YES
Input TRS:
    1: f(g(x)) -> g(f(f(x)))
    2: f(h(x)) -> h(h(f(x)))
    3: f(x) -> x
    4: g(x) -> x
Infeasibility test:
    f(x) --> f(h(x))
Co-Order(NegReal,≥,Sum) ...Co-QLPOpS ...Co-QWPOpS(PosReal,>,Sum) ... succeeded.
     h(x1)	weight: x1	status: [x1]	precedence above:
     f(x1)	weight: x1	status: [x1]	precedence above: h g
    #(x1)	weight: x1	status: x1
     g(x1)	weight: (/ 1 2) + x1	status: [x1]	precedence above: