YES
Input TRS:
      1: a(p(x1)) -> p(a(A(x1)))
      2: a(A(x1)) -> A(a(x1))
      3: p(A(A(x1))) -> a(p(x1))
Number of strict rules: 3
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #a(A(x1)) -> #a(x1)
     #2: #p(A(A(x1))) -> #a(p(x1))
     #3: #p(A(A(x1))) -> #p(x1)
     #4: #a(p(x1)) -> #p(a(A(x1)))
     #5: #a(p(x1)) -> #a(A(x1))
Number of SCCs: 1, DPs: 5
  SCC { #1..5 }
POLO(Sum)... succeeded.
      a 	w: x1
      #p 	w: x1 + 1
      p 	w: x1 + 1
      A 	w: x1
      #a 	w: x1
    USABLE RULES: { 1..3 }
    Removed DPs: #5
Number of SCCs: 1, DPs: 4
  SCC { #1..4 }
POLO(Sum)... succeeded.
      a 	w: x1
      #p 	w: 1
      p 	w: 1
      A 	w: x1 + 32286
      #a 	w: x1
    USABLE RULES: { 1..3 }
    Removed DPs: #1
Number of SCCs: 1, DPs: 3
  SCC { #2..4 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded.
      a 	w: [1,1;0,1] * x1 + [1;0]
      #p 	w: [0,1;0,0] * x1 + [0;1]
      p 	w: [0,1;0,0] * x1 + [1;1]
      A 	w: [0,0;0,1] * x1 + [31675;2]
      #a 	w: x1 + [2;0]
    USABLE RULES: { 1..3 }
    Removed DPs: #2..4
Number of SCCs: 0, DPs: 0