Input TRS:
    1: a__from(X) -> cons(mark(X),from(s(X)))
    2: a__first(0(),Z) -> nil()
    3: a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
    4: a__sel(0(),cons(X,Z)) -> mark(X)
    5: a__sel(s(X),cons(Y,Z)) -> a__sel(mark(X),mark(Z))
    6: mark(from(X)) -> a__from(mark(X))
    7: mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
    8: mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
    9: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    10: mark(s(X)) -> s(mark(X))
    11: mark(0()) -> 0()
    12: mark(nil()) -> nil()
    13: a__from(X) -> from(X)
    14: a__first(X1,X2) -> first(X1,X2)
    15: a__sel(X1,X2) -> sel(X1,X2)
Number of strict rules: 15
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #mark(from(X)) -> #a__from(mark(X))
   #2: #mark(from(X)) -> #mark(X)
   #3: #mark(cons(X1,X2)) -> #mark(X1)
   #4: #mark(first(X1,X2)) -> #a__first(mark(X1),mark(X2))
   #5: #mark(first(X1,X2)) -> #mark(X1)
   #6: #mark(first(X1,X2)) -> #mark(X2)
   #7: #mark(s(X)) -> #mark(X)
   #8: #a__sel(s(X),cons(Y,Z)) -> #a__sel(mark(X),mark(Z))
   #9: #a__sel(s(X),cons(Y,Z)) -> #mark(X)
   #10: #a__sel(s(X),cons(Y,Z)) -> #mark(Z)
   #11: #a__first(s(X),cons(Y,Z)) -> #mark(Y)
   #12: #a__from(X) -> #mark(X)
   #13: #mark(sel(X1,X2)) -> #a__sel(mark(X1),mark(X2))
   #14: #mark(sel(X1,X2)) -> #mark(X1)
   #15: #mark(sel(X1,X2)) -> #mark(X2)
   #16: #a__sel(0(),cons(X,Z)) -> #mark(X)
Number of SCCs: 1, DPs: 16, edges: 130
	SCC { #1..16 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
     s(x1)	weight: x1
#a__from(x1)	weight: (/ 1 8) + x1
#a__first(x1,x2)	weight: max{0, (/ 1 8) + x2}
a__from(x1)	weight: (/ 1 4) + x1
#mark(x1)	weight: (/ 1 16) + x1
     0()	weight: (/ 1 16)
  from(x1)	weight: (/ 1 4) + x1
   sel(x1,x2)	weight: max{(/ 3 16) + x2, (/ 1 2) + x1}
   nil()	weight: (/ 1 4)
#a__sel(x1,x2)	weight: max{(/ 1 8) + x2, (/ 3 16) + x1}
  mark(x1)	weight: x1
a__sel(x1,x2)	weight: max{(/ 3 16) + x2, (/ 1 2) + x1}
 first(x1,x2)	weight: max{(/ 1 8) + x2, (/ 3 16) + x1}
a__first(x1,x2)	weight: max{(/ 1 8) + x2, (/ 3 16) + x1}
  cons(x1,x2)	weight: max{x2, (/ 1 4) + x1}
    Usable rules: { 1..15 }
    Removed DPs: #1..6 #9..16
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #7 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
     s(x1)	weight: (/ 3 8) + x1
#a__from(x1)	weight: 0
#a__first(x1,x2)	weight: 0
a__from(x1)	weight: (/ 5 8)
#mark(x1)	weight: x1
     0()	weight: 0
  from(x1)	weight: (/ 1 8) + x1
   sel(x1,x2)	weight: (/ 1 8) + x1 + x2
   nil()	weight: 0
#a__sel(x1,x2)	weight: 0
  mark(x1)	weight: (/ 3 8) + x1
a__sel(x1,x2)	weight: x1 + x2
 first(x1,x2)	weight: (/ 1 8)
a__first(x1,x2)	weight: 0
  cons(x1,x2)	weight: (/ 1 4) + x2
    Usable rules: { }
    Removed DPs: #7
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #8 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
     s(x1)	weight: max{0, (/ 1 16) + x1}
#a__from(x1)	weight: 0
#a__first(x1,x2)	weight: 0
a__from(x1)	weight: max{0, (/ 1 4) + x1}
#mark(x1)	weight: 0
     0()	weight: (/ 1 8)
  from(x1)	weight: max{0, (/ 1 4) + x1}
   sel(x1,x2)	weight: max{0, (- (/ 1 16)) + x2 + x1}
   nil()	weight: (/ 1 16)
#a__sel(x1,x2)	weight: max{0, (/ 1 16) + x1}
  mark(x1)	weight: max{0, x1}
a__sel(x1,x2)	weight: max{0, (- (/ 1 16)) + x2 + x1}
 first(x1,x2)	weight: max{0, (/ 1 8) + x2 + x1}
a__first(x1,x2)	weight: max{0, (/ 1 8) + x2 + x1}
  cons(x1,x2)	weight: max{0, (/ 1 4) + x1, (- (/ 1 16)) + x2}
    Usable rules: { 1..15 }
    Removed DPs: #8
Number of SCCs: 0, DPs: 0, edges: 0
YES