YES

Problem:
 a(c(a(x1))) -> c(a(c(x1)))
 a(a(b(x1))) -> a(d(b(x1)))
 a(b(x1)) -> b(a(a(x1)))
 d(d(x1)) -> a(d(b(x1)))
 b(b(x1)) -> b(c(x1))
 a(d(c(x1))) -> c(a(x1))
 b(c(x1)) -> a(a(a(x1)))

Proof:
 DP Processor:
  DPs:
   a#(c(a(x1))) -> a#(c(x1))
   a#(a(b(x1))) -> d#(b(x1))
   a#(a(b(x1))) -> a#(d(b(x1)))
   a#(b(x1)) -> a#(x1)
   a#(b(x1)) -> a#(a(x1))
   a#(b(x1)) -> b#(a(a(x1)))
   d#(d(x1)) -> b#(x1)
   d#(d(x1)) -> d#(b(x1))
   d#(d(x1)) -> a#(d(b(x1)))
   b#(b(x1)) -> b#(c(x1))
   a#(d(c(x1))) -> a#(x1)
   b#(c(x1)) -> a#(x1)
   b#(c(x1)) -> a#(a(x1))
   b#(c(x1)) -> a#(a(a(x1)))
  TRS:
   a(c(a(x1))) -> c(a(c(x1)))
   a(a(b(x1))) -> a(d(b(x1)))
   a(b(x1)) -> b(a(a(x1)))
   d(d(x1)) -> a(d(b(x1)))
   b(b(x1)) -> b(c(x1))
   a(d(c(x1))) -> c(a(x1))
   b(c(x1)) -> a(a(a(x1)))
  TDG Processor:
   DPs:
    a#(c(a(x1))) -> a#(c(x1))
    a#(a(b(x1))) -> d#(b(x1))
    a#(a(b(x1))) -> a#(d(b(x1)))
    a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> a#(a(x1))
    a#(b(x1)) -> b#(a(a(x1)))
    d#(d(x1)) -> b#(x1)
    d#(d(x1)) -> d#(b(x1))
    d#(d(x1)) -> a#(d(b(x1)))
    b#(b(x1)) -> b#(c(x1))
    a#(d(c(x1))) -> a#(x1)
    b#(c(x1)) -> a#(x1)
    b#(c(x1)) -> a#(a(x1))
    b#(c(x1)) -> a#(a(a(x1)))
   TRS:
    a(c(a(x1))) -> c(a(c(x1)))
    a(a(b(x1))) -> a(d(b(x1)))
    a(b(x1)) -> b(a(a(x1)))
    d(d(x1)) -> a(d(b(x1)))
    b(b(x1)) -> b(c(x1))
    a(d(c(x1))) -> c(a(x1))
    b(c(x1)) -> a(a(a(x1)))
   graph:
    b#(b(x1)) -> b#(c(x1)) -> b#(c(x1)) -> a#(a(a(x1)))
    b#(b(x1)) -> b#(c(x1)) -> b#(c(x1)) -> a#(a(x1))
    b#(b(x1)) -> b#(c(x1)) -> b#(c(x1)) -> a#(x1)
    b#(b(x1)) -> b#(c(x1)) -> b#(b(x1)) -> b#(c(x1))
    b#(c(x1)) -> a#(a(a(x1))) -> a#(d(c(x1))) -> a#(x1)
    b#(c(x1)) -> a#(a(a(x1))) -> a#(b(x1)) -> b#(a(a(x1)))
    b#(c(x1)) -> a#(a(a(x1))) -> a#(b(x1)) -> a#(a(x1))
    b#(c(x1)) -> a#(a(a(x1))) -> a#(b(x1)) -> a#(x1)
    b#(c(x1)) -> a#(a(a(x1))) -> a#(a(b(x1))) -> a#(d(b(x1)))
    b#(c(x1)) -> a#(a(a(x1))) -> a#(a(b(x1))) -> d#(b(x1))
    b#(c(x1)) -> a#(a(a(x1))) -> a#(c(a(x1))) -> a#(c(x1))
    b#(c(x1)) -> a#(a(x1)) -> a#(d(c(x1))) -> a#(x1)
    b#(c(x1)) -> a#(a(x1)) -> a#(b(x1)) -> b#(a(a(x1)))
    b#(c(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(a(x1))
    b#(c(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(x1)
    b#(c(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(d(b(x1)))
    b#(c(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> d#(b(x1))
    b#(c(x1)) -> a#(a(x1)) -> a#(c(a(x1))) -> a#(c(x1))
    b#(c(x1)) -> a#(x1) -> a#(d(c(x1))) -> a#(x1)
    b#(c(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(a(x1)))
    b#(c(x1)) -> a#(x1) -> a#(b(x1)) -> a#(a(x1))
    b#(c(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
    b#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(d(b(x1)))
    b#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> d#(b(x1))
    b#(c(x1)) -> a#(x1) -> a#(c(a(x1))) -> a#(c(x1))
    d#(d(x1)) -> b#(x1) -> b#(c(x1)) -> a#(a(a(x1)))
    d#(d(x1)) -> b#(x1) -> b#(c(x1)) -> a#(a(x1))
    d#(d(x1)) -> b#(x1) -> b#(c(x1)) -> a#(x1)
    d#(d(x1)) -> b#(x1) -> b#(b(x1)) -> b#(c(x1))
    d#(d(x1)) -> d#(b(x1)) -> d#(d(x1)) -> a#(d(b(x1)))
    d#(d(x1)) -> d#(b(x1)) -> d#(d(x1)) -> d#(b(x1))
    d#(d(x1)) -> d#(b(x1)) -> d#(d(x1)) -> b#(x1)
    d#(d(x1)) -> a#(d(b(x1))) -> a#(d(c(x1))) -> a#(x1)
    d#(d(x1)) -> a#(d(b(x1))) -> a#(b(x1)) -> b#(a(a(x1)))
    d#(d(x1)) -> a#(d(b(x1))) -> a#(b(x1)) -> a#(a(x1))
    d#(d(x1)) -> a#(d(b(x1))) -> a#(b(x1)) -> a#(x1)
    d#(d(x1)) -> a#(d(b(x1))) -> a#(a(b(x1))) -> a#(d(b(x1)))
    d#(d(x1)) -> a#(d(b(x1))) -> a#(a(b(x1))) -> d#(b(x1))
    d#(d(x1)) -> a#(d(b(x1))) -> a#(c(a(x1))) -> a#(c(x1))
    a#(d(c(x1))) -> a#(x1) -> a#(d(c(x1))) -> a#(x1)
    a#(d(c(x1))) -> a#(x1) -> a#(b(x1)) -> b#(a(a(x1)))
    a#(d(c(x1))) -> a#(x1) -> a#(b(x1)) -> a#(a(x1))
    a#(d(c(x1))) -> a#(x1) -> a#(b(x1)) -> a#(x1)
    a#(d(c(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(d(b(x1)))
    a#(d(c(x1))) -> a#(x1) -> a#(a(b(x1))) -> d#(b(x1))
    a#(d(c(x1))) -> a#(x1) -> a#(c(a(x1))) -> a#(c(x1))
    a#(b(x1)) -> b#(a(a(x1))) -> b#(c(x1)) -> a#(a(a(x1)))
    a#(b(x1)) -> b#(a(a(x1))) -> b#(c(x1)) -> a#(a(x1))
    a#(b(x1)) -> b#(a(a(x1))) -> b#(c(x1)) -> a#(x1)
    a#(b(x1)) -> b#(a(a(x1))) -> b#(b(x1)) -> b#(c(x1))
    a#(b(x1)) -> a#(a(x1)) -> a#(d(c(x1))) -> a#(x1)
    a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> b#(a(a(x1)))
    a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(a(x1))
    a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(d(b(x1)))
    a#(b(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> d#(b(x1))
    a#(b(x1)) -> a#(a(x1)) -> a#(c(a(x1))) -> a#(c(x1))
    a#(b(x1)) -> a#(x1) -> a#(d(c(x1))) -> a#(x1)
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(a(x1)))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(a(x1))
    a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(d(b(x1)))
    a#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> d#(b(x1))
    a#(b(x1)) -> a#(x1) -> a#(c(a(x1))) -> a#(c(x1))
    a#(c(a(x1))) -> a#(c(x1)) -> a#(d(c(x1))) -> a#(x1)
    a#(c(a(x1))) -> a#(c(x1)) -> a#(b(x1)) -> b#(a(a(x1)))
    a#(c(a(x1))) -> a#(c(x1)) -> a#(b(x1)) -> a#(a(x1))
    a#(c(a(x1))) -> a#(c(x1)) -> a#(b(x1)) -> a#(x1)
    a#(c(a(x1))) -> a#(c(x1)) -> a#(a(b(x1))) -> a#(d(b(x1)))
    a#(c(a(x1))) -> a#(c(x1)) -> a#(a(b(x1))) -> d#(b(x1))
    a#(c(a(x1))) -> a#(c(x1)) -> a#(c(a(x1))) -> a#(c(x1))
    a#(a(b(x1))) -> d#(b(x1)) -> d#(d(x1)) -> a#(d(b(x1)))
    a#(a(b(x1))) -> d#(b(x1)) -> d#(d(x1)) -> d#(b(x1))
    a#(a(b(x1))) -> d#(b(x1)) -> d#(d(x1)) -> b#(x1)
    a#(a(b(x1))) -> a#(d(b(x1))) -> a#(d(c(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(d(b(x1))) -> a#(b(x1)) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(d(b(x1))) -> a#(b(x1)) -> a#(a(x1))
    a#(a(b(x1))) -> a#(d(b(x1))) -> a#(b(x1)) -> a#(x1)
    a#(a(b(x1))) -> a#(d(b(x1))) -> a#(a(b(x1))) -> a#(d(b(x1)))
    a#(a(b(x1))) -> a#(d(b(x1))) -> a#(a(b(x1))) -> d#(b(x1))
    a#(a(b(x1))) -> a#(d(b(x1))) -> a#(c(a(x1))) -> a#(c(x1))
   EDG Processor:
    DPs:
     a#(c(a(x1))) -> a#(c(x1))
     a#(a(b(x1))) -> d#(b(x1))
     a#(a(b(x1))) -> a#(d(b(x1)))
     a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> a#(a(x1))
     a#(b(x1)) -> b#(a(a(x1)))
     d#(d(x1)) -> b#(x1)
     d#(d(x1)) -> d#(b(x1))
     d#(d(x1)) -> a#(d(b(x1)))
     b#(b(x1)) -> b#(c(x1))
     a#(d(c(x1))) -> a#(x1)
     b#(c(x1)) -> a#(x1)
     b#(c(x1)) -> a#(a(x1))
     b#(c(x1)) -> a#(a(a(x1)))
    TRS:
     a(c(a(x1))) -> c(a(c(x1)))
     a(a(b(x1))) -> a(d(b(x1)))
     a(b(x1)) -> b(a(a(x1)))
     d(d(x1)) -> a(d(b(x1)))
     b(b(x1)) -> b(c(x1))
     a(d(c(x1))) -> c(a(x1))
     b(c(x1)) -> a(a(a(x1)))
    graph:
     b#(b(x1)) -> b#(c(x1)) -> b#(c(x1)) -> a#(x1)
     b#(b(x1)) -> b#(c(x1)) -> b#(c(x1)) -> a#(a(x1))
     b#(b(x1)) -> b#(c(x1)) -> b#(c(x1)) -> a#(a(a(x1)))
     b#(c(x1)) -> a#(a(a(x1))) -> a#(c(a(x1))) -> a#(c(x1))
     b#(c(x1)) -> a#(a(a(x1))) -> a#(a(b(x1))) -> d#(b(x1))
     b#(c(x1)) -> a#(a(a(x1))) -> a#(a(b(x1))) -> a#(d(b(x1)))
     b#(c(x1)) -> a#(a(a(x1))) -> a#(b(x1)) -> a#(x1)
     b#(c(x1)) -> a#(a(a(x1))) -> a#(b(x1)) -> a#(a(x1))
     b#(c(x1)) -> a#(a(a(x1))) -> a#(b(x1)) -> b#(a(a(x1)))
     b#(c(x1)) -> a#(a(x1)) -> a#(c(a(x1))) -> a#(c(x1))
     b#(c(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> d#(b(x1))
     b#(c(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(d(b(x1)))
     b#(c(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(x1)
     b#(c(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(a(x1))
     b#(c(x1)) -> a#(a(x1)) -> a#(b(x1)) -> b#(a(a(x1)))
     b#(c(x1)) -> a#(x1) -> a#(c(a(x1))) -> a#(c(x1))
     b#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> d#(b(x1))
     b#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(d(b(x1)))
     b#(c(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
     b#(c(x1)) -> a#(x1) -> a#(b(x1)) -> a#(a(x1))
     b#(c(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(a(x1)))
     b#(c(x1)) -> a#(x1) -> a#(d(c(x1))) -> a#(x1)
     d#(d(x1)) -> b#(x1) -> b#(b(x1)) -> b#(c(x1))
     d#(d(x1)) -> b#(x1) -> b#(c(x1)) -> a#(x1)
     d#(d(x1)) -> b#(x1) -> b#(c(x1)) -> a#(a(x1))
     d#(d(x1)) -> b#(x1) -> b#(c(x1)) -> a#(a(a(x1)))
     d#(d(x1)) -> a#(d(b(x1))) -> a#(c(a(x1))) -> a#(c(x1))
     d#(d(x1)) -> a#(d(b(x1))) -> a#(a(b(x1))) -> d#(b(x1))
     d#(d(x1)) -> a#(d(b(x1))) -> a#(a(b(x1))) -> a#(d(b(x1)))
     d#(d(x1)) -> a#(d(b(x1))) -> a#(b(x1)) -> a#(x1)
     d#(d(x1)) -> a#(d(b(x1))) -> a#(b(x1)) -> a#(a(x1))
     d#(d(x1)) -> a#(d(b(x1))) -> a#(b(x1)) -> b#(a(a(x1)))
     d#(d(x1)) -> a#(d(b(x1))) -> a#(d(c(x1))) -> a#(x1)
     a#(d(c(x1))) -> a#(x1) -> a#(c(a(x1))) -> a#(c(x1))
     a#(d(c(x1))) -> a#(x1) -> a#(a(b(x1))) -> d#(b(x1))
     a#(d(c(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(d(b(x1)))
     a#(d(c(x1))) -> a#(x1) -> a#(b(x1)) -> a#(x1)
     a#(d(c(x1))) -> a#(x1) -> a#(b(x1)) -> a#(a(x1))
     a#(d(c(x1))) -> a#(x1) -> a#(b(x1)) -> b#(a(a(x1)))
     a#(d(c(x1))) -> a#(x1) -> a#(d(c(x1))) -> a#(x1)
     a#(b(x1)) -> b#(a(a(x1))) -> b#(b(x1)) -> b#(c(x1))
     a#(b(x1)) -> b#(a(a(x1))) -> b#(c(x1)) -> a#(x1)
     a#(b(x1)) -> b#(a(a(x1))) -> b#(c(x1)) -> a#(a(x1))
     a#(b(x1)) -> b#(a(a(x1))) -> b#(c(x1)) -> a#(a(a(x1)))
     a#(b(x1)) -> a#(a(x1)) -> a#(c(a(x1))) -> a#(c(x1))
     a#(b(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> d#(b(x1))
     a#(b(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(d(b(x1)))
     a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(a(x1))
     a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> b#(a(a(x1)))
     a#(b(x1)) -> a#(x1) -> a#(c(a(x1))) -> a#(c(x1))
     a#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> d#(b(x1))
     a#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(d(b(x1)))
     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(a(x1))
     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(a(x1)))
     a#(b(x1)) -> a#(x1) -> a#(d(c(x1))) -> a#(x1)
     a#(c(a(x1))) -> a#(c(x1)) -> a#(c(a(x1))) -> a#(c(x1))
     a#(a(b(x1))) -> a#(d(b(x1))) -> a#(c(a(x1))) -> a#(c(x1))
     a#(a(b(x1))) -> a#(d(b(x1))) -> a#(a(b(x1))) -> d#(b(x1))
     a#(a(b(x1))) -> a#(d(b(x1))) -> a#(a(b(x1))) -> a#(d(b(x1)))
     a#(a(b(x1))) -> a#(d(b(x1))) -> a#(b(x1)) -> a#(x1)
     a#(a(b(x1))) -> a#(d(b(x1))) -> a#(b(x1)) -> a#(a(x1))
     a#(a(b(x1))) -> a#(d(b(x1))) -> a#(b(x1)) -> b#(a(a(x1)))
     a#(a(b(x1))) -> a#(d(b(x1))) -> a#(d(c(x1))) -> a#(x1)
    CDG Processor:
     DPs:
      a#(c(a(x1))) -> a#(c(x1))
      a#(a(b(x1))) -> d#(b(x1))
      a#(a(b(x1))) -> a#(d(b(x1)))
      a#(b(x1)) -> a#(x1)
      a#(b(x1)) -> a#(a(x1))
      a#(b(x1)) -> b#(a(a(x1)))
      d#(d(x1)) -> b#(x1)
      d#(d(x1)) -> d#(b(x1))
      d#(d(x1)) -> a#(d(b(x1)))
      b#(b(x1)) -> b#(c(x1))
      a#(d(c(x1))) -> a#(x1)
      b#(c(x1)) -> a#(x1)
      b#(c(x1)) -> a#(a(x1))
      b#(c(x1)) -> a#(a(a(x1)))
     TRS:
      a(c(a(x1))) -> c(a(c(x1)))
      a(a(b(x1))) -> a(d(b(x1)))
      a(b(x1)) -> b(a(a(x1)))
      d(d(x1)) -> a(d(b(x1)))
      b(b(x1)) -> b(c(x1))
      a(d(c(x1))) -> c(a(x1))
      b(c(x1)) -> a(a(a(x1)))
     graph:
      b#(b(x1)) -> b#(c(x1)) -> b#(c(x1)) -> a#(a(a(x1)))
      b#(b(x1)) -> b#(c(x1)) -> b#(c(x1)) -> a#(a(x1))
      b#(b(x1)) -> b#(c(x1)) -> b#(c(x1)) -> a#(x1)
      b#(c(x1)) -> a#(a(a(x1))) -> a#(b(x1)) -> b#(a(a(x1)))
      b#(c(x1)) -> a#(a(a(x1))) -> a#(b(x1)) -> a#(a(x1))
      b#(c(x1)) -> a#(a(a(x1))) -> a#(b(x1)) -> a#(x1)
      b#(c(x1)) -> a#(a(a(x1))) -> a#(a(b(x1))) -> a#(d(b(x1)))
      b#(c(x1)) -> a#(a(a(x1))) -> a#(a(b(x1))) -> d#(b(x1))
      b#(c(x1)) -> a#(a(a(x1))) -> a#(c(a(x1))) -> a#(c(x1))
      b#(c(x1)) -> a#(a(x1)) -> a#(b(x1)) -> b#(a(a(x1)))
      b#(c(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(a(x1))
      b#(c(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(x1)
      b#(c(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(d(b(x1)))
      b#(c(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> d#(b(x1))
      b#(c(x1)) -> a#(a(x1)) -> a#(c(a(x1))) -> a#(c(x1))
      b#(c(x1)) -> a#(x1) -> a#(d(c(x1))) -> a#(x1)
      b#(c(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(a(x1)))
      b#(c(x1)) -> a#(x1) -> a#(b(x1)) -> a#(a(x1))
      b#(c(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
      b#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(d(b(x1)))
      b#(c(x1)) -> a#(x1) -> a#(a(b(x1))) -> d#(b(x1))
      b#(c(x1)) -> a#(x1) -> a#(c(a(x1))) -> a#(c(x1))
      d#(d(x1)) -> b#(x1) -> b#(c(x1)) -> a#(a(a(x1)))
      d#(d(x1)) -> b#(x1) -> b#(c(x1)) -> a#(a(x1))
      d#(d(x1)) -> b#(x1) -> b#(c(x1)) -> a#(x1)
      d#(d(x1)) -> b#(x1) -> b#(b(x1)) -> b#(c(x1))
      d#(d(x1)) -> a#(d(b(x1))) -> a#(d(c(x1))) -> a#(x1)
      d#(d(x1)) -> a#(d(b(x1))) -> a#(b(x1)) -> b#(a(a(x1)))
      d#(d(x1)) -> a#(d(b(x1))) -> a#(b(x1)) -> a#(a(x1))
      d#(d(x1)) -> a#(d(b(x1))) -> a#(b(x1)) -> a#(x1)
      d#(d(x1)) -> a#(d(b(x1))) -> a#(a(b(x1))) -> a#(d(b(x1)))
      d#(d(x1)) -> a#(d(b(x1))) -> a#(a(b(x1))) -> d#(b(x1))
      d#(d(x1)) -> a#(d(b(x1))) -> a#(c(a(x1))) -> a#(c(x1))
      a#(d(c(x1))) -> a#(x1) -> a#(d(c(x1))) -> a#(x1)
      a#(d(c(x1))) -> a#(x1) -> a#(b(x1)) -> b#(a(a(x1)))
      a#(d(c(x1))) -> a#(x1) -> a#(b(x1)) -> a#(a(x1))
      a#(d(c(x1))) -> a#(x1) -> a#(b(x1)) -> a#(x1)
      a#(d(c(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(d(b(x1)))
      a#(d(c(x1))) -> a#(x1) -> a#(a(b(x1))) -> d#(b(x1))
      a#(d(c(x1))) -> a#(x1) -> a#(c(a(x1))) -> a#(c(x1))
      a#(b(x1)) -> b#(a(a(x1))) -> b#(c(x1)) -> a#(a(a(x1)))
      a#(b(x1)) -> b#(a(a(x1))) -> b#(c(x1)) -> a#(a(x1))
      a#(b(x1)) -> b#(a(a(x1))) -> b#(c(x1)) -> a#(x1)
      a#(b(x1)) -> b#(a(a(x1))) -> b#(b(x1)) -> b#(c(x1))
      a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> b#(a(a(x1)))
      a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(a(x1))
      a#(b(x1)) -> a#(a(x1)) -> a#(b(x1)) -> a#(x1)
      a#(b(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(d(b(x1)))
      a#(b(x1)) -> a#(a(x1)) -> a#(a(b(x1))) -> d#(b(x1))
      a#(b(x1)) -> a#(a(x1)) -> a#(c(a(x1))) -> a#(c(x1))
      a#(b(x1)) -> a#(x1) -> a#(d(c(x1))) -> a#(x1)
      a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> b#(a(a(x1)))
      a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(a(x1))
      a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
      a#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> a#(d(b(x1)))
      a#(b(x1)) -> a#(x1) -> a#(a(b(x1))) -> d#(b(x1))
      a#(b(x1)) -> a#(x1) -> a#(c(a(x1))) -> a#(c(x1))
      a#(a(b(x1))) -> a#(d(b(x1))) -> a#(d(c(x1))) -> a#(x1)
      a#(a(b(x1))) -> a#(d(b(x1))) -> a#(b(x1)) -> b#(a(a(x1)))
      a#(a(b(x1))) -> a#(d(b(x1))) -> a#(b(x1)) -> a#(a(x1))
      a#(a(b(x1))) -> a#(d(b(x1))) -> a#(b(x1)) -> a#(x1)
      a#(a(b(x1))) -> a#(d(b(x1))) -> a#(a(b(x1))) -> a#(d(b(x1)))
      a#(a(b(x1))) -> a#(d(b(x1))) -> a#(a(b(x1))) -> d#(b(x1))
      a#(a(b(x1))) -> a#(d(b(x1))) -> a#(c(a(x1))) -> a#(c(x1))
     SCC Processor:
      #sccs: 1
      #rules: 9
      #arcs: 64/196
      DPs:
       b#(b(x1)) -> b#(c(x1))
       b#(c(x1)) -> a#(x1)
       a#(a(b(x1))) -> a#(d(b(x1)))
       a#(b(x1)) -> a#(x1)
       a#(b(x1)) -> a#(a(x1))
       a#(b(x1)) -> b#(a(a(x1)))
       b#(c(x1)) -> a#(a(x1))
       b#(c(x1)) -> a#(a(a(x1)))
       a#(d(c(x1))) -> a#(x1)
      TRS:
       a(c(a(x1))) -> c(a(c(x1)))
       a(a(b(x1))) -> a(d(b(x1)))
       a(b(x1)) -> b(a(a(x1)))
       d(d(x1)) -> a(d(b(x1)))
       b(b(x1)) -> b(c(x1))
       a(d(c(x1))) -> c(a(x1))
       b(c(x1)) -> a(a(a(x1)))
      Matrix Interpretation Processor: dim=3
       
       interpretation:
        [b#](x0) = [0 0 1]x0 + [1],
        
        [a#](x0) = [0 1 1]x0,
        
                  [1 0 1]     [0]
        [d](x0) = [0 0 0]x0 + [0]
                  [1 0 0]     [1],
        
                  [0 0 1]     [0]
        [b](x0) = [0 0 1]x0 + [1]
                  [0 1 1]     [1],
        
                  [0 1 1]  
        [c](x0) = [0 0 0]x0
                  [0 1 1]  ,
        
                  [0 0 1]  
        [a](x0) = [0 1 0]x0
                  [0 0 1]  
       orientation:
        b#(b(x1)) = [0 1 1]x1 + [2] >= [0 1 1]x1 + [1] = b#(c(x1))
        
        b#(c(x1)) = [0 1 1]x1 + [1] >= [0 1 1]x1 = a#(x1)
        
        a#(a(b(x1))) = [0 1 2]x1 + [2] >= [0 0 1]x1 + [1] = a#(d(b(x1)))
        
        a#(b(x1)) = [0 1 2]x1 + [2] >= [0 1 1]x1 = a#(x1)
        
        a#(b(x1)) = [0 1 2]x1 + [2] >= [0 1 1]x1 = a#(a(x1))
        
        a#(b(x1)) = [0 1 2]x1 + [2] >= [0 0 1]x1 + [1] = b#(a(a(x1)))
        
        b#(c(x1)) = [0 1 1]x1 + [1] >= [0 1 1]x1 = a#(a(x1))
        
        b#(c(x1)) = [0 1 1]x1 + [1] >= [0 1 1]x1 = a#(a(a(x1)))
        
        a#(d(c(x1))) = [0 1 1]x1 + [1] >= [0 1 1]x1 = a#(x1)
        
                      [0 1 1]      [0 1 1]                
        a(c(a(x1))) = [0 0 0]x1 >= [0 0 0]x1 = c(a(c(x1)))
                      [0 1 1]      [0 1 1]                
        
                      [0 1 1]     [1]    [0 0 1]     [1]              
        a(a(b(x1))) = [0 0 1]x1 + [1] >= [0 0 0]x1 + [0] = a(d(b(x1)))
                      [0 1 1]     [1]    [0 0 1]     [1]              
        
                   [0 1 1]     [1]    [0 0 1]     [0]              
        a(b(x1)) = [0 0 1]x1 + [1] >= [0 0 1]x1 + [1] = b(a(a(x1)))
                   [0 1 1]     [1]    [0 1 1]     [1]              
        
                   [2 0 1]     [1]    [0 0 1]     [1]              
        d(d(x1)) = [0 0 0]x1 + [0] >= [0 0 0]x1 + [0] = a(d(b(x1)))
                   [1 0 1]     [1]    [0 0 1]     [1]              
        
                   [0 1 1]     [1]    [0 1 1]     [0]           
        b(b(x1)) = [0 1 1]x1 + [2] >= [0 1 1]x1 + [1] = b(c(x1))
                   [0 1 2]     [3]    [0 1 1]     [1]           
        
                      [0 1 1]     [1]    [0 1 1]             
        a(d(c(x1))) = [0 0 0]x1 + [0] >= [0 0 0]x1 = c(a(x1))
                      [0 1 1]     [1]    [0 1 1]             
        
                   [0 1 1]     [0]    [0 0 1]                
        b(c(x1)) = [0 1 1]x1 + [1] >= [0 1 0]x1 = a(a(a(x1)))
                   [0 1 1]     [1]    [0 0 1]                
       problem:
        DPs:
         
        TRS:
         a(c(a(x1))) -> c(a(c(x1)))
         a(a(b(x1))) -> a(d(b(x1)))
         a(b(x1)) -> b(a(a(x1)))
         d(d(x1)) -> a(d(b(x1)))
         b(b(x1)) -> b(c(x1))
         a(d(c(x1))) -> c(a(x1))
         b(c(x1)) -> a(a(a(x1)))
       Qed