YES

Problem:
 q0(a(x1)) -> x(q1(x1))
 q1(a(x1)) -> a(q1(x1))
 q1(y(x1)) -> y(q1(x1))
 a(q1(b(x1))) -> q2(a(y(x1)))
 a(q2(a(x1))) -> q2(a(a(x1)))
 a(q2(y(x1))) -> q2(a(y(x1)))
 y(q1(b(x1))) -> q2(y(y(x1)))
 y(q2(a(x1))) -> q2(y(a(x1)))
 y(q2(y(x1))) -> q2(y(y(x1)))
 q2(x(x1)) -> x(q0(x1))
 q0(y(x1)) -> y(q3(x1))
 q3(y(x1)) -> y(q3(x1))
 q3(bl(x1)) -> bl(q4(x1))

Proof:
 DP Processor:
  DPs:
   q0#(a(x1)) -> q1#(x1)
   q1#(a(x1)) -> q1#(x1)
   q1#(a(x1)) -> a#(q1(x1))
   q1#(y(x1)) -> q1#(x1)
   q1#(y(x1)) -> y#(q1(x1))
   a#(q1(b(x1))) -> y#(x1)
   a#(q1(b(x1))) -> a#(y(x1))
   a#(q1(b(x1))) -> q2#(a(y(x1)))
   a#(q2(a(x1))) -> a#(a(x1))
   a#(q2(a(x1))) -> q2#(a(a(x1)))
   a#(q2(y(x1))) -> a#(y(x1))
   a#(q2(y(x1))) -> q2#(a(y(x1)))
   y#(q1(b(x1))) -> y#(x1)
   y#(q1(b(x1))) -> y#(y(x1))
   y#(q1(b(x1))) -> q2#(y(y(x1)))
   y#(q2(a(x1))) -> y#(a(x1))
   y#(q2(a(x1))) -> q2#(y(a(x1)))
   y#(q2(y(x1))) -> y#(y(x1))
   y#(q2(y(x1))) -> q2#(y(y(x1)))
   q2#(x(x1)) -> q0#(x1)
   q0#(y(x1)) -> q3#(x1)
   q0#(y(x1)) -> y#(q3(x1))
   q3#(y(x1)) -> q3#(x1)
   q3#(y(x1)) -> y#(q3(x1))
  TRS:
   q0(a(x1)) -> x(q1(x1))
   q1(a(x1)) -> a(q1(x1))
   q1(y(x1)) -> y(q1(x1))
   a(q1(b(x1))) -> q2(a(y(x1)))
   a(q2(a(x1))) -> q2(a(a(x1)))
   a(q2(y(x1))) -> q2(a(y(x1)))
   y(q1(b(x1))) -> q2(y(y(x1)))
   y(q2(a(x1))) -> q2(y(a(x1)))
   y(q2(y(x1))) -> q2(y(y(x1)))
   q2(x(x1)) -> x(q0(x1))
   q0(y(x1)) -> y(q3(x1))
   q3(y(x1)) -> y(q3(x1))
   q3(bl(x1)) -> bl(q4(x1))
  KBO Processor:
   weight function:
    w0 = 1
    w(q3#) = w(q2#) = w(y#) = w(a#) = w(q1#) = w(q0#) = w(q4) = w(bl) = w(
    q3) = w(q2) = w(b) = w(y) = w(x) = w(q1) = w(q0) = w(a) = 1
   precedence:
    q0 > q3 ~ q1 > q1# ~ y ~ a > q3# > q0# > y# > a# ~ q2 > q2# ~ q4 ~ bl ~ b ~ x
   problem:
    DPs:
     
    TRS:
     
   Qed