YES

TRS:

  a__zeros() -> cons(0(),zeros())
  a__U11(tt(),V1) -> a__U12(a__isNatIListKind(V1),V1)
  a__U12(tt(),V1) -> a__U13(a__isNatList(V1))
  a__U13(tt()) -> tt()
  a__U21(tt(),V1) -> a__U22(a__isNatKind(V1),V1)
  a__U22(tt(),V1) -> a__U23(a__isNat(V1))
  a__U23(tt()) -> tt()
  a__U31(tt(),V) -> a__U32(a__isNatIListKind(V),V)
  a__U32(tt(),V) -> a__U33(a__isNatList(V))
  a__U33(tt()) -> tt()
  a__U41(tt(),V1,V2) -> a__U42(a__isNatKind(V1),V1,V2)
  a__U42(tt(),V1,V2) -> a__U43(a__isNatIListKind(V2),V1,V2)
  a__U43(tt(),V1,V2) -> a__U44(a__isNatIListKind(V2),V1,V2)
  a__U44(tt(),V1,V2) -> a__U45(a__isNat(V1),V2)
  a__U45(tt(),V2) -> a__U46(a__isNatIList(V2))
  a__U46(tt()) -> tt()
  a__U51(tt(),V2) -> a__U52(a__isNatIListKind(V2))
  a__U52(tt()) -> tt()
  a__U61(tt()) -> tt()
  a__U71(tt()) -> tt()
  a__U81(tt(),V1,V2) -> a__U82(a__isNatKind(V1),V1,V2)
  a__U82(tt(),V1,V2) -> a__U83(a__isNatIListKind(V2),V1,V2)
  a__U83(tt(),V1,V2) -> a__U84(a__isNatIListKind(V2),V1,V2)
  a__U84(tt(),V1,V2) -> a__U85(a__isNat(V1),V2)
  a__U85(tt(),V2) -> a__U86(a__isNatList(V2))
  a__U86(tt()) -> tt()
  a__U91(tt(),L,N) -> a__U92(a__isNatIListKind(L),L,N)
  a__U92(tt(),L,N) -> a__U93(a__isNat(N),L,N)
  a__U93(tt(),L,N) -> a__U94(a__isNatKind(N),L)
  a__U94(tt(),L) -> s(a__length(mark(L)))
  a__isNat(0()) -> tt()
  a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1)
  a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1)
  a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V)
  a__isNatIList(zeros()) -> tt()
  a__isNatIList(cons(V1,V2)) -> a__U41(a__isNatKind(V1),V1,V2)
  a__isNatIListKind(nil()) -> tt()
  a__isNatIListKind(zeros()) -> tt()
  a__isNatIListKind(cons(V1,V2)) -> a__U51(a__isNatKind(V1),V2)
  a__isNatKind(0()) -> tt()
  a__isNatKind(length(V1)) -> a__U61(a__isNatIListKind(V1))
  a__isNatKind(s(V1)) -> a__U71(a__isNatKind(V1))
  a__isNatList(nil()) -> tt()
  a__isNatList(cons(V1,V2)) -> a__U81(a__isNatKind(V1),V1,V2)
  a__length(nil()) -> 0()
  a__length(cons(N,L)) -> a__U91(a__isNatList(L),L,N)
  mark(zeros()) -> a__zeros()
  mark(U11(X1,X2)) -> a__U11(mark(X1),X2)
  mark(U12(X1,X2)) -> a__U12(mark(X1),X2)
  mark(isNatIListKind(X)) -> a__isNatIListKind(X)
  mark(U13(X)) -> a__U13(mark(X))
  mark(isNatList(X)) -> a__isNatList(X)
  mark(U21(X1,X2)) -> a__U21(mark(X1),X2)
  mark(U22(X1,X2)) -> a__U22(mark(X1),X2)
  mark(isNatKind(X)) -> a__isNatKind(X)
  mark(U23(X)) -> a__U23(mark(X))
  mark(isNat(X)) -> a__isNat(X)
  mark(U31(X1,X2)) -> a__U31(mark(X1),X2)
  mark(U32(X1,X2)) -> a__U32(mark(X1),X2)
  mark(U33(X)) -> a__U33(mark(X))
  mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3)
  mark(U42(X1,X2,X3)) -> a__U42(mark(X1),X2,X3)
  mark(U43(X1,X2,X3)) -> a__U43(mark(X1),X2,X3)
  mark(U44(X1,X2,X3)) -> a__U44(mark(X1),X2,X3)
  mark(U45(X1,X2)) -> a__U45(mark(X1),X2)
  mark(U46(X)) -> a__U46(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(U61(X)) -> a__U61(mark(X))
  mark(U71(X)) -> a__U71(mark(X))
  mark(U81(X1,X2,X3)) -> a__U81(mark(X1),X2,X3)
  mark(U82(X1,X2,X3)) -> a__U82(mark(X1),X2,X3)
  mark(U83(X1,X2,X3)) -> a__U83(mark(X1),X2,X3)
  mark(U84(X1,X2,X3)) -> a__U84(mark(X1),X2,X3)
  mark(U85(X1,X2)) -> a__U85(mark(X1),X2)
  mark(U86(X)) -> a__U86(mark(X))
  mark(U91(X1,X2,X3)) -> a__U91(mark(X1),X2,X3)
  mark(U92(X1,X2,X3)) -> a__U92(mark(X1),X2,X3)
  mark(U93(X1,X2,X3)) -> a__U93(mark(X1),X2,X3)
  mark(U94(X1,X2)) -> a__U94(mark(X1),X2)
  mark(length(X)) -> a__length(mark(X))
  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(X1,X2) -> U11(X1,X2)
  a__U12(X1,X2) -> U12(X1,X2)
  a__isNatIListKind(X) -> isNatIListKind(X)
  a__U13(X) -> U13(X)
  a__isNatList(X) -> isNatList(X)
  a__U21(X1,X2) -> U21(X1,X2)
  a__U22(X1,X2) -> U22(X1,X2)
  a__isNatKind(X) -> isNatKind(X)
  a__U23(X) -> U23(X)
  a__isNat(X) -> isNat(X)
  a__U31(X1,X2) -> U31(X1,X2)
  a__U32(X1,X2) -> U32(X1,X2)
  a__U33(X) -> U33(X)
  a__U41(X1,X2,X3) -> U41(X1,X2,X3)
  a__U42(X1,X2,X3) -> U42(X1,X2,X3)
  a__U43(X1,X2,X3) -> U43(X1,X2,X3)
  a__U44(X1,X2,X3) -> U44(X1,X2,X3)
  a__U45(X1,X2) -> U45(X1,X2)
  a__U46(X) -> U46(X)
  a__isNatIList(X) -> isNatIList(X)
  a__U51(X1,X2) -> U51(X1,X2)
  a__U52(X) -> U52(X)
  a__U61(X) -> U61(X)
  a__U71(X) -> U71(X)
  a__U81(X1,X2,X3) -> U81(X1,X2,X3)
  a__U82(X1,X2,X3) -> U82(X1,X2,X3)
  a__U83(X1,X2,X3) -> U83(X1,X2,X3)
  a__U84(X1,X2,X3) -> U84(X1,X2,X3)
  a__U85(X1,X2) -> U85(X1,X2)
  a__U86(X) -> U86(X)
  a__U91(X1,X2,X3) -> U91(X1,X2,X3)
  a__U92(X1,X2,X3) -> U92(X1,X2,X3)
  a__U93(X1,X2,X3) -> U93(X1,X2,X3)
  a__U94(X1,X2) -> U94(X1,X2)
  a__length(X) -> length(X)

max/plus interpretations on N:

  a__zeros_A = 791
  a__zeros#_A = 791
  cons_A(x1,x2) = max{229, 328 + x1, 755 + x2}
  cons#_A(x1,x2) = max{229, 328 + x1, 755 + x2}
  0_A = 462
  0#_A = 462
  zeros_A = 0
  zeros#_A = 0
  a__U11_A(x1,x2) = max{618, 35 + x1, 88 + x2}
  a__U11#_A(x1,x2) = max{618, 35 + x1, 88 + x2}
  tt_A = 460
  tt#_A = 460
  a__U12_A(x1,x2) = max{618, 1 + x1, 87 + x2}
  a__U12#_A(x1,x2) = max{618, 1 + x1, 87 + x2}
  a__isNatIListKind_A(x1) = max{493, 1 + x1}
  a__isNatIListKind#_A(x1) = max{493, 1 + x1}
  a__U13_A(x1) = max{618, 1 + x1}
  a__U13#_A(x1) = max{618, 1 + x1}
  a__isNatList_A(x1) = max{329, 85 + x1}
  a__isNatList#_A(x1) = max{329, 85 + x1}
  a__U21_A(x1,x2) = max{1, x1, 93 + x2}
  a__U21#_A(x1,x2) = max{1, x1, 93 + x2}
  a__U22_A(x1,x2) = max{460, 2 + x1, 93 + x2}
  a__U22#_A(x1,x2) = max{460, 2 + x1, 93 + x2}
  a__isNatKind_A(x1) = max{412, 39 + x1}
  a__isNatKind#_A(x1) = max{412, 39 + x1}
  a__U23_A(x1) = max{461, 1 + x1}
  a__U23#_A(x1) = max{461, 1 + x1}
  a__isNat_A(x1) = max{91, 89 + x1}
  a__isNat#_A(x1) = max{91, 89 + x1}
  a__U31_A(x1,x2) = max{794, 230 + x1, 552 + x2}
  a__U31#_A(x1,x2) = max{794, 230 + x1, 552 + x2}
  a__U32_A(x1,x2) = max{794, 301 + x1, 551 + x2}
  a__U32#_A(x1,x2) = max{794, 301 + x1, 551 + x2}
  a__U33_A(x1) = max{794, 465 + x1}
  a__U33#_A(x1) = max{794, 465 + x1}
  a__U41_A(x1,x2,x3) = max{228, x1, 790 + x2, 972 + x3}
  a__U41#_A(x1,x2,x3) = max{228, x1, 790 + x2, 972 + x3}
  a__U42_A(x1,x2,x3) = max{789, 559 + x1, 787 + x2, 787 + x3}
  a__U42#_A(x1,x2,x3) = max{789, 559 + x1, 787 + x2, 787 + x3}
  a__U43_A(x1,x2,x3) = max{788, 525 + x1, 786 + x2, 786 + x3}
  a__U43#_A(x1,x2,x3) = max{788, 525 + x1, 786 + x2, 786 + x3}
  a__U44_A(x1,x2,x3) = max{984, 419 + x1, 785 + x2, 785 + x3}
  a__U44#_A(x1,x2,x3) = max{984, 419 + x1, 785 + x2, 785 + x3}
  a__U45_A(x1,x2) = max{983, 564 + x1, 784 + x2}
  a__U45#_A(x1,x2) = max{983, 564 + x1, 784 + x2}
  a__U46_A(x1) = max{1024, 230 + x1}
  a__U46#_A(x1) = max{1024, 230 + x1}
  a__isNatIList_A(x1) = max{794, 553 + x1}
  a__isNatIList#_A(x1) = max{794, 553 + x1}
  a__U51_A(x1,x2) = max{723, 230 + x1, 690 + x2}
  a__U51#_A(x1,x2) = max{723, 230 + x1, 690 + x2}
  a__U52_A(x1) = max{691, 230 + x1}
  a__U52#_A(x1) = max{691, 230 + x1}
  a__U61_A(x1) = max{530, 37 + x1}
  a__U61#_A(x1) = max{530, 37 + x1}
  a__U71_A(x1) = max{565, 1 + x1}
  a__U71#_A(x1) = max{565, 1 + x1}
  a__U81_A(x1,x2,x3) = max{228, 290 + x1, 327 + x2, 754 + x3}
  a__U81#_A(x1,x2,x3) = max{228, 290 + x1, 327 + x2, 754 + x3}
  a__U82_A(x1,x2,x3) = max{751, 287 + x1, 326 + x2, 753 + x3}
  a__U82#_A(x1,x2,x3) = max{751, 287 + x1, 326 + x2, 753 + x3}
  a__U83_A(x1,x2,x3) = max{753, 259 + x1, 325 + x2, 721 + x3}
  a__U83#_A(x1,x2,x3) = max{753, 259 + x1, 325 + x2, 721 + x3}
  a__U84_A(x1,x2,x3) = max{720, 229 + x1, 324 + x2, 324 + x3}
  a__U84#_A(x1,x2,x3) = max{720, 229 + x1, 324 + x2, 324 + x3}
  a__U85_A(x1,x2) = max{719, 232 + x1, 231 + x2}
  a__U85#_A(x1,x2) = max{719, 232 + x1, 231 + x2}
  a__U86_A(x1) = max{719, x1}
  a__U86#_A(x1) = max{719, x1}
  a__U91_A(x1,x2,x3) = max{791, 462 + x1, 661 + x2, 327 + x3}
  a__U91#_A(x1,x2,x3) = max{791, 462 + x1, 661 + x2, 327 + x3}
  a__U92_A(x1,x2,x3) = max{793, 428 + x1, 660 + x2, 320 + x3}
  a__U92#_A(x1,x2,x3) = max{793, 428 + x1, 660 + x2, 320 + x3}
  a__U93_A(x1,x2,x3) = max{887, 230 + x1, 659 + x2, 319 + x3}
  a__U93#_A(x1,x2,x3) = max{887, 230 + x1, 659 + x2, 319 + x3}
  a__U94_A(x1,x2) = max{886, 279 + x1, 658 + x2}
  a__U94#_A(x1,x2) = max{886, 279 + x1, 658 + x2}
  s_A(x1) = max{740, 94 + x1}
  s#_A(x1) = max{740, 94 + x1}
  a__length_A(x1) = max{792, x1}
  a__length#_A(x1) = max{792, x1}
  mark_A(x1) = max{792, 563 + x1}
  mark#_A(x1) = max{792, 563 + x1}
  length_A(x1) = max{529, x1}
  length#_A(x1) = max{529, x1}
  nil_A = 461
  nil#_A = 461
  U11_A(x1,x2) = max{264, 35 + x1, x2}
  U11#_A(x1,x2) = max{264, 35 + x1, x2}
  U12_A(x1,x2) = max{230, 1 + x1, x2}
  U12#_A(x1,x2) = max{230, 1 + x1, x2}
  isNatIListKind_A(x1) = max{0, x1}
  isNatIListKind#_A(x1) = max{0, x1}
  U13_A(x1) = max{230, 1 + x1}
  U13#_A(x1) = max{230, 1 + x1}
  isNatList_A(x1) = max{0, x1}
  isNatList#_A(x1) = max{0, x1}
  U21_A(x1,x2) = max{2, x1, x2}
  U21#_A(x1,x2) = max{2, x1, x2}
  U22_A(x1,x2) = max{231, 2 + x1, x2}
  U22#_A(x1,x2) = max{231, 2 + x1, x2}
  isNatKind_A(x1) = max{0, x1}
  isNatKind#_A(x1) = max{0, x1}
  U23_A(x1) = max{230, 1 + x1}
  U23#_A(x1) = max{230, 1 + x1}
  isNat_A(x1) = max{0, x1}
  isNat#_A(x1) = max{0, x1}
  U31_A(x1,x2) = max{793, 230 + x1, 230 + x2}
  U31#_A(x1,x2) = max{793, 230 + x1, 230 + x2}
  U32_A(x1,x2) = max{552, 301 + x1, 230 + x2}
  U32#_A(x1,x2) = max{552, 301 + x1, 230 + x2}
  U33_A(x1) = max{694, 465 + x1}
  U33#_A(x1) = max{694, 465 + x1}
  U41_A(x1,x2,x3) = max{1, x1, 227 + x2, 409 + x3}
  U41#_A(x1,x2,x3) = max{1, x1, 227 + x2, 409 + x3}
  U42_A(x1,x2,x3) = max{788, 559 + x1, 230 + x2, 225 + x3}
  U42#_A(x1,x2,x3) = max{788, 559 + x1, 230 + x2, 225 + x3}
  U43_A(x1,x2,x3) = max{787, 525 + x1, 223 + x2, 230 + x3}
  U43#_A(x1,x2,x3) = max{787, 525 + x1, 223 + x2, 230 + x3}
  U44_A(x1,x2,x3) = max{420, 419 + x1, 230 + x2, 648 + x3}
  U44#_A(x1,x2,x3) = max{420, 419 + x1, 230 + x2, 648 + x3}
  U45_A(x1,x2) = max{793, 564 + x1, 419 + x2}
  U45#_A(x1,x2) = max{793, 564 + x1, 419 + x2}
  U46_A(x1) = max{793, 230 + x1}
  U46#_A(x1) = max{793, 230 + x1}
  isNatIList_A(x1) = max{232, 552 + x1}
  isNatIList#_A(x1) = max{232, 552 + x1}
  U51_A(x1,x2) = max{691, 230 + x1, 458 + x2}
  U51#_A(x1,x2) = max{691, 230 + x1, 458 + x2}
  U52_A(x1) = max{459, 230 + x1}
  U52#_A(x1) = max{459, 230 + x1}
  U61_A(x1) = max{266, 37 + x1}
  U61#_A(x1) = max{266, 37 + x1}
  U71_A(x1) = max{230, 1 + x1}
  U71#_A(x1) = max{230, 1 + x1}
  U81_A(x1,x2,x3) = max{0, 290 + x1, x2, 519 + x3}
  U81#_A(x1,x2,x3) = max{0, 290 + x1, x2, 519 + x3}
  U82_A(x1,x2,x3) = max{752, 287 + x1, 230 + x2, 230 + x3}
  U82#_A(x1,x2,x3) = max{752, 287 + x1, 230 + x2, 230 + x3}
  U83_A(x1,x2,x3) = max{722, 259 + x1, 230 + x2, 230 + x3}
  U83#_A(x1,x2,x3) = max{722, 259 + x1, 230 + x2, 230 + x3}
  U84_A(x1,x2,x3) = max{458, 229 + x1, 230 + x2, 230 + x3}
  U84#_A(x1,x2,x3) = max{458, 229 + x1, 230 + x2, 230 + x3}
  U85_A(x1,x2) = max{461, 232 + x1, 230 + x2}
  U85#_A(x1,x2) = max{461, 232 + x1, 230 + x2}
  U86_A(x1) = max{1, x1}
  U86#_A(x1) = max{1, x1}
  U91_A(x1,x2,x3) = max{691, 462 + x1, 227 + x2, 227 + x3}
  U91#_A(x1,x2,x3) = max{691, 462 + x1, 227 + x2, 227 + x3}
  U92_A(x1,x2,x3) = max{661, 428 + x1, 656 + x2, 319 + x3}
  U92#_A(x1,x2,x3) = max{661, 428 + x1, 656 + x2, 319 + x3}
  U93_A(x1,x2,x3) = max{793, 230 + x1, 230 + x2, 318 + x3}
  U93#_A(x1,x2,x3) = max{793, 230 + x1, 230 + x2, 318 + x3}
  U94_A(x1,x2) = max{659, 279 + x1, 322 + x2}
  U94#_A(x1,x2) = max{659, 279 + x1, 322 + x2}

precedence:

  zeros > a__zeros > 0 > mark > cons = a__isNatIList > a__U31 = a__U41 = a__U91 > a__U32 = a__U42 = a__U92 = U31 = U41 = U91 > a__U33 = a__U43 = a__U93 = U32 = U42 = U92 > a__U44 = a__U94 = U33 = U43 = U93 > a__U45 = a__U82 = s = U44 = U94 > a__U21 = a__U46 = a__U83 = U45 = U82 > a__U22 = a__U84 = a__length = U21 = U46 = U83 > a__U23 = a__isNat = a__U85 = length = U22 = U84 > a__U11 = a__U86 = U23 = isNat = isNatIList = U85 > a__U12 = U11 = U86 > a__U13 = U12 > tt = U13 > a__isNatList = nil > a__U71 = a__U81 = isNatList > a__isNatIListKind = a__isNatKind = U71 = U81 > a__U51 = a__U61 = isNatIListKind = isNatKind > a__U52 = U51 = U61 > U52