YES

Problem:
 op(i(x),op(y,z)) -> op(x,op(i(i(y)),z))
 op(i(x),op(y,op(z,w))) -> op(x,op(z,op(y,w)))
 i(x) -> 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)) -> op#(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))) -> op#(x,op(z,op(y,w)))
  TRS:
   op(i(x),op(y,z)) -> op(x,op(i(i(y)),z))
   op(i(x),op(y,op(z,w))) -> op(x,op(z,op(y,w)))
   i(x) -> x
  TDG 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)) -> op#(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))) -> op#(x,op(z,op(y,w)))
   TRS:
    op(i(x),op(y,z)) -> op(x,op(i(i(y)),z))
    op(i(x),op(y,op(z,w))) -> op(x,op(z,op(y,w)))
    i(x) -> x
   graph:
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w)) ->
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w)))
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w)) ->
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w))
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w)) ->
    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,z)) -> op#(x,op(i(i(y)),z))
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w)) ->
    op#(i(x),op(y,z)) -> op#(i(i(y)),z)
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w)) ->
    op#(i(x),op(y,z)) -> i#(i(y))
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w)) ->
    op#(i(x),op(y,z)) -> i#(y)
    op#(i(x),op(y,op(z,w))) -> op#(y,w) ->
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w)))
    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))) -> op#(y,w) ->
    op#(i(x),op(y,op(z,w))) -> op#(y,w)
    op#(i(x),op(y,op(z,w))) -> op#(y,w) ->
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z))
    op#(i(x),op(y,op(z,w))) -> op#(y,w) ->
    op#(i(x),op(y,z)) -> op#(i(i(y)),z)
    op#(i(x),op(y,op(z,w))) -> op#(y,w) ->
    op#(i(x),op(y,z)) -> i#(i(y))
    op#(i(x),op(y,op(z,w))) -> op#(y,w) ->
    op#(i(x),op(y,z)) -> i#(y)
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w))) ->
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w)))
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w))) ->
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w))
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w))) ->
    op#(i(x),op(y,op(z,w))) -> op#(y,w)
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w))) ->
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z))
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w))) ->
    op#(i(x),op(y,z)) -> op#(i(i(y)),z)
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w))) ->
    op#(i(x),op(y,z)) -> i#(i(y))
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w))) ->
    op#(i(x),op(y,z)) -> i#(y)
    op#(i(x),op(y,z)) -> op#(i(i(y)),z) ->
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w)))
    op#(i(x),op(y,z)) -> op#(i(i(y)),z) ->
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w))
    op#(i(x),op(y,z)) -> op#(i(i(y)),z) ->
    op#(i(x),op(y,op(z,w))) -> op#(y,w)
    op#(i(x),op(y,z)) -> op#(i(i(y)),z) ->
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z))
    op#(i(x),op(y,z)) -> op#(i(i(y)),z) ->
    op#(i(x),op(y,z)) -> op#(i(i(y)),z)
    op#(i(x),op(y,z)) -> op#(i(i(y)),z) ->
    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)) -> i#(y)
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z)) ->
    op#(i(x),op(y,op(z,w))) -> op#(x,op(z,op(y,w)))
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z)) ->
    op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w))
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z)) ->
    op#(i(x),op(y,op(z,w))) -> op#(y,w)
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z)) ->
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z))
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z)) ->
    op#(i(x),op(y,z)) -> op#(i(i(y)),z)
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z)) ->
    op#(i(x),op(y,z)) -> i#(i(y))
    op#(i(x),op(y,z)) -> op#(x,op(i(i(y)),z)) -> op#(i(x),op(y,z)) -> i#(y)
   SCC Processor:
    #sccs: 1
    #rules: 5
    #arcs: 35/49
    DPs:
     op#(i(x),op(y,op(z,w))) -> op#(z,op(y,w))
     op#(i(x),op(y,z)) -> op#(i(i(y)),z)
     op#(i(x),op(y,z)) -> op#(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#(x,op(z,op(y,w)))
    TRS:
     op(i(x),op(y,z)) -> op(x,op(i(i(y)),z))
     op(i(x),op(y,op(z,w))) -> op(x,op(z,op(y,w)))
     i(x) -> x
    KBO Processor:
     argument filtering:
      pi(i) = [0]
      pi(op) = [0,1]
      pi(op#) = [0,1]
     weight function:
      w0 = 1
      w(op#) = 1
      w(op) = w(i) = 0
     precedence:
      op# ~ op ~ i
     problem:
      DPs:
       
      TRS:
       op(i(x),op(y,z)) -> op(x,op(i(i(y)),z))
       op(i(x),op(y,op(z,w))) -> op(x,op(z,op(y,w)))
       i(x) -> x
     Qed