Input TRS:
    1: f(f(x)) -> f(c(f(x)))
    2: f(f(x)) -> f(d(f(x)))
    3: g(c(x)) -> x
    4: g(d(x)) -> x
    5: g(c(h(|0|()))) -> g(d(|1|()))
    6: g(c(|1|())) -> g(d(h(|0|())))
    7: g(h(x)) -> g(x)
Number of strict rules: 7
Direct Order(PosReal,>,Poly) ... removes: 4 3
   |0|()	weight: 0
     h(x1)	weight: x1
     d(x1)	weight: x1
     c(x1)	weight: x1
     f(x1)	weight: (/ 1 8) + 2 * x1
   |1|()	weight: 0
     g(x1)	weight: (/ 1 8) + x1
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... failed.
Freezing g
1: f(f(x)) -> f(c(f(x)))
2: f(f(x)) -> f(d(f(x)))
5: g❆1_c(h(|0|())) -> g❆1_d(|1|())
6: g❆1_c(|1|()) -> g❆1_d(h(|0|()))
7: g❆1_h(x) -> g(x)
8: g(h(_1)) ->= g❆1_h(_1)
9: g(d(_1)) ->= g❆1_d(_1)
10: g(c(_1)) ->= g❆1_c(_1)
Number of strict rules: 5
Direct Order(PosReal,>,Poly) ... removes: 8 5 10 7 9 6
   |0|()	weight: 0
     h(x1)	weight: (/ 1 4) + x1
     d(x1)	weight: x1
g❆1_c(x1)	weight: (/ 3 8) + x1
     c(x1)	weight: x1
g❆1_d(x1)	weight: x1
g❆1_h(x1)	weight: (/ 5 8) + x1
     f(x1)	weight: (/ 61753 8) + x1
   |1|()	weight: 0
     g(x1)	weight: (/ 1 2) + x1
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Dependency Pairs:
   #1: #f(f(x)) -> #f(d(f(x)))
   #2: #f(f(x)) -> #f(c(f(x)))
Number of SCCs: 0, DPs: 0, edges: 0
YES