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)))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
      [p#](x0, x1) = [0 0 1]x0 + [0 0 1]x1,
      
                    [0 0 0]     [0 0 0]     [0]
      [p](x0, x1) = [0 0 1]x0 + [0 1 0]x1 + [1]
                    [0 1 1]     [0 1 0]     [0],
      
                [0 0 0]     [0]
      [b](x0) = [1 0 0]x0 + [1]
                [1 1 0]     [0],
      
                [0 0 0]  
      [a](x0) = [0 0 0]x0
                [0 1 1]  
     orientation:
      p#(a(x0),p(b(x1),p(a(x2),x3))) = [0 1 1]x0 + [2 1 0]x1 + [0 1 1]x2 + [0 1 0]x3 + [2] >= [0 1 1]x0 + [2 1 0]x1 + [0 1 0]x3 + [1] = p#(a(a(x0)),p(b(x1),x3))
      
      p#(a(x0),p(b(x1),p(a(x2),x3))) = [0 1 1]x0 + [2 1 0]x1 + [0 1 1]x2 + [0 1 0]x3 + [2] >= [0 1 1]x0 + [1 1 0]x1 + [0 0 1]x2 + [0 1 0]x3 + [1] = p#(x2,p(a(a(x0)),p(b(x1),x3)))
      
                                      [0 0 0]     [0 0 0]     [0 0 0]     [0 0 0]     [0]    [0 0 0]     [0 0 0]     [0 0 0]     [0 0 0]     [0]                                
      p(a(x0),p(b(x1),p(a(x2),x3))) = [0 1 1]x0 + [1 1 0]x1 + [0 1 1]x2 + [0 1 0]x3 + [3] >= [0 1 1]x0 + [1 1 0]x1 + [0 0 1]x2 + [0 1 0]x3 + [3] = p(x2,p(a(a(x0)),p(b(x1),x3)))
                                      [0 1 1]     [1 1 0]     [0 1 1]     [0 1 0]     [2]    [0 1 1]     [1 1 0]     [0 1 1]     [0 1 0]     [2]                                
     problem:
      DPs:
       
      TRS:
       p(a(x0),p(b(x1),p(a(x2),x3))) -> p(x2,p(a(a(x0)),p(b(x1),x3)))
     Qed