Input TRS:
    1: a__pairNs() -> cons(0(),incr(oddNs()))
    2: a__oddNs() -> a__incr(a__pairNs())
    3: a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
    4: a__take(0(),XS) -> nil()
    5: a__take(s(N),cons(X,XS)) -> cons(mark(X),take(N,XS))
    6: a__zip(nil(),XS) -> nil()
    7: a__zip(X,nil()) -> nil()
    8: a__zip(cons(X,XS),cons(Y,YS)) -> cons(pair(mark(X),mark(Y)),zip(XS,YS))
    9: a__tail(cons(X,XS)) -> mark(XS)
    10: a__repItems(nil()) -> nil()
    11: a__repItems(cons(X,XS)) -> cons(mark(X),cons(X,repItems(XS)))
    12: mark(pairNs()) -> a__pairNs()
    13: mark(incr(X)) -> a__incr(mark(X))
    14: mark(oddNs()) -> a__oddNs()
    15: mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
    16: mark(zip(X1,X2)) -> a__zip(mark(X1),mark(X2))
    17: mark(tail(X)) -> a__tail(mark(X))
    18: mark(repItems(X)) -> a__repItems(mark(X))
    19: mark(cons(X1,X2)) -> cons(mark(X1),X2)
    20: mark(0()) -> 0()
    21: mark(s(X)) -> s(mark(X))
    22: mark(nil()) -> nil()
    23: mark(pair(X1,X2)) -> pair(mark(X1),mark(X2))
    24: a__pairNs() -> pairNs()
    25: a__incr(X) -> incr(X)
    26: a__oddNs() -> oddNs()
    27: a__take(X1,X2) -> take(X1,X2)
    28: a__zip(X1,X2) -> zip(X1,X2)
    29: a__tail(X) -> tail(X)
    30: a__repItems(X) -> repItems(X)
Number of strict rules: 30
Direct Order(PosReal,>,Poly) ... removes: 4 10 7 9 6
repItems(x1)	weight: (/ 1 8) + 2 * x1
  incr(x1)	weight: x1
     s(x1)	weight: x1
a__incr(x1)	weight: x1
  take(x1,x2)	weight: (/ 1 8) + x1 + x2
  pair(x1,x2)	weight: x1 + x2
  tail(x1)	weight: (/ 1 8) + x1
     0()	weight: 0
a__repItems(x1)	weight: (/ 1 8) + 2 * x1
   nil()	weight: 0
  mark(x1)	weight: x1
pairNs()	weight: 0
a__zip(x1,x2)	weight: (/ 1 8) + x1 + x2
 oddNs()	weight: 0
  cons(x1,x2)	weight: x1 + x2
a__oddNs()	weight: 0
a__take(x1,x2)	weight: (/ 1 8) + x1 + x2
a__pairNs()	weight: 0
a__tail(x1)	weight: (/ 1 8) + x1
   zip(x1,x2)	weight: (/ 1 8) + x1 + x2
Number of strict rules: 25
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #a__oddNs() -> #a__incr(a__pairNs())
   #2: #a__oddNs() -> #a__pairNs()
   #3: #mark(incr(X)) -> #a__incr(mark(X))
   #4: #mark(incr(X)) -> #mark(X)
   #5: #a__repItems(cons(X,XS)) -> #mark(X)
   #6: #mark(pair(X1,X2)) -> #mark(X1)
   #7: #mark(pair(X1,X2)) -> #mark(X2)
   #8: #mark(pairNs()) -> #a__pairNs()
   #9: #mark(oddNs()) -> #a__oddNs()
   #10: #a__take(s(N),cons(X,XS)) -> #mark(X)
   #11: #mark(tail(X)) -> #a__tail(mark(X))
   #12: #mark(tail(X)) -> #mark(X)
   #13: #mark(cons(X1,X2)) -> #mark(X1)
   #14: #mark(s(X)) -> #mark(X)
   #15: #mark(zip(X1,X2)) -> #a__zip(mark(X1),mark(X2))
   #16: #mark(zip(X1,X2)) -> #mark(X1)
   #17: #mark(zip(X1,X2)) -> #mark(X2)
   #18: #a__incr(cons(X,XS)) -> #mark(X)
   #19: #a__zip(cons(X,XS),cons(Y,YS)) -> #mark(X)
   #20: #a__zip(cons(X,XS),cons(Y,YS)) -> #mark(Y)
   #21: #mark(take(X1,X2)) -> #a__take(mark(X1),mark(X2))
   #22: #mark(take(X1,X2)) -> #mark(X1)
   #23: #mark(take(X1,X2)) -> #mark(X2)
   #24: #mark(repItems(X)) -> #a__repItems(mark(X))
   #25: #mark(repItems(X)) -> #mark(X)
Number of SCCs: 1, DPs: 22, edges: 263
	SCC { #1 #3..7 #9 #10 #12..25 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
repItems(x1)	weight: (/ 1 2) + x1
  incr(x1)	weight: x1
     s(x1)	weight: x1
#a__zip(x1,x2)	weight: (/ 1 4) + x1 + x2
a__incr(x1)	weight: x1
  take(x1,x2)	weight: (/ 1 2) + x1 + x2
  pair(x1,x2)	weight: (/ 1 4) + x1 + x2
#a__take(x1,x2)	weight: (/ 1 4) + x2
#a__pairNs()	weight: 0
  tail(x1)	weight: (/ 1 4) + x1
#mark(x1)	weight: x1
     0()	weight: 0
a__repItems(x1)	weight: (/ 1 2) + x1
   nil()	weight: 0
#a__oddNs()	weight: 0
  mark(x1)	weight: x1
pairNs()	weight: 0
a__zip(x1,x2)	weight: (/ 1 2) + x1 + x2
#a__repItems(x1)	weight: (/ 1 4) + x1
 oddNs()	weight: 0
#a__incr(x1)	weight: x1
  cons(x1,x2)	weight: x1
a__oddNs()	weight: 0
a__take(x1,x2)	weight: (/ 1 2) + x1 + x2
a__pairNs()	weight: 0
a__tail(x1)	weight: (/ 1 4) + x1
#a__tail(x1)	weight: 0
   zip(x1,x2)	weight: (/ 1 2) + x1 + x2
    Usable rules: { 1..3 5 8 11..30 }
    Removed DPs: #5..7 #10 #12 #15..17 #19..25
Number of SCCs: 1, DPs: 7, edges: 23
	SCC { #1 #3 #4 #9 #13 #14 #18 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... succeeded.
repItems(x1)	weight: (/ 1 8) + x1
  incr(x1)	weight: (/ 1 4) + x1
     s(x1)	weight: (/ 1 8) + x1
#a__zip(x1,x2)	weight: 0
a__incr(x1)	weight: (/ 1 4) + x1
  take(x1,x2)	weight: max{0, (/ 1 8) + x2}
  pair(x1,x2)	weight: 0
#a__take(x1,x2)	weight: 0
#a__pairNs()	weight: 0
  tail(x1)	weight: (/ 1 8)
#mark(x1)	weight: x1
     0()	weight: (/ 1 8)
a__repItems(x1)	weight: (/ 1 8) + x1
   nil()	weight: (/ 1 8)
#a__oddNs()	weight: (/ 5 8)
  mark(x1)	weight: x1
pairNs()	weight: (/ 3 8)
a__zip(x1,x2)	weight: max{0, (/ 1 4) + x2}
#a__repItems(x1)	weight: 0
 oddNs()	weight: (/ 3 4)
#a__incr(x1)	weight: (/ 1 8) + x1
  cons(x1,x2)	weight: max{0, (/ 1 4) + x1}
a__oddNs()	weight: (/ 3 4)
a__take(x1,x2)	weight: max{0, (/ 1 8) + x2}
a__pairNs()	weight: (/ 3 8)
a__tail(x1)	weight: (/ 1 8)
#a__tail(x1)	weight: 0
   zip(x1,x2)	weight: max{0, (/ 1 4) + x2}
    Usable rules: { 1..3 5 8 11..30 }
    Removed DPs: #1 #3 #4 #9 #13 #14 #18
Number of SCCs: 0, DPs: 0, edges: 0
YES