MAYBE
Time: 0.001543
TRS:
 {                   from X -> cons(X, n__from s X),
                     from X -> n__from X,
              first(X1, X2) -> n__first(X1, X2),
     first(s X, cons(Y, Z)) -> cons(Y, n__first(X, activate Z)),
              first(0(), Z) -> nil(),
                 activate X -> X,
         activate n__from X -> from X,
  activate n__first(X1, X2) -> first(X1, X2),
       sel(s X, cons(Y, Z)) -> sel(X, activate Z),
       sel(0(), cons(X, Z)) -> X}
 DP:
  DP:
   {   first#(s X, cons(Y, Z)) -> activate# Z,
           activate# n__from X -> from# X,
    activate# n__first(X1, X2) -> first#(X1, X2),
         sel#(s X, cons(Y, Z)) -> activate# Z,
         sel#(s X, cons(Y, Z)) -> sel#(X, activate Z)}
  TRS:
  {                   from X -> cons(X, n__from s X),
                      from X -> n__from X,
               first(X1, X2) -> n__first(X1, X2),
      first(s X, cons(Y, Z)) -> cons(Y, n__first(X, activate Z)),
               first(0(), Z) -> nil(),
                  activate X -> X,
          activate n__from X -> from X,
   activate n__first(X1, X2) -> first(X1, X2),
        sel(s X, cons(Y, Z)) -> sel(X, activate Z),
        sel(0(), cons(X, Z)) -> X}
  EDG:
   {(sel#(s X, cons(Y, Z)) -> activate# Z, activate# n__first(X1, X2) -> first#(X1, X2))
    (sel#(s X, cons(Y, Z)) -> activate# Z, activate# n__from X -> from# X)
    (activate# n__first(X1, X2) -> first#(X1, X2), first#(s X, cons(Y, Z)) -> activate# Z)
    (sel#(s X, cons(Y, Z)) -> sel#(X, activate Z), sel#(s X, cons(Y, Z)) -> activate# Z)
    (sel#(s X, cons(Y, Z)) -> sel#(X, activate Z), sel#(s X, cons(Y, Z)) -> sel#(X, activate Z))
    (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))}
   STATUS:
    arrows: 0.720000
    SCCS (2):
     Scc:
      {sel#(s X, cons(Y, Z)) -> sel#(X, activate Z)}
     Scc:
      {   first#(s X, cons(Y, Z)) -> activate# Z,
       activate# n__first(X1, X2) -> first#(X1, X2)}
     
     SCC (1):
      Strict:
       {sel#(s X, cons(Y, Z)) -> sel#(X, activate Z)}
      Weak:
      {                   from X -> cons(X, n__from s X),
                          from X -> n__from X,
                   first(X1, X2) -> n__first(X1, X2),
          first(s X, cons(Y, Z)) -> cons(Y, n__first(X, activate Z)),
                   first(0(), Z) -> nil(),
                      activate X -> X,
              activate n__from X -> from X,
       activate n__first(X1, X2) -> first(X1, X2),
            sel(s X, cons(Y, Z)) -> sel(X, activate Z),
            sel(0(), cons(X, Z)) -> X}
      Open
     
     SCC (2):
      Strict:
       {   first#(s X, cons(Y, Z)) -> activate# Z,
        activate# n__first(X1, X2) -> first#(X1, X2)}
      Weak:
      {                   from X -> cons(X, n__from s X),
                          from X -> n__from X,
                   first(X1, X2) -> n__first(X1, X2),
          first(s X, cons(Y, Z)) -> cons(Y, n__first(X, activate Z)),
                   first(0(), Z) -> nil(),
                      activate X -> X,
              activate n__from X -> from X,
       activate n__first(X1, X2) -> first(X1, X2),
            sel(s X, cons(Y, Z)) -> sel(X, activate Z),
            sel(0(), cons(X, Z)) -> X}
      Open