MAYBE

Problem:
 a(a(x1)) -> b(b(b(x1)))
 a(x1) -> c(d(x1))
 b(b(x1)) -> c(c(c(x1)))
 c(c(x1)) -> d(d(d(x1)))
 e(d(x1)) -> a(b(c(d(e(x1)))))
 b(x1) -> d(d(x1))
 e(c(x1)) -> b(a(a(e(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)))
   a#(x1) -> c#(d(x1))
   b#(b(x1)) -> c#(x1)
   b#(b(x1)) -> c#(c(x1))
   b#(b(x1)) -> c#(c(c(x1)))
   e#(d(x1)) -> e#(x1)
   e#(d(x1)) -> c#(d(e(x1)))
   e#(d(x1)) -> b#(c(d(e(x1))))
   e#(d(x1)) -> a#(b(c(d(e(x1)))))
   e#(c(x1)) -> e#(x1)
   e#(c(x1)) -> a#(e(x1))
   e#(c(x1)) -> a#(a(e(x1)))
   e#(c(x1)) -> b#(a(a(e(x1))))
   c#(d(d(x1))) -> a#(x1)
  TRS:
   a(a(x1)) -> b(b(b(x1)))
   a(x1) -> c(d(x1))
   b(b(x1)) -> c(c(c(x1)))
   c(c(x1)) -> d(d(d(x1)))
   e(d(x1)) -> a(b(c(d(e(x1)))))
   b(x1) -> d(d(x1))
   e(c(x1)) -> b(a(a(e(x1))))
   c(d(d(x1))) -> a(x1)
  Open