Input TRS:
    1: active(f(X,X)) -> mark(f(a(),b()))
    2: active(b()) -> mark(a())
    3: active(f(X1,X2)) -> f(active(X1),X2)
    4: f(mark(X1),X2) -> mark(f(X1,X2))
    5: proper(f(X1,X2)) -> f(proper(X1),proper(X2))
    6: proper(a()) -> ok(a())
    7: proper(b()) -> ok(b())
    8: f(ok(X1),ok(X2)) -> ok(f(X1,X2))
    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: #top(mark(X)) -> #top(proper(X))
   #2: #top(mark(X)) -> #proper(X)
   #3: #top(ok(X)) -> #top(active(X))
   #4: #top(ok(X)) -> #active(X)
   #5: #proper(f(X1,X2)) -> #f(proper(X1),proper(X2))
   #6: #proper(f(X1,X2)) -> #proper(X1)
   #7: #proper(f(X1,X2)) -> #proper(X2)
   #8: #active(f(X1,X2)) -> #f(active(X1),X2)
   #9: #active(f(X1,X2)) -> #active(X1)
   #10: #active(f(X,X)) -> #f(a(),b())
   #11: #f(ok(X1),ok(X2)) -> #f(X1,X2)
   #12: #f(mark(X1),X2) -> #f(X1,X2)
Number of SCCs: 4, DPs: 7, edges: 13
	SCC { #9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     b()	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: 0
     f(x1,x2)	weight: (/ 1 2) + x1
proper(x1)	weight: 0
    ok(x1)	weight: 0
  mark(x1)	weight: 0
   #f(x1,x2)	weight: 0
#proper(x1)	weight: 0
active(x1)	weight: 0
#active(x1)	weight: x1
    Usable rules: { }
    Removed DPs: #9
Number of SCCs: 3, DPs: 6, edges: 12
	SCC { #6 #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     b()	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: 0
     f(x1,x2)	weight: (/ 1 2) + x1 + x2
proper(x1)	weight: 0
    ok(x1)	weight: 0
  mark(x1)	weight: 0
   #f(x1,x2)	weight: 0
#proper(x1)	weight: x1
active(x1)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #6 #7
Number of SCCs: 2, DPs: 4, edges: 8
	SCC { #1 #3 }
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...  failed.
MAYBE