Input TRS:
    1: active(from(X)) -> mark(cons(X,from(s(X))))
    2: active(sel(0(),cons(X,Y))) -> mark(X)
    3: active(sel(s(X),cons(Y,Z))) -> mark(sel(X,Z))
    4: mark(from(X)) -> active(from(mark(X)))
    5: mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
    6: mark(s(X)) -> active(s(mark(X)))
    7: mark(sel(X1,X2)) -> active(sel(mark(X1),mark(X2)))
    8: mark(0()) -> active(0())
    9: from(mark(X)) -> from(X)
    10: from(active(X)) -> from(X)
    11: cons(mark(X1),X2) -> cons(X1,X2)
    12: cons(X1,mark(X2)) -> cons(X1,X2)
    13: cons(active(X1),X2) -> cons(X1,X2)
    14: cons(X1,active(X2)) -> cons(X1,X2)
    15: s(mark(X)) -> s(X)
    16: s(active(X)) -> s(X)
    17: sel(mark(X1),X2) -> sel(X1,X2)
    18: sel(X1,mark(X2)) -> sel(X1,X2)
    19: sel(active(X1),X2) -> sel(X1,X2)
    20: sel(X1,active(X2)) -> sel(X1,X2)
Number of strict rules: 20
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #active(sel(0(),cons(X,Y))) -> #mark(X)
   #2: #mark(s(X)) -> #active(s(mark(X)))
   #3: #mark(s(X)) -> #s(mark(X))
   #4: #mark(s(X)) -> #mark(X)
   #5: #cons(active(X1),X2) -> #cons(X1,X2)
   #6: #from(mark(X)) -> #from(X)
   #7: #cons(mark(X1),X2) -> #cons(X1,X2)
   #8: #cons(X1,mark(X2)) -> #cons(X1,X2)
   #9: #cons(X1,active(X2)) -> #cons(X1,X2)
   #10: #sel(X1,active(X2)) -> #sel(X1,X2)
   #11: #mark(sel(X1,X2)) -> #active(sel(mark(X1),mark(X2)))
   #12: #mark(sel(X1,X2)) -> #sel(mark(X1),mark(X2))
   #13: #mark(sel(X1,X2)) -> #mark(X1)
   #14: #mark(sel(X1,X2)) -> #mark(X2)
   #15: #from(active(X)) -> #from(X)
   #16: #mark(cons(X1,X2)) -> #active(cons(mark(X1),X2))
   #17: #mark(cons(X1,X2)) -> #cons(mark(X1),X2)
   #18: #mark(cons(X1,X2)) -> #mark(X1)
   #19: #sel(mark(X1),X2) -> #sel(X1,X2)
   #20: #sel(active(X1),X2) -> #sel(X1,X2)
   #21: #s(active(X)) -> #s(X)
   #22: #active(sel(s(X),cons(Y,Z))) -> #mark(sel(X,Z))
   #23: #active(sel(s(X),cons(Y,Z))) -> #sel(X,Z)
   #24: #active(from(X)) -> #mark(cons(X,from(s(X))))
   #25: #active(from(X)) -> #cons(X,from(s(X)))
   #26: #active(from(X)) -> #from(s(X))
   #27: #active(from(X)) -> #s(X)
   #28: #mark(0()) -> #active(0())
   #29: #s(mark(X)) -> #s(X)
   #30: #mark(from(X)) -> #active(from(mark(X)))
   #31: #mark(from(X)) -> #from(mark(X))
   #32: #mark(from(X)) -> #mark(X)
   #33: #sel(X1,mark(X2)) -> #sel(X1,X2)
Number of SCCs: 5, DPs: 22, edges: 89
	SCC { #21 #29 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
  from(x1)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: x1
  mark(x1)	weight: (/ 1 2) + x1
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #21 #29
Number of SCCs: 4, DPs: 20, edges: 85
	SCC { #6 #15 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
  from(x1)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#from(x1)	weight: x1
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #6 #15
Number of SCCs: 3, DPs: 18, edges: 81
	SCC { #10 #19 #20 #33 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: x2
  from(x1)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #10 #33
Number of SCCs: 3, DPs: 16, edges: 69
	SCC { #19 #20 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: x1
  from(x1)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #19 #20
Number of SCCs: 2, DPs: 14, edges: 65
	SCC { #5 #7..9 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: x2
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
  from(x1)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #8 #9
Number of SCCs: 3, DPs: 12, edges: 53
	SCC { #5 #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: x1
     s(x1)	weight: 0
#mark(x1)	weight: 0
     0()	weight: 0
 #sel(x1,x2)	weight: 0
  from(x1)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  cons(x1,x2)	weight: 0
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #5 #7
Number of SCCs: 2, DPs: 10, edges: 49
	SCC { #1 #4 #11 #13 #14 #18 #22 #24 #30 #32 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: x1
#mark(x1)	weight: x1
     0()	weight: 0
 #sel(x1,x2)	weight: 0
  from(x1)	weight: (/ 1 2) + x1
   sel(x1,x2)	weight: max{(/ 1 2) + x2, (/ 1 4) + x1}
   #s(x1)	weight: 0
  mark(x1)	weight: x1
#from(x1)	weight: 0
active(x1)	weight: x1
  cons(x1,x2)	weight: max{x2, (/ 1 4) + x1}
#active(x1)	weight: x1
    Usable rules: { 1..20 }
    Removed DPs: #1 #13 #14 #18 #32
Number of SCCs: 4, DPs: 3, edges: 3
	SCC { #4 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
#mark(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
 #sel(x1,x2)	weight: 0
  from(x1)	weight: (/ 1 4)
   sel(x1,x2)	weight: (/ 1 4)
   #s(x1)	weight: 0
  mark(x1)	weight: (/ 1 4)
#from(x1)	weight: 0
active(x1)	weight: (/ 1 2)
  cons(x1,x2)	weight: (/ 1 4)
#active(x1)	weight: 0
    Usable rules: { }
    Removed DPs: #4
Number of SCCs: 3, DPs: 2, edges: 2
	SCC { #11 #22 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
#cons(x1,x2)	weight: (/ 1 8) + x2 + x1	status: [x1,x2]	precedence above:
     s(x1)	weight: x1	status: [x1]	precedence above: sel
#mark(x1)	weight: (/ 3 8) + x1	status: [x1]	precedence above: s sel #active
     0()	weight: (/ 1 8)	status: []	precedence above:
 #sel(x1,x2)	weight: (/ 1 8) + x2 + x1	status: [x2,x1]	precedence above:
  from(x1)	weight: (/ 3 8) + x1	status: []	precedence above: s sel cons
   sel(x1,x2)	weight: (/ 1 8) + x2 + x1	status: [x1]	precedence above: s
   #s(x1)	weight: (/ 1 8)	status: []	precedence above:
  mark(x1)	weight: x1	status: x1
#from(x1)	weight: (/ 1 8)	status: []	precedence above:
active(x1)	weight: x1	status: x1
  cons(x1,x2)	weight: max{x2, (/ 1 4) + x1}	status: [x1]	precedence above:
#active(x1)	weight: (/ 3 8) + x1	status: [x1]	precedence above: s #mark sel
    Usable rules: { 1..20 }
    Removed DPs: #22
Number of SCCs: 2, DPs: 0, edges: 0
YES