Input TRS:
    1: f(g(a())) -> f(s(g(b())))
    2: f(f(x)) -> b()
    3: g(x) -> f(g(x))
Number of strict rules: 3
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #g(x) -> #f(g(x))
   #2: #g(x) -> #g(x)
   #3: #f(g(a())) -> #f(s(g(b())))
   #4: #f(g(a())) -> #g(b())
Number of SCCs: 1, DPs: 3, edges: 5
	SCC { #1 #2 #4 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     a()	weight: (/ 3 8)
     s(x1)	weight: (/ 1 8)
     b()	weight: (/ 1 8)
     f(x1)	weight: (/ 1 8)
   #f(x1)	weight: x1
   #g(x1)	weight: (/ 1 4) + x1
     g(x1)	weight: (/ 1 8) + x1
    Usable rules: { 1..3 }
    Removed DPs: #1 #4
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #2 }
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.
  #g(x_{1})	-#2->
  #g(x_{1})	--->*
  #g(x_{1})
  Looping with: [ x_{1} := x_{1}; ]
NO