Input TRS:
    1: active(f(f(a()))) -> mark(c(f(g(f(a())))))
    2: active(f(X)) -> f(active(X))
    3: active(g(X)) -> g(active(X))
    4: f(mark(X)) -> mark(f(X))
    5: g(mark(X)) -> mark(g(X))
    6: proper(f(X)) -> f(proper(X))
    7: proper(a()) -> ok(a())
    8: proper(c(X)) -> c(proper(X))
    9: proper(g(X)) -> g(proper(X))
    10: f(ok(X)) -> ok(f(X))
    11: c(ok(X)) -> ok(c(X))
    12: g(ok(X)) -> ok(g(X))
    13: top(mark(X)) -> top(proper(X))
    14: top(ok(X)) -> top(active(X))
Number of strict rules: 14
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #active(f(X)) -> #f(active(X))
   #2: #active(f(X)) -> #active(X)
   #3: #proper(f(X)) -> #f(proper(X))
   #4: #proper(f(X)) -> #proper(X)
   #5: #top(mark(X)) -> #top(proper(X))
   #6: #top(mark(X)) -> #proper(X)
   #7: #proper(g(X)) -> #g(proper(X))
   #8: #proper(g(X)) -> #proper(X)
   #9: #c(ok(X)) -> #c(X)
   #10: #g(ok(X)) -> #g(X)
   #11: #top(ok(X)) -> #top(active(X))
   #12: #top(ok(X)) -> #active(X)
   #13: #f(ok(X)) -> #f(X)
   #14: #g(mark(X)) -> #g(X)
   #15: #active(g(X)) -> #g(active(X))
   #16: #active(g(X)) -> #active(X)
   #17: #active(f(f(a()))) -> #c(f(g(f(a()))))
   #18: #active(f(f(a()))) -> #f(g(f(a())))
   #19: #active(f(f(a()))) -> #g(f(a()))
   #20: #proper(c(X)) -> #c(proper(X))
   #21: #proper(c(X)) -> #proper(X)
   #22: #f(mark(X)) -> #f(X)
Number of SCCs: 6, DPs: 12, edges: 26
	SCC { #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: 0
     c(x1)	weight: 0
     f(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
  mark(x1)	weight: 0
   #f(x1)	weight: 0
   #g(x1)	weight: 0
#proper(x1)	weight: 0
   #c(x1)	weight: x1
active(x1)	weight: 0
#active(x1)	weight: 0
     g(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #9
Number of SCCs: 5, DPs: 11, edges: 25
	SCC { #10 #14 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: 0
     c(x1)	weight: 0
     f(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
  mark(x1)	weight: (/ 1 2) + x1
   #f(x1)	weight: 0
   #g(x1)	weight: x1
#proper(x1)	weight: 0
   #c(x1)	weight: 0
active(x1)	weight: 0
#active(x1)	weight: 0
     g(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #10 #14
Number of SCCs: 4, DPs: 9, edges: 21
	SCC { #13 #22 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: 0
     c(x1)	weight: 0
     f(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
  mark(x1)	weight: (/ 1 2) + x1
   #f(x1)	weight: x1
   #g(x1)	weight: 0
#proper(x1)	weight: 0
   #c(x1)	weight: 0
active(x1)	weight: 0
#active(x1)	weight: 0
     g(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #13 #22
Number of SCCs: 3, DPs: 7, edges: 17
	SCC { #2 #16 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: 0
     c(x1)	weight: 0
     f(x1)	weight: (/ 1 2) + x1
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2)
  mark(x1)	weight: (/ 1 2)
   #f(x1)	weight: 0
   #g(x1)	weight: 0
#proper(x1)	weight: 0
   #c(x1)	weight: 0
active(x1)	weight: 0
#active(x1)	weight: x1
     g(x1)	weight: (/ 1 2) + x1
    Usable rules: { }
    Removed DPs: #2 #16
Number of SCCs: 2, DPs: 5, edges: 13
	SCC { #5 #11 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: x1
     c(x1)	weight: (/ 1 8)
     f(x1)	weight: (/ 3 16) + x1
proper(x1)	weight: (/ 1 8) + x1
    ok(x1)	weight: x1
  mark(x1)	weight: (/ 1 4) + x1
   #f(x1)	weight: 0
   #g(x1)	weight: 0
#proper(x1)	weight: 0
   #c(x1)	weight: 0
active(x1)	weight: x1
#active(x1)	weight: 0
     g(x1)	weight: (/ 1 8) + x1
    Usable rules: { 1..12 }
    Removed DPs: #5
Number of SCCs: 2, DPs: 4, edges: 10
	SCC { #11 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: x1
     c(x1)	weight: (/ 1 2) + x1
     f(x1)	weight: (/ 3 4) + x1
proper(x1)	weight: 2 + x1
    ok(x1)	weight: 2 + x1
  mark(x1)	weight: (/ 1 2) + x1
   #f(x1)	weight: 0
   #g(x1)	weight: 0
#proper(x1)	weight: 0
   #c(x1)	weight: 0
active(x1)	weight: (/ 3 2) + x1
#active(x1)	weight: 0
     g(x1)	weight: (/ 1 2) + x1
    Usable rules: { 1..5 10..12 }
    Removed DPs: #11
Number of SCCs: 1, DPs: 3, edges: 9
	SCC { #4 #8 #21 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: x1
     c(x1)	weight: (/ 1 2) + x1
     f(x1)	weight: (/ 3 4) + x1
proper(x1)	weight: 2 + x1
    ok(x1)	weight: 2 + x1
  mark(x1)	weight: (/ 1 2) + x1
   #f(x1)	weight: 0
   #g(x1)	weight: 0
#proper(x1)	weight: x1
   #c(x1)	weight: 0
active(x1)	weight: (/ 3 2) + x1
#active(x1)	weight: 0
     g(x1)	weight: (/ 1 2) + x1
    Usable rules: { }
    Removed DPs: #4 #8 #21
Number of SCCs: 1, DPs: 0, edges: 0
YES