YES
Input TRS:
      1: f(f(a(),x),a()) -> f(a(),f(f(x,f(a(),a())),a()))
Number of strict rules: 1
Direct POLO(bPol) ... failed.
Uncurrying f
      1: f^2_a(x,a()) -> f^1_a(f(f(x,f^1_a(a())),a()))
      2: f(a(),_1) ->= f^1_a(_1)
      3: f(f^1_a(_1),_2) ->= f^2_a(_1,_2)
Number of strict rules: 1
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #f(f^1_a(_1),_2) ->? #f^2_a(_1,_2)
     #2: #f^2_a(x,a()) -> #f(f(x,f^1_a(a())),a())
     #3: #f^2_a(x,a()) -> #f(x,f^1_a(a()))
Number of SCCs: 1, DPs: 3
  SCC { #1..3 }
POLO(Sum)... succeeded.
      a 	w: 3
      f 	w: 1
      #f^2_a	w: x2
      f^1_a	w: 2
      #f 	w: x2
      f^2_a	w: x1 + x2 + 2
    USABLE RULES: { }
    Removed DPs: #3
Number of SCCs: 1, DPs: 2
  SCC { #1 #2 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded.
      a 	w: [1;26995]
      f 	w: [0,1;0,0] * x1 + [0,1;0,0] * x2 + [28470;26994]
      #f^2_a	w: [0,1;0,0] * x1 + [1,0;1,1] * x2 + [55465;0]
      f^1_a	w: [0,1;0,0] * x1 + [55465;26994]
      #f 	w: [1,0;0,0] * x1 + [1,0;1,1] * x2
      f^2_a	w: [0,1;0,0] * x2 + [55464;26994]
    USABLE RULES: { 1..3 }
    Removed DPs: #2
Number of SCCs: 0, DPs: 0