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))
  TDG 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))
   graph:
    plus#(n,s(m)) -> plus#(n,m) -> plus#(n,s(m)) -> plus#(n,m)
    cond#(true(),x,y,z) -> plus#(s(y),z) ->
    plus#(n,s(m)) -> plus#(n,m)
    cond#(true(),x,y,z) -> d#(x,s(y),plus(s(y),z)) ->
    d#(x,s(y),z) -> cond#(ge(x,z),x,y,z)
    cond#(true(),x,y,z) -> d#(x,s(y),plus(s(y),z)) ->
    d#(x,s(y),z) -> ge#(x,z)
    ge#(s(u),s(v)) -> ge#(u,v) -> ge#(s(u),s(v)) -> ge#(u,v)
    d#(x,s(y),z) -> cond#(ge(x,z),x,y,z) ->
    cond#(true(),x,y,z) -> d#(x,s(y),plus(s(y),z))
    d#(x,s(y),z) -> cond#(ge(x,z),x,y,z) ->
    cond#(true(),x,y,z) -> plus#(s(y),z)
    d#(x,s(y),z) -> ge#(x,z) -> ge#(s(u),s(v)) -> ge#(u,v)
    div#(x,s(y)) -> d#(x,s(y),0()) ->
    d#(x,s(y),z) -> cond#(ge(x,z),x,y,z)
    div#(x,s(y)) -> d#(x,s(y),0()) -> d#(x,s(y),z) -> ge#(x,z)
   SCC Processor:
    #sccs: 3
    #rules: 4
    #arcs: 10/49
    DPs:
     cond#(true(),x,y,z) -> d#(x,s(y),plus(s(y),z))
     d#(x,s(y),z) -> cond#(ge(x,z),x,y,z)
    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))
    Open
    
    DPs:
     ge#(s(u),s(v)) -> ge#(u,v)
    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))
    Subterm Criterion Processor:
     simple projection:
      pi(ge#) = 1
     problem:
      DPs:
       
      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))
     Qed
    
    DPs:
     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))
    Subterm Criterion Processor:
     simple projection:
      pi(plus#) = 1
     problem:
      DPs:
       
      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))
     Qed