MAYBE

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

Proof:
 DP Processor:
  DPs:
   a#(a(x1)) -> b#(x1)
   a#(a(x1)) -> b#(b(x1))
   a#(a(x1)) -> b#(b(b(x1)))
   b#(b(x1)) -> c#(x1)
   b#(b(x1)) -> c#(c(x1))
   b#(b(x1)) -> c#(c(c(x1)))
   c#(d(d(x1))) -> a#(x1)
  TRS:
   a(a(x1)) -> b(b(b(x1)))
   b(b(x1)) -> c(c(c(x1)))
   c(c(x1)) -> d(d(d(x1)))
   b(x1) -> d(d(x1))
   c(d(d(x1))) -> a(x1)
  TDG Processor:
   DPs:
    a#(a(x1)) -> b#(x1)
    a#(a(x1)) -> b#(b(x1))
    a#(a(x1)) -> b#(b(b(x1)))
    b#(b(x1)) -> c#(x1)
    b#(b(x1)) -> c#(c(x1))
    b#(b(x1)) -> c#(c(c(x1)))
    c#(d(d(x1))) -> a#(x1)
   TRS:
    a(a(x1)) -> b(b(b(x1)))
    b(b(x1)) -> c(c(c(x1)))
    c(c(x1)) -> d(d(d(x1)))
    b(x1) -> d(d(x1))
    c(d(d(x1))) -> a(x1)
   graph:
    c#(d(d(x1))) -> a#(x1) -> a#(a(x1)) -> b#(b(b(x1)))
    c#(d(d(x1))) -> a#(x1) -> a#(a(x1)) -> b#(b(x1))
    c#(d(d(x1))) -> a#(x1) -> a#(a(x1)) -> b#(x1)
    b#(b(x1)) -> c#(c(c(x1))) -> c#(d(d(x1))) -> a#(x1)
    b#(b(x1)) -> c#(c(x1)) -> c#(d(d(x1))) -> a#(x1)
    b#(b(x1)) -> c#(x1) -> c#(d(d(x1))) -> a#(x1)
    a#(a(x1)) -> b#(b(b(x1))) -> b#(b(x1)) -> c#(c(c(x1)))
    a#(a(x1)) -> b#(b(b(x1))) -> b#(b(x1)) -> c#(c(x1))
    a#(a(x1)) -> b#(b(b(x1))) -> b#(b(x1)) -> c#(x1)
    a#(a(x1)) -> b#(b(x1)) -> b#(b(x1)) -> c#(c(c(x1)))
    a#(a(x1)) -> b#(b(x1)) -> b#(b(x1)) -> c#(c(x1))
    a#(a(x1)) -> b#(b(x1)) -> b#(b(x1)) -> c#(x1)
    a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> c#(c(c(x1)))
    a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> c#(c(x1))
    a#(a(x1)) -> b#(x1) -> b#(b(x1)) -> c#(x1)
   Open