MAYBE
* Step 1: Failure MAYBE
  + Considered Problem:
      - Strict TRS:
          app(l,nil()) -> l
          app(cons(x,l),k) -> cons(x,app(l,k))
          app(nil(),k) -> k
          gt(s(x),s(y)) -> gt(x,y)
          gt(s(x),zero()) -> true()
          gt(zero(),y) -> false()
          id(x) -> x
          if(false(),x,y) -> y
          if(true(),x,y) -> x
          not(x) -> if(x,false(),true())
          plus(id(x),s(y)) -> s(plus(x,if(gt(s(y),y),y,s(y))))
          plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x))
          plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))))
          plus(zero(),y) -> y
          sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k)))))
          sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l))
          sum(cons(x,nil())) -> cons(x,nil())
      - Signature:
          {app/2,gt/2,id/1,if/3,not/1,plus/2,sum/1} / {cons/2,false/0,nil/0,s/1,true/0,zero/0}
      - Obligation:
          innermost runtime complexity wrt. defined symbols {app,gt,id,if,not,plus,sum} and constructors {cons,false
          ,nil,s,true,zero}
  + Applied Processor:
      NaturalMI {miDimension = 3, miDegree = 3, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}
  + Details:
      Incompatible
MAYBE