MAYBE

Problem:
 d(0()) -> 0()
 d(s(x)) -> s(s(d(x)))
 e(s(x),y) -> e(x,d(y))
 sup(s(x),e(0(),y)) -> sup(x,e(y,s(0())))

Proof:
 DP Processor:
  DPs:
   d#(s(x)) -> d#(x)
   e#(s(x),y) -> d#(y)
   e#(s(x),y) -> e#(x,d(y))
   sup#(s(x),e(0(),y)) -> e#(y,s(0()))
   sup#(s(x),e(0(),y)) -> sup#(x,e(y,s(0())))
  TRS:
   d(0()) -> 0()
   d(s(x)) -> s(s(d(x)))
   e(s(x),y) -> e(x,d(y))
   sup(s(x),e(0(),y)) -> sup(x,e(y,s(0())))
  Usable Rule Processor:
   DPs:
    d#(s(x)) -> d#(x)
    e#(s(x),y) -> d#(y)
    e#(s(x),y) -> e#(x,d(y))
    sup#(s(x),e(0(),y)) -> e#(y,s(0()))
    sup#(s(x),e(0(),y)) -> sup#(x,e(y,s(0())))
   TRS:
    d(0()) -> 0()
    d(s(x)) -> s(s(d(x)))
    e(s(x),y) -> e(x,d(y))
   TDG Processor:
    DPs:
     d#(s(x)) -> d#(x)
     e#(s(x),y) -> d#(y)
     e#(s(x),y) -> e#(x,d(y))
     sup#(s(x),e(0(),y)) -> e#(y,s(0()))
     sup#(s(x),e(0(),y)) -> sup#(x,e(y,s(0())))
    TRS:
     d(0()) -> 0()
     d(s(x)) -> s(s(d(x)))
     e(s(x),y) -> e(x,d(y))
    graph:
     sup#(s(x),e(0(),y)) -> sup#(x,e(y,s(0()))) ->
     sup#(s(x),e(0(),y)) -> sup#(x,e(y,s(0())))
     sup#(s(x),e(0(),y)) -> sup#(x,e(y,s(0()))) ->
     sup#(s(x),e(0(),y)) -> e#(y,s(0()))
     sup#(s(x),e(0(),y)) -> e#(y,s(0())) ->
     e#(s(x),y) -> e#(x,d(y))
     sup#(s(x),e(0(),y)) -> e#(y,s(0())) -> e#(s(x),y) -> d#(y)
     e#(s(x),y) -> e#(x,d(y)) -> e#(s(x),y) -> e#(x,d(y))
     e#(s(x),y) -> e#(x,d(y)) -> e#(s(x),y) -> d#(y)
     e#(s(x),y) -> d#(y) -> d#(s(x)) -> d#(x)
     d#(s(x)) -> d#(x) -> d#(s(x)) -> d#(x)
    Restore Modifier:
     DPs:
      d#(s(x)) -> d#(x)
      e#(s(x),y) -> d#(y)
      e#(s(x),y) -> e#(x,d(y))
      sup#(s(x),e(0(),y)) -> e#(y,s(0()))
      sup#(s(x),e(0(),y)) -> sup#(x,e(y,s(0())))
     TRS:
      d(0()) -> 0()
      d(s(x)) -> s(s(d(x)))
      e(s(x),y) -> e(x,d(y))
      sup(s(x),e(0(),y)) -> sup(x,e(y,s(0())))
     SCC Processor:
      #sccs: 3
      #rules: 3
      #arcs: 8/25
      DPs:
       sup#(s(x),e(0(),y)) -> sup#(x,e(y,s(0())))
      TRS:
       d(0()) -> 0()
       d(s(x)) -> s(s(d(x)))
       e(s(x),y) -> e(x,d(y))
       sup(s(x),e(0(),y)) -> sup(x,e(y,s(0())))
      Open
      
      DPs:
       e#(s(x),y) -> e#(x,d(y))
      TRS:
       d(0()) -> 0()
       d(s(x)) -> s(s(d(x)))
       e(s(x),y) -> e(x,d(y))
       sup(s(x),e(0(),y)) -> sup(x,e(y,s(0())))
      Open
      
      DPs:
       d#(s(x)) -> d#(x)
      TRS:
       d(0()) -> 0()
       d(s(x)) -> s(s(d(x)))
       e(s(x),y) -> e(x,d(y))
       sup(s(x),e(0(),y)) -> sup(x,e(y,s(0())))
      Open