NO
Input TRS:
      1: f(g(X),Y) -> f(X,n__f(g(X),activate(Y)))
      2: f(X1,X2) -> n__f(X1,X2)
      3: activate(n__f(X1,X2)) -> f(X1,X2)
      4: activate(X) -> X
Number of strict rules: 4
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #activate(n__f(X1,X2)) -> #f(X1,X2)
     #2: #f(g(X),Y) -> #f(X,n__f(g(X),activate(Y)))
     #3: #f(g(X),Y) -> #activate(Y)
Number of SCCs: 1, DPs: 3
  SCC { #1..3 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  found.
  #activate(n__f(g(g(X_{2})),Y_{1}))	-#1->
  #f(g(g(X_{2})),Y_{1})	--->*
  #f(g(g(X_{2})),Y_{1})	-#2->
  #f(g(X_{2}),n__f(g(g(X_{2})),activate(Y_{1})))	--->*
  #f(g(X_{2}),n__f(g(g(X_{2})),activate(Y_{1})))	-#3->
  #activate(n__f(g(g(X_{2})),activate(Y_{1})))	--->*
  #activate(n__f(g(g(X_{2})),activate(Y_{1})))
  Looping with: [ Y_{1} := activate(Y_{1}); X_{2} := X_{2}; ]