Input TRS:
    1: active(f(a(),X,X)) -> mark(f(X,b(),b()))
    2: active(b()) -> mark(a())
    3: mark(f(X1,X2,X3)) -> active(f(X1,mark(X2),X3))
    4: mark(a()) -> active(a())
    5: mark(b()) -> active(b())
    6: f(mark(X1),X2,X3) -> f(X1,X2,X3)
    7: f(X1,mark(X2),X3) -> f(X1,X2,X3)
    8: f(X1,X2,mark(X3)) -> f(X1,X2,X3)
    9: f(active(X1),X2,X3) -> f(X1,X2,X3)
    10: f(X1,active(X2),X3) -> f(X1,X2,X3)
    11: f(X1,X2,active(X3)) -> f(X1,X2,X3)
Number of strict rules: 11
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #active(b()) -> #mark(a())
   #2: #f(mark(X1),X2,X3) -> #f(X1,X2,X3)
   #3: #f(active(X1),X2,X3) -> #f(X1,X2,X3)
   #4: #f(X1,X2,active(X3)) -> #f(X1,X2,X3)
   #5: #f(X1,mark(X2),X3) -> #f(X1,X2,X3)
   #6: #f(X1,active(X2),X3) -> #f(X1,X2,X3)
   #7: #mark(b()) -> #active(b())
   #8: #mark(f(X1,X2,X3)) -> #active(f(X1,mark(X2),X3))
   #9: #mark(f(X1,X2,X3)) -> #f(X1,mark(X2),X3)
   #10: #mark(f(X1,X2,X3)) -> #mark(X2)
   #11: #active(f(a(),X,X)) -> #mark(f(X,b(),b()))
   #12: #active(f(a(),X,X)) -> #f(X,b(),b())
   #13: #f(X1,X2,mark(X3)) -> #f(X1,X2,X3)
   #14: #mark(a()) -> #active(a())
Number of SCCs: 2, DPs: 9, edges: 41
	SCC { #8 #10 #11 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     b()	weight: 0
     f(x1,x2,x3)	weight: (/ 1 2) + x1 + x2 + x3
#mark(x1)	weight: x1
  mark(x1)	weight: x1
   #f(x1,x2,x3)	weight: 0
active(x1)	weight: x1
#active(x1)	weight: x1
    Usable rules: { 1..11 }
    Removed DPs: #10
Number of SCCs: 2, DPs: 8, edges: 38
	SCC { #8 #11 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     a()	weight: (/ 7 16)
     b()	weight: 0
     f(x1,x2,x3)	weight: max{0, (/ 3 8) + x3, (/ 1 8) + x1}
#mark(x1)	weight: (/ 3 16) + x1
  mark(x1)	weight: (/ 1 16) + x1
   #f(x1,x2,x3)	weight: 0
active(x1)	weight: (/ 1 8) + x1
#active(x1)	weight: x1
    Usable rules: { 6..11 }
    Removed DPs: #8
Number of SCCs: 1, DPs: 6, edges: 36
	SCC { #2..6 #13 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     a()	weight: 0
     b()	weight: 0
     f(x1,x2,x3)	weight: (/ 1 4)
#mark(x1)	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
   #f(x1,x2,x3)	weight: x1 + x2 + x3
active(x1)	weight: (/ 1 2) + x1
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #2..6 #13
Number of SCCs: 1, DPs: 0, edges: 0
YES