YES

Problem:
 strict:
  o(lambda(x),y) -> lambda(o(x,d(1(),o(y,p()))))
  o(d(x,y),z) -> d(o(x,z),o(y,z))
  o(o(x,y),z) -> o(x,o(y,z))
  lambda(x) -> x
  o(x,y) -> x
  o(x,y) -> y
  d(x,y) -> x
  d(x,y) -> y
 weak:
  o(x,y) -> d(x,y)
  o(x,y) -> d(y,x)

Proof:
 RT Transformation Processor:
  o(lambda(x),y) -> lambda(o(x,d(1(),o(y,p()))))
  o(d(x,y),z) -> d(o(x,z),o(y,z))
  o(o(x,y),z) -> o(x,o(y,z))
  lambda(x) -> x
  o(x,y) -> x
  o(x,y) -> y
  d(x,y) -> x
  d(x,y) -> y
  o(x,y) -> d(x,y)
  o(x,y) -> d(y,x)
  DP Processor:
   DPs:
    o#(lambda(x),y) -> o#(y,p())
    o#(lambda(x),y) -> d#(1(),o(y,p()))
    o#(lambda(x),y) -> o#(x,d(1(),o(y,p())))
    o#(lambda(x),y) -> lambda#(o(x,d(1(),o(y,p()))))
    o#(d(x,y),z) -> o#(y,z)
    o#(d(x,y),z) -> o#(x,z)
    o#(d(x,y),z) -> d#(o(x,z),o(y,z))
    o#(o(x,y),z) -> o#(y,z)
    o#(o(x,y),z) -> o#(x,o(y,z))
    o#(x,y) -> d#(x,y)
    o#(x,y) -> d#(y,x)
   TRS:
    o(lambda(x),y) -> lambda(o(x,d(1(),o(y,p()))))
    o(d(x,y),z) -> d(o(x,z),o(y,z))
    o(o(x,y),z) -> o(x,o(y,z))
    lambda(x) -> x
    o(x,y) -> x
    o(x,y) -> y
    d(x,y) -> x
    d(x,y) -> y
    o(x,y) -> d(x,y)
    o(x,y) -> d(y,x)
   TDG Processor:
    DPs:
     o#(lambda(x),y) -> o#(y,p())
     o#(lambda(x),y) -> d#(1(),o(y,p()))
     o#(lambda(x),y) -> o#(x,d(1(),o(y,p())))
     o#(lambda(x),y) -> lambda#(o(x,d(1(),o(y,p()))))
     o#(d(x,y),z) -> o#(y,z)
     o#(d(x,y),z) -> o#(x,z)
     o#(d(x,y),z) -> d#(o(x,z),o(y,z))
     o#(o(x,y),z) -> o#(y,z)
     o#(o(x,y),z) -> o#(x,o(y,z))
     o#(x,y) -> d#(x,y)
     o#(x,y) -> d#(y,x)
    TRS:
     o(lambda(x),y) -> lambda(o(x,d(1(),o(y,p()))))
     o(d(x,y),z) -> d(o(x,z),o(y,z))
     o(o(x,y),z) -> o(x,o(y,z))
     lambda(x) -> x
     o(x,y) -> x
     o(x,y) -> y
     d(x,y) -> x
     d(x,y) -> y
     o(x,y) -> d(x,y)
     o(x,y) -> d(y,x)
    graph:
     o#(d(x,y),z) -> o#(y,z) -> o#(x,y) -> d#(y,x)
     o#(d(x,y),z) -> o#(y,z) -> o#(x,y) -> d#(x,y)
     o#(d(x,y),z) -> o#(y,z) -> o#(o(x,y),z) -> o#(x,o(y,z))
     o#(d(x,y),z) -> o#(y,z) -> o#(o(x,y),z) -> o#(y,z)
     o#(d(x,y),z) -> o#(y,z) -> o#(d(x,y),z) -> d#(o(x,z),o(y,z))
     o#(d(x,y),z) -> o#(y,z) -> o#(d(x,y),z) -> o#(x,z)
     o#(d(x,y),z) -> o#(y,z) -> o#(d(x,y),z) -> o#(y,z)
     o#(d(x,y),z) -> o#(y,z) ->
     o#(lambda(x),y) -> lambda#(o(x,d(1(),o(y,p()))))
     o#(d(x,y),z) -> o#(y,z) -> o#(lambda(x),y) -> o#(x,d(1(),o(y,p())))
     o#(d(x,y),z) -> o#(y,z) -> o#(lambda(x),y) -> d#(1(),o(y,p()))
     o#(d(x,y),z) -> o#(y,z) -> o#(lambda(x),y) -> o#(y,p())
     o#(d(x,y),z) -> o#(x,z) -> o#(x,y) -> d#(y,x)
     o#(d(x,y),z) -> o#(x,z) -> o#(x,y) -> d#(x,y)
     o#(d(x,y),z) -> o#(x,z) -> o#(o(x,y),z) -> o#(x,o(y,z))
     o#(d(x,y),z) -> o#(x,z) -> o#(o(x,y),z) -> o#(y,z)
     o#(d(x,y),z) -> o#(x,z) -> o#(d(x,y),z) -> d#(o(x,z),o(y,z))
     o#(d(x,y),z) -> o#(x,z) -> o#(d(x,y),z) -> o#(x,z)
     o#(d(x,y),z) -> o#(x,z) -> o#(d(x,y),z) -> o#(y,z)
     o#(d(x,y),z) -> o#(x,z) ->
     o#(lambda(x),y) -> lambda#(o(x,d(1(),o(y,p()))))
     o#(d(x,y),z) -> o#(x,z) -> o#(lambda(x),y) -> o#(x,d(1(),o(y,p())))
     o#(d(x,y),z) -> o#(x,z) -> o#(lambda(x),y) -> d#(1(),o(y,p()))
     o#(d(x,y),z) -> o#(x,z) -> o#(lambda(x),y) -> o#(y,p())
     o#(o(x,y),z) -> o#(y,z) -> o#(x,y) -> d#(y,x)
     o#(o(x,y),z) -> o#(y,z) -> o#(x,y) -> d#(x,y)
     o#(o(x,y),z) -> o#(y,z) -> o#(o(x,y),z) -> o#(x,o(y,z))
     o#(o(x,y),z) -> o#(y,z) -> o#(o(x,y),z) -> o#(y,z)
     o#(o(x,y),z) -> o#(y,z) -> o#(d(x,y),z) -> d#(o(x,z),o(y,z))
     o#(o(x,y),z) -> o#(y,z) -> o#(d(x,y),z) -> o#(x,z)
     o#(o(x,y),z) -> o#(y,z) -> o#(d(x,y),z) -> o#(y,z)
     o#(o(x,y),z) -> o#(y,z) ->
     o#(lambda(x),y) -> lambda#(o(x,d(1(),o(y,p()))))
     o#(o(x,y),z) -> o#(y,z) -> o#(lambda(x),y) -> o#(x,d(1(),o(y,p())))
     o#(o(x,y),z) -> o#(y,z) -> o#(lambda(x),y) -> d#(1(),o(y,p()))
     o#(o(x,y),z) -> o#(y,z) -> o#(lambda(x),y) -> o#(y,p())
     o#(o(x,y),z) -> o#(x,o(y,z)) -> o#(x,y) -> d#(y,x)
     o#(o(x,y),z) -> o#(x,o(y,z)) -> o#(x,y) -> d#(x,y)
     o#(o(x,y),z) -> o#(x,o(y,z)) -> o#(o(x,y),z) -> o#(x,o(y,z))
     o#(o(x,y),z) -> o#(x,o(y,z)) -> o#(o(x,y),z) -> o#(y,z)
     o#(o(x,y),z) -> o#(x,o(y,z)) -> o#(d(x,y),z) -> d#(o(x,z),o(y,z))
     o#(o(x,y),z) -> o#(x,o(y,z)) -> o#(d(x,y),z) -> o#(x,z)
     o#(o(x,y),z) -> o#(x,o(y,z)) -> o#(d(x,y),z) -> o#(y,z)
     o#(o(x,y),z) -> o#(x,o(y,z)) ->
     o#(lambda(x),y) -> lambda#(o(x,d(1(),o(y,p()))))
     o#(o(x,y),z) -> o#(x,o(y,z)) ->
     o#(lambda(x),y) -> o#(x,d(1(),o(y,p())))
     o#(o(x,y),z) -> o#(x,o(y,z)) ->
     o#(lambda(x),y) -> d#(1(),o(y,p()))
     o#(o(x,y),z) -> o#(x,o(y,z)) -> o#(lambda(x),y) -> o#(y,p())
     o#(lambda(x),y) -> o#(y,p()) -> o#(x,y) -> d#(y,x)
     o#(lambda(x),y) -> o#(y,p()) -> o#(x,y) -> d#(x,y)
     o#(lambda(x),y) -> o#(y,p()) -> o#(o(x,y),z) -> o#(x,o(y,z))
     o#(lambda(x),y) -> o#(y,p()) -> o#(o(x,y),z) -> o#(y,z)
     o#(lambda(x),y) -> o#(y,p()) -> o#(d(x,y),z) -> d#(o(x,z),o(y,z))
     o#(lambda(x),y) -> o#(y,p()) -> o#(d(x,y),z) -> o#(x,z)
     o#(lambda(x),y) -> o#(y,p()) -> o#(d(x,y),z) -> o#(y,z)
     o#(lambda(x),y) -> o#(y,p()) ->
     o#(lambda(x),y) -> lambda#(o(x,d(1(),o(y,p()))))
     o#(lambda(x),y) -> o#(y,p()) ->
     o#(lambda(x),y) -> o#(x,d(1(),o(y,p())))
     o#(lambda(x),y) -> o#(y,p()) ->
     o#(lambda(x),y) -> d#(1(),o(y,p()))
     o#(lambda(x),y) -> o#(y,p()) ->
     o#(lambda(x),y) -> o#(y,p())
     o#(lambda(x),y) -> o#(x,d(1(),o(y,p()))) ->
     o#(x,y) -> d#(y,x)
     o#(lambda(x),y) -> o#(x,d(1(),o(y,p()))) ->
     o#(x,y) -> d#(x,y)
     o#(lambda(x),y) -> o#(x,d(1(),o(y,p()))) ->
     o#(o(x,y),z) -> o#(x,o(y,z))
     o#(lambda(x),y) -> o#(x,d(1(),o(y,p()))) ->
     o#(o(x,y),z) -> o#(y,z)
     o#(lambda(x),y) -> o#(x,d(1(),o(y,p()))) ->
     o#(d(x,y),z) -> d#(o(x,z),o(y,z))
     o#(lambda(x),y) -> o#(x,d(1(),o(y,p()))) ->
     o#(d(x,y),z) -> o#(x,z)
     o#(lambda(x),y) -> o#(x,d(1(),o(y,p()))) ->
     o#(d(x,y),z) -> o#(y,z)
     o#(lambda(x),y) -> o#(x,d(1(),o(y,p()))) ->
     o#(lambda(x),y) -> lambda#(o(x,d(1(),o(y,p()))))
     o#(lambda(x),y) -> o#(x,d(1(),o(y,p()))) ->
     o#(lambda(x),y) -> o#(x,d(1(),o(y,p())))
     o#(lambda(x),y) -> o#(x,d(1(),o(y,p()))) ->
     o#(lambda(x),y) -> d#(1(),o(y,p()))
     o#(lambda(x),y) -> o#(x,d(1(),o(y,p()))) -> o#(lambda(x),y) -> o#(y,p())
    SCC Processor:
     #sccs: 1
     #rules: 6
     #arcs: 66/121
     DPs:
      o#(d(x,y),z) -> o#(y,z)
      o#(lambda(x),y) -> o#(y,p())
      o#(lambda(x),y) -> o#(x,d(1(),o(y,p())))
      o#(d(x,y),z) -> o#(x,z)
      o#(o(x,y),z) -> o#(y,z)
      o#(o(x,y),z) -> o#(x,o(y,z))
     TRS:
      o(lambda(x),y) -> lambda(o(x,d(1(),o(y,p()))))
      o(d(x,y),z) -> d(o(x,z),o(y,z))
      o(o(x,y),z) -> o(x,o(y,z))
      lambda(x) -> x
      o(x,y) -> x
      o(x,y) -> y
      d(x,y) -> x
      d(x,y) -> y
      o(x,y) -> d(x,y)
      o(x,y) -> d(y,x)
     Maximal Polynomial Processor:
      usable rules:
       o(lambda(x),y) -> lambda(o(x,d(1(),o(y,p()))))
       o(d(x,y),z) -> d(o(x,z),o(y,z))
       o(o(x,y),z) -> o(x,o(y,z))
       lambda(x) -> x
       o(x,y) -> x
       o(x,y) -> y
       d(x,y) -> x
       d(x,y) -> y
       o(x,y) -> d(x,y)
       o(x,y) -> d(y,x)
      interpretations:
       o#(x0, x1) = max(0, 0 + x0 + x1)
       d(x0, x1) = max(0, x0, x1)
       p = 0
       1 = 0
       o(x0, x1) = max(0, 0 + x0 + x1)
       lambda(x0) = max(0, 0 + 1 + x0)
      problem:
       DPs:
        o#(d(x,y),z) -> o#(y,z)
        o#(d(x,y),z) -> o#(x,z)
        o#(o(x,y),z) -> o#(y,z)
        o#(o(x,y),z) -> o#(x,o(y,z))
       TRS:
        o(lambda(x),y) -> lambda(o(x,d(1(),o(y,p()))))
        o(d(x,y),z) -> d(o(x,z),o(y,z))
        o(o(x,y),z) -> o(x,o(y,z))
        lambda(x) -> x
        o(x,y) -> x
        o(x,y) -> y
        d(x,y) -> x
        d(x,y) -> y
        o(x,y) -> d(x,y)
        o(x,y) -> d(y,x)
      Restore Modifier:
       DPs:
        o#(d(x,y),z) -> o#(y,z)
        o#(d(x,y),z) -> o#(x,z)
        o#(o(x,y),z) -> o#(y,z)
        o#(o(x,y),z) -> o#(x,o(y,z))
       TRS:
        o(lambda(x),y) -> lambda(o(x,d(1(),o(y,p()))))
        o(d(x,y),z) -> d(o(x,z),o(y,z))
        o(o(x,y),z) -> o(x,o(y,z))
        lambda(x) -> x
        o(x,y) -> x
        o(x,y) -> y
        d(x,y) -> x
        d(x,y) -> y
        o(x,y) -> d(x,y)
        o(x,y) -> d(y,x)
       Size-Change Termination Processor:
        DPs:
         
        TRS:
         o(lambda(x),y) -> lambda(o(x,d(1(),o(y,p()))))
         o(d(x,y),z) -> d(o(x,z),o(y,z))
         o(o(x,y),z) -> o(x,o(y,z))
         lambda(x) -> x
         o(x,y) -> x
         o(x,y) -> y
         d(x,y) -> x
         d(x,y) -> y
         o(x,y) -> d(x,y)
         o(x,y) -> d(y,x)
        The DP: o#(d(x,y),z) -> o#(y,z) has the edges:
          0 >   0
          1 >=  1
        The DP: o#(d(x,y),z) -> o#(x,z) has the edges:
          0 >   0
          1 >=  1
        The DP: o#(o(x,y),z) -> o#(y,z) has the edges:
          0 >   0
          1 >=  1
        The DP: o#(o(x,y),z) -> o#(x,o(y,z)) has the edges:
          0 >   0
        Qed