YES

Problem:
 a(x1) -> x1
 a(a(b(x1))) -> b(a(b(a(a(x1)))))
 b(b(x1)) -> b(x1)

Proof:
 DP Processor:
  DPs:
   a#(a(b(x1))) -> a#(x1)
   a#(a(b(x1))) -> a#(a(x1))
   a#(a(b(x1))) -> b#(a(a(x1)))
   a#(a(b(x1))) -> a#(b(a(a(x1))))
   a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
  TRS:
   a(x1) -> x1
   a(a(b(x1))) -> b(a(b(a(a(x1)))))
   b(b(x1)) -> b(x1)
  TDG Processor:
   DPs:
    a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(b(a(a(x1))))
    a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
   TRS:
    a(x1) -> x1
    a(a(b(x1))) -> b(a(b(a(a(x1)))))
    b(b(x1)) -> b(x1)
   graph:
    a#(a(b(x1))) -> a#(b(a(a(x1)))) ->
    a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
    a#(a(b(x1))) -> a#(b(a(a(x1)))) ->
    a#(a(b(x1))) -> a#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(b(a(a(x1)))) -> a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(b(a(a(x1)))) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(b(a(a(x1)))) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1)
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(b(a(a(x1))))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1)))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1))
    a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
   EDG Processor:
    DPs:
     a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> a#(a(x1))
     a#(a(b(x1))) -> b#(a(a(x1)))
     a#(a(b(x1))) -> a#(b(a(a(x1))))
     a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
    TRS:
     a(x1) -> x1
     a(a(b(x1))) -> b(a(b(a(a(x1)))))
     b(b(x1)) -> b(x1)
    graph:
     a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(a(x1))
     a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(a(x1)))
     a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> a#(b(a(a(x1))))
     a#(a(b(x1))) -> a#(a(x1)) -> a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(a(x1))
     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(a(x1)))
     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(b(a(a(x1))))
     a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> b#(a(b(a(a(x1)))))
    SCC Processor:
     #sccs: 1
     #rules: 2
     #arcs: 10/25
     DPs:
      a#(a(b(x1))) -> a#(a(x1))
      a#(a(b(x1))) -> a#(x1)
     TRS:
      a(x1) -> x1
      a(a(b(x1))) -> b(a(b(a(a(x1)))))
      b(b(x1)) -> b(x1)
     Bounds Processor:
      bound: 0
      enrichment: match-dp
      automaton:
       final states: {1}
       transitions:
        a{#,0}(3) -> 1*
        b0(12) -> 13*
        b0(10) -> 11*
        a0(2) -> 3*
        a0(11) -> 12*
        a0(9) -> 10*
        f40() -> 2*
        11 -> 13,3,10,12
        2 -> 3*
        13 -> 11,12,3
        9 -> 10*
        3 -> 9*
      problem:
       DPs:
        a#(a(b(x1))) -> a#(x1)
       TRS:
        a(x1) -> x1
        a(a(b(x1))) -> b(a(b(a(a(x1)))))
        b(b(x1)) -> b(x1)
      Restore Modifier:
       DPs:
        a#(a(b(x1))) -> a#(x1)
       TRS:
        a(x1) -> x1
        a(a(b(x1))) -> b(a(b(a(a(x1)))))
        b(b(x1)) -> b(x1)
       EDG Processor:
        DPs:
         a#(a(b(x1))) -> a#(x1)
        TRS:
         a(x1) -> x1
         a(a(b(x1))) -> b(a(b(a(a(x1)))))
         b(b(x1)) -> b(x1)
        graph:
         a#(a(b(x1))) -> a#(x1) -> a#(a(b(x1))) -> a#(x1)
        Usable Rule Processor:
         DPs:
          a#(a(b(x1))) -> a#(x1)
         TRS:
          
         Arctic Interpretation Processor:
          dimension: 1
          usable rules:
           
          interpretation:
           [b](x0) = 1x0 + 13,
           
           [a](x0) = x0 + 0,
           
           [a#](x0) = x0
          orientation:
           a#(a(b(x1))) = 1x1 + 13 >= x1 = a#(x1)
          problem:
           DPs:
            
           TRS:
            
          Qed