Input TRS:
    1: f(nil()) -> nil()
    2: f(.(nil(),y)) -> .(nil(),f(y))
    3: f(.(.(x,y),z)) -> f(.(x,.(y,z)))
    4: g(nil()) -> nil()
    5: g(.(x,nil())) -> .(g(x),nil())
    6: g(.(x,.(y,z))) -> g(.(.(x,y),z))
Number of strict rules: 6
Direct Order(PosReal,>,Poly) ... removes: 4 1
     f(x1)	weight: (/ 224801 8) + x1
   nil()	weight: 0
     .(x1,x2)	weight: (/ 1 8) + x1 + x2
     g(x1)	weight: (/ 1 8) + x1
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... removes: 2
     f(x1)	weight: (/ 224801 8) + 2 * x1
   nil()	weight: 0
     .(x1,x2)	weight: (/ 1 8) + x1 + x2
     g(x1)	weight: (/ 1 8) + x1
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... removes: 5
     f(x1)	weight: (/ 224801 8) + 2 * x1
   nil()	weight: 0
     .(x1,x2)	weight: (/ 1 8) + x1 + x2
     g(x1)	weight: (/ 1 8) + 2 * x1
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Freezing f g
3: f❆1_.(.(x,y),z) -> f❆1_.(x,.(y,z))
6: g❆1_.(x,.(y,z)) -> g❆1_.(.(x,y),z)
7: g(.(_1,_2)) ->= g❆1_.(_1,_2)
8: f(.(_1,_2)) ->= f❆1_.(_1,_2)
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... removes: 8 3 7
g❆1_.(x1,x2)	weight: x1 + x2
     f(x1)	weight: 2 * x1
   nil()	weight: 0
     .(x1,x2)	weight: (/ 1 4) + x1 + x2
f❆1_.(x1,x2)	weight: 2 * x1 + x2
     g(x1)	weight: 2 * x1
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... removes: 6
g❆1_.(x1,x2)	weight: x1 + 2 * x2
     f(x1)	weight: 2 * x1
   nil()	weight: 0
     .(x1,x2)	weight: (/ 1 4) + x1 + x2
f❆1_.(x1,x2)	weight: 2 * x1 + x2
     g(x1)	weight: 2 * x1
Number of strict rules: 0
YES