YES

Problem:
 op(i(x),op(y,z)) -> op(f(x,i(x)),op(i(i(y)),z))
 op(i(x),op(y,op(z,w))) -> op(f(x,i(x)),op(z,op(y,w)))
 i(x) -> x
 f(x,y) -> x

Proof:
 DP Processor:
  DPs:
   op#(i(x),op(y,z)) -> i#(y)
   op#(i(x),op(y,z)) -> i#(i(y))
   op#(i(x),op(y,z)) -> op#(i(i(y)),z)
   op#(i(x),op(y,z)) -> f#(x,i(x))
   op#(i(x),op(y,z)) -> op#(f(x,i(x)),op(i(i(y)),z))
   op#(i(x),op(y,op(z,w))) -> op#(y,w)
   op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w))
   op#(i(x),op(y,op(z,w))) -> f#(x,i(x))
   op#(i(x),op(y,op(z,w))) -> op#(f(x,i(x)),op(z,op(y,w)))
  TRS:
   op(i(x),op(y,z)) -> op(f(x,i(x)),op(i(i(y)),z))
   op(i(x),op(y,op(z,w))) -> op(f(x,i(x)),op(z,op(y,w)))
   i(x) -> x
   f(x,y) -> x
  KBO Processor:
   argument filtering:
    pi(i) = [0]
    pi(op) = [0,1]
    pi(f) = 0
    pi(op#) = [0,1]
    pi(i#) = 0
    pi(f#) = 1
   usable rules:
    op(i(x),op(y,z)) -> op(f(x,i(x)),op(i(i(y)),z))
    op(i(x),op(y,op(z,w))) -> op(f(x,i(x)),op(z,op(y,w)))
    i(x) -> x
    f(x,y) -> x
   weight function:
    w0 = 1
    w(f#) = w(op#) = w(f) = 1
    w(i#) = w(op) = w(i) = 0
   precedence:
    f# ~ i# ~ op# ~ f ~ op ~ i
   problem:
    DPs:
     
    TRS:
     op(i(x),op(y,z)) -> op(f(x,i(x)),op(i(i(y)),z))
     op(i(x),op(y,op(z,w))) -> op(f(x,i(x)),op(z,op(y,w)))
     i(x) -> x
     f(x,y) -> x
   Qed