NO

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

Proof:
 String Reversal Processor:
  c(b(x1)) -> b(b(a(x1)))
  a(b(x1)) -> b(c(a(x1)))
  DP Processor:
   DPs:
    c#(b(x1)) -> a#(x1)
    a#(b(x1)) -> a#(x1)
    a#(b(x1)) -> c#(a(x1))
   TRS:
    c(b(x1)) -> b(b(a(x1)))
    a(b(x1)) -> b(c(a(x1)))
   TDG Processor:
    DPs:
     c#(b(x1)) -> a#(x1)
     a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> c#(a(x1))
    TRS:
     c(b(x1)) -> b(b(a(x1)))
     a(b(x1)) -> b(c(a(x1)))
    graph:
     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(a(x1))
     a#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
     a#(b(x1)) -> c#(a(x1)) -> c#(b(x1)) -> a#(x1)
     c#(b(x1)) -> a#(x1) -> a#(b(x1)) -> c#(a(x1))
     c#(b(x1)) -> a#(x1) -> a#(b(x1)) -> a#(x1)
    Loop Processor:
     loop length: 13
     terms:
      a(c(a(b(b(b(b(x1)))))))
      a(c(b(c(a(b(b(b(x1))))))))
      a(c(b(c(b(c(a(b(b(x1)))))))))
      a(c(b(c(b(c(b(c(a(b(x1))))))))))
      a(b(b(a(c(b(c(b(c(a(b(x1)))))))))))
      b(c(a(b(a(c(b(c(b(c(a(b(x1))))))))))))
      b(c(b(c(a(a(c(b(c(b(c(a(b(x1)))))))))))))
      b(c(b(c(a(a(c(b(b(b(a(c(a(b(x1))))))))))))))
      b(c(b(c(a(a(b(b(a(b(b(a(c(a(b(x1)))))))))))))))
      b(c(b(c(a(a(b(b(b(c(a(b(a(c(a(b(x1))))))))))))))))
      b(c(b(c(a(b(c(a(b(b(c(a(b(a(c(a(b(x1)))))))))))))))))
      b(c(b(c(a(b(c(a(b(b(c(b(c(a(a(c(a(b(x1))))))))))))))))))
      b(c(b(c(b(c(a(c(a(b(b(c(b(c(a(a(c(a(b(x1)))))))))))))))))))
     context: b(c(b(c(b(c([]))))))
     substitution:
      x1 -> a(c(a(a(c(a(b(x1)))))))
     Qed