Input TRS:
    1: f(h(x)) -> f(i(x))
    2: g(i(x)) -> g(h(x))
    3: h(a()) -> b()
    4: i(a()) -> b()
Number of strict rules: 4
Direct Order(PosReal,>,Poly) ... removes: 4 3
     h(x1)	weight: (/ 1 4) + 2 * x1
     a()	weight: 0
     b()	weight: 0
     f(x1)	weight: x1
     i(x1)	weight: (/ 1 4) + 2 * x1
     g(x1)	weight: x1
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Freezing f g
1: f❆1_h(x) -> f❆1_i(x)
2: g❆1_i(x) -> g❆1_h(x)
5: g(h(_1)) ->= g❆1_h(_1)
6: g(i(_1)) ->= g❆1_i(_1)
7: f(h(_1)) ->= f❆1_h(_1)
8: f(i(_1)) ->= f❆1_i(_1)
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... removes: 8 1 5 7 6 2
     h(x1)	weight: (/ 9749 4) + x1
     a()	weight: 0
f❆1_i(x1)	weight: x1
     b()	weight: 0
g❆1_h(x1)	weight: x1
     f(x1)	weight: (/ 1 2) + 2 * x1
f❆1_h(x1)	weight: (/ 1 4) + x1
     i(x1)	weight: (/ 1 4) + x1
g❆1_i(x1)	weight: (/ 1 4) + x1
     g(x1)	weight: 2 * x1
Number of strict rules: 0
YES