Input TRS:
    1: f(c(s(x),y)) -> f(c(x,s(y)))
    2: f(c(s(x),s(y))) -> g(c(x,y))
    3: g(c(x,s(y))) -> g(c(s(x),y))
    4: g(c(s(x),s(y))) -> f(c(x,y))
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... removes: 4 2
     s(x1)	weight: (/ 1 4) + x1
     c(x1,x2)	weight: (/ 112401 4) + x1 + x2
     f(x1)	weight: (/ 1 4) + x1
     g(x1)	weight: x1
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Freezing f g
1: f❆1_c(s(x),y) -> f❆1_c(x,s(y))
3: g❆1_c(x,s(y)) -> g❆1_c(s(x),y)
5: g(c(_1,_2)) ->= g❆1_c(_1,_2)
6: f(c(_1,_2)) ->= f❆1_c(_1,_2)
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... removes: 3 5 6
     s(x1)	weight: (/ 1 4) + x1
g❆1_c(x1,x2)	weight: x1 + 2 * x2
     c(x1,x2)	weight: (/ 1 4) + x1 + x2
f❆1_c(x1,x2)	weight: (/ 1 4) + x1 + x2
     f(x1)	weight: 2 * x1
     g(x1)	weight: 2 * x1
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... removes: 1
     s(x1)	weight: (/ 1 4) + x1
g❆1_c(x1,x2)	weight: x1 + 2 * x2
     c(x1,x2)	weight: (/ 1 4) + x1 + x2
f❆1_c(x1,x2)	weight: (/ 1 4) + 2 * x1 + x2
     f(x1)	weight: 2 * x1
     g(x1)	weight: 2 * x1
Number of strict rules: 0
YES