YES

Problem:
 p(a(x0),p(b(x1),p(a(x2),x3))) -> p(x2,p(a(a(x0)),p(b(x1),x3)))

Proof:
 DP Processor:
  DPs:
   p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(b(x1),x3)
   p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(a(a(x0)),p(b(x1),x3))
   p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(x2,p(a(a(x0)),p(b(x1),x3)))
  TRS:
   p(a(x0),p(b(x1),p(a(x2),x3))) -> p(x2,p(a(a(x0)),p(b(x1),x3)))
  EDG Processor:
   DPs:
    p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(b(x1),x3)
    p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(a(a(x0)),p(b(x1),x3))
    p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(x2,p(a(a(x0)),p(b(x1),x3)))
   TRS:
    p(a(x0),p(b(x1),p(a(x2),x3))) -> p(x2,p(a(a(x0)),p(b(x1),x3)))
   graph:
    p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(a(a(x0)),p(b(x1),x3)) ->
    p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(b(x1),x3)
    p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(a(a(x0)),p(b(x1),x3)) ->
    p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(a(a(x0)),p(b(x1),x3))
    p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(a(a(x0)),p(b(x1),x3)) ->
    p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(x2,p(a(a(x0)),p(b(x1),x3)))
    p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(x2,p(a(a(x0)),p(b(x1),x3))) ->
    p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(b(x1),x3)
    p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(x2,p(a(a(x0)),p(b(x1),x3))) ->
    p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(a(a(x0)),p(b(x1),x3))
    p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(x2,p(a(a(x0)),p(b(x1),x3))) ->
    p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(x2,p(a(a(x0)),p(b(x1),x3)))
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 6/9
    DPs:
     p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(a(a(x0)),p(b(x1),x3))
     p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(x2,p(a(a(x0)),p(b(x1),x3)))
    TRS:
     p(a(x0),p(b(x1),p(a(x2),x3))) -> p(x2,p(a(a(x0)),p(b(x1),x3)))
    Subterm Criterion Processor:
     simple projection:
      pi(p) = [1,1]
      pi(p#) = [1,1]
     problem:
      DPs:
       p#(a(x0),p(b(x1),p(a(x2),x3))) -> p#(x2,p(a(a(x0)),p(b(x1),x3)))
      TRS:
       p(a(x0),p(b(x1),p(a(x2),x3))) -> p(x2,p(a(a(x0)),p(b(x1),x3)))
     Semantic Labeling Processor:
      dimension: 2
      usable rules:
       
      interpretation:
                 [0]
       [b](x0) = [1],
       
                 [1 1]  
       [a](x0) = [0 0]x0,
       
                     [1 1]     [0 1]     [1]
       [p](x0, x1) = [1 0]x0 + [0 1]x1 + [0]
       labeled:
        p#
       usable (for model):
        p#
        a
        p
        b
       argument filtering:
        pi(a) = 0
        pi(b) = []
        pi(p) = 0
        pi(p#) = []
      precedence:
       p# ~ p ~ b ~ a
      problem:
       DPs:
        
       TRS:
        p(a(x0),p(b(x1),p(a(x2),x3))) -> p(x2,p(a(a(x0)),p(b(x1),x3)))
      Qed