MAYBE
Input TRS:
      1: zeros() -> cons(0(),n__zeros())
      2: U11(tt(),V1) -> U12(isNatList(activate(V1)))
      3: U12(tt()) -> tt()
      4: U21(tt(),V1) -> U22(isNat(activate(V1)))
      5: U22(tt()) -> tt()
      6: U31(tt(),V) -> U32(isNatList(activate(V)))
      7: U32(tt()) -> tt()
      8: U41(tt(),V1,V2) -> U42(isNat(activate(V1)),activate(V2))
      9: U42(tt(),V2) -> U43(isNatIList(activate(V2)))
      10: U43(tt()) -> tt()
      11: U51(tt(),V1,V2) -> U52(isNat(activate(V1)),activate(V2))
      12: U52(tt(),V2) -> U53(isNatList(activate(V2)))
      13: U53(tt()) -> tt()
      14: U61(tt(),V1,V2) -> U62(isNat(activate(V1)),activate(V2))
      15: U62(tt(),V2) -> U63(isNatIList(activate(V2)))
      16: U63(tt()) -> tt()
      17: U71(tt(),L) -> s(length(activate(L)))
      18: U81(tt()) -> nil()
      19: U91(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL)))
      20: and(tt(),X) -> activate(X)
      21: isNat(n__0()) -> tt()
      22: isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)),activate(V1))
      23: isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
      24: isNatIList(V) -> U31(isNatIListKind(activate(V)),activate(V))
      25: isNatIList(n__zeros()) -> tt()
      26: isNatIList(n__cons(V1,V2)) -> U41(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
      27: isNatIListKind(n__nil()) -> tt()
      28: isNatIListKind(n__zeros()) -> tt()
      29: isNatIListKind(n__cons(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
      30: isNatIListKind(n__take(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
      31: isNatKind(n__0()) -> tt()
      32: isNatKind(n__length(V1)) -> isNatIListKind(activate(V1))
      33: isNatKind(n__s(V1)) -> isNatKind(activate(V1))
      34: isNatList(n__nil()) -> tt()
      35: isNatList(n__cons(V1,V2)) -> U51(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
      36: isNatList(n__take(V1,V2)) -> U61(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
      37: length(nil()) -> 0()
      38: length(cons(N,L)) -> U71(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))),n__and(n__isNat(N),n__isNatKind(N))),activate(L))
      39: take(0(),IL) -> U81(and(isNatIList(IL),n__isNatIListKind(IL)))
      40: take(s(M),cons(N,IL)) -> U91(and(and(isNatIList(activate(IL)),n__isNatIListKind(activate(IL))),n__and(n__and(n__isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N)))),activate(IL),M,N)
      41: zeros() -> n__zeros()
      42: take(X1,X2) -> n__take(X1,X2)
      43: 0() -> n__0()
      44: length(X) -> n__length(X)
      45: s(X) -> n__s(X)
      46: cons(X1,X2) -> n__cons(X1,X2)
      47: isNatIListKind(X) -> n__isNatIListKind(X)
      48: nil() -> n__nil()
      49: and(X1,X2) -> n__and(X1,X2)
      50: isNat(X) -> n__isNat(X)
      51: isNatKind(X) -> n__isNatKind(X)
      52: activate(n__zeros()) -> zeros()
      53: activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
      54: activate(n__0()) -> 0()
      55: activate(n__length(X)) -> length(activate(X))
      56: activate(n__s(X)) -> s(activate(X))
      57: activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
      58: activate(n__isNatIListKind(X)) -> isNatIListKind(X)
      59: activate(n__nil()) -> nil()
      60: activate(n__and(X1,X2)) -> and(activate(X1),X2)
      61: activate(n__isNat(X)) -> isNat(X)
      62: activate(n__isNatKind(X)) -> isNatKind(X)
      63: activate(X) -> X
Number of strict rules: 63
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #U11(tt(),V1) -> #U12(isNatList(activate(V1)))
     #2: #U11(tt(),V1) -> #isNatList(activate(V1))
     #3: #U11(tt(),V1) -> #activate(V1)
     #4: #isNatIListKind(n__cons(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
     #5: #isNatIListKind(n__cons(V1,V2)) -> #isNatKind(activate(V1))
     #6: #isNatIListKind(n__cons(V1,V2)) -> #activate(V1)
     #7: #isNatIListKind(n__cons(V1,V2)) -> #activate(V2)
     #8: #isNatList(n__cons(V1,V2)) -> #U51(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
     #9: #isNatList(n__cons(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
     #10: #isNatList(n__cons(V1,V2)) -> #isNatKind(activate(V1))
     #11: #isNatList(n__cons(V1,V2)) -> #activate(V1)
     #12: #isNatList(n__cons(V1,V2)) -> #activate(V2)
     #13: #isNatList(n__cons(V1,V2)) -> #activate(V1)
     #14: #isNatList(n__cons(V1,V2)) -> #activate(V2)
     #15: #length(nil()) -> #0()
     #16: #activate(n__take(X1,X2)) -> #take(activate(X1),activate(X2))
     #17: #activate(n__take(X1,X2)) -> #activate(X1)
     #18: #activate(n__take(X1,X2)) -> #activate(X2)
     #19: #activate(n__isNatIListKind(X)) -> #isNatIListKind(X)
     #20: #activate(n__isNat(X)) -> #isNat(X)
     #21: #length(cons(N,L)) -> #U71(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))),n__and(n__isNat(N),n__isNatKind(N))),activate(L))
     #22: #length(cons(N,L)) -> #and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))),n__and(n__isNat(N),n__isNatKind(N)))
     #23: #length(cons(N,L)) -> #and(isNatList(activate(L)),n__isNatIListKind(activate(L)))
     #24: #length(cons(N,L)) -> #isNatList(activate(L))
     #25: #length(cons(N,L)) -> #activate(L)
     #26: #length(cons(N,L)) -> #activate(L)
     #27: #length(cons(N,L)) -> #activate(L)
     #28: #U31(tt(),V) -> #U32(isNatList(activate(V)))
     #29: #U31(tt(),V) -> #isNatList(activate(V))
     #30: #U31(tt(),V) -> #activate(V)
     #31: #activate(n__nil()) -> #nil()
     #32: #activate(n__length(X)) -> #length(activate(X))
     #33: #activate(n__length(X)) -> #activate(X)
     #34: #take(s(M),cons(N,IL)) -> #U91(and(and(isNatIList(activate(IL)),n__isNatIListKind(activate(IL))),n__and(n__and(n__isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N)))),activate(IL),M,N)
     #35: #take(s(M),cons(N,IL)) -> #and(and(isNatIList(activate(IL)),n__isNatIListKind(activate(IL))),n__and(n__and(n__isNat(M),n__isNatKind(M)),n__and(n__isNat(N),n__isNatKind(N))))
     #36: #take(s(M),cons(N,IL)) -> #and(isNatIList(activate(IL)),n__isNatIListKind(activate(IL)))
     #37: #take(s(M),cons(N,IL)) -> #isNatIList(activate(IL))
     #38: #take(s(M),cons(N,IL)) -> #activate(IL)
     #39: #take(s(M),cons(N,IL)) -> #activate(IL)
     #40: #take(s(M),cons(N,IL)) -> #activate(IL)
     #41: #U42(tt(),V2) -> #U43(isNatIList(activate(V2)))
     #42: #U42(tt(),V2) -> #isNatIList(activate(V2))
     #43: #U42(tt(),V2) -> #activate(V2)
     #44: #U51(tt(),V1,V2) -> #U52(isNat(activate(V1)),activate(V2))
     #45: #U51(tt(),V1,V2) -> #isNat(activate(V1))
     #46: #U51(tt(),V1,V2) -> #activate(V1)
     #47: #U51(tt(),V1,V2) -> #activate(V2)
     #48: #activate(n__cons(X1,X2)) -> #cons(activate(X1),X2)
     #49: #activate(n__cons(X1,X2)) -> #activate(X1)
     #50: #isNatIList(V) -> #U31(isNatIListKind(activate(V)),activate(V))
     #51: #isNatIList(V) -> #isNatIListKind(activate(V))
     #52: #isNatIList(V) -> #activate(V)
     #53: #isNatIList(V) -> #activate(V)
     #54: #isNat(n__s(V1)) -> #U21(isNatKind(activate(V1)),activate(V1))
     #55: #isNat(n__s(V1)) -> #isNatKind(activate(V1))
     #56: #isNat(n__s(V1)) -> #activate(V1)
     #57: #isNat(n__s(V1)) -> #activate(V1)
     #58: #U52(tt(),V2) -> #U53(isNatList(activate(V2)))
     #59: #U52(tt(),V2) -> #isNatList(activate(V2))
     #60: #U52(tt(),V2) -> #activate(V2)
     #61: #activate(n__s(X)) -> #s(activate(X))
     #62: #activate(n__s(X)) -> #activate(X)
     #63: #U61(tt(),V1,V2) -> #U62(isNat(activate(V1)),activate(V2))
     #64: #U61(tt(),V1,V2) -> #isNat(activate(V1))
     #65: #U61(tt(),V1,V2) -> #activate(V1)
     #66: #U61(tt(),V1,V2) -> #activate(V2)
     #67: #activate(n__isNatKind(X)) -> #isNatKind(X)
     #68: #isNatIListKind(n__take(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
     #69: #isNatIListKind(n__take(V1,V2)) -> #isNatKind(activate(V1))
     #70: #isNatIListKind(n__take(V1,V2)) -> #activate(V1)
     #71: #isNatIListKind(n__take(V1,V2)) -> #activate(V2)
     #72: #activate(n__zeros()) -> #zeros()
     #73: #and(tt(),X) -> #activate(X)
     #74: #take(0(),IL) -> #U81(and(isNatIList(IL),n__isNatIListKind(IL)))
     #75: #take(0(),IL) -> #and(isNatIList(IL),n__isNatIListKind(IL))
     #76: #take(0(),IL) -> #isNatIList(IL)
     #77: #isNatKind(n__s(V1)) -> #isNatKind(activate(V1))
     #78: #isNatKind(n__s(V1)) -> #activate(V1)
     #79: #isNat(n__length(V1)) -> #U11(isNatIListKind(activate(V1)),activate(V1))
     #80: #isNat(n__length(V1)) -> #isNatIListKind(activate(V1))
     #81: #isNat(n__length(V1)) -> #activate(V1)
     #82: #isNat(n__length(V1)) -> #activate(V1)
     #83: #activate(n__and(X1,X2)) -> #and(activate(X1),X2)
     #84: #activate(n__and(X1,X2)) -> #activate(X1)
     #85: #U71(tt(),L) -> #s(length(activate(L)))
     #86: #U71(tt(),L) -> #length(activate(L))
     #87: #U71(tt(),L) -> #activate(L)
     #88: #isNatKind(n__length(V1)) -> #isNatIListKind(activate(V1))
     #89: #isNatKind(n__length(V1)) -> #activate(V1)
     #90: #U91(tt(),IL,M,N) -> #cons(activate(N),n__take(activate(M),activate(IL)))
     #91: #U91(tt(),IL,M,N) -> #activate(N)
     #92: #U91(tt(),IL,M,N) -> #activate(M)
     #93: #U91(tt(),IL,M,N) -> #activate(IL)
     #94: #isNatIList(n__cons(V1,V2)) -> #U41(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
     #95: #isNatIList(n__cons(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
     #96: #isNatIList(n__cons(V1,V2)) -> #isNatKind(activate(V1))
     #97: #isNatIList(n__cons(V1,V2)) -> #activate(V1)
     #98: #isNatIList(n__cons(V1,V2)) -> #activate(V2)
     #99: #isNatIList(n__cons(V1,V2)) -> #activate(V1)
     #100: #isNatIList(n__cons(V1,V2)) -> #activate(V2)
     #101: #isNatList(n__take(V1,V2)) -> #U61(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2))
     #102: #isNatList(n__take(V1,V2)) -> #and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2)))
     #103: #isNatList(n__take(V1,V2)) -> #isNatKind(activate(V1))
     #104: #isNatList(n__take(V1,V2)) -> #activate(V1)
     #105: #isNatList(n__take(V1,V2)) -> #activate(V2)
     #106: #isNatList(n__take(V1,V2)) -> #activate(V1)
     #107: #isNatList(n__take(V1,V2)) -> #activate(V2)
     #108: #zeros() -> #cons(0(),n__zeros())
     #109: #zeros() -> #0()
     #110: #activate(n__0()) -> #0()
     #111: #U41(tt(),V1,V2) -> #U42(isNat(activate(V1)),activate(V2))
     #112: #U41(tt(),V1,V2) -> #isNat(activate(V1))
     #113: #U41(tt(),V1,V2) -> #activate(V1)
     #114: #U41(tt(),V1,V2) -> #activate(V2)
     #115: #U62(tt(),V2) -> #U63(isNatIList(activate(V2)))
     #116: #U62(tt(),V2) -> #isNatIList(activate(V2))
     #117: #U62(tt(),V2) -> #activate(V2)
     #118: #U21(tt(),V1) -> #U22(isNat(activate(V1)))
     #119: #U21(tt(),V1) -> #isNat(activate(V1))
     #120: #U21(tt(),V1) -> #activate(V1)
     #121: #U81(tt()) -> #nil()
Number of SCCs: 1, DPs: 103
  SCC { #2..14 #16..27 #29 #30 #32..40 #42..47 #49..57 #59 #60 #62..71 #73 #75..84 #86..89 #91..107 #111..114 #116 #117 #119 #120 }
POLO(Sum)... POLO(max)... succeeded.
      #0 	w: 0
      #U32	w: 0
      #isNatIListKind	w: x1
      isNatKind	w: x1 + 12076
      U21	w: max(x2 + 4)
      isNatList	w: x1
      U11	w: max(x1 + 89, x2 + 2)
      #cons	w: 0
      s 	w: x1
      #isNat	w: x1 + 1
      #take	w: max(x1 + 24147, x2 + 36217)
      U42	w: max(x2 + 24146)
      U91	w: max(x1 + 12073, x2 + 36219, x3 + 36218, x4 + 48295)
      activate	w: x1
      n__isNatIListKind	w: x1
      take	w: max(x1 + 36218, x2 + 36219)
      U71	w: max(x1 + 32701, x2 + 32705)
      n__isNatKind	w: x1 + 12076
      #U81	w: 0
      and	w: max(x1, x2)
      n__zeros	w: 12272
      isNatIList	w: x1 + 24146
      U43	w: x1
      #activate	w: x1
      #U53	w: 0
      #U43	w: 0
      U63	w: 18750
      zeros	w: 12272
      n__nil	w: 3567
      #U52	w: max(x1 + 1906, x2)
      U12	w: 3
      n__s	w: x1
      #U42	w: max(x2 + 12077)
      #U12	w: 0
      #U62	w: max(x1 + 12076, x2 + 12078)
      0 	w: 196
      #zeros	w: 0
      n__take	w: max(x1 + 36218, x2 + 36219)
      #isNatList	w: x1
      #s 	w: 0
      n__cons	w: max(x1 + 12076, x2)
      nil	w: 3567
      isNatIListKind	w: x1
      n__isNat	w: x1 + 4
      U62	w: max(x1 + 18747, x2 + 18750)
      #U63	w: 0
      #nil	w: 0
      U32	w: 15803
      n__0	w: 196
      n__length	w: x1 + 32705
      isNat	w: x1 + 4
      U52	w: max(x1, x2)
      U61	w: max(x2 + 36218, x3 + 18750)
      #U51	w: max(x1, x2 + 1910, x3)
      #U11	w: max(x2 + 96)
      U31	w: max(x1 + 15800, x2 + 23611)
      #U41	w: max(x1 + 12077, x2 + 6108, x3 + 12077)
      cons	w: max(x1 + 12076, x2)
      #isNatIList	w: x1 + 12077
      #U21	w: max(x2 + 1)
      U81	w: 36414
      #U22	w: 0
      tt	w: 2
      n__and	w: max(x1, x2)
      #U71	w: max(x2)
      U22	w: x1
      U51	w: max(x2 + 4, x3)
      #isNatKind	w: x1
      U53	w: 2
      length	w: x1 + 32705
      #length	w: x1
      U41	w: max(x3 + 24146)
      #U31	w: max(x1 + 5009, x2 + 6628)
      #and	w: max(x1, x2)
      #U91	w: max(x1 + 12071, x2 + 36216, x3 + 11668, x4 + 36216)
      #U61	w: max(x1 + 24141, x2 + 12081, x3 + 12081)
    USABLE RULES: { 1..63 }
    Removed DPs: #2 #3 #5 #6 #10 #11 #13 #16..18 #20 #29 #30 #32 #33 #35..40 #43 #45 #46 #49..53 #55..57 #63..71 #75 #76 #79..82 #88 #89 #91..93 #95..107 #112..114 #116 #117 #120
Number of SCCs: 6, DPs: 18
  SCC { #77 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.