MAYBE
* Step 1: Failure MAYBE
  + Considered Problem:
      - Strict TRS:
          a__add(X1,X2) -> add(X1,X2)
          a__add(0(),X) -> mark(X)
          a__add(s(X),Y) -> s(a__add(mark(X),mark(Y)))
          a__dbl(X) -> dbl(X)
          a__dbl(0()) -> 0()
          a__dbl(s(X)) -> s(s(a__dbl(mark(X))))
          a__first(X1,X2) -> first(X1,X2)
          a__first(0(),X) -> nil()
          a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
          a__sqr(X) -> sqr(X)
          a__sqr(0()) -> 0()
          a__sqr(s(X)) -> s(a__add(a__sqr(mark(X)),a__dbl(mark(X))))
          a__terms(N) -> cons(recip(a__sqr(mark(N))),terms(s(N)))
          a__terms(X) -> terms(X)
          mark(0()) -> 0()
          mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
          mark(cons(X1,X2)) -> cons(mark(X1),X2)
          mark(dbl(X)) -> a__dbl(mark(X))
          mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
          mark(nil()) -> nil()
          mark(recip(X)) -> recip(mark(X))
          mark(s(X)) -> s(mark(X))
          mark(sqr(X)) -> a__sqr(mark(X))
          mark(terms(X)) -> a__terms(mark(X))
      - Signature:
          {a__add/2,a__dbl/1,a__first/2,a__sqr/1,a__terms/1,mark/1} / {0/0,add/2,cons/2,dbl/1,first/2,nil/0,recip/1
          ,s/1,sqr/1,terms/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {a__add,a__dbl,a__first,a__sqr,a__terms
          ,mark} and constructors {0,add,cons,dbl,first,nil,recip,s,sqr,terms}
  + Applied Processor:
      Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT}
  + Details:
      The input can not be schown compatible.
MAYBE