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 = 100
  a__zeros#_A = 367
  cons_A(x1,x2) = max{25, x1, 27 + x2}
  cons#_A(x1,x2) = max{364, 366, 363}
  0_A = 100
  0#_A = 354
  zeros_A = 1
  zeros#_A = 354
  a__U11_A(x1) = max{392, 233 + x1}
  a__U11#_A(x1) = max{444, 444}
  tt_A = 231
  tt#_A = 353
  a__U21_A(x1) = max{263, 1 + x1}
  a__U21#_A(x1) = max{1, 1}
  a__U31_A(x1) = max{263, 13 + x1}
  a__U31#_A(x1) = max{361, 197}
  a__U41_A(x1,x2) = max{263, 37 + x1, 176 + x2}
  a__U41#_A(x1,x2) = max{365, 362, 361}
  a__U42_A(x1) = max{264, 5 + x1}
  a__U42#_A(x1) = max{188, 186}
  a__isNatIList_A(x1) = max{263, 171 + x1}
  a__isNatIList#_A(x1) = max{354, 361}
  a__U51_A(x1,x2) = max{159, x1, 157 + x2}
  a__U51#_A(x1,x2) = max{178, 342, 342}
  a__U52_A(x1) = max{160, 1 + x1}
  a__U52#_A(x1) = max{0, 342}
  a__isNatList_A(x1) = max{159, 131 + x1}
  a__isNatList#_A(x1) = max{342, 179}
  a__U61_A(x1,x2) = max{606, 293 + x1, 433 + x2}
  a__U61#_A(x1,x2) = max{361, 361, 353}
  a__U62_A(x1) = max{525, 262 + x1}
  a__U62#_A(x1) = max{352, 361}
  a__U71_A(x1,x2,x3) = max{286, 156 + x1, 287 + x2, 151 + x3}
  a__U71#_A(x1,x2,x3) = max{342, 236 + x1, 365 + x2, 182}
  a__U72_A(x1,x2) = max{387, x1, 287 + x2}
  a__U72#_A(x1,x2) = max{447, 442, 364 + x2}
  a__isNat_A(x1) = max{159, 131 + x1}
  a__isNat#_A(x1) = max{180, 181}
  s_A(x1) = max{288, 27 + x1}
  s#_A(x1) = max{2, 3 + x1}
  a__length_A(x1) = max{360, 260 + x1}
  a__length#_A(x1) = max{445, 343 + x1}
  mark_A(x1) = max{100, x1}
  mark#_A(x1) = max{446, 184 + x1}
  a__U81_A(x1) = max{574, 270 + x1}
  a__U81#_A(x1) = max{443, 445}
  nil_A = 101
  nil#_A = 444
  a__U91_A(x1,x2,x3,x4) = max{529, 270 + x1, 468 + x2, 501 + x3, 441 + x4}
  a__U91#_A(x1,x2,x3,x4) = max{453, 453, 453 + x2, 453, 451 + x4}
  a__U92_A(x1,x2,x3,x4) = max{100, 370 + x1, 468 + x2, 501 + x3, 369 + x4}
  a__U92#_A(x1,x2,x3,x4) = max{453, 453, 452, 448, 450 + x4}
  a__U93_A(x1,x2,x3,x4) = max{601, 186 + x1, 468 + x2, 501 + x3, 187 + x4}
  a__U93#_A(x1,x2,x3,x4) = max{369, 449, 367, 447, 371 + x4}
  take_A(x1,x2) = max{574, 474 + x1, 441 + x2}
  take#_A(x1,x2) = max{361, 179, 353}
  length_A(x1) = max{360, 260 + x1}
  length#_A(x1) = max{444, 183}
  a__take_A(x1,x2) = max{574, 474 + x1, 441 + x2}
  a__take#_A(x1,x2) = max{758, 659, 453 + x2}
  U11_A(x1) = max{392, 233 + x1}
  U11#_A(x1) = max{444, 444}
  U21_A(x1) = max{263, 1 + x1}
  U21#_A(x1) = max{0, 1}
  U31_A(x1) = max{263, 13 + x1}
  U31#_A(x1) = max{198, 183}
  U41_A(x1,x2) = max{263, 37 + x1, 176 + x2}
  U41#_A(x1,x2) = max{0, 360, 360}
  U42_A(x1) = max{264, 5 + x1}
  U42#_A(x1) = max{187, 185}
  isNatIList_A(x1) = max{263, 171 + x1}
  isNatIList#_A(x1) = max{360, 355}
  U51_A(x1,x2) = max{159, x1, 157 + x2}
  U51#_A(x1,x2) = max{185, 177, 177}
  U52_A(x1) = max{160, 1 + x1}
  U52#_A(x1) = max{183, -1}
  isNatList_A(x1) = max{159, 131 + x1}
  isNatList#_A(x1) = max{341, 178}
  U61_A(x1,x2) = max{606, 293 + x1, 433 + x2}
  U61#_A(x1,x2) = max{361, 361, 183}
  U62_A(x1) = max{525, 262 + x1}
  U62#_A(x1) = max{361, 351}
  U71_A(x1,x2,x3) = max{157, 156 + x1, 287 + x2, 151 + x3}
  U71#_A(x1,x2,x3) = max{343, 364, 343, 183}
  U72_A(x1,x2) = max{387, x1, 287 + x2}
  U72#_A(x1,x2) = max{0, 441, 441}
  isNat_A(x1) = max{159, 131 + x1}
  isNat#_A(x1) = max{0, 179}
  U81_A(x1) = max{574, 270 + x1}
  U81#_A(x1) = max{0, 183}
  U91_A(x1,x2,x3,x4) = max{529, 270 + x1, 468 + x2, 501 + x3, 441 + x4}
  U91#_A(x1,x2,x3,x4) = max{445, 445, 445 + x2, 183, 445 + x4}
  U92_A(x1,x2,x3,x4) = max{469, 370 + x1, 468 + x2, 501 + x3, 369 + x4}
  U92#_A(x1,x2,x3,x4) = max{453, 183, 453, 445, 453}
  U93_A(x1,x2,x3,x4) = max{601, 186 + x1, 468 + x2, 501 + x3, 187 + x4}
  U93#_A(x1,x2,x3,x4) = max{369, 370, 368, 448, 368}

precedence:

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