Input TRS:
    1: g(c(x,s(y))) -> g(c(s(x),y))
    2: f(c(s(x),y)) -> f(c(x,s(y)))
    3: f(f(x)) -> f(d(f(x)))
    4: f(x) -> x
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... removes: 4
     d(x1)	weight: x1
     s(x1)	weight: (/ 1 8) + x1
     c(x1,x2)	weight: 32285 + x1 + x2
     f(x1)	weight: (/ 1 8) + 2 * x1
     g(x1)	weight: x1
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing g
1: g❆1_c(x,s(y)) -> g❆1_c(s(x),y)
2: f(c(s(x),y)) -> f(c(x,s(y)))
3: f(f(x)) -> f(d(f(x)))
5: g(c(_1,_2)) ->= g❆1_c(_1,_2)
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... removes: 1 5 2
     d(x1)	weight: x1
     s(x1)	weight: (/ 1 4) + x1
g❆1_c(x1,x2)	weight: x1 + 2 * x2
     c(x1,x2)	weight: (/ 41801 4) + 2 * x1 + x2
     f(x1)	weight: (/ 129141 4) + x1
     g(x1)	weight: (/ 1 4) + 2 * x1
Number of strict rules: 1
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #f(f(x)) -> #f(d(f(x)))
Number of SCCs: 0, DPs: 0, edges: 0
YES