Input TRS:
    1: active(f(f(a()))) -> mark(f(g(f(a()))))
    2: mark(f(X)) -> active(f(mark(X)))
    3: mark(a()) -> active(a())
    4: mark(g(X)) -> active(g(X))
    5: f(mark(X)) -> f(X)
    6: f(active(X)) -> f(X)
    7: g(mark(X)) -> g(X)
    8: g(active(X)) -> g(X)
Number of strict rules: 8
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #mark(f(X)) -> #active(f(mark(X)))
   #2: #mark(f(X)) -> #f(mark(X))
   #3: #mark(f(X)) -> #mark(X)
   #4: #f(active(X)) -> #f(X)
   #5: #g(mark(X)) -> #g(X)
   #6: #f(mark(X)) -> #f(X)
   #7: #mark(a()) -> #active(a())
   #8: #active(f(f(a()))) -> #mark(f(g(f(a()))))
   #9: #active(f(f(a()))) -> #f(g(f(a())))
   #10: #active(f(f(a()))) -> #g(f(a()))
   #11: #g(active(X)) -> #g(X)
   #12: #mark(g(X)) -> #active(g(X))
Number of SCCs: 3, DPs: 7, edges: 13
	SCC { #4 #6 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     f(x1)	weight: 0
#mark(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
   #f(x1)	weight: x1
   #g(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
#active(x1)	weight: 0
     g(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #4 #6
Number of SCCs: 2, DPs: 5, edges: 9
	SCC { #5 #11 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     f(x1)	weight: 0
#mark(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
   #f(x1)	weight: 0
   #g(x1)	weight: x1
active(x1)	weight: (/ 1 2) + x1
#active(x1)	weight: 0
     g(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #5 #11
Number of SCCs: 1, DPs: 3, edges: 5
	SCC { #1 #3 #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     f(x1)	weight: (/ 1 4) + x1
#mark(x1)	weight: x1
  mark(x1)	weight: x1
   #f(x1)	weight: 0
   #g(x1)	weight: 0
active(x1)	weight: x1
#active(x1)	weight: x1
     g(x1)	weight: x1
    Usable rules: { 1..8 }
    Removed DPs: #3
Number of SCCs: 1, DPs: 2, edges: 2
	SCC { #1 #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     f(x1)	weight: (/ 1 4) + x1
#mark(x1)	weight: (/ 1 8) + x1
  mark(x1)	weight: (/ 1 16) + x1
   #f(x1)	weight: 0
   #g(x1)	weight: 0
active(x1)	weight: x1
#active(x1)	weight: x1
     g(x1)	weight: (/ 1 16)
    Usable rules: { 1..8 }
    Removed DPs: #1 #8
Number of SCCs: 0, DPs: 0, edges: 0
YES