MAYBE

Problem:
 prod(xs) -> prodIter(xs,s(0()))
 prodIter(xs,x) -> ifProd(isempty(xs),xs,x)
 ifProd(true(),xs,x) -> x
 ifProd(false(),xs,x) -> prodIter(tail(xs),times(x,head(xs)))
 plus(0(),y) -> y
 plus(s(x),y) -> s(plus(x,y))
 times(x,y) -> timesIter(x,y,0(),0())
 timesIter(x,y,z,u) -> ifTimes(ge(u,x),x,y,z,u)
 ifTimes(true(),x,y,z,u) -> z
 ifTimes(false(),x,y,z,u) -> timesIter(x,y,plus(y,z),s(u))
 isempty(nil()) -> true()
 isempty(cons(x,xs)) -> false()
 head(nil()) -> error()
 head(cons(x,xs)) -> x
 tail(nil()) -> nil()
 tail(cons(x,xs)) -> xs
 ge(x,0()) -> true()
 ge(0(),s(y)) -> false()
 ge(s(x),s(y)) -> ge(x,y)
 a() -> b()
 a() -> c()

Proof:
 DP Processor:
  DPs:
   prod#(xs) -> prodIter#(xs,s(0()))
   prodIter#(xs,x) -> isempty#(xs)
   prodIter#(xs,x) -> ifProd#(isempty(xs),xs,x)
   ifProd#(false(),xs,x) -> head#(xs)
   ifProd#(false(),xs,x) -> times#(x,head(xs))
   ifProd#(false(),xs,x) -> tail#(xs)
   ifProd#(false(),xs,x) -> prodIter#(tail(xs),times(x,head(xs)))
   plus#(s(x),y) -> plus#(x,y)
   times#(x,y) -> timesIter#(x,y,0(),0())
   timesIter#(x,y,z,u) -> ge#(u,x)
   timesIter#(x,y,z,u) -> ifTimes#(ge(u,x),x,y,z,u)
   ifTimes#(false(),x,y,z,u) -> plus#(y,z)
   ifTimes#(false(),x,y,z,u) -> timesIter#(x,y,plus(y,z),s(u))
   ge#(s(x),s(y)) -> ge#(x,y)
  TRS:
   prod(xs) -> prodIter(xs,s(0()))
   prodIter(xs,x) -> ifProd(isempty(xs),xs,x)
   ifProd(true(),xs,x) -> x
   ifProd(false(),xs,x) -> prodIter(tail(xs),times(x,head(xs)))
   plus(0(),y) -> y
   plus(s(x),y) -> s(plus(x,y))
   times(x,y) -> timesIter(x,y,0(),0())
   timesIter(x,y,z,u) -> ifTimes(ge(u,x),x,y,z,u)
   ifTimes(true(),x,y,z,u) -> z
   ifTimes(false(),x,y,z,u) -> timesIter(x,y,plus(y,z),s(u))
   isempty(nil()) -> true()
   isempty(cons(x,xs)) -> false()
   head(nil()) -> error()
   head(cons(x,xs)) -> x
   tail(nil()) -> nil()
   tail(cons(x,xs)) -> xs
   ge(x,0()) -> true()
   ge(0(),s(y)) -> false()
   ge(s(x),s(y)) -> ge(x,y)
   a() -> b()
   a() -> c()
  Usable Rule Processor:
   DPs:
    prod#(xs) -> prodIter#(xs,s(0()))
    prodIter#(xs,x) -> isempty#(xs)
    prodIter#(xs,x) -> ifProd#(isempty(xs),xs,x)
    ifProd#(false(),xs,x) -> head#(xs)
    ifProd#(false(),xs,x) -> times#(x,head(xs))
    ifProd#(false(),xs,x) -> tail#(xs)
    ifProd#(false(),xs,x) -> prodIter#(tail(xs),times(x,head(xs)))
    plus#(s(x),y) -> plus#(x,y)
    times#(x,y) -> timesIter#(x,y,0(),0())
    timesIter#(x,y,z,u) -> ge#(u,x)
    timesIter#(x,y,z,u) -> ifTimes#(ge(u,x),x,y,z,u)
    ifTimes#(false(),x,y,z,u) -> plus#(y,z)
    ifTimes#(false(),x,y,z,u) -> timesIter#(x,y,plus(y,z),s(u))
    ge#(s(x),s(y)) -> ge#(x,y)
   TRS:
    isempty(nil()) -> true()
    isempty(cons(x,xs)) -> false()
    head(nil()) -> error()
    head(cons(x,xs)) -> x
    times(x,y) -> timesIter(x,y,0(),0())
    timesIter(x,y,z,u) -> ifTimes(ge(u,x),x,y,z,u)
    ifTimes(true(),x,y,z,u) -> z
    ifTimes(false(),x,y,z,u) -> timesIter(x,y,plus(y,z),s(u))
    ge(x,0()) -> true()
    ge(0(),s(y)) -> false()
    ge(s(x),s(y)) -> ge(x,y)
    plus(0(),y) -> y
    plus(s(x),y) -> s(plus(x,y))
    tail(nil()) -> nil()
    tail(cons(x,xs)) -> xs
   Open