MAYBE
Time: 0.000914
TRS:
 {            first(X1, X2) -> n__first(X1, X2),
              first(0(), X) -> nil(),
     first(s X, cons(Y, Z)) -> cons(Y, n__first(X, activate Z)),
                 activate X -> X,
  activate n__first(X1, X2) -> first(X1, X2),
         activate n__from X -> from X,
                     from X -> cons(X, n__from s X),
                     from X -> n__from X}
 DP:
  DP:
   {   first#(s X, cons(Y, Z)) -> activate# Z,
    activate# n__first(X1, X2) -> first#(X1, X2),
           activate# n__from X -> from# X}
  TRS:
  {            first(X1, X2) -> n__first(X1, X2),
               first(0(), X) -> nil(),
      first(s X, cons(Y, Z)) -> cons(Y, n__first(X, activate Z)),
                  activate X -> X,
   activate n__first(X1, X2) -> first(X1, X2),
          activate n__from X -> from X,
                      from X -> cons(X, n__from s X),
                      from X -> n__from X}
  EDG:
   {(first#(s X, cons(Y, Z)) -> activate# Z, activate# n__from X -> from# X)
    (first#(s X, cons(Y, Z)) -> activate# Z, activate# n__first(X1, X2) -> first#(X1, X2))
    (activate# n__first(X1, X2) -> first#(X1, X2), first#(s X, cons(Y, Z)) -> activate# Z)}
   STATUS:
    arrows: 0.666667
    SCCS (1):
     Scc:
      {   first#(s X, cons(Y, Z)) -> activate# Z,
       activate# n__first(X1, X2) -> first#(X1, X2)}
     
     SCC (2):
      Strict:
       {   first#(s X, cons(Y, Z)) -> activate# Z,
        activate# n__first(X1, X2) -> first#(X1, X2)}
      Weak:
      {            first(X1, X2) -> n__first(X1, X2),
                   first(0(), X) -> nil(),
          first(s X, cons(Y, Z)) -> cons(Y, n__first(X, activate Z)),
                      activate X -> X,
       activate n__first(X1, X2) -> first(X1, X2),
              activate n__from X -> from X,
                          from X -> cons(X, n__from s X),
                          from X -> n__from X}
      Open