MAYBE

Problem:
 div(x,s(y)) -> d(x,s(y),0())
 d(x,s(y),z) -> cond(ge(x,z),x,y,z)
 cond(true(),x,y,z) -> s(d(x,s(y),plus(s(y),z)))
 cond(false(),x,y,z) -> 0()
 ge(u,0()) -> true()
 ge(0(),s(v)) -> false()
 ge(s(u),s(v)) -> ge(u,v)
 plus(n,0()) -> n
 plus(n,s(m)) -> s(plus(n,m))

Proof:
 DP Processor:
  DPs:
   div#(x,s(y)) -> d#(x,s(y),0())
   d#(x,s(y),z) -> ge#(x,z)
   d#(x,s(y),z) -> cond#(ge(x,z),x,y,z)
   cond#(true(),x,y,z) -> plus#(s(y),z)
   cond#(true(),x,y,z) -> d#(x,s(y),plus(s(y),z))
   ge#(s(u),s(v)) -> ge#(u,v)
   plus#(n,s(m)) -> plus#(n,m)
  TRS:
   div(x,s(y)) -> d(x,s(y),0())
   d(x,s(y),z) -> cond(ge(x,z),x,y,z)
   cond(true(),x,y,z) -> s(d(x,s(y),plus(s(y),z)))
   cond(false(),x,y,z) -> 0()
   ge(u,0()) -> true()
   ge(0(),s(v)) -> false()
   ge(s(u),s(v)) -> ge(u,v)
   plus(n,0()) -> n
   plus(n,s(m)) -> s(plus(n,m))
  Usable Rule Processor:
   DPs:
    div#(x,s(y)) -> d#(x,s(y),0())
    d#(x,s(y),z) -> ge#(x,z)
    d#(x,s(y),z) -> cond#(ge(x,z),x,y,z)
    cond#(true(),x,y,z) -> plus#(s(y),z)
    cond#(true(),x,y,z) -> d#(x,s(y),plus(s(y),z))
    ge#(s(u),s(v)) -> ge#(u,v)
    plus#(n,s(m)) -> plus#(n,m)
   TRS:
    ge(u,0()) -> true()
    ge(0(),s(v)) -> false()
    ge(s(u),s(v)) -> ge(u,v)
    plus(n,0()) -> n
    plus(n,s(m)) -> s(plus(n,m))
   Open