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
  EDG 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,z)) -> i#(y)
    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)) -> 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#(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#(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,z)) -> i#(y)
    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)) -> 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,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,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#(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,z)) -> i#(y)
    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)) -> 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#(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,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#(x,op(z,op(y,w)))
    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#(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)) -> 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)) -> 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#(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)) -> op#(x,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,z)) -> i#(i(y))
    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)) -> 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,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#(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)))
   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,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,z)) -> op#(x,op(i(i(y)),z))
     op#(i(x),op(y,z)) -> op#(i(i(y)),z)
    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
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [op#](x0, x1) = x1,
      
      [op](x0, x1) = x0 + x1 + 1,
      
      [i](x0) = x0
     orientation:
      op#(i(x),op(y,op(z,w))) = w + y + z + 2 >= w + y + 1 = op#(z,op(y,w))
      
      op#(i(x),op(y,op(z,w))) = w + y + z + 2 >= w + y + z + 2 = op#(x,op(z,op(y,w)))
      
      op#(i(x),op(y,op(z,w))) = w + y + z + 2 >= w = op#(y,w)
      
      op#(i(x),op(y,z)) = y + z + 1 >= y + z + 1 = op#(x,op(i(i(y)),z))
      
      op#(i(x),op(y,z)) = y + z + 1 >= z = op#(i(i(y)),z)
      
      op(i(x),op(y,z)) = x + y + z + 2 >= x + y + z + 2 = op(x,op(i(i(y)),z))
      
      op(i(x),op(y,op(z,w))) = w + x + y + z + 3 >= w + x + y + z + 3 = op(x,op(z,op(y,w)))
      
      i(x) = x >= x = x
     problem:
      DPs:
       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))
      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
     Subterm Criterion Processor:
      simple projection:
       pi(op#) = 0
      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