Problem Transformed CSR 04 Ex6 Luc98 Z

Tool CaT

Execution Time	Unknown
Answer	MAYBE
Input	Transformed CSR 04 Ex6 Luc98 Z

stdout:

MAYBE

Problem:
first(0(),X) -> nil()
first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
from(X) -> cons(X,n__from(s(X)))
first(X1,X2) -> n__first(X1,X2)
from(X) -> n__from(X)
activate(n__first(X1,X2)) -> first(X1,X2)
activate(n__from(X)) -> from(X)
activate(X) -> X

Proof:
Open

Tool IRC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex6 Luc98 Z

stdout:

YES(?,O(n^1))

Tool IRC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex6 Luc98 Z

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  first(0(), X) -> nil()
     , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
     , from(X) -> cons(X, n__from(s(X)))
     , first(X1, X2) -> n__first(X1, X2)
     , from(X) -> n__from(X)
     , activate(n__first(X1, X2)) -> first(X1, X2)
     , activate(n__from(X)) -> from(X)
     , activate(X) -> X}

Proof Output:
  'matrix-interpretation of dimension 1' proved the best result:

  Details:
  --------
    'matrix-interpretation of dimension 1' succeeded with the following output:
     'matrix-interpretation of dimension 1'
     --------------------------------------
     Answer:           YES(?,O(n^1))
     Input Problem:    innermost runtime-complexity with respect to
       Rules:
         {  first(0(), X) -> nil()
          , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
          , from(X) -> cons(X, n__from(s(X)))
          , first(X1, X2) -> n__first(X1, X2)
          , from(X) -> n__from(X)
          , activate(n__first(X1, X2)) -> first(X1, X2)
          , activate(n__from(X)) -> from(X)
          , activate(X) -> X}

     Proof Output:
       The following argument positions are usable:
         Uargs(first) = {}, Uargs(s) = {}, Uargs(cons) = {2},
         Uargs(n__first) = {2}, Uargs(activate) = {}, Uargs(from) = {},
         Uargs(n__from) = {}
       We have the following constructor-restricted matrix interpretation:
       Interpretation Functions:
        first(x1, x2) = [2] x1 + [2] x2 + [5]
        0() = [2]
        nil() = [0]
        s(x1) = [1] x1 + [2]
        cons(x1, x2) = [0] x1 + [1] x2 + [0]
        n__first(x1, x2) = [1] x1 + [1] x2 + [4]
        activate(x1) = [2] x1 + [4]
        from(x1) = [0] x1 + [3]
        n__from(x1) = [0] x1 + [0]

Tool RC1

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex6 Luc98 Z

stdout:

YES(?,O(n^1))

Tool RC2

Execution Time	Unknown
Answer	YES(?,O(n^1))
Input	Transformed CSR 04 Ex6 Luc98 Z

stdout:

YES(?,O(n^1))

'Fastest (timeout of 60.0 seconds)'
-----------------------------------
Answer:           YES(?,O(n^1))
Input Problem:    runtime-complexity with respect to
  Rules:
    {  first(0(), X) -> nil()
     , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
     , from(X) -> cons(X, n__from(s(X)))
     , first(X1, X2) -> n__first(X1, X2)
     , from(X) -> n__from(X)
     , activate(n__first(X1, X2)) -> first(X1, X2)
     , activate(n__from(X)) -> from(X)
     , activate(X) -> X}

Proof Output:
  'matrix-interpretation of dimension 1' proved the best result:

  Details:
  --------
    'matrix-interpretation of dimension 1' succeeded with the following output:
     'matrix-interpretation of dimension 1'
     --------------------------------------
     Answer:           YES(?,O(n^1))
     Input Problem:    runtime-complexity with respect to
       Rules:
         {  first(0(), X) -> nil()
          , first(s(X), cons(Y, Z)) -> cons(Y, n__first(X, activate(Z)))
          , from(X) -> cons(X, n__from(s(X)))
          , first(X1, X2) -> n__first(X1, X2)
          , from(X) -> n__from(X)
          , activate(n__first(X1, X2)) -> first(X1, X2)
          , activate(n__from(X)) -> from(X)
          , activate(X) -> X}

     Proof Output:
       The following argument positions are usable:
         Uargs(first) = {}, Uargs(s) = {}, Uargs(cons) = {2},
         Uargs(n__first) = {2}, Uargs(activate) = {}, Uargs(from) = {},
         Uargs(n__from) = {}
       We have the following constructor-restricted matrix interpretation:
       Interpretation Functions:
        first(x1, x2) = [2] x1 + [2] x2 + [5]
        0() = [2]
        nil() = [0]
        s(x1) = [1] x1 + [2]
        cons(x1, x2) = [0] x1 + [1] x2 + [0]
        n__first(x1, x2) = [1] x1 + [1] x2 + [4]
        activate(x1) = [2] x1 + [4]
        from(x1) = [0] x1 + [3]
        n__from(x1) = [0] x1 + [0]