Input TRS:
    1: active(f(f(a()))) -> mark(f(g(f(a()))))
    2: active(g(X)) -> g(active(X))
    3: g(mark(X)) -> mark(g(X))
    4: proper(f(X)) -> f(proper(X))
    5: proper(a()) -> ok(a())
    6: proper(g(X)) -> g(proper(X))
    7: f(ok(X)) -> ok(f(X))
    8: g(ok(X)) -> ok(g(X))
    9: top(mark(X)) -> top(proper(X))
    10: top(ok(X)) -> top(active(X))
Number of strict rules: 10
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #active(g(X)) -> #g(active(X))
   #2: #active(g(X)) -> #active(X)
   #3: #proper(g(X)) -> #g(proper(X))
   #4: #proper(g(X)) -> #proper(X)
   #5: #top(mark(X)) -> #top(proper(X))
   #6: #top(mark(X)) -> #proper(X)
   #7: #f(ok(X)) -> #f(X)
   #8: #top(ok(X)) -> #top(active(X))
   #9: #top(ok(X)) -> #active(X)
   #10: #g(mark(X)) -> #g(X)
   #11: #active(f(f(a()))) -> #f(g(f(a())))
   #12: #active(f(f(a()))) -> #g(f(a()))
   #13: #g(ok(X)) -> #g(X)
   #14: #proper(f(X)) -> #f(proper(X))
   #15: #proper(f(X)) -> #proper(X)
Number of SCCs: 5, DPs: 8, edges: 14
	SCC { #2 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: 0
     f(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: 0
  mark(x1)	weight: 0
   #f(x1)	weight: 0
   #g(x1)	weight: 0
#proper(x1)	weight: 0
active(x1)	weight: 0
#active(x1)	weight: x1
     g(x1)	weight: (/ 1 2) + x1
    Usable rules: { }
    Removed DPs: #2
Number of SCCs: 4, DPs: 7, edges: 13
	SCC { #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: 0
     f(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
  mark(x1)	weight: 0
   #f(x1)	weight: x1
   #g(x1)	weight: 0
#proper(x1)	weight: 0
active(x1)	weight: 0
#active(x1)	weight: 0
     g(x1)	weight: (/ 1 2)
    Usable rules: { }
    Removed DPs: #7
Number of SCCs: 3, DPs: 6, edges: 12
	SCC { #10 #13 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
   top(x1)	weight: 0
 #top(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
active(x1)	weight: 0
#active(x1)	weight: 0
     g(x1)	weight: (/ 1 2)
    Usable rules: { }
    Removed DPs: #10 #13
Number of SCCs: 2, DPs: 4, edges: 8
	SCC { #4 #15 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
   top(x1)	weight: 0
 #top(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: x1
active(x1)	weight: 0
#active(x1)	weight: 0
     g(x1)	weight: (/ 1 2) + x1
    Usable rules: { }
    Removed DPs: #4 #15
Number of SCCs: 1, DPs: 2, edges: 4
	SCC { #5 #8 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... succeeded.
     a()	weight: (/ 1 4); (/ 1 8)
   top(x1)	weight: 0; 0
 #top(x1)	weight: x1_2; 0
     f(x1)	weight: (/ 1 8) + x1_1; (/ 1 8) + x1_1
proper(x1)	weight: (/ 1 8) + x1_1; (/ 1 8) + x1_2
    ok(x1)	weight: x1_1; x1_2
  mark(x1)	weight: (/ 1 8); (/ 1 4) + x1_2
   #f(x1)	weight: 0; 0
   #g(x1)	weight: 0; 0
#proper(x1)	weight: 0; 0
active(x1)	weight: (/ 1 8); x1_2
#active(x1)	weight: 0; 0
     g(x1)	weight: (/ 1 8); x1_2
    Usable rules: { 1..8 }
    Removed DPs: #5
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: x1
     f(x1)	weight: (/ 1 2)
proper(x1)	weight: (/ 1 2) + x1
    ok(x1)	weight: (/ 1 2)
  mark(x1)	weight: (/ 1 4)
   #f(x1)	weight: 0
   #g(x1)	weight: 0
#proper(x1)	weight: 0
active(x1)	weight: (/ 1 4)
#active(x1)	weight: 0
     g(x1)	weight: x1
    Usable rules: { 1..3 7 8 }
    Removed DPs: #8
Number of SCCs: 0, DPs: 0, edges: 0
YES