Input TRS:
    1: f(h(x)) -> f(i(x))
    2: f(i(x)) -> a()
    3: i(x) -> h(x)
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... removes: 2
     h(x1)	weight: 7720 + x1
     a()	weight: 0
     f(x1)	weight: 2 * x1
     i(x1)	weight: 7720 + x1
Number of strict rules: 2
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #f(h(x)) -> #f(i(x))
   #2: #f(h(x)) -> #i(x)
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #1 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... Order(PosReal,>,MaxSum-Sum; NegReal,≥,Sum)... failed.
Removing edges: failed.
Finding a loop...  found.
  #f(h(x_{1}))	-#1->
  #f(i(x_{1}))	--->*
  #f(h(x_{1}))
  Looping with: [ x_{1} := x_{1}; ]
NO