YES

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

Proof:
 DP Processor:
  DPs:
   p#(a(x0),p(b(a(x1)),x2)) -> a#(b(a(x1)))
   p#(a(x0),p(b(a(x1)),x2)) -> p#(a(b(a(x1))),x2)
   p#(a(x0),p(b(a(x1)),x2)) -> p#(x1,p(a(b(a(x1))),x2))
   a#(b(a(x0))) -> a#(b(x0))
  TRS:
   p(a(x0),p(b(a(x1)),x2)) -> p(x1,p(a(b(a(x1))),x2))
   a(b(a(x0))) -> b(a(b(x0)))
  TDG Processor:
   DPs:
    p#(a(x0),p(b(a(x1)),x2)) -> a#(b(a(x1)))
    p#(a(x0),p(b(a(x1)),x2)) -> p#(a(b(a(x1))),x2)
    p#(a(x0),p(b(a(x1)),x2)) -> p#(x1,p(a(b(a(x1))),x2))
    a#(b(a(x0))) -> a#(b(x0))
   TRS:
    p(a(x0),p(b(a(x1)),x2)) -> p(x1,p(a(b(a(x1))),x2))
    a(b(a(x0))) -> b(a(b(x0)))
   graph:
    a#(b(a(x0))) -> a#(b(x0)) -> a#(b(a(x0))) -> a#(b(x0))
    p#(a(x0),p(b(a(x1)),x2)) -> a#(b(a(x1))) ->
    a#(b(a(x0))) -> a#(b(x0))
    p#(a(x0),p(b(a(x1)),x2)) -> p#(a(b(a(x1))),x2) ->
    p#(a(x0),p(b(a(x1)),x2)) -> p#(x1,p(a(b(a(x1))),x2))
    p#(a(x0),p(b(a(x1)),x2)) -> p#(a(b(a(x1))),x2) ->
    p#(a(x0),p(b(a(x1)),x2)) -> p#(a(b(a(x1))),x2)
    p#(a(x0),p(b(a(x1)),x2)) -> p#(a(b(a(x1))),x2) ->
    p#(a(x0),p(b(a(x1)),x2)) -> a#(b(a(x1)))
    p#(a(x0),p(b(a(x1)),x2)) -> p#(x1,p(a(b(a(x1))),x2)) ->
    p#(a(x0),p(b(a(x1)),x2)) -> p#(x1,p(a(b(a(x1))),x2))
    p#(a(x0),p(b(a(x1)),x2)) -> p#(x1,p(a(b(a(x1))),x2)) ->
    p#(a(x0),p(b(a(x1)),x2)) -> p#(a(b(a(x1))),x2)
    p#(a(x0),p(b(a(x1)),x2)) -> p#(x1,p(a(b(a(x1))),x2)) ->
    p#(a(x0),p(b(a(x1)),x2)) -> a#(b(a(x1)))
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 8/16
    DPs:
     p#(a(x0),p(b(a(x1)),x2)) -> p#(a(b(a(x1))),x2)
     p#(a(x0),p(b(a(x1)),x2)) -> p#(x1,p(a(b(a(x1))),x2))
    TRS:
     p(a(x0),p(b(a(x1)),x2)) -> p(x1,p(a(b(a(x1))),x2))
     a(b(a(x0))) -> b(a(b(x0)))
    Matrix Interpretation Processor: dim=4
     
     interpretation:
      [p#](x0, x1) = [0 0 1 0]x0 + [1 1 0 0]x1,
      
                    [0 0 0 1]     [1 0 1 1]  
                    [0 0 1 1]     [0 1 0 0]  
      [p](x0, x1) = [0 0 1 0]x0 + [1 0 1 1]x1
                    [0 0 1 1]     [0 1 0 0]  ,
      
                [0 0 0 0]  
                [0 0 0 0]  
      [b](x0) = [1 0 0 0]x0
                [0 1 0 0]  ,
      
                [0 0 1 1]     [1]
                [1 1 0 0]     [0]
      [a](x0) = [0 0 0 1]x0 + [1]
                [0 0 0 0]     [0]
     orientation:
      p#(a(x0),p(b(a(x1)),x2)) = [0 0 0 1]x0 + [2 2 1 1]x1 + [1 1 1 1]x2 + [2] >= [1 1 0 0]x1 + [1 1 0 0]x2 + [1] = p#(a(b(a(x1))),x2)
      
      p#(a(x0),p(b(a(x1)),x2)) = [0 0 0 1]x0 + [2 2 1 1]x1 + [1 1 1 1]x2 + [2] >= [1 1 1 0]x1 + [1 1 1 1]x2 + [1] = p#(x1,p(a(b(a(x1))),x2))
      
                                [0 0 0 0]     [2 2 2 2]     [2 1 2 2]     [2]    [2 2 0 1]     [2 1 2 2]     [2]                          
                                [0 0 0 1]     [1 1 1 1]     [0 1 0 0]     [2]    [1 1 1 1]     [0 1 0 0]     [1]                          
      p(a(x0),p(b(a(x1)),x2)) = [0 0 0 1]x0 + [2 2 2 2]x1 + [2 1 2 2]x2 + [3] >= [2 2 1 0]x1 + [2 1 2 2]x2 + [2] = p(x1,p(a(b(a(x1))),x2))
                                [0 0 0 1]     [1 1 1 1]     [0 1 0 0]     [2]    [1 1 1 1]     [0 1 0 0]     [1]                          
      
                    [1 1 1 1]     [2]    [0 0 0 0]     [0]              
                    [0 0 0 0]     [0]    [0 0 0 0]     [0]              
      a(b(a(x0))) = [1 1 0 0]x0 + [1] >= [1 1 0 0]x0 + [1] = b(a(b(x0)))
                    [0 0 0 0]     [0]    [0 0 0 0]     [0]              
     problem:
      DPs:
       
      TRS:
       p(a(x0),p(b(a(x1)),x2)) -> p(x1,p(a(b(a(x1))),x2))
       a(b(a(x0))) -> b(a(b(x0)))
     Qed
    
    DPs:
     a#(b(a(x0))) -> a#(b(x0))
    TRS:
     p(a(x0),p(b(a(x1)),x2)) -> p(x1,p(a(b(a(x1))),x2))
     a(b(a(x0))) -> b(a(b(x0)))
    KBO Processor:
     argument filtering:
      pi(a) = [0]
      pi(b) = 0
      pi(p) = []
      pi(a#) = [0]
     weight function:
      w0 = 1
      w(a#) = w(p) = 1
      w(b) = w(a) = 0
     precedence:
      a# ~ p ~ b ~ a
     problem:
      DPs:
       
      TRS:
       p(a(x0),p(b(a(x1)),x2)) -> p(x1,p(a(b(a(x1))),x2))
       a(b(a(x0))) -> b(a(b(x0)))
     Qed