Input TRS:
    1: f(f(X)) -> c(n__f(n__g(n__f(X))))
    2: c(X) -> d(activate(X))
    3: h(X) -> c(n__d(X))
    4: f(X) -> n__f(X)
    5: g(X) -> n__g(X)
    6: d(X) -> n__d(X)
    7: activate(n__f(X)) -> f(activate(X))
    8: activate(n__g(X)) -> g(X)
    9: activate(n__d(X)) -> d(X)
    10: activate(X) -> X
Number of strict rules: 10
Direct Order(PosReal,>,Poly) ... removes: 3
     h(x1)	weight: (/ 1 8) + 2 * x1
     d(x1)	weight: x1
activate(x1)	weight: x1
     c(x1)	weight: x1
     f(x1)	weight: (/ 1 8) + x1
  n__f(x1)	weight: (/ 1 8) + x1
  n__g(x1)	weight: x1
  n__d(x1)	weight: x1
     g(x1)	weight: x1
Number of strict rules: 9
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #c(X) -> #d(activate(X))
   #2: #c(X) -> #activate(X)
   #3: #activate(n__d(X)) -> #d(X)
   #4: #activate(n__f(X)) -> #f(activate(X))
   #5: #activate(n__f(X)) -> #activate(X)
   #6: #f(f(X)) -> #c(n__f(n__g(n__f(X))))
   #7: #activate(n__g(X)) -> #g(X)
Number of SCCs: 1, DPs: 4, edges: 6
	SCC { #2 #4..6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     h(x1)	weight: 0
     d(x1)	weight: (/ 1 4)
activate(x1)	weight: x1
#activate(x1)	weight: x1
     c(x1)	weight: (/ 1 4)
     f(x1)	weight: (/ 1 4) + x1
  n__f(x1)	weight: (/ 1 4) + x1
   #d(x1)	weight: 0
   #f(x1)	weight: (/ 1 4) + x1
   #g(x1)	weight: 0
  n__g(x1)	weight: x1
   #c(x1)	weight: x1
  n__d(x1)	weight: (/ 1 4)
     g(x1)	weight: x1
    Usable rules: { 1 2 4..10 }
    Removed DPs: #5
Number of SCCs: 1, DPs: 3, edges: 3
	SCC { #2 #4 #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     h(x1)	weight: 0
     d(x1)	weight: (/ 1 2)
activate(x1)	weight: x1
#activate(x1)	weight: x1
     c(x1)	weight: (/ 1 2)
     f(x1)	weight: 2 + x1
  n__f(x1)	weight: 2 + x1
   #d(x1)	weight: 0
   #f(x1)	weight: (/ 3 2) + x1
   #g(x1)	weight: 0
  n__g(x1)	weight: (/ 1 2)
   #c(x1)	weight: (/ 1 2) + x1
  n__d(x1)	weight: (/ 1 2)
     g(x1)	weight: (/ 1 2)
    Usable rules: { 1 2 4..10 }
    Removed DPs: #2 #4 #6
Number of SCCs: 0, DPs: 0, edges: 0
YES