Input TRS:
    1: active(f(b(),X,c())) -> mark(f(X,c(),X))
    2: active(c()) -> mark(b())
    3: active(f(X1,X2,X3)) -> f(X1,active(X2),X3)
    4: f(X1,mark(X2),X3) -> mark(f(X1,X2,X3))
    5: proper(f(X1,X2,X3)) -> f(proper(X1),proper(X2),proper(X3))
    6: proper(b()) -> ok(b())
    7: proper(c()) -> ok(c())
    8: f(ok(X1),ok(X2),ok(X3)) -> ok(f(X1,X2,X3))
    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,X3)) -> #f(proper(X1),proper(X2),proper(X3))
   #6: #proper(f(X1,X2,X3)) -> #proper(X1)
   #7: #proper(f(X1,X2,X3)) -> #proper(X2)
   #8: #proper(f(X1,X2,X3)) -> #proper(X3)
   #9: #active(f(X1,X2,X3)) -> #f(X1,active(X2),X3)
   #10: #active(f(X1,X2,X3)) -> #active(X2)
   #11: #active(f(b(),X,c())) -> #f(X,c(),X)
   #12: #f(ok(X1),ok(X2),ok(X3)) -> #f(X1,X2,X3)
   #13: #f(X1,mark(X2),X3) -> #f(X1,X2,X3)
Number of SCCs: 4, DPs: 8, edges: 18
	SCC { #10 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     b()	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: 0
     c()	weight: 0
     f(x1,x2,x3)	weight: (/ 1 2) + x2
proper(x1)	weight: 0
    ok(x1)	weight: 0
  mark(x1)	weight: 0
   #f(x1,x2,x3)	weight: 0
#proper(x1)	weight: 0
active(x1)	weight: 0
#active(x1)	weight: x1
    Usable rules: { }
    Removed DPs: #10
Number of SCCs: 3, DPs: 7, edges: 17
	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)... succeeded.
     b()	weight: (/ 1 2); (/ 1 4)
   top(x1)	weight: 0; 0
 #top(x1)	weight: x1_1 + x1_2; 0
     c()	weight: (/ 1 4); (/ 3 4)
     f(x1,x2,x3)	weight: (/ 1 4) + x3_2 + x2_1 + x2_2 + x1_1; 0
proper(x1)	weight: x1_1; x1_2
    ok(x1)	weight: x1_1; x1_2
  mark(x1)	weight: (/ 1 4) + x1_1 + x1_2; 0
   #f(x1,x2,x3)	weight: 0; 0
#proper(x1)	weight: 0; 0
active(x1)	weight: x1_1 + x1_2; 0
#active(x1)	weight: 0; 0
    Usable rules: { 1..8 }
    Removed DPs: #1
Number of SCCs: 3, DPs: 6, edges: 14
	SCC { #3 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     b()	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: x1
     c()	weight: 0
     f(x1,x2,x3)	weight: x2
proper(x1)	weight: (/ 1 2)
    ok(x1)	weight: (/ 1 2) + x1
  mark(x1)	weight: (/ 1 4)
   #f(x1,x2,x3)	weight: 0
#proper(x1)	weight: 0
active(x1)	weight: (/ 1 4) + x1
#active(x1)	weight: 0
    Usable rules: { 1..4 8 }
    Removed DPs: #3
Number of SCCs: 2, DPs: 5, edges: 13
	SCC { #12 #13 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     b()	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: x1
     c()	weight: 0
     f(x1,x2,x3)	weight: x2
proper(x1)	weight: (/ 1 2)
    ok(x1)	weight: (/ 1 2) + x1
  mark(x1)	weight: (/ 1 2)
   #f(x1,x2,x3)	weight: x3
#proper(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #12
Number of SCCs: 3, DPs: 4, edges: 10
	SCC { #13 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     b()	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: x1
     c()	weight: 0
     f(x1,x2,x3)	weight: x2
proper(x1)	weight: (/ 1 2)
    ok(x1)	weight: (/ 1 2) + x1
  mark(x1)	weight: (/ 1 2) + x1
   #f(x1,x2,x3)	weight: x2
#proper(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #13
Number of SCCs: 2, DPs: 3, edges: 9
	SCC { #6..8 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     b()	weight: 0
   top(x1)	weight: 0
 #top(x1)	weight: 0
     c()	weight: 0
     f(x1,x2,x3)	weight: (/ 1 4) + x1 + x2 + x3
proper(x1)	weight: 0
    ok(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
   #f(x1,x2,x3)	weight: 0
#proper(x1)	weight: x1
active(x1)	weight: (/ 1 4) + x1
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #6..8
Number of SCCs: 2, DPs: 0, edges: 0
YES