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__fact(X) -> a__if(a__zero(mark(X)),s(0()),prod(X,fact(p(X))))
          a__fact(X) -> fact(X)
          a__if(X1,X2,X3) -> if(X1,X2,X3)
          a__if(false(),X,Y) -> mark(Y)
          a__if(true(),X,Y) -> mark(X)
          a__p(X) -> p(X)
          a__p(s(X)) -> mark(X)
          a__prod(X1,X2) -> prod(X1,X2)
          a__prod(0(),X) -> 0()
          a__prod(s(X),Y) -> a__add(mark(Y),a__prod(mark(X),mark(Y)))
          a__zero(X) -> zero(X)
          a__zero(0()) -> true()
          a__zero(s(X)) -> false()
          mark(0()) -> 0()
          mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
          mark(fact(X)) -> a__fact(mark(X))
          mark(false()) -> false()
          mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
          mark(p(X)) -> a__p(mark(X))
          mark(prod(X1,X2)) -> a__prod(mark(X1),mark(X2))
          mark(s(X)) -> s(mark(X))
          mark(true()) -> true()
          mark(zero(X)) -> a__zero(mark(X))
      - Signature:
          {a__add/2,a__fact/1,a__if/3,a__p/1,a__prod/2,a__zero/1,mark/1} / {0/0,add/2,fact/1,false/0,if/3,p/1,prod/2
          ,s/1,true/0,zero/1}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {a__add,a__fact,a__if,a__p,a__prod,a__zero
          ,mark} and constructors {0,add,fact,false,if,p,prod,s,true,zero}
  + Applied Processor:
      MI {miKind = Automaton Nothing, miDimension = 3, miUArgs = NoUArgs, miURules = NoURules, miSelector = Nothing}
  + Details:
      Incompatible
MAYBE