Input TRS:
    1: active(U11(tt(),N,X,XS)) -> mark(U12(splitAt(N,XS),X))
    2: active(U12(pair(YS,ZS),X)) -> mark(pair(cons(X,YS),ZS))
    3: active(afterNth(N,XS)) -> mark(snd(splitAt(N,XS)))
    4: active(and(tt(),X)) -> mark(X)
    5: active(fst(pair(X,Y))) -> mark(X)
    6: active(head(cons(N,XS))) -> mark(N)
    7: active(natsFrom(N)) -> mark(cons(N,natsFrom(s(N))))
    8: active(sel(N,XS)) -> mark(head(afterNth(N,XS)))
    9: active(snd(pair(X,Y))) -> mark(Y)
    10: active(splitAt(0(),XS)) -> mark(pair(nil(),XS))
    11: active(splitAt(s(N),cons(X,XS))) -> mark(U11(tt(),N,X,XS))
    12: active(tail(cons(N,XS))) -> mark(XS)
    13: active(take(N,XS)) -> mark(fst(splitAt(N,XS)))
    14: active(U11(X1,X2,X3,X4)) -> U11(active(X1),X2,X3,X4)
    15: active(U12(X1,X2)) -> U12(active(X1),X2)
    16: active(splitAt(X1,X2)) -> splitAt(active(X1),X2)
    17: active(splitAt(X1,X2)) -> splitAt(X1,active(X2))
    18: active(pair(X1,X2)) -> pair(active(X1),X2)
    19: active(pair(X1,X2)) -> pair(X1,active(X2))
    20: active(cons(X1,X2)) -> cons(active(X1),X2)
    21: active(afterNth(X1,X2)) -> afterNth(active(X1),X2)
    22: active(afterNth(X1,X2)) -> afterNth(X1,active(X2))
    23: active(snd(X)) -> snd(active(X))
    24: active(and(X1,X2)) -> and(active(X1),X2)
    25: active(fst(X)) -> fst(active(X))
    26: active(head(X)) -> head(active(X))
    27: active(natsFrom(X)) -> natsFrom(active(X))
    28: active(s(X)) -> s(active(X))
    29: active(sel(X1,X2)) -> sel(active(X1),X2)
    30: active(sel(X1,X2)) -> sel(X1,active(X2))
    31: active(tail(X)) -> tail(active(X))
    32: active(take(X1,X2)) -> take(active(X1),X2)
    33: active(take(X1,X2)) -> take(X1,active(X2))
    34: U11(mark(X1),X2,X3,X4) -> mark(U11(X1,X2,X3,X4))
    35: U12(mark(X1),X2) -> mark(U12(X1,X2))
    36: splitAt(mark(X1),X2) -> mark(splitAt(X1,X2))
    37: splitAt(X1,mark(X2)) -> mark(splitAt(X1,X2))
    38: pair(mark(X1),X2) -> mark(pair(X1,X2))
    39: pair(X1,mark(X2)) -> mark(pair(X1,X2))
    40: cons(mark(X1),X2) -> mark(cons(X1,X2))
    41: afterNth(mark(X1),X2) -> mark(afterNth(X1,X2))
    42: afterNth(X1,mark(X2)) -> mark(afterNth(X1,X2))
    43: snd(mark(X)) -> mark(snd(X))
    44: and(mark(X1),X2) -> mark(and(X1,X2))
    45: fst(mark(X)) -> mark(fst(X))
    46: head(mark(X)) -> mark(head(X))
    47: natsFrom(mark(X)) -> mark(natsFrom(X))
    48: s(mark(X)) -> mark(s(X))
    49: sel(mark(X1),X2) -> mark(sel(X1,X2))
    50: sel(X1,mark(X2)) -> mark(sel(X1,X2))
    51: tail(mark(X)) -> mark(tail(X))
    52: take(mark(X1),X2) -> mark(take(X1,X2))
    53: take(X1,mark(X2)) -> mark(take(X1,X2))
    54: proper(U11(X1,X2,X3,X4)) -> U11(proper(X1),proper(X2),proper(X3),proper(X4))
    55: proper(tt()) -> ok(tt())
    56: proper(U12(X1,X2)) -> U12(proper(X1),proper(X2))
    57: proper(splitAt(X1,X2)) -> splitAt(proper(X1),proper(X2))
    58: proper(pair(X1,X2)) -> pair(proper(X1),proper(X2))
    59: proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    60: proper(afterNth(X1,X2)) -> afterNth(proper(X1),proper(X2))
    61: proper(snd(X)) -> snd(proper(X))
    62: proper(and(X1,X2)) -> and(proper(X1),proper(X2))
    63: proper(fst(X)) -> fst(proper(X))
    64: proper(head(X)) -> head(proper(X))
    65: proper(natsFrom(X)) -> natsFrom(proper(X))
    66: proper(s(X)) -> s(proper(X))
    67: proper(sel(X1,X2)) -> sel(proper(X1),proper(X2))
    68: proper(0()) -> ok(0())
    69: proper(nil()) -> ok(nil())
    70: proper(tail(X)) -> tail(proper(X))
    71: proper(take(X1,X2)) -> take(proper(X1),proper(X2))
    72: U11(ok(X1),ok(X2),ok(X3),ok(X4)) -> ok(U11(X1,X2,X3,X4))
    73: U12(ok(X1),ok(X2)) -> ok(U12(X1,X2))
    74: splitAt(ok(X1),ok(X2)) -> ok(splitAt(X1,X2))
    75: pair(ok(X1),ok(X2)) -> ok(pair(X1,X2))
    76: cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    77: afterNth(ok(X1),ok(X2)) -> ok(afterNth(X1,X2))
    78: snd(ok(X)) -> ok(snd(X))
    79: and(ok(X1),ok(X2)) -> ok(and(X1,X2))
    80: fst(ok(X)) -> ok(fst(X))
    81: head(ok(X)) -> ok(head(X))
    82: natsFrom(ok(X)) -> ok(natsFrom(X))
    83: s(ok(X)) -> ok(s(X))
    84: sel(ok(X1),ok(X2)) -> ok(sel(X1,X2))
    85: tail(ok(X)) -> ok(tail(X))
    86: take(ok(X1),ok(X2)) -> ok(take(X1,X2))
    87: top(mark(X)) -> top(proper(X))
    88: top(ok(X)) -> top(active(X))
Number of strict rules: 88
Direct Order(PosReal,>,Poly) ... failed.
Freezing ... failed.
Dependency Pairs:
   #1: #active(U12(pair(YS,ZS),X)) -> #pair(cons(X,YS),ZS)
   #2: #active(U12(pair(YS,ZS),X)) -> #cons(X,YS)
   #3: #take(ok(X1),ok(X2)) -> #take(X1,X2)
   #4: #snd(mark(X)) -> #snd(X)
   #5: #active(sel(X1,X2)) -> #sel(active(X1),X2)
   #6: #active(sel(X1,X2)) -> #active(X1)
   #7: #U12(mark(X1),X2) -> #U12(X1,X2)
   #8: #s(ok(X)) -> #s(X)
   #9: #proper(s(X)) -> #s(proper(X))
   #10: #proper(s(X)) -> #proper(X)
   #11: #head(mark(X)) -> #head(X)
   #12: #afterNth(X1,mark(X2)) -> #afterNth(X1,X2)
   #13: #afterNth(mark(X1),X2) -> #afterNth(X1,X2)
   #14: #splitAt(X1,mark(X2)) -> #splitAt(X1,X2)
   #15: #U12(ok(X1),ok(X2)) -> #U12(X1,X2)
   #16: #natsFrom(mark(X)) -> #natsFrom(X)
   #17: #take(X1,mark(X2)) -> #take(X1,X2)
   #18: #proper(take(X1,X2)) -> #take(proper(X1),proper(X2))
   #19: #proper(take(X1,X2)) -> #proper(X1)
   #20: #proper(take(X1,X2)) -> #proper(X2)
   #21: #s(mark(X)) -> #s(X)
   #22: #pair(ok(X1),ok(X2)) -> #pair(X1,X2)
   #23: #splitAt(ok(X1),ok(X2)) -> #splitAt(X1,X2)
   #24: #proper(pair(X1,X2)) -> #pair(proper(X1),proper(X2))
   #25: #proper(pair(X1,X2)) -> #proper(X1)
   #26: #proper(pair(X1,X2)) -> #proper(X2)
   #27: #proper(snd(X)) -> #snd(proper(X))
   #28: #proper(snd(X)) -> #proper(X)
   #29: #pair(mark(X1),X2) -> #pair(X1,X2)
   #30: #proper(cons(X1,X2)) -> #cons(proper(X1),proper(X2))
   #31: #proper(cons(X1,X2)) -> #proper(X1)
   #32: #proper(cons(X1,X2)) -> #proper(X2)
   #33: #proper(sel(X1,X2)) -> #sel(proper(X1),proper(X2))
   #34: #proper(sel(X1,X2)) -> #proper(X1)
   #35: #proper(sel(X1,X2)) -> #proper(X2)
   #36: #cons(mark(X1),X2) -> #cons(X1,X2)
   #37: #tail(mark(X)) -> #tail(X)
   #38: #active(take(N,XS)) -> #fst(splitAt(N,XS))
   #39: #active(take(N,XS)) -> #splitAt(N,XS)
   #40: #active(splitAt(s(N),cons(X,XS))) -> #U11(tt(),N,X,XS)
   #41: #proper(splitAt(X1,X2)) -> #splitAt(proper(X1),proper(X2))
   #42: #proper(splitAt(X1,X2)) -> #proper(X1)
   #43: #proper(splitAt(X1,X2)) -> #proper(X2)
   #44: #cons(ok(X1),ok(X2)) -> #cons(X1,X2)
   #45: #active(and(X1,X2)) -> #and(active(X1),X2)
   #46: #active(and(X1,X2)) -> #active(X1)
   #47: #proper(tail(X)) -> #tail(proper(X))
   #48: #proper(tail(X)) -> #proper(X)
   #49: #active(snd(X)) -> #snd(active(X))
   #50: #active(snd(X)) -> #active(X)
   #51: #head(ok(X)) -> #head(X)
   #52: #snd(ok(X)) -> #snd(X)
   #53: #fst(mark(X)) -> #fst(X)
   #54: #active(tail(X)) -> #tail(active(X))
   #55: #active(tail(X)) -> #active(X)
   #56: #and(ok(X1),ok(X2)) -> #and(X1,X2)
   #57: #proper(U12(X1,X2)) -> #U12(proper(X1),proper(X2))
   #58: #proper(U12(X1,X2)) -> #proper(X1)
   #59: #proper(U12(X1,X2)) -> #proper(X2)
   #60: #natsFrom(ok(X)) -> #natsFrom(X)
   #61: #active(U11(X1,X2,X3,X4)) -> #U11(active(X1),X2,X3,X4)
   #62: #active(U11(X1,X2,X3,X4)) -> #active(X1)
   #63: #proper(and(X1,X2)) -> #and(proper(X1),proper(X2))
   #64: #proper(and(X1,X2)) -> #proper(X1)
   #65: #proper(and(X1,X2)) -> #proper(X2)
   #66: #active(sel(X1,X2)) -> #sel(X1,active(X2))
   #67: #active(sel(X1,X2)) -> #active(X2)
   #68: #take(mark(X1),X2) -> #take(X1,X2)
   #69: #sel(mark(X1),X2) -> #sel(X1,X2)
   #70: #active(fst(X)) -> #fst(active(X))
   #71: #active(fst(X)) -> #active(X)
   #72: #active(cons(X1,X2)) -> #cons(active(X1),X2)
   #73: #active(cons(X1,X2)) -> #active(X1)
   #74: #top(ok(X)) -> #top(active(X))
   #75: #top(ok(X)) -> #active(X)
   #76: #active(natsFrom(N)) -> #cons(N,natsFrom(s(N)))
   #77: #active(natsFrom(N)) -> #natsFrom(s(N))
   #78: #active(natsFrom(N)) -> #s(N)
   #79: #pair(X1,mark(X2)) -> #pair(X1,X2)
   #80: #active(splitAt(0(),XS)) -> #pair(nil(),XS)
   #81: #proper(head(X)) -> #head(proper(X))
   #82: #proper(head(X)) -> #proper(X)
   #83: #active(take(X1,X2)) -> #take(X1,active(X2))
   #84: #active(take(X1,X2)) -> #active(X2)
   #85: #U11(ok(X1),ok(X2),ok(X3),ok(X4)) -> #U11(X1,X2,X3,X4)
   #86: #and(mark(X1),X2) -> #and(X1,X2)
   #87: #proper(natsFrom(X)) -> #natsFrom(proper(X))
   #88: #proper(natsFrom(X)) -> #proper(X)
   #89: #active(s(X)) -> #s(active(X))
   #90: #active(s(X)) -> #active(X)
   #91: #active(afterNth(X1,X2)) -> #afterNth(X1,active(X2))
   #92: #active(afterNth(X1,X2)) -> #active(X2)
   #93: #U11(mark(X1),X2,X3,X4) -> #U11(X1,X2,X3,X4)
   #94: #sel(ok(X1),ok(X2)) -> #sel(X1,X2)
   #95: #top(mark(X)) -> #top(proper(X))
   #96: #top(mark(X)) -> #proper(X)
   #97: #active(natsFrom(X)) -> #natsFrom(active(X))
   #98: #active(natsFrom(X)) -> #active(X)
   #99: #proper(afterNth(X1,X2)) -> #afterNth(proper(X1),proper(X2))
   #100: #proper(afterNth(X1,X2)) -> #proper(X1)
   #101: #proper(afterNth(X1,X2)) -> #proper(X2)
   #102: #active(splitAt(X1,X2)) -> #splitAt(X1,active(X2))
   #103: #active(splitAt(X1,X2)) -> #active(X2)
   #104: #active(take(X1,X2)) -> #take(active(X1),X2)
   #105: #active(take(X1,X2)) -> #active(X1)
   #106: #active(pair(X1,X2)) -> #pair(X1,active(X2))
   #107: #active(pair(X1,X2)) -> #active(X2)
   #108: #proper(fst(X)) -> #fst(proper(X))
   #109: #proper(fst(X)) -> #proper(X)
   #110: #active(head(X)) -> #head(active(X))
   #111: #active(head(X)) -> #active(X)
   #112: #tail(ok(X)) -> #tail(X)
   #113: #splitAt(mark(X1),X2) -> #splitAt(X1,X2)
   #114: #active(afterNth(X1,X2)) -> #afterNth(active(X1),X2)
   #115: #active(afterNth(X1,X2)) -> #active(X1)
   #116: #active(splitAt(X1,X2)) -> #splitAt(active(X1),X2)
   #117: #active(splitAt(X1,X2)) -> #active(X1)
   #118: #active(afterNth(N,XS)) -> #snd(splitAt(N,XS))
   #119: #active(afterNth(N,XS)) -> #splitAt(N,XS)
   #120: #afterNth(ok(X1),ok(X2)) -> #afterNth(X1,X2)
   #121: #active(U11(tt(),N,X,XS)) -> #U12(splitAt(N,XS),X)
   #122: #active(U11(tt(),N,X,XS)) -> #splitAt(N,XS)
   #123: #proper(U11(X1,X2,X3,X4)) -> #U11(proper(X1),proper(X2),proper(X3),proper(X4))
   #124: #proper(U11(X1,X2,X3,X4)) -> #proper(X1)
   #125: #proper(U11(X1,X2,X3,X4)) -> #proper(X2)
   #126: #proper(U11(X1,X2,X3,X4)) -> #proper(X3)
   #127: #proper(U11(X1,X2,X3,X4)) -> #proper(X4)
   #128: #active(sel(N,XS)) -> #head(afterNth(N,XS))
   #129: #active(sel(N,XS)) -> #afterNth(N,XS)
   #130: #active(U12(X1,X2)) -> #U12(active(X1),X2)
   #131: #active(U12(X1,X2)) -> #active(X1)
   #132: #fst(ok(X)) -> #fst(X)
   #133: #sel(X1,mark(X2)) -> #sel(X1,X2)
   #134: #active(pair(X1,X2)) -> #pair(active(X1),X2)
   #135: #active(pair(X1,X2)) -> #active(X1)
Number of SCCs: 18, DPs: 83, edges: 1165
	SCC { #53 #132 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: 0
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: 0
  pair(x1,x2)	weight: 0
   fst(x1)	weight: 0
 #top(x1)	weight: 0
natsFrom(x1)	weight: 0
#head(x1)	weight: 0
splitAt(x1,x2)	weight: 0
 #fst(x1)	weight: x1
   U12(x1,x2)	weight: 0
 #U12(x1,x2)	weight: 0
  tail(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
afterNth(x1,x2)	weight: 0
   nil()	weight: 0
#tail(x1)	weight: 0
#splitAt(x1,x2)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#afterNth(x1,x2)	weight: 0
#proper(x1)	weight: 0
 #U11(x1,x2,x3,x4)	weight: 0
active(x1)	weight: 0
  head(x1)	weight: 0
 #snd(x1)	weight: 0
  cons(x1,x2)	weight: 0
#natsFrom(x1)	weight: 0
#active(x1)	weight: 0
   snd(x1)	weight: 0
    tt()	weight: 0
#pair(x1,x2)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #53 #132
Number of SCCs: 17, DPs: 81, edges: 1161
	SCC { #16 #60 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: 0
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: 0
  pair(x1,x2)	weight: 0
   fst(x1)	weight: 0
 #top(x1)	weight: 0
natsFrom(x1)	weight: 0
#head(x1)	weight: 0
splitAt(x1,x2)	weight: 0
 #fst(x1)	weight: 0
   U12(x1,x2)	weight: 0
 #U12(x1,x2)	weight: 0
  tail(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
afterNth(x1,x2)	weight: 0
   nil()	weight: 0
#tail(x1)	weight: 0
#splitAt(x1,x2)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#afterNth(x1,x2)	weight: 0
#proper(x1)	weight: 0
 #U11(x1,x2,x3,x4)	weight: 0
active(x1)	weight: 0
  head(x1)	weight: 0
 #snd(x1)	weight: 0
  cons(x1,x2)	weight: 0
#natsFrom(x1)	weight: x1
#active(x1)	weight: 0
   snd(x1)	weight: 0
    tt()	weight: 0
#pair(x1,x2)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #16 #60
Number of SCCs: 16, DPs: 79, edges: 1157
	SCC { #11 #51 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: 0
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: 0
  pair(x1,x2)	weight: 0
   fst(x1)	weight: 0
 #top(x1)	weight: 0
natsFrom(x1)	weight: 0
#head(x1)	weight: x1
splitAt(x1,x2)	weight: 0
 #fst(x1)	weight: 0
   U12(x1,x2)	weight: 0
 #U12(x1,x2)	weight: 0
  tail(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
afterNth(x1,x2)	weight: 0
   nil()	weight: 0
#tail(x1)	weight: 0
#splitAt(x1,x2)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#afterNth(x1,x2)	weight: 0
#proper(x1)	weight: 0
 #U11(x1,x2,x3,x4)	weight: 0
active(x1)	weight: 0
  head(x1)	weight: 0
 #snd(x1)	weight: 0
  cons(x1,x2)	weight: 0
#natsFrom(x1)	weight: 0
#active(x1)	weight: 0
   snd(x1)	weight: 0
    tt()	weight: 0
#pair(x1,x2)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #11 #51
Number of SCCs: 15, DPs: 77, edges: 1153
	SCC { #37 #112 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: 0
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: 0
  pair(x1,x2)	weight: 0
   fst(x1)	weight: 0
 #top(x1)	weight: 0
natsFrom(x1)	weight: 0
#head(x1)	weight: 0
splitAt(x1,x2)	weight: 0
 #fst(x1)	weight: 0
   U12(x1,x2)	weight: 0
 #U12(x1,x2)	weight: 0
  tail(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
afterNth(x1,x2)	weight: 0
   nil()	weight: 0
#tail(x1)	weight: x1
#splitAt(x1,x2)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#afterNth(x1,x2)	weight: 0
#proper(x1)	weight: 0
 #U11(x1,x2,x3,x4)	weight: 0
active(x1)	weight: 0
  head(x1)	weight: 0
 #snd(x1)	weight: 0
  cons(x1,x2)	weight: 0
#natsFrom(x1)	weight: 0
#active(x1)	weight: 0
   snd(x1)	weight: 0
    tt()	weight: 0
#pair(x1,x2)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #37 #112
Number of SCCs: 14, DPs: 75, edges: 1149
	SCC { #4 #52 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: 0
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: 0
  pair(x1,x2)	weight: 0
   fst(x1)	weight: 0
 #top(x1)	weight: 0
natsFrom(x1)	weight: 0
#head(x1)	weight: 0
splitAt(x1,x2)	weight: 0
 #fst(x1)	weight: 0
   U12(x1,x2)	weight: 0
 #U12(x1,x2)	weight: 0
  tail(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
afterNth(x1,x2)	weight: 0
   nil()	weight: 0
#tail(x1)	weight: 0
#splitAt(x1,x2)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#afterNth(x1,x2)	weight: 0
#proper(x1)	weight: 0
 #U11(x1,x2,x3,x4)	weight: 0
active(x1)	weight: 0
  head(x1)	weight: 0
 #snd(x1)	weight: x1
  cons(x1,x2)	weight: 0
#natsFrom(x1)	weight: 0
#active(x1)	weight: 0
   snd(x1)	weight: 0
    tt()	weight: 0
#pair(x1,x2)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #4 #52
Number of SCCs: 13, DPs: 73, edges: 1145
	SCC { #8 #21 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: 0
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: 0
   top(x1)	weight: 0
   and(x1,x2)	weight: 0
  pair(x1,x2)	weight: 0
   fst(x1)	weight: 0
 #top(x1)	weight: 0
natsFrom(x1)	weight: 0
#head(x1)	weight: 0
splitAt(x1,x2)	weight: 0
 #fst(x1)	weight: 0
   U12(x1,x2)	weight: 0
 #U12(x1,x2)	weight: 0
  tail(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: x1
afterNth(x1,x2)	weight: 0
   nil()	weight: 0
#tail(x1)	weight: 0
#splitAt(x1,x2)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#afterNth(x1,x2)	weight: 0
#proper(x1)	weight: 0
 #U11(x1,x2,x3,x4)	weight: 0
active(x1)	weight: 0
  head(x1)	weight: 0
 #snd(x1)	weight: 0
  cons(x1,x2)	weight: 0
#natsFrom(x1)	weight: 0
#active(x1)	weight: 0
   snd(x1)	weight: 0
    tt()	weight: 0
#pair(x1,x2)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #8 #21
Number of SCCs: 12, DPs: 71, edges: 1141
	SCC { #74 #95 }
Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... succeeded.
   U11(x1,x2,x3,x4)	weight: max{(/ 1 2) + x4, (/ 1 2) + x3, (/ 1 16) + x2, (/ 1 2) + x1}	status: [x2,x4,x1]	precedence above: pair splitAt U12 proper nil mark cons
#cons(x1,x2)	weight: (/ 1 16) + x1	status: [x1]	precedence above:
     s(x1)	weight: x1	status: [x1]	precedence above: proper mark
#take(x1,x2)	weight: x1	status: []	precedence above:
  take(x1,x2)	weight: (/ 9 16) + x2 + x1	status: [x2,x1]	precedence above: U11 pair splitAt U12 proper nil mark cons
   top(x1)	weight: x1	status: []	precedence above:
   and(x1,x2)	weight: (/ 1 16) + x2 + x1	status: [x1,x2]	precedence above: proper mark
  pair(x1,x2)	weight: max{(/ 3 16) + x2, (/ 1 4) + x1}	status: [x1,x2]	precedence above: proper mark
   fst(x1)	weight: x1	status: x1
 #top(x1)	weight: (/ 1 16) + x1	status: [x1]	precedence above:
natsFrom(x1)	weight: (/ 1 8) + x1	status: [x1]	precedence above: s proper mark cons
#head(x1)	weight: (/ 1 16)	status: []	precedence above:
splitAt(x1,x2)	weight: max{(/ 1 2) + x2, (/ 1 16) + x1}	status: [x1,x2]	precedence above: U11 pair U12 proper nil mark cons
 #fst(x1)	weight: x1	status: []	precedence above:
   U12(x1,x2)	weight: max{(/ 1 2) + x2, x1}	status: [x1]	precedence above: pair proper mark cons
 #U12(x1,x2)	weight: (/ 1 16) + x2 + x1	status: [x2,x1]	precedence above:
  tail(x1)	weight: (/ 1 16) + x1	status: [x1]	precedence above: proper mark
proper(x1)	weight: x1	status: x1
    ok(x1)	weight: x1	status: x1
     0()	weight: (/ 1 16)	status: []	precedence above: proper mark
 #sel(x1,x2)	weight: x1	status: [x1]	precedence above:
   sel(x1,x2)	weight: (/ 3 4) + x2 + x1	status: [x1,x2]	precedence above: proper ok afterNth mark head snd
   #s(x1)	weight: (/ 1 16)	status: []	precedence above:
afterNth(x1,x2)	weight: (/ 5 8) + x2 + x1	status: [x1,x2]	precedence above: proper mark snd
   nil()	weight: (/ 3 16)	status: []	precedence above:
#tail(x1)	weight: (/ 1 16)	status: []	precedence above:
#splitAt(x1,x2)	weight: (/ 1 16) + x1	status: [x1]	precedence above:
  mark(x1)	weight: x1	status: [x1]	precedence above: proper
#afterNth(x1,x2)	weight: (/ 1 16) + x2	status: [x2]	precedence above:
#proper(x1)	weight: x1	status: []	precedence above:
 #U11(x1,x2,x3,x4)	weight: (/ 1 16) + x4 + x2	status: [x4,x2]	precedence above:
active(x1)	weight: x1	status: x1
  head(x1)	weight: (/ 1 16) + x1	status: [x1]	precedence above: proper mark
 #snd(x1)	weight: (/ 1 16)	status: []	precedence above:
  cons(x1,x2)	weight: max{x2, (/ 1 8) + x1}	status: [x1]	precedence above: proper mark
#natsFrom(x1)	weight: (/ 1 16)	status: []	precedence above:
#active(x1)	weight: x1	status: []	precedence above:
   snd(x1)	weight: (/ 1 16) + x1	status: [x1]	precedence above: proper mark
    tt()	weight: (/ 1 8)	status: []	precedence above:
#pair(x1,x2)	weight: (/ 1 16) + x2 + x1	status: [x1,x2]	precedence above:
 #and(x1,x2)	weight: (/ 1 16) + x2 + x1	status: [x1,x2]	precedence above:
    Usable rules: { 1..86 }
    Removed DPs: #95
Number of SCCs: 12, DPs: 70, edges: 1138
	SCC { #74 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: x3
#cons(x1,x2)	weight: 0
     s(x1)	weight: x1
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: x1
   top(x1)	weight: 0
   and(x1,x2)	weight: x2
  pair(x1,x2)	weight: x2
   fst(x1)	weight: x1
 #top(x1)	weight: x1
natsFrom(x1)	weight: x1
#head(x1)	weight: 0
splitAt(x1,x2)	weight: x1
 #fst(x1)	weight: 0
   U12(x1,x2)	weight: x2
 #U12(x1,x2)	weight: 0
  tail(x1)	weight: x1
proper(x1)	weight: (/ 1 2)
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: x2
   #s(x1)	weight: 0
afterNth(x1,x2)	weight: x2
   nil()	weight: 0
#tail(x1)	weight: 0
#splitAt(x1,x2)	weight: 0
  mark(x1)	weight: 0
#afterNth(x1,x2)	weight: 0
#proper(x1)	weight: 0
 #U11(x1,x2,x3,x4)	weight: 0
active(x1)	weight: (/ 1 4) + x1
  head(x1)	weight: x1
 #snd(x1)	weight: 0
  cons(x1,x2)	weight: x1
#natsFrom(x1)	weight: 0
#active(x1)	weight: 0
   snd(x1)	weight: x1
    tt()	weight: 0
#pair(x1,x2)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { 1..53 72..86 }
    Removed DPs: #74
Number of SCCs: 11, DPs: 69, edges: 1137
	SCC { #56 #86 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: x3
#cons(x1,x2)	weight: 0
     s(x1)	weight: x1
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: x1
   top(x1)	weight: 0
   and(x1,x2)	weight: x2
  pair(x1,x2)	weight: x2
   fst(x1)	weight: x1
 #top(x1)	weight: x1
natsFrom(x1)	weight: x1
#head(x1)	weight: 0
splitAt(x1,x2)	weight: x1
 #fst(x1)	weight: 0
   U12(x1,x2)	weight: x2
 #U12(x1,x2)	weight: 0
  tail(x1)	weight: x1
proper(x1)	weight: (/ 1 2)
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: x2
   #s(x1)	weight: 0
afterNth(x1,x2)	weight: x2
   nil()	weight: 0
#tail(x1)	weight: 0
#splitAt(x1,x2)	weight: 0
  mark(x1)	weight: 0
#afterNth(x1,x2)	weight: 0
#proper(x1)	weight: 0
 #U11(x1,x2,x3,x4)	weight: 0
active(x1)	weight: (/ 1 4) + x1
  head(x1)	weight: x1
 #snd(x1)	weight: 0
  cons(x1,x2)	weight: x1
#natsFrom(x1)	weight: 0
#active(x1)	weight: 0
   snd(x1)	weight: x1
    tt()	weight: 0
#pair(x1,x2)	weight: 0
 #and(x1,x2)	weight: x2
    Usable rules: { }
    Removed DPs: #56
Number of SCCs: 12, DPs: 68, edges: 1134
	SCC { #86 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: x3
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: x2
   top(x1)	weight: 0
   and(x1,x2)	weight: x2
  pair(x1,x2)	weight: 0
   fst(x1)	weight: 0
 #top(x1)	weight: 0
natsFrom(x1)	weight: x1
#head(x1)	weight: 0
splitAt(x1,x2)	weight: 0
 #fst(x1)	weight: 0
   U12(x1,x2)	weight: x2
 #U12(x1,x2)	weight: 0
  tail(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
afterNth(x1,x2)	weight: x2
   nil()	weight: 0
#tail(x1)	weight: 0
#splitAt(x1,x2)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#afterNth(x1,x2)	weight: 0
#proper(x1)	weight: 0
 #U11(x1,x2,x3,x4)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
 #snd(x1)	weight: 0
  cons(x1,x2)	weight: 0
#natsFrom(x1)	weight: 0
#active(x1)	weight: 0
   snd(x1)	weight: 0
    tt()	weight: 0
#pair(x1,x2)	weight: 0
 #and(x1,x2)	weight: x1
    Usable rules: { }
    Removed DPs: #86
Number of SCCs: 11, DPs: 67, edges: 1133
	SCC { #7 #15 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: x3
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: x2
   top(x1)	weight: 0
   and(x1,x2)	weight: x2
  pair(x1,x2)	weight: 0
   fst(x1)	weight: 0
 #top(x1)	weight: 0
natsFrom(x1)	weight: x1
#head(x1)	weight: 0
splitAt(x1,x2)	weight: 0
 #fst(x1)	weight: 0
   U12(x1,x2)	weight: x2
 #U12(x1,x2)	weight: x1 + x2
  tail(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
afterNth(x1,x2)	weight: x2
   nil()	weight: 0
#tail(x1)	weight: 0
#splitAt(x1,x2)	weight: 0
  mark(x1)	weight: (/ 1 4) + x1
#afterNth(x1,x2)	weight: 0
#proper(x1)	weight: 0
 #U11(x1,x2,x3,x4)	weight: 0
active(x1)	weight: (/ 1 4) + x1
  head(x1)	weight: 0
 #snd(x1)	weight: 0
  cons(x1,x2)	weight: 0
#natsFrom(x1)	weight: 0
#active(x1)	weight: 0
   snd(x1)	weight: 0
    tt()	weight: 0
#pair(x1,x2)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #7 #15
Number of SCCs: 11, DPs: 65, edges: 1129
	SCC { #36 #44 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: x3
#cons(x1,x2)	weight: x2
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: x2
   top(x1)	weight: 0
   and(x1,x2)	weight: x2
  pair(x1,x2)	weight: 0
   fst(x1)	weight: 0
 #top(x1)	weight: 0
natsFrom(x1)	weight: x1
#head(x1)	weight: 0
splitAt(x1,x2)	weight: 0
 #fst(x1)	weight: 0
   U12(x1,x2)	weight: x2
 #U12(x1,x2)	weight: 0
  tail(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
afterNth(x1,x2)	weight: x2
   nil()	weight: 0
#tail(x1)	weight: 0
#splitAt(x1,x2)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#afterNth(x1,x2)	weight: 0
#proper(x1)	weight: 0
 #U11(x1,x2,x3,x4)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
 #snd(x1)	weight: 0
  cons(x1,x2)	weight: 0
#natsFrom(x1)	weight: 0
#active(x1)	weight: 0
   snd(x1)	weight: 0
    tt()	weight: 0
#pair(x1,x2)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #44
Number of SCCs: 11, DPs: 64, edges: 1126
	SCC { #36 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: x3
#cons(x1,x2)	weight: x1
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: x2
   top(x1)	weight: 0
   and(x1,x2)	weight: x2
  pair(x1,x2)	weight: 0
   fst(x1)	weight: 0
 #top(x1)	weight: 0
natsFrom(x1)	weight: x1
#head(x1)	weight: 0
splitAt(x1,x2)	weight: 0
 #fst(x1)	weight: 0
   U12(x1,x2)	weight: x2
 #U12(x1,x2)	weight: 0
  tail(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
afterNth(x1,x2)	weight: x2
   nil()	weight: 0
#tail(x1)	weight: 0
#splitAt(x1,x2)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#afterNth(x1,x2)	weight: 0
#proper(x1)	weight: 0
 #U11(x1,x2,x3,x4)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
 #snd(x1)	weight: 0
  cons(x1,x2)	weight: 0
#natsFrom(x1)	weight: 0
#active(x1)	weight: 0
   snd(x1)	weight: 0
    tt()	weight: 0
#pair(x1,x2)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #36
Number of SCCs: 10, DPs: 63, edges: 1125
	SCC { #12 #13 #120 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: x3
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: x2
   top(x1)	weight: 0
   and(x1,x2)	weight: x2
  pair(x1,x2)	weight: 0
   fst(x1)	weight: 0
 #top(x1)	weight: 0
natsFrom(x1)	weight: x1
#head(x1)	weight: 0
splitAt(x1,x2)	weight: 0
 #fst(x1)	weight: 0
   U12(x1,x2)	weight: x2
 #U12(x1,x2)	weight: 0
  tail(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
afterNth(x1,x2)	weight: x2
   nil()	weight: 0
#tail(x1)	weight: 0
#splitAt(x1,x2)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#afterNth(x1,x2)	weight: x2
#proper(x1)	weight: 0
 #U11(x1,x2,x3,x4)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
 #snd(x1)	weight: 0
  cons(x1,x2)	weight: 0
#natsFrom(x1)	weight: 0
#active(x1)	weight: 0
   snd(x1)	weight: 0
    tt()	weight: 0
#pair(x1,x2)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #12 #120
Number of SCCs: 11, DPs: 61, edges: 1117
	SCC { #13 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: x3
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
  take(x1,x2)	weight: x2
   top(x1)	weight: 0
   and(x1,x2)	weight: x2
  pair(x1,x2)	weight: 0
   fst(x1)	weight: 0
 #top(x1)	weight: 0
natsFrom(x1)	weight: x1
#head(x1)	weight: 0
splitAt(x1,x2)	weight: 0
 #fst(x1)	weight: 0
   U12(x1,x2)	weight: x2
 #U12(x1,x2)	weight: 0
  tail(x1)	weight: 0
proper(x1)	weight: 0
    ok(x1)	weight: (/ 1 2) + x1
     0()	weight: 0
 #sel(x1,x2)	weight: 0
   sel(x1,x2)	weight: 0
   #s(x1)	weight: 0
afterNth(x1,x2)	weight: x2
   nil()	weight: 0
#tail(x1)	weight: 0
#splitAt(x1,x2)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#afterNth(x1,x2)	weight: x1
#proper(x1)	weight: 0
 #U11(x1,x2,x3,x4)	weight: 0
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
 #snd(x1)	weight: 0
  cons(x1,x2)	weight: 0
#natsFrom(x1)	weight: 0
#active(x1)	weight: 0
   snd(x1)	weight: 0
    tt()	weight: 0
#pair(x1,x2)	weight: 0
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #13
Number of SCCs: 10, DPs: 60, edges: 1116
	SCC { #14 #23 #113 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: x3
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
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proper(x1)	weight: 0
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active(x1)	weight: (/ 1 2) + x1
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    tt()	weight: 0
#pair(x1,x2)	weight: 0
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    Usable rules: { }
    Removed DPs: #23 #113
Number of SCCs: 11, DPs: 58, edges: 1108
	SCC { #14 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: x3
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
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proper(x1)	weight: 0
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#proper(x1)	weight: 0
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active(x1)	weight: (/ 1 2) + x1
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    tt()	weight: 0
#pair(x1,x2)	weight: 0
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    Usable rules: { }
    Removed DPs: #14
Number of SCCs: 10, DPs: 57, edges: 1107
	SCC { #69 #94 #133 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: x3
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
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proper(x1)	weight: 0
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afterNth(x1,x2)	weight: x2
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#afterNth(x1,x2)	weight: 0
#proper(x1)	weight: 0
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active(x1)	weight: (/ 1 2) + x1
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#pair(x1,x2)	weight: 0
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    Usable rules: { }
    Removed DPs: #94 #133
Number of SCCs: 11, DPs: 55, edges: 1099
	SCC { #69 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: x3
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
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   top(x1)	weight: 0
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proper(x1)	weight: 0
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afterNth(x1,x2)	weight: x2
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#splitAt(x1,x2)	weight: 0
  mark(x1)	weight: (/ 1 2) + x1
#afterNth(x1,x2)	weight: 0
#proper(x1)	weight: 0
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active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
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   snd(x1)	weight: 0
    tt()	weight: 0
#pair(x1,x2)	weight: 0
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    Usable rules: { }
    Removed DPs: #69
Number of SCCs: 10, DPs: 54, edges: 1098
	SCC { #22 #29 #79 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: x3
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
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active(x1)	weight: (/ 1 2) + x1
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   snd(x1)	weight: 0
    tt()	weight: 0
#pair(x1,x2)	weight: x2
 #and(x1,x2)	weight: 0
    Usable rules: { }
    Removed DPs: #22 #79
Number of SCCs: 11, DPs: 52, edges: 1090
	SCC { #29 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: x3
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: 0
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active(x1)	weight: (/ 1 2) + x1
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#pair(x1,x2)	weight: x1
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    Usable rules: { }
    Removed DPs: #29
Number of SCCs: 10, DPs: 51, edges: 1089
	SCC { #3 #17 #68 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: x3
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: x2
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active(x1)	weight: (/ 1 2) + x1
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    Usable rules: { }
    Removed DPs: #3 #17
Number of SCCs: 11, DPs: 49, edges: 1081
	SCC { #68 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: x3
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
#take(x1,x2)	weight: x1
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active(x1)	weight: (/ 1 2) + x1
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    tt()	weight: 0
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    Usable rules: { }
    Removed DPs: #68
Number of SCCs: 10, DPs: 48, edges: 1080
	SCC { #85 #93 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: x3
#cons(x1,x2)	weight: 0
     s(x1)	weight: 0
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 #U11(x1,x2,x3,x4)	weight: x3 + x4
active(x1)	weight: (/ 1 4) + x1
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#pair(x1,x2)	weight: 0
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    Usable rules: { }
    Removed DPs: #85
Number of SCCs: 11, DPs: 47, edges: 1077
	SCC { #93 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: x3
#cons(x1,x2)	weight: 0
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#proper(x1)	weight: 0
 #U11(x1,x2,x3,x4)	weight: x1
active(x1)	weight: (/ 1 2) + x1
  head(x1)	weight: 0
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    tt()	weight: 0
#pair(x1,x2)	weight: 0
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    Usable rules: { }
    Removed DPs: #93
Number of SCCs: 10, DPs: 46, edges: 1076
	SCC { #6 #46 #50 #55 #62 #67 #71 #73 #84 #90 #92 #98 #103 #105 #107 #111 #115 #117 #131 #135 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: (/ 1 4) + x1 + x3
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
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splitAt(x1,x2)	weight: (/ 1 4) + x1 + x2
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#proper(x1)	weight: 0
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active(x1)	weight: 0
  head(x1)	weight: (/ 1 4) + x1
 #snd(x1)	weight: 0
  cons(x1,x2)	weight: (/ 1 4) + x1 + x2
#natsFrom(x1)	weight: 0
#active(x1)	weight: x1
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    tt()	weight: 0
#pair(x1,x2)	weight: 0
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    Usable rules: { }
    Removed DPs: #6 #46 #50 #55 #62 #67 #71 #73 #84 #90 #92 #98 #103 #105 #107 #111 #115 #117 #131 #135
Number of SCCs: 10, DPs: 26, edges: 676
	SCC { #10 #19 #20 #25 #26 #28 #31 #32 #34 #35 #42 #43 #48 #58 #59 #64 #65 #82 #88 #100 #101 #109 #124..127 }
Removing DPs: Order(PosReal,>,Sum)... succeeded.
   U11(x1,x2,x3,x4)	weight: (/ 1 4) + x1 + x2 + x3 + x4
#cons(x1,x2)	weight: 0
     s(x1)	weight: (/ 1 4) + x1
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  take(x1,x2)	weight: (/ 1 4) + x1 + x2
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   fst(x1)	weight: (/ 1 4) + x1
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natsFrom(x1)	weight: (/ 1 4) + x1
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splitAt(x1,x2)	weight: (/ 1 4) + x1 + x2
 #fst(x1)	weight: 0
   U12(x1,x2)	weight: (/ 1 4) + x1 + x2
 #U12(x1,x2)	weight: 0
  tail(x1)	weight: (/ 1 4) + x1
proper(x1)	weight: 0
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     0()	weight: 0
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afterNth(x1,x2)	weight: (/ 1 4) + x1 + x2
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#tail(x1)	weight: 0
#splitAt(x1,x2)	weight: 0
  mark(x1)	weight: x1
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#proper(x1)	weight: x1
 #U11(x1,x2,x3,x4)	weight: 0
active(x1)	weight: 0
  head(x1)	weight: (/ 1 4) + x1
 #snd(x1)	weight: 0
  cons(x1,x2)	weight: (/ 1 4) + x1 + x2
#natsFrom(x1)	weight: 0
#active(x1)	weight: 0
   snd(x1)	weight: (/ 1 4) + x1
    tt()	weight: 0
#pair(x1,x2)	weight: 0
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    Usable rules: { }
    Removed DPs: #10 #19 #20 #25 #26 #28 #31 #32 #34 #35 #42 #43 #48 #58 #59 #64 #65 #82 #88 #100 #101 #109 #124..127
Number of SCCs: 9, DPs: 0, edges: 0
YES