Input TRS:
    1: a(f(),a(g(),a(f(),x))) -> a(f(),a(g(),a(g(),a(f(),x))))
    2: a(g(),a(f(),a(g(),x))) -> a(g(),a(f(),a(f(),a(g(),x))))
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Freezing a
1: a❆1_f(a❆1_g(a❆1_f(x))) -> a❆1_f(a❆1_g(a❆1_g(a❆1_f(x))))
2: a❆1_g(a❆1_f(a❆1_g(x))) -> a❆1_g(a❆1_f(a❆1_f(a❆1_g(x))))
3: a(g(),_1) ->= a❆1_g(_1)
4: a(f(),_1) ->= a❆1_f(_1)
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... removes: 4 3
     a(x1,x2)	weight: (/ 1 2) + x1 + x2
a❆1_f(x1)	weight: x1
a❆1_g(x1)	weight: x1
     f()	weight: 0
     g()	weight: 0
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #a❆1_g(a❆1_f(a❆1_g(x))) -> #a❆1_g(a❆1_f(a❆1_f(a❆1_g(x))))
   #2: #a❆1_g(a❆1_f(a❆1_g(x))) -> #a❆1_f(a❆1_f(a❆1_g(x)))
   #3: #a❆1_f(a❆1_g(a❆1_f(x))) -> #a❆1_f(a❆1_g(a❆1_g(a❆1_f(x))))
   #4: #a❆1_f(a❆1_g(a❆1_f(x))) -> #a❆1_g(a❆1_g(a❆1_f(x)))
Number of SCCs: 0, DPs: 0, edges: 0
YES