NO
Input TRS:
      1: U11(tt()) -> snd(splitAt(N,XS))
      2: U161(tt()) -> cons(N)
      3: U171(tt()) -> head(afterNth(N,XS))
      4: U181(tt()) -> Y
      5: U191(tt()) -> pair(nil(),XS)
      6: U201(tt()) -> U202(splitAt(N,XS))
      7: U202(pair(YS,ZS)) -> pair(cons(X),ZS)
      8: U21(tt()) -> X
      9: U211(tt()) -> XS
      10: U221(tt()) -> fst(splitAt(N,XS))
      11: U31(tt()) -> N
      12: and(tt()) -> X
      13: U101(tt()) -> U102(isNatural())
      14: U102(tt()) -> U103(isLNat())
      15: U103(tt()) -> tt()
      16: U111(tt()) -> U112(isLNat())
      17: U112(tt()) -> tt()
      18: U121(tt()) -> U122(isNatural())
      19: U122(tt()) -> tt()
      20: U131(tt()) -> U132(isNatural())
      21: U132(tt()) -> U133(isLNat())
      22: U133(tt()) -> tt()
      23: U141(tt()) -> U142(isLNat())
      24: U142(tt()) -> U143(isLNat())
      25: U143(tt()) -> tt()
      26: U151(tt()) -> U152(isNatural())
      27: U152(tt()) -> U153(isLNat())
      28: U153(tt()) -> tt()
      29: U41(tt()) -> U42(isNatural())
      30: U42(tt()) -> U43(isLNat())
      31: U43(tt()) -> tt()
      32: U51(tt()) -> U52(isNatural())
      33: U52(tt()) -> U53(isLNat())
      34: U53(tt()) -> tt()
      35: U61(tt()) -> U62(isPLNat())
      36: U62(tt()) -> tt()
      37: U71(tt()) -> U72(isNatural())
      38: U72(tt()) -> tt()
      39: U81(tt()) -> U82(isPLNat())
      40: U82(tt()) -> tt()
      41: U91(tt()) -> U92(isLNat())
      42: U92(tt()) -> tt()
      43: afterNth(N,XS) -> U11(and(and(isNatural())))
      44: fst(pair(X,Y)) -> U21(and(and(isLNat())))
      45: head(cons(N)) -> U31(and(and(isNatural())))
      46: isLNat() -> tt()
      47: isLNat() -> U41(and(isNaturalKind()))
      48: isLNat() -> U51(and(isNaturalKind()))
      49: isLNat() -> U61(isPLNatKind())
      50: isLNat() -> U71(isNaturalKind())
      51: isLNat() -> U81(isPLNatKind())
      52: isLNat() -> U91(isLNatKind())
      53: isLNat() -> U101(and(isNaturalKind()))
      54: isLNatKind() -> tt()
      55: isLNatKind() -> and(isNaturalKind())
      56: isLNatKind() -> isPLNatKind()
      57: isLNatKind() -> isNaturalKind()
      58: isLNatKind() -> isLNatKind()
      59: isNatural() -> tt()
      60: isNatural() -> U111(isLNatKind())
      61: isNatural() -> U121(isNaturalKind())
      62: isNatural() -> U131(and(isNaturalKind()))
      63: isNaturalKind() -> tt()
      64: isNaturalKind() -> isLNatKind()
      65: isNaturalKind() -> isNaturalKind()
      66: isNaturalKind() -> and(isNaturalKind())
      67: isPLNat() -> U141(and(isLNatKind()))
      68: isPLNat() -> U151(and(isNaturalKind()))
      69: isPLNatKind() -> and(isLNatKind())
      70: isPLNatKind() -> and(isNaturalKind())
      71: natsFrom(N) -> U161(and(isNatural()))
      72: sel(N,XS) -> U171(and(and(isNatural())))
      73: snd(pair(X,Y)) -> U181(and(and(isLNat())))
      74: splitAt(0(),XS) -> U191(and(isLNat()))
      75: splitAt(s(N),cons(X)) -> U201(and(and(isNatural())))
      76: tail(cons(N)) -> U211(and(and(isNatural())))
      77: take(N,XS) -> U221(and(and(isNatural())))
Extra variable in rule 2.