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)))
    Arctic Interpretation Processor:
     dimension: 1
     usable rules:
      p(a(x0),p(b(a(x1)),x2)) -> p(x1,p(a(b(a(x1))),x2))
     interpretation:
      [p#](x0, x1) = x1,
      
      [p](x0, x1) = 4x1,
      
      [b](x0) = x0 + -4,
      
      [a](x0) = 1x0 + -6
     orientation:
      p#(a(x0),p(b(a(x1)),x2)) = 4x2 >= x2 = p#(a(b(a(x1))),x2)
      
      p#(a(x0),p(b(a(x1)),x2)) = 4x2 >= 4x2 = p#(x1,p(a(b(a(x1))),x2))
      
      p(a(x0),p(b(a(x1)),x2)) = 8x2 >= 8x2 = p(x1,p(a(b(a(x1))),x2))
      
      a(b(a(x0))) = 2x0 + -3 >= 1x0 + -3 = b(a(b(x0)))
     problem:
      DPs:
       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)))
     Restore Modifier:
      DPs:
       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=3
       
       usable rules:
        p(a(x0),p(b(a(x1)),x2)) -> p(x1,p(a(b(a(x1))),x2))
        a(b(a(x0))) -> b(a(b(x0)))
       interpretation:
        [p#](x0, x1) = [0 1 0]x0 + [0 0 1]x1,
        
                      [0 0 0]     [0 0 1]     [0]
        [p](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                      [0 1 0]     [0 0 1]     [0],
        
                  [1 0 0]  
        [b](x0) = [0 0 1]x0
                  [0 0 0]  ,
        
                  [0 0 1]     [0]
        [a](x0) = [1 0 0]x0 + [1]
                  [0 1 1]     [1]
       orientation:
        p#(a(x0),p(b(a(x1)),x2)) = [1 0 0]x0 + [0 1 1]x1 + [0 0 1]x2 + [2] >= [0 1 1]x1 + [0 0 1]x2 + [1] = p#(x1,p(a(b(a(x1))),x2))
        
                                  [0 0 0]     [0 1 1]     [0 0 1]     [1]    [0 0 1]     [0 0 1]     [1]                          
        p(a(x0),p(b(a(x1)),x2)) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2 + [1] >= [0 0 0]x1 + [0 0 0]x2 + [1] = p(x1,p(a(b(a(x1))),x2))
                                  [1 0 0]     [0 1 1]     [0 0 1]     [2]    [0 1 1]     [0 0 1]     [1]                          
        
                      [0 0 0]     [0]    [0 0 0]     [0]              
        a(b(a(x0))) = [0 0 1]x0 + [1] >= [0 0 1]x0 + [1] = b(a(b(x0)))
                      [0 1 1]     [2]    [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)))
    Usable Rule Processor:
     DPs:
      a#(b(a(x0))) -> a#(b(x0))
     TRS:
      
     Semantic Labeling Processor:
      dimension: 1
      usable rules:
       
      interpretation:
       [b](x0) = x0,
       
       [a](x0) = x0 + 1
       labeled:
        a#
       usable (for model):
        a#
        b
        a
       argument filtering:
        pi(a) = []
        pi(b) = 0
        pi(a#) = []
      precedence:
       a# ~ b ~ a
      problem:
       DPs:
        
       TRS:
        
      Qed