YES

TRS:

  a__zeros() -> cons(0(),zeros())
  a__U11(tt()) -> tt()
  a__U21(tt()) -> tt()
  a__U31(tt()) -> tt()
  a__U41(tt(),V2) -> a__U42(a__isNatIList(V2))
  a__U42(tt()) -> tt()
  a__U51(tt(),V2) -> a__U52(a__isNatList(V2))
  a__U52(tt()) -> tt()
  a__U61(tt(),V2) -> a__U62(a__isNatIList(V2))
  a__U62(tt()) -> tt()
  a__U71(tt(),L,N) -> a__U72(a__isNat(N),L)
  a__U72(tt(),L) -> s(a__length(mark(L)))
  a__U81(tt()) -> nil()
  a__U91(tt(),IL,M,N) -> a__U92(a__isNat(M),IL,M,N)
  a__U92(tt(),IL,M,N) -> a__U93(a__isNat(N),IL,M,N)
  a__U93(tt(),IL,M,N) -> cons(mark(N),take(M,IL))
  a__isNat(0()) -> tt()
  a__isNat(length(V1)) -> a__U11(a__isNatList(V1))
  a__isNat(s(V1)) -> a__U21(a__isNat(V1))
  a__isNatIList(V) -> a__U31(a__isNatList(V))
  a__isNatIList(zeros()) -> tt()
  a__isNatIList(cons(V1,V2)) -> a__U41(a__isNat(V1),V2)
  a__isNatList(nil()) -> tt()
  a__isNatList(cons(V1,V2)) -> a__U51(a__isNat(V1),V2)
  a__isNatList(take(V1,V2)) -> a__U61(a__isNat(V1),V2)
  a__length(nil()) -> 0()
  a__length(cons(N,L)) -> a__U71(a__isNatList(L),L,N)
  a__take(0(),IL) -> a__U81(a__isNatIList(IL))
  a__take(s(M),cons(N,IL)) -> a__U91(a__isNatIList(IL),IL,M,N)
  mark(zeros()) -> a__zeros()
  mark(U11(X)) -> a__U11(mark(X))
  mark(U21(X)) -> a__U21(mark(X))
  mark(U31(X)) -> a__U31(mark(X))
  mark(U41(X1,X2)) -> a__U41(mark(X1),X2)
  mark(U42(X)) -> a__U42(mark(X))
  mark(isNatIList(X)) -> a__isNatIList(X)
  mark(U51(X1,X2)) -> a__U51(mark(X1),X2)
  mark(U52(X)) -> a__U52(mark(X))
  mark(isNatList(X)) -> a__isNatList(X)
  mark(U61(X1,X2)) -> a__U61(mark(X1),X2)
  mark(U62(X)) -> a__U62(mark(X))
  mark(U71(X1,X2,X3)) -> a__U71(mark(X1),X2,X3)
  mark(U72(X1,X2)) -> a__U72(mark(X1),X2)
  mark(isNat(X)) -> a__isNat(X)
  mark(length(X)) -> a__length(mark(X))
  mark(U81(X)) -> a__U81(mark(X))
  mark(U91(X1,X2,X3,X4)) -> a__U91(mark(X1),X2,X3,X4)
  mark(U92(X1,X2,X3,X4)) -> a__U92(mark(X1),X2,X3,X4)
  mark(U93(X1,X2,X3,X4)) -> a__U93(mark(X1),X2,X3,X4)
  mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
  mark(cons(X1,X2)) -> cons(mark(X1),X2)
  mark(0()) -> 0()
  mark(tt()) -> tt()
  mark(s(X)) -> s(mark(X))
  mark(nil()) -> nil()
  a__zeros() -> zeros()
  a__U11(X) -> U11(X)
  a__U21(X) -> U21(X)
  a__U31(X) -> U31(X)
  a__U41(X1,X2) -> U41(X1,X2)
  a__U42(X) -> U42(X)
  a__isNatIList(X) -> isNatIList(X)
  a__U51(X1,X2) -> U51(X1,X2)
  a__U52(X) -> U52(X)
  a__isNatList(X) -> isNatList(X)
  a__U61(X1,X2) -> U61(X1,X2)
  a__U62(X) -> U62(X)
  a__U71(X1,X2,X3) -> U71(X1,X2,X3)
  a__U72(X1,X2) -> U72(X1,X2)
  a__isNat(X) -> isNat(X)
  a__length(X) -> length(X)
  a__U81(X) -> U81(X)
  a__U91(X1,X2,X3,X4) -> U91(X1,X2,X3,X4)
  a__U92(X1,X2,X3,X4) -> U92(X1,X2,X3,X4)
  a__U93(X1,X2,X3,X4) -> U93(X1,X2,X3,X4)
  a__take(X1,X2) -> take(X1,X2)

max/plus interpretations on N:

  a__zeros_A = 42
  a__zeros#_A = 42
  cons_A(x1,x2) = max{42, x1, 11 + x2}
  cons#_A(x1,x2) = max{42, x1, 11 + x2}
  0_A = 0
  0#_A = 0
  zeros_A = 30
  zeros#_A = 30
  a__U11_A(x1) = max{103, 43 + x1}
  a__U11#_A(x1) = max{103, 43 + x1}
  tt_A = 57
  tt#_A = 57
  a__U21_A(x1) = max{99, 10 + x1}
  a__U21#_A(x1) = max{99, 10 + x1}
  a__U31_A(x1) = max{27, x1}
  a__U31#_A(x1) = max{27, x1}
  a__U41_A(x1,x2) = max{10, x1, 30 + x2}
  a__U41#_A(x1,x2) = max{10, x1, 30 + x2}
  a__U42_A(x1) = max{57, 1 + x1}
  a__U42#_A(x1) = max{57, 1 + x1}
  a__isNatIList_A(x1) = max{10, 28 + x1}
  a__isNatIList#_A(x1) = max{10, 28 + x1}
  a__U51_A(x1,x2) = max{43, x1, 25 + x2}
  a__U51#_A(x1,x2) = max{43, x1, 25 + x2}
  a__U52_A(x1) = max{42, x1}
  a__U52#_A(x1) = max{42, x1}
  a__isNatList_A(x1) = max{24, 15 + x1}
  a__isNatList#_A(x1) = max{24, 15 + x1}
  a__U61_A(x1,x2) = max{43, 1 + x1, 29 + x2}
  a__U61#_A(x1,x2) = max{43, 1 + x1, 29 + x2}
  a__U62_A(x1) = max{42, x1}
  a__U62#_A(x1) = max{42, x1}
  a__U71_A(x1,x2,x3) = max{101, 55 + x1, 70 + x2, 58 + x3}
  a__U71#_A(x1,x2,x3) = max{101, 55 + x1, 70 + x2, 58 + x3}
  a__U72_A(x1,x2) = max{97, 55 + x1, 70 + x2}
  a__U72#_A(x1,x2) = max{97, 55 + x1, 70 + x2}
  a__isNat_A(x1) = max{57, 2 + x1}
  a__isNat#_A(x1) = max{57, 2 + x1}
  s_A(x1) = max{98, 11 + x1}
  s#_A(x1) = max{98, 11 + x1}
  a__length_A(x1) = max{101, 59 + x1}
  a__length#_A(x1) = max{101, 59 + x1}
  mark_A(x1) = max{42, x1}
  mark#_A(x1) = max{42, x1}
  a__U81_A(x1) = max{2, x1}
  a__U81#_A(x1) = max{2, x1}
  nil_A = 43
  nil#_A = 43
  a__U91_A(x1,x2,x3,x4) = max{107, x1, 41 + x2, 20 + x3, 29 + x4}
  a__U91#_A(x1,x2,x3,x4) = max{107, x1, 41 + x2, 20 + x3, 29 + x4}
  a__U92_A(x1,x2,x3,x4) = max{83, 17 + x1, 41 + x2, 20 + x3, 28 + x4}
  a__U92#_A(x1,x2,x3,x4) = max{83, 17 + x1, 41 + x2, 20 + x3, 28 + x4}
  a__U93_A(x1,x2,x3,x4) = max{83, 16 + x1, 41 + x2, 20 + x3, 27 + x4}
  a__U93#_A(x1,x2,x3,x4) = max{83, 16 + x1, 41 + x2, 20 + x3, 27 + x4}
  take_A(x1,x2) = max{72, 9 + x1, 30 + x2}
  take#_A(x1,x2) = max{72, 9 + x1, 30 + x2}
  length_A(x1) = max{101, 59 + x1}
  length#_A(x1) = max{101, 59 + x1}
  a__take_A(x1,x2) = max{72, 9 + x1, 30 + x2}
  a__take#_A(x1,x2) = max{72, 9 + x1, 30 + x2}
  U11_A(x1) = max{103, 43 + x1}
  U11#_A(x1) = max{103, 43 + x1}
  U21_A(x1) = max{99, 10 + x1}
  U21#_A(x1) = max{99, 10 + x1}
  U31_A(x1) = max{1, x1}
  U31#_A(x1) = max{1, x1}
  U41_A(x1,x2) = max{1, x1, 30 + x2}
  U41#_A(x1,x2) = max{1, x1, 30 + x2}
  U42_A(x1) = max{57, 1 + x1}
  U42#_A(x1) = max{57, 1 + x1}
  isNatIList_A(x1) = max{28, 28 + x1}
  isNatIList#_A(x1) = max{28, 28 + x1}
  U51_A(x1,x2) = max{43, x1, 25 + x2}
  U51#_A(x1,x2) = max{43, x1, 25 + x2}
  U52_A(x1) = max{41, x1}
  U52#_A(x1) = max{41, x1}
  isNatList_A(x1) = max{24, 15 + x1}
  isNatList#_A(x1) = max{24, 15 + x1}
  U61_A(x1,x2) = max{43, 1 + x1, 29 + x2}
  U61#_A(x1,x2) = max{43, 1 + x1, 29 + x2}
  U62_A(x1) = max{1, x1}
  U62#_A(x1) = max{1, x1}
  U71_A(x1,x2,x3) = max{101, 55 + x1, 70 + x2, 58 + x3}
  U71#_A(x1,x2,x3) = max{101, 55 + x1, 70 + x2, 58 + x3}
  U72_A(x1,x2) = max{97, 55 + x1, 70 + x2}
  U72#_A(x1,x2) = max{97, 55 + x1, 70 + x2}
  isNat_A(x1) = max{57, 2 + x1}
  isNat#_A(x1) = max{57, 2 + x1}
  U81_A(x1) = max{1, x1}
  U81#_A(x1) = max{1, x1}
  U91_A(x1,x2,x3,x4) = max{107, x1, 41 + x2, 20 + x3, 29 + x4}
  U91#_A(x1,x2,x3,x4) = max{107, x1, 41 + x2, 20 + x3, 29 + x4}
  U92_A(x1,x2,x3,x4) = max{83, 17 + x1, 41 + x2, 20 + x3, 28 + x4}
  U92#_A(x1,x2,x3,x4) = max{83, 17 + x1, 41 + x2, 20 + x3, 28 + x4}
  U93_A(x1,x2,x3,x4) = max{83, 16 + x1, 41 + x2, 20 + x3, 27 + x4}
  U93#_A(x1,x2,x3,x4) = max{83, 16 + x1, 41 + x2, 20 + x3, 27 + x4}

precedence:

  mark > a__take > a__U91 > zeros = a__U92 = U91 > a__zeros = a__U93 = U92 > cons = a__length = take = U93 > a__U41 = a__U71 = length > a__U42 = a__U72 = U41 = U71 > a__isNatIList = s = U42 = U72 > a__isNatList = a__isNat = isNatIList > tt = a__U51 = a__U61 = isNatList = isNat > a__U11 = a__U21 = a__U31 = a__U52 = a__U62 = nil = U51 = U61 > 0 = a__U81 = U11 = U21 = U31 = U52 = U62 > U81