≤ X₂ ∧ 1 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

X₄ {O(n)}

MPRF:

l12 [X₁ ]
l6 [X₁-1 ]
l7 [X₁-1 ]
l5 [X₁ ]
l11 [X₁-1 ]
n_l14___1 [X₁ ]
n_l14___3 [X₁ ]
n_l12___2 [X₁ ]

MPRF for transition t₁₀₄: n_l14___1(X₀, X₁, X₂, X₃, X₄) → n_l12___2(X₀, X₁, X₂-1, X₃, X₄) :|: X₁ ≤ X₄ ∧ 1+X₂ ≤ X₃ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ 1 ≤ X₂ ∧ 1 ≤ X₁ ∧ X₂ ≤ X₃ ∧ X₁ ≤ X₄ ∧ 1 ≤ X₄ ∧ 3 ≤ X₃+X₄ ∧ 2 ≤ X₂+X₄ ∧ 2 ≤ X₁+X₄ ∧ X₁ ≤ X₄ ∧ 2 ≤ X₃ ∧ 3 ≤ X₂+X₃ ∧ 1+X₂ ≤ X₃ ∧ 3 ≤ X₁+X₃ ∧ 1 ≤ X₂ ∧ 2 ≤ X₁+X₂ ∧ 1 ≤ X₁ of depth 1:

new bound:

2⋅X₃⋅X₄ {O(n^2)}

MPRF:

n_l14___3 [0 ]
l12 [0 ]
l6 [0 ]
l7 [0 ]
l5 [0 ]
l11 [0 ]
n_l14___1 [X₂ ]
n_l12___2 [X₂ ]

CFR did not improve the program. Rolling back

All Bounds

Timebounds

Overall timebound:2⋅X₃⋅X₄+2⋅X₃+5⋅X₄+12 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₇: 1 {O(1)}
t₁₃: X₄+1 {O(n)}
t₁₀: X₃⋅X₄+X₃ {O(n^2)}
t₁₁: X₄+1 {O(n)}
t₁₆: 1 {O(1)}
t₁₂: X₃⋅X₄+X₃ {O(n^2)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₈: X₄ {O(n)}
t₉: 1 {O(1)}
t₁₄: X₄ {O(n)}
t₁₅: X₄ {O(n)}
t₅: 1 {O(1)}
t₆: 1 {O(1)}

Costbounds

Overall costbound: 2⋅X₃⋅X₄+2⋅X₃+5⋅X₄+12 {O(n^2)}
t₀: 1 {O(1)}
t₃: 1 {O(1)}
t₇: 1 {O(1)}
t₁₃: X₄+1 {O(n)}
t₁₀: X₃⋅X₄+X₃ {O(n^2)}
t₁₁: X₄+1 {O(n)}
t₁₆: 1 {O(1)}
t₁₂: X₃⋅X₄+X₃ {O(n^2)}
t₁: 1 {O(1)}
t₂: 1 {O(1)}
t₄: 1 {O(1)}
t₈: X₄ {O(n)}
t₉: 1 {O(1)}
t₁₄: X₄ {O(n)}
t₁₅: X₄ {O(n)}
t₅: 1 {O(1)}
t₆: 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)}
t₇, X₀: X₀ {O(n)}
t₇, X₁: X₄ {O(n)}
t₇, X₂: X₂ {O(n)}
t₇, X₃: X₃ {O(n)}
t₇, X₄: X₄ {O(n)}
t₁₃, X₀: X₄ {O(n)}
t₁₃, X₁: X₄ {O(n)}
t₁₃, X₂: 4⋅X₃ {O(n)}
t₁₃, X₃: X₃ {O(n)}
t₁₃, X₄: X₄ {O(n)}
t₁₀, X₀: X₀+X₄ {O(n)}
t₁₀, X₁: X₄ {O(n)}
t₁₀, X₂: 2⋅X₃ {O(n)}
t₁₀, X₃: X₃ {O(n)}
t₁₀, X₄: X₄ {O(n)}
t₁₁, X₀: 2⋅X₀+2⋅X₄ {O(n)}
t₁₁, X₁: X₄ {O(n)}
t₁₁, X₂: 4⋅X₃ {O(n)}
t₁₁, X₃: X₃ {O(n)}
t₁₁, X₄: X₄ {O(n)}
t₁₆, X₀: X₀+X₄ {O(n)}
t₁₆, X₁: 2⋅X₄ {O(n)}
t₁₆, X₂: 4⋅X₃+X₂ {O(n)}
t₁₆, X₃: 2⋅X₃ {O(n)}
t₁₆, X₄: 2⋅X₄ {O(n)}
t₁₂, X₀: X₀+X₄ {O(n)}
t₁₂, X₁: X₄ {O(n)}
t₁₂, X₂: 2⋅X₃ {O(n)}
t₁₂, X₃: X₃ {O(n)}
t₁₂, X₄: X₄ {O(n)}
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)}
t₈, X₀: X₀+X₄ {O(n)}
t₈, X₁: X₄ {O(n)}
t₈, X₂: 2⋅X₃ {O(n)}
t₈, X₃: X₃ {O(n)}
t₈, X₄: X₄ {O(n)}
t₉, X₀: X₀+X₄ {O(n)}
t₉, X₁: 2⋅X₄ {O(n)}
t₉, X₂: 4⋅X₃+X₂ {O(n)}
t₉, X₃: 2⋅X₃ {O(n)}
t₉, X₄: 2⋅X₄ {O(n)}
t₁₄, X₀: X₄ {O(n)}
t₁₄, X₁: X₄ {O(n)}
t₁₄, X₂: 4⋅X₃ {O(n)}
t₁₄, X₃: X₃ {O(n)}
t₁₄, X₄: X₄ {O(n)}
t₁₅, X₀: X₄ {O(n)}
t₁₅, X₁: X₄ {O(n)}
t₁₅, X₂: 4⋅X₃ {O(n)}
t₁₅, X₃: X₃ {O(n)}
t₁₅, 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)}