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))
  EDG 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)) -> e#(x)
    e#(q(x)) -> e#(x) -> e#(q(x)) -> d#(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))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [e#](x0) = x0 + 1,
       
       [q](x0) = x0 + 1,
       
       [e](x0) = 0,
       
       [s](x0) = 0,
       
       [d](x0) = 0,
       
       [0] = 0
      orientation:
       e#(q(x)) = x + 2 >= x + 1 = e#(x)
       
       d(0()) = 0 >= 0 = 0()
       
       d(s(x)) = 0 >= 0 = s(s(d(x)))
       
       e(0()) = 0 >= 0 = s(0())
       
       e(q(x)) = 0 >= 0 = d(e(x))
      problem:
       DPs:
        
       TRS:
        d(0()) -> 0()
        d(s(x)) -> s(s(d(x)))
        e(0()) -> s(0())
        e(q(x)) -> d(e(x))
      Qed
     
     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