YES
Input TRS:
      1: f(a(),f(a(),x)) -> f(a(),f(f(a(),x),f(a(),a())))
Number of strict rules: 1
Direct POLO(bPol) ... failed.
Uncurrying f
      1: f^1_a(f^1_a(x)) -> f^1_a(f(f^1_a(x),f^1_a(a())))
      2: f(a(),_1) ->= f^1_a(_1)
Number of strict rules: 1
Direct POLO(bPol) ... failed.
Dependency Pairs:
     #1: #f(a(),_1) ->? #f^1_a(_1)
     #2: #f^1_a(f^1_a(x)) -> #f^1_a(f(f^1_a(x),f^1_a(a())))
     #3: #f^1_a(f^1_a(x)) -> #f(f^1_a(x),f^1_a(a()))
     #4: #f^1_a(f^1_a(x)) -> #f^1_a(a())
Number of SCCs: 0, DPs: 0