MAYBE

Problem:
 d(0()) -> 0()
 d(s(x)) -> s(s(d(x)))
 e(0()) -> s(0())
 e(q(x)) -> d(e(x))

Proof:
 DP Processor:
  DPs:
   d#(s(x)) -> d#(x)
   e#(q(x)) -> e#(x)
   e#(q(x)) -> d#(e(x))
  TRS:
   d(0()) -> 0()
   d(s(x)) -> s(s(d(x)))
   e(0()) -> s(0())
   e(q(x)) -> d(e(x))
  TDG Processor:
   DPs:
    d#(s(x)) -> d#(x)
    e#(q(x)) -> e#(x)
    e#(q(x)) -> d#(e(x))
   TRS:
    d(0()) -> 0()
    d(s(x)) -> s(s(d(x)))
    e(0()) -> s(0())
    e(q(x)) -> d(e(x))
   graph:
    e#(q(x)) -> e#(x) -> e#(q(x)) -> d#(e(x))
    e#(q(x)) -> e#(x) -> e#(q(x)) -> e#(x)
    e#(q(x)) -> d#(e(x)) -> d#(s(x)) -> d#(x)
    d#(s(x)) -> d#(x) -> d#(s(x)) -> d#(x)
   Restore Modifier:
    DPs:
     d#(s(x)) -> d#(x)
     e#(q(x)) -> e#(x)
     e#(q(x)) -> d#(e(x))
    TRS:
     d(0()) -> 0()
     d(s(x)) -> s(s(d(x)))
     e(0()) -> s(0())
     e(q(x)) -> d(e(x))
    SCC Processor:
     #sccs: 2
     #rules: 2
     #arcs: 4/9
     DPs:
      e#(q(x)) -> e#(x)
     TRS:
      d(0()) -> 0()
      d(s(x)) -> s(s(d(x)))
      e(0()) -> s(0())
      e(q(x)) -> d(e(x))
     Open
     
     DPs:
      d#(s(x)) -> d#(x)
     TRS:
      d(0()) -> 0()
      d(s(x)) -> s(s(d(x)))
      e(0()) -> s(0())
      e(q(x)) -> d(e(x))
     Open