MAYBE
* Step 1: Failure MAYBE
  + Considered Problem:
      - Strict TRS:
          append(ConsNat(x,xs),ys) -> ConsNat(x,append(xs,ys))
          append(NilNat(),ys) -> ys
          filterLeq(nr,ConsNat(x,xs)) -> ite(leq(nr,x),ConsNat(x,filterLeq(nr,xs)),filterLeq(nr,xs))
          filterLeq(nr,NilNat()) -> NilNat()
          takeWhileLeq(nr,Leaf(data)) -> data
          takeWhileLeq(nr,Node(ConsNat(up,nrs),ConsBTree(t,ts))) -> ite(leq(nr,up)
                                                                       ,append(takeWhileLeq(nr,t)
                                                                              ,takeWhileLeq(nr,Node(nrs,ts)))
                                                                       ,NilNat())
          takeWhileLeq(nr,Node(ConsNat(up,NilNat()),ConsBTree(tLeq,ConsBTree(tGt,NilBTree())))) -> ite(leq(nr,up)
                                                                                                      ,append(takeWhileLeq(nr
                                                                                                                          ,tLeq)
                                                                                                             ,filterLeq(nr
                                                                                                                       ,takeWhileLeq(nr
                                                                                                                                    ,tGt)))
                                                                                                      ,NilNat())
      - Weak TRS:
          ite(False(),t,e) -> e
          ite(True(),t,e) -> t
          leq(0(),0()) -> True()
          leq(0(),S(m)) -> True()
          leq(S(n),0()) -> False()
          leq(S(n),S(m)) -> leq(n,m)
      - Signature:
          {append/2,filterLeq/2,ite/3,leq/2,takeWhileLeq/2} / {0/0,ConsBTree/2,ConsNat/2,False/0,Leaf/1,NilBTree/0
          ,NilNat/0,Node/2,S/1,True/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {append,filterLeq,ite,leq
          ,takeWhileLeq} and constructors {0,ConsBTree,ConsNat,False,Leaf,NilBTree,NilNat,Node,S,True}
  + Applied Processor:
      EmptyProcessor
  + Details:
      The problem is still open.
MAYBE