Input TRS:
    1: a__from(X) -> cons(mark(X),from(s(X)))
    2: a__sel(0(),cons(X,XS)) -> mark(X)
    3: a__sel(s(N),cons(X,XS)) -> a__sel(mark(N),mark(XS))
    4: a__minus(X,0()) -> 0()
    5: a__minus(s(X),s(Y)) -> a__minus(mark(X),mark(Y))
    6: a__quot(0(),s(Y)) -> 0()
    7: a__quot(s(X),s(Y)) -> s(a__quot(a__minus(mark(X),mark(Y)),s(mark(Y))))
    8: a__zWquot(XS,nil()) -> nil()
    9: a__zWquot(nil(),XS) -> nil()
    10: a__zWquot(cons(X,XS),cons(Y,YS)) -> cons(a__quot(mark(X),mark(Y)),zWquot(XS,YS))
    11: mark(from(X)) -> a__from(mark(X))
    12: mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
    13: mark(minus(X1,X2)) -> a__minus(mark(X1),mark(X2))
    14: mark(quot(X1,X2)) -> a__quot(mark(X1),mark(X2))
    15: mark(zWquot(X1,X2)) -> a__zWquot(mark(X1),mark(X2))
    16: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    17: mark(s(X)) -> s(mark(X))
    18: mark(0()) -> 0()
    19: mark(nil()) -> nil()
    20: a__from(X) -> from(X)
    21: a__sel(X1,X2) -> sel(X1,X2)
    22: a__minus(X1,X2) -> minus(X1,X2)
    23: a__quot(X1,X2) -> quot(X1,X2)
    24: a__zWquot(X1,X2) -> zWquot(X1,X2)
Number of strict rules: 24
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__sel(0(),cons(X,XS)) -> #mark(X)
   #2: #mark(minus(X1,X2)) -> #a__minus(mark(X1),mark(X2))
   #3: #mark(minus(X1,X2)) -> #mark(X1)
   #4: #mark(minus(X1,X2)) -> #mark(X2)
   #5: #mark(from(X)) -> #a__from(mark(X))
   #6: #mark(from(X)) -> #mark(X)
   #7: #mark(sel(X1,X2)) -> #a__sel(mark(X1),mark(X2))
   #8: #mark(sel(X1,X2)) -> #mark(X1)
   #9: #mark(sel(X1,X2)) -> #mark(X2)
   #10: #mark(quot(X1,X2)) -> #a__quot(mark(X1),mark(X2))
   #11: #mark(quot(X1,X2)) -> #mark(X1)
   #12: #mark(quot(X1,X2)) -> #mark(X2)
   #13: #a__quot(s(X),s(Y)) -> #a__quot(a__minus(mark(X),mark(Y)),s(mark(Y)))
   #14: #a__quot(s(X),s(Y)) -> #a__minus(mark(X),mark(Y))
   #15: #a__quot(s(X),s(Y)) -> #mark(X)
   #16: #a__quot(s(X),s(Y)) -> #mark(Y)
   #17: #a__quot(s(X),s(Y)) -> #mark(Y)
   #18: #a__zWquot(cons(X,XS),cons(Y,YS)) -> #a__quot(mark(X),mark(Y))
   #19: #a__zWquot(cons(X,XS),cons(Y,YS)) -> #mark(X)
   #20: #a__zWquot(cons(X,XS),cons(Y,YS)) -> #mark(Y)
   #21: #a__minus(s(X),s(Y)) -> #a__minus(mark(X),mark(Y))
   #22: #a__minus(s(X),s(Y)) -> #mark(X)
   #23: #a__minus(s(X),s(Y)) -> #mark(Y)
   #24: #mark(s(X)) -> #mark(X)
   #25: #mark(cons(X1,X2)) -> #mark(X1)
   #26: #a__sel(s(N),cons(X,XS)) -> #a__sel(mark(N),mark(XS))
   #27: #a__sel(s(N),cons(X,XS)) -> #mark(N)
   #28: #a__sel(s(N),cons(X,XS)) -> #mark(XS)
   #29: #a__from(X) -> #mark(X)
   #30: #mark(zWquot(X1,X2)) -> #a__zWquot(mark(X1),mark(X2))
   #31: #mark(zWquot(X1,X2)) -> #mark(X1)
   #32: #mark(zWquot(X1,X2)) -> #mark(X2)
Number of SCCs: 1, DPs: 31, edges: 381
	SCC { #1..12 #14..32 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
a__minus(x1,x2)	weight: max{(/ 1 4) + x2, x1}
     s(x1)	weight: x1
#a__zWquot(x1,x2)	weight: max{(/ 3 4) + x2, (/ 1 2) + x1}
#a__from(x1)	weight: (/ 1 4) + x1
#a__quot(x1,x2)	weight: max{(/ 3 8) + x2, (/ 3 8) + x1}
 minus(x1,x2)	weight: max{(/ 1 4) + x2, x1}
a__from(x1)	weight: (/ 1 4) + x1
a__zWquot(x1,x2)	weight: max{(/ 3 4) + x2, (/ 1 2) + x1}
zWquot(x1,x2)	weight: max{(/ 3 4) + x2, (/ 1 2) + x1}
a__quot(x1,x2)	weight: max{(/ 3 4) + x2, (/ 3 8) + x1}
#mark(x1)	weight: (/ 1 8) + x1
     0()	weight: (/ 7 8)
  quot(x1,x2)	weight: max{(/ 3 4) + x2, (/ 3 8) + x1}
  from(x1)	weight: (/ 1 4) + x1
   sel(x1,x2)	weight: max{(/ 1 2) + x2, (/ 3 4) + x1}
#a__minus(x1,x2)	weight: max{(/ 1 4) + x2, (/ 1 8) + x1}
   nil()	weight: (/ 7 8)
#a__sel(x1,x2)	weight: max{(/ 1 4) + x2, (/ 1 2) + x1}
  mark(x1)	weight: x1
a__sel(x1,x2)	weight: max{(/ 1 2) + x2, (/ 3 4) + x1}
  cons(x1,x2)	weight: max{x2, (/ 1 8) + x1}
    Usable rules: { 1..24 }
    Removed DPs: #1 #4..12 #14..20 #23 #25 #27..32
Number of SCCs: 2, DPs: 6, edges: 14
	SCC { #26 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
a__minus(x1,x2)	weight: 0
     s(x1)	weight: max{0, (/ 1 4) + x1}
#a__zWquot(x1,x2)	weight: 0
#a__from(x1)	weight: 0
#a__quot(x1,x2)	weight: 0
 minus(x1,x2)	weight: 0
a__from(x1)	weight: max{0, (/ 3 8) + x1}
a__zWquot(x1,x2)	weight: max{0, (/ 3 8) + x1}
zWquot(x1,x2)	weight: max{0, (/ 3 8) + x1}
a__quot(x1,x2)	weight: max{0, (/ 3 8) + x1}
#mark(x1)	weight: 0
     0()	weight: 0
  quot(x1,x2)	weight: max{0, (/ 3 8) + x1}
  from(x1)	weight: max{0, (/ 3 8) + x1}
   sel(x1,x2)	weight: max{0, (/ 1 4) + x2 + x1}
#a__minus(x1,x2)	weight: 0
   nil()	weight: (/ 1 8)
#a__sel(x1,x2)	weight: max{0, (- (/ 1 8)) + x1}
  mark(x1)	weight: max{0, x1}
a__sel(x1,x2)	weight: max{0, (/ 1 4) + x2 + x1}
  cons(x1,x2)	weight: max{0, (- (/ 1 8)) + x1, (- (/ 1 4)) + x2}
    Usable rules: { 1..24 }
    Removed DPs: #26
Number of SCCs: 1, DPs: 5, edges: 13
	SCC { #2 #3 #21 #22 #24 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
a__minus(x1,x2)	weight: max{(/ 1 4) + x2, (/ 3 8) + x1}
     s(x1)	weight: x1
#a__zWquot(x1,x2)	weight: 0
#a__from(x1)	weight: (/ 1 4)
#a__quot(x1,x2)	weight: 0
 minus(x1,x2)	weight: max{(/ 1 4) + x2, (/ 3 8) + x1}
a__from(x1)	weight: (/ 1 8) + x1
a__zWquot(x1,x2)	weight: max{0, (/ 1 2) + x2}
zWquot(x1,x2)	weight: max{0, (/ 1 2) + x2}
a__quot(x1,x2)	weight: max{0, (/ 1 2) + x2}
#mark(x1)	weight: (/ 1 8) + x1
     0()	weight: (/ 1 2)
  quot(x1,x2)	weight: max{0, (/ 1 2) + x2}
  from(x1)	weight: (/ 1 8) + x1
   sel(x1,x2)	weight: max{(/ 1 4) + x2, (/ 1 8) + x1}
#a__minus(x1,x2)	weight: max{0, (/ 1 4) + x1}
   nil()	weight: (/ 1 8)
#a__sel(x1,x2)	weight: 0
  mark(x1)	weight: x1
a__sel(x1,x2)	weight: max{(/ 1 4) + x2, (/ 1 8) + x1}
  cons(x1,x2)	weight: max{x2, x1}
    Usable rules: { 1..24 }
    Removed DPs: #2 #3 #22
Number of SCCs: 2, DPs: 2, edges: 2
	SCC { #24 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
a__minus(x1,x2)	weight: (/ 1 4)
     s(x1)	weight: (/ 1 8) + x1
#a__zWquot(x1,x2)	weight: 0
#a__from(x1)	weight: (/ 3 8)
#a__quot(x1,x2)	weight: 0
 minus(x1,x2)	weight: (/ 3 8) + x1
a__from(x1)	weight: (/ 1 4)
a__zWquot(x1,x2)	weight: (/ 1 4)
zWquot(x1,x2)	weight: (/ 3 8) + x1 + x2
a__quot(x1,x2)	weight: (/ 1 4)
#mark(x1)	weight: (/ 3 8) + x1
     0()	weight: 0
  quot(x1,x2)	weight: (/ 3 8) + x2
  from(x1)	weight: (/ 3 8) + x1
   sel(x1,x2)	weight: (/ 1 4)
#a__minus(x1,x2)	weight: (/ 3 8)
   nil()	weight: 0
#a__sel(x1,x2)	weight: (/ 3 8)
  mark(x1)	weight: (/ 1 8)
a__sel(x1,x2)	weight: (/ 1 8) + x2
  cons(x1,x2)	weight: (/ 1 4) + x2
    Usable rules: { }
    Removed DPs: #24
Number of SCCs: 1, DPs: 1, edges: 1
	SCC { #21 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... succeeded.
a__minus(x1,x2)	weight: 0
     s(x1)	weight: max{0, (/ 1 4) + x1}
#a__zWquot(x1,x2)	weight: 0
#a__from(x1)	weight: 0
#a__quot(x1,x2)	weight: 0
 minus(x1,x2)	weight: 0
a__from(x1)	weight: max{0, (/ 3 8) + x1}
a__zWquot(x1,x2)	weight: max{0, (/ 3 8) + x1}
zWquot(x1,x2)	weight: max{0, (/ 3 8) + x1}
a__quot(x1,x2)	weight: max{0, (/ 3 8) + x1}
#mark(x1)	weight: 0
     0()	weight: 0
  quot(x1,x2)	weight: max{0, (/ 3 8) + x1}
  from(x1)	weight: max{0, (/ 3 8) + x1}
   sel(x1,x2)	weight: max{0, (/ 1 4) + x2 + x1}
#a__minus(x1,x2)	weight: max{0, (/ 1 8) + x1}
   nil()	weight: (/ 1 8)
#a__sel(x1,x2)	weight: max{0, x1}
  mark(x1)	weight: max{0, x1}
a__sel(x1,x2)	weight: max{0, (/ 1 4) + x2 + x1}
  cons(x1,x2)	weight: max{0, (- (/ 1 8)) + x1, (- (/ 1 4)) + x2}
    Usable rules: { 1..24 }
    Removed DPs: #21
Number of SCCs: 0, DPs: 0, edges: 0
YES