MAYBE
Time: 0.007430
TRS:
 {                  sqr s X -> s n__add(sqr activate X, dbl activate X),
                    sqr 0() -> 0(),
                        s X -> n__s X,
                    terms N -> cons(recip sqr N, n__terms s N),
                    terms X -> n__terms X,
                 activate X -> X,
        activate n__terms X -> terms X,
    activate n__add(X1, X2) -> add(X1, X2),
            activate n__s X -> s X,
          activate n__dbl X -> dbl X,
  activate n__first(X1, X2) -> first(X1, X2),
                      dbl X -> n__dbl X,
                    dbl s X -> s n__s n__dbl activate X,
                    dbl 0() -> 0(),
                add(X1, X2) -> n__add(X1, X2),
                add(s X, Y) -> s n__add(activate X, Y),
                add(0(), X) -> X,
              first(X1, X2) -> n__first(X1, X2),
     first(s X, cons(Y, Z)) -> cons(Y, n__first(activate X, activate Z)),
              first(0(), X) -> nil()}
 DP:
  DP:
   {                  sqr# s X -> sqr# activate X,
                      sqr# s X -> s# n__add(sqr activate X, dbl activate X),
                      sqr# s X -> activate# X,
                      sqr# s X -> dbl# activate X,
                      terms# N -> sqr# N,
                      terms# N -> s# N,
          activate# n__terms X -> terms# X,
      activate# n__add(X1, X2) -> add#(X1, X2),
              activate# n__s X -> s# X,
            activate# n__dbl X -> dbl# X,
    activate# n__first(X1, X2) -> first#(X1, X2),
                      dbl# s X -> s# n__s n__dbl activate X,
                      dbl# s X -> activate# X,
                  add#(s X, Y) -> s# n__add(activate X, Y),
                  add#(s X, Y) -> activate# X,
       first#(s X, cons(Y, Z)) -> activate# X,
       first#(s X, cons(Y, Z)) -> activate# Z}
  TRS:
  {                  sqr s X -> s n__add(sqr activate X, dbl activate X),
                     sqr 0() -> 0(),
                         s X -> n__s X,
                     terms N -> cons(recip sqr N, n__terms s N),
                     terms X -> n__terms X,
                  activate X -> X,
         activate n__terms X -> terms X,
     activate n__add(X1, X2) -> add(X1, X2),
             activate n__s X -> s X,
           activate n__dbl X -> dbl X,
   activate n__first(X1, X2) -> first(X1, X2),
                       dbl X -> n__dbl X,
                     dbl s X -> s n__s n__dbl activate X,
                     dbl 0() -> 0(),
                 add(X1, X2) -> n__add(X1, X2),
                 add(s X, Y) -> s n__add(activate X, Y),
                 add(0(), X) -> X,
               first(X1, X2) -> n__first(X1, X2),
      first(s X, cons(Y, Z)) -> cons(Y, n__first(activate X, activate Z)),
               first(0(), X) -> nil()}
  UR:
   {                  sqr s X -> s n__add(sqr activate X, dbl activate X),
                      sqr 0() -> 0(),
                          s X -> n__s X,
                      terms N -> cons(recip sqr N, n__terms s N),
                      terms X -> n__terms X,
                   activate X -> X,
          activate n__terms X -> terms X,
      activate n__add(X1, X2) -> add(X1, X2),
              activate n__s X -> s X,
            activate n__dbl X -> dbl X,
    activate n__first(X1, X2) -> first(X1, X2),
                        dbl X -> n__dbl X,
                      dbl s X -> s n__s n__dbl activate X,
                      dbl 0() -> 0(),
                  add(X1, X2) -> n__add(X1, X2),
                  add(s X, Y) -> s n__add(activate X, Y),
                  add(0(), X) -> X,
                first(X1, X2) -> n__first(X1, X2),
       first(s X, cons(Y, Z)) -> cons(Y, n__first(activate X, activate Z)),
                first(0(), X) -> nil(),
                      a(x, y) -> x,
                      a(x, y) -> y}
   EDG:
    {(sqr# s X -> dbl# activate X, dbl# s X -> activate# X)
     (sqr# s X -> dbl# activate X, dbl# s X -> s# n__s n__dbl activate X)
     (activate# n__add(X1, X2) -> add#(X1, X2), add#(s X, Y) -> activate# X)
     (activate# n__add(X1, X2) -> add#(X1, X2), add#(s X, Y) -> s# n__add(activate X, Y))
     (first#(s X, cons(Y, Z)) -> activate# Z, activate# n__first(X1, X2) -> first#(X1, X2))
     (first#(s X, cons(Y, Z)) -> activate# Z, activate# n__dbl X -> dbl# X)
     (first#(s X, cons(Y, Z)) -> activate# Z, activate# n__s X -> s# X)
     (first#(s X, cons(Y, Z)) -> activate# Z, activate# n__add(X1, X2) -> add#(X1, X2))
     (first#(s X, cons(Y, Z)) -> activate# Z, activate# n__terms X -> terms# X)
     (activate# n__terms X -> terms# X, terms# N -> s# N)
     (activate# n__terms X -> terms# X, terms# N -> sqr# N)
     (activate# n__dbl X -> dbl# X, dbl# s X -> activate# X)
     (activate# n__dbl X -> dbl# X, dbl# s X -> s# n__s n__dbl activate X)
     (add#(s X, Y) -> activate# X, activate# n__first(X1, X2) -> first#(X1, X2))
     (add#(s X, Y) -> activate# X, activate# n__dbl X -> dbl# X)
     (add#(s X, Y) -> activate# X, activate# n__s X -> s# X)
     (add#(s X, Y) -> activate# X, activate# n__add(X1, X2) -> add#(X1, X2))
     (add#(s X, Y) -> activate# X, activate# n__terms X -> terms# X)
     (terms# N -> sqr# N, sqr# s X -> dbl# activate X)
     (terms# N -> sqr# N, sqr# s X -> activate# X)
     (terms# N -> sqr# N, sqr# s X -> s# n__add(sqr activate X, dbl activate X))
     (terms# N -> sqr# N, sqr# s X -> sqr# activate X)
     (first#(s X, cons(Y, Z)) -> activate# X, activate# n__terms X -> terms# X)
     (first#(s X, cons(Y, Z)) -> activate# X, activate# n__add(X1, X2) -> add#(X1, X2))
     (first#(s X, cons(Y, Z)) -> activate# X, activate# n__s X -> s# X)
     (first#(s X, cons(Y, Z)) -> activate# X, activate# n__dbl X -> dbl# X)
     (first#(s X, cons(Y, Z)) -> activate# X, activate# n__first(X1, X2) -> first#(X1, X2))
     (dbl# s X -> activate# X, activate# n__terms X -> terms# X)
     (dbl# s X -> activate# X, activate# n__add(X1, X2) -> add#(X1, X2))
     (dbl# s X -> activate# X, activate# n__s X -> s# X)
     (dbl# s X -> activate# X, activate# n__dbl X -> dbl# X)
     (dbl# s X -> activate# X, activate# n__first(X1, X2) -> first#(X1, X2))
     (sqr# s X -> activate# X, activate# n__terms X -> terms# X)
     (sqr# s X -> activate# X, activate# n__add(X1, X2) -> add#(X1, X2))
     (sqr# s X -> activate# X, activate# n__s X -> s# X)
     (sqr# s X -> activate# X, activate# n__dbl X -> dbl# X)
     (sqr# s X -> activate# X, activate# n__first(X1, X2) -> first#(X1, X2))
     (activate# n__first(X1, X2) -> first#(X1, X2), first#(s X, cons(Y, Z)) -> activate# X)
     (activate# n__first(X1, X2) -> first#(X1, X2), first#(s X, cons(Y, Z)) -> activate# Z)
     (sqr# s X -> sqr# activate X, sqr# s X -> sqr# activate X)
     (sqr# s X -> sqr# activate X, sqr# s X -> s# n__add(sqr activate X, dbl activate X))
     (sqr# s X -> sqr# activate X, sqr# s X -> activate# X)
     (sqr# s X -> sqr# activate X, sqr# s X -> dbl# activate X)}
    STATUS:
     arrows: 0.851211
     SCCS (1):
      Scc:
       {                  sqr# s X -> sqr# activate X,
                          sqr# s X -> activate# X,
                          sqr# s X -> dbl# activate X,
                          terms# N -> sqr# N,
              activate# n__terms X -> terms# X,
          activate# n__add(X1, X2) -> add#(X1, X2),
                activate# n__dbl X -> dbl# X,
        activate# n__first(X1, X2) -> first#(X1, X2),
                          dbl# s X -> activate# X,
                      add#(s X, Y) -> activate# X,
           first#(s X, cons(Y, Z)) -> activate# X,
           first#(s X, cons(Y, Z)) -> activate# Z}
      
      SCC (12):
       Strict:
        {                  sqr# s X -> sqr# activate X,
                           sqr# s X -> activate# X,
                           sqr# s X -> dbl# activate X,
                           terms# N -> sqr# N,
               activate# n__terms X -> terms# X,
           activate# n__add(X1, X2) -> add#(X1, X2),
                 activate# n__dbl X -> dbl# X,
         activate# n__first(X1, X2) -> first#(X1, X2),
                           dbl# s X -> activate# X,
                       add#(s X, Y) -> activate# X,
            first#(s X, cons(Y, Z)) -> activate# X,
            first#(s X, cons(Y, Z)) -> activate# Z}
       Weak:
       {                  sqr s X -> s n__add(sqr activate X, dbl activate X),
                          sqr 0() -> 0(),
                              s X -> n__s X,
                          terms N -> cons(recip sqr N, n__terms s N),
                          terms X -> n__terms X,
                       activate X -> X,
              activate n__terms X -> terms X,
          activate n__add(X1, X2) -> add(X1, X2),
                  activate n__s X -> s X,
                activate n__dbl X -> dbl X,
        activate n__first(X1, X2) -> first(X1, X2),
                            dbl X -> n__dbl X,
                          dbl s X -> s n__s n__dbl activate X,
                          dbl 0() -> 0(),
                      add(X1, X2) -> n__add(X1, X2),
                      add(s X, Y) -> s n__add(activate X, Y),
                      add(0(), X) -> X,
                    first(X1, X2) -> n__first(X1, X2),
           first(s X, cons(Y, Z)) -> cons(Y, n__first(activate X, activate Z)),
                    first(0(), X) -> nil()}
       Open