MAYBE
Input TRS:
      1: zeros() -> cons(0(),n__zeros())
      2: U11(tt()) -> tt()
      3: U21(tt()) -> tt()
      4: U31(tt()) -> tt()
      5: U41(tt(),V2) -> U42(isNatIList(activate(V2)))
      6: U42(tt()) -> tt()
      7: U51(tt(),V2) -> U52(isNatList(activate(V2)))
      8: U52(tt()) -> tt()
      9: U61(tt(),V2) -> U62(isNatIList(activate(V2)))
      10: U62(tt()) -> tt()
      11: U71(tt(),L,N) -> U72(isNat(activate(N)),activate(L))
      12: U72(tt(),L) -> s(length(activate(L)))
      13: U81(tt()) -> nil()
      14: U91(tt(),IL,M,N) -> U92(isNat(activate(M)),activate(IL),activate(M),activate(N))
      15: U92(tt(),IL,M,N) -> U93(isNat(activate(N)),activate(IL),activate(M),activate(N))
      16: U93(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL)))
      17: isNat(n__0()) -> tt()
      18: isNat(n__length(V1)) -> U11(isNatList(activate(V1)))
      19: isNat(n__s(V1)) -> U21(isNat(activate(V1)))
      20: isNatIList(V) -> U31(isNatList(activate(V)))
      21: isNatIList(n__zeros()) -> tt()
      22: isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2))
      23: isNatList(n__nil()) -> tt()
      24: isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2))
      25: isNatList(n__take(V1,V2)) -> U61(isNat(activate(V1)),activate(V2))
      26: length(nil()) -> 0()
      27: length(cons(N,L)) -> U71(isNatList(activate(L)),activate(L),N)
      28: take(0(),IL) -> U81(isNatIList(IL))
      29: take(s(M),cons(N,IL)) -> U91(isNatIList(activate(IL)),activate(IL),M,N)
      30: zeros() -> n__zeros()
      31: take(X1,X2) -> n__take(X1,X2)
      32: 0() -> n__0()
      33: length(X) -> n__length(X)
      34: s(X) -> n__s(X)
      35: cons(X1,X2) -> n__cons(X1,X2)
      36: nil() -> n__nil()
      37: activate(n__zeros()) -> zeros()
      38: activate(n__take(X1,X2)) -> take(activate(X1),activate(X2))
      39: activate(n__0()) -> 0()
      40: activate(n__length(X)) -> length(activate(X))
      41: activate(n__s(X)) -> s(activate(X))
      42: activate(n__cons(X1,X2)) -> cons(activate(X1),X2)
      43: activate(n__nil()) -> nil()
      44: activate(X) -> X
Number of strict rules: 44
Direct POLO(bPol) ... failed.
Uncurrying ... failed.
Dependency Pairs:
     #1: #activate(n__nil()) -> #nil()
     #2: #take(s(M),cons(N,IL)) -> #U91(isNatIList(activate(IL)),activate(IL),M,N)
     #3: #take(s(M),cons(N,IL)) -> #isNatIList(activate(IL))
     #4: #take(s(M),cons(N,IL)) -> #activate(IL)
     #5: #take(s(M),cons(N,IL)) -> #activate(IL)
     #6: #activate(n__cons(X1,X2)) -> #cons(activate(X1),X2)
     #7: #activate(n__cons(X1,X2)) -> #activate(X1)
     #8: #activate(n__s(X)) -> #s(activate(X))
     #9: #activate(n__s(X)) -> #activate(X)
     #10: #activate(n__zeros()) -> #zeros()
     #11: #activate(n__take(X1,X2)) -> #take(activate(X1),activate(X2))
     #12: #activate(n__take(X1,X2)) -> #activate(X1)
     #13: #activate(n__take(X1,X2)) -> #activate(X2)
     #14: #activate(n__length(X)) -> #length(activate(X))
     #15: #activate(n__length(X)) -> #activate(X)
     #16: #U81(tt()) -> #nil()
     #17: #U61(tt(),V2) -> #U62(isNatIList(activate(V2)))
     #18: #U61(tt(),V2) -> #isNatIList(activate(V2))
     #19: #U61(tt(),V2) -> #activate(V2)
     #20: #U71(tt(),L,N) -> #U72(isNat(activate(N)),activate(L))
     #21: #U71(tt(),L,N) -> #isNat(activate(N))
     #22: #U71(tt(),L,N) -> #activate(N)
     #23: #U71(tt(),L,N) -> #activate(L)
     #24: #isNatList(n__cons(V1,V2)) -> #U51(isNat(activate(V1)),activate(V2))
     #25: #isNatList(n__cons(V1,V2)) -> #isNat(activate(V1))
     #26: #isNatList(n__cons(V1,V2)) -> #activate(V1)
     #27: #isNatList(n__cons(V1,V2)) -> #activate(V2)
     #28: #U72(tt(),L) -> #s(length(activate(L)))
     #29: #U72(tt(),L) -> #length(activate(L))
     #30: #U72(tt(),L) -> #activate(L)
     #31: #U91(tt(),IL,M,N) -> #U92(isNat(activate(M)),activate(IL),activate(M),activate(N))
     #32: #U91(tt(),IL,M,N) -> #isNat(activate(M))
     #33: #U91(tt(),IL,M,N) -> #activate(M)
     #34: #U91(tt(),IL,M,N) -> #activate(IL)
     #35: #U91(tt(),IL,M,N) -> #activate(M)
     #36: #U91(tt(),IL,M,N) -> #activate(N)
     #37: #isNatList(n__take(V1,V2)) -> #U61(isNat(activate(V1)),activate(V2))
     #38: #isNatList(n__take(V1,V2)) -> #isNat(activate(V1))
     #39: #isNatList(n__take(V1,V2)) -> #activate(V1)
     #40: #isNatList(n__take(V1,V2)) -> #activate(V2)
     #41: #isNatIList(V) -> #U31(isNatList(activate(V)))
     #42: #isNatIList(V) -> #isNatList(activate(V))
     #43: #isNatIList(V) -> #activate(V)
     #44: #U51(tt(),V2) -> #U52(isNatList(activate(V2)))
     #45: #U51(tt(),V2) -> #isNatList(activate(V2))
     #46: #U51(tt(),V2) -> #activate(V2)
     #47: #activate(n__0()) -> #0()
     #48: #U41(tt(),V2) -> #U42(isNatIList(activate(V2)))
     #49: #U41(tt(),V2) -> #isNatIList(activate(V2))
     #50: #U41(tt(),V2) -> #activate(V2)
     #51: #take(0(),IL) -> #U81(isNatIList(IL))
     #52: #take(0(),IL) -> #isNatIList(IL)
     #53: #isNatIList(n__cons(V1,V2)) -> #U41(isNat(activate(V1)),activate(V2))
     #54: #isNatIList(n__cons(V1,V2)) -> #isNat(activate(V1))
     #55: #isNatIList(n__cons(V1,V2)) -> #activate(V1)
     #56: #isNatIList(n__cons(V1,V2)) -> #activate(V2)
     #57: #length(cons(N,L)) -> #U71(isNatList(activate(L)),activate(L),N)
     #58: #length(cons(N,L)) -> #isNatList(activate(L))
     #59: #length(cons(N,L)) -> #activate(L)
     #60: #length(cons(N,L)) -> #activate(L)
     #61: #isNat(n__s(V1)) -> #U21(isNat(activate(V1)))
     #62: #isNat(n__s(V1)) -> #isNat(activate(V1))
     #63: #isNat(n__s(V1)) -> #activate(V1)
     #64: #length(nil()) -> #0()
     #65: #U93(tt(),IL,M,N) -> #cons(activate(N),n__take(activate(M),activate(IL)))
     #66: #U93(tt(),IL,M,N) -> #activate(N)
     #67: #U93(tt(),IL,M,N) -> #activate(M)
     #68: #U93(tt(),IL,M,N) -> #activate(IL)
     #69: #zeros() -> #cons(0(),n__zeros())
     #70: #zeros() -> #0()
     #71: #U92(tt(),IL,M,N) -> #U93(isNat(activate(N)),activate(IL),activate(M),activate(N))
     #72: #U92(tt(),IL,M,N) -> #isNat(activate(N))
     #73: #U92(tt(),IL,M,N) -> #activate(N)
     #74: #U92(tt(),IL,M,N) -> #activate(IL)
     #75: #U92(tt(),IL,M,N) -> #activate(M)
     #76: #U92(tt(),IL,M,N) -> #activate(N)
     #77: #isNat(n__length(V1)) -> #U11(isNatList(activate(V1)))
     #78: #isNat(n__length(V1)) -> #isNatList(activate(V1))
     #79: #isNat(n__length(V1)) -> #activate(V1)
Number of SCCs: 1, DPs: 61
  SCC { #2..5 #7 #9 #11..15 #18..27 #29..40 #42 #43 #45 #46 #49 #50 #52..60 #62 #63 #66..68 #71..76 #78 #79 }
POLO(Sum)... succeeded.
      #0 	w: 0
      #U72	w: x2
      U21	w: x1 + 1
      isNatList	w: 1
      U11	w: 2
      #cons	w: 0
      s 	w: x1
      #isNat	w: x1
      #take	w: x1 + x2 + 2
      U42	w: x1 + 2
      U91	w: x2 + x3 + x4 + 24326
      activate	w: x1
      take	w: x1 + x2 + 24326
      U71	w: x2 + x3 + 32539
      #U81	w: 0
      #U92	w: x2 + x3 + x4
      n__zeros	w: 1
      isNatIList	w: 1
      #U93	w: x2 + x3 + x4
      #activate	w: x1
      U93	w: x2 + x3 + x4 + 24326
      U72	w: x2 + 32539
      zeros	w: 1
      n__nil	w: 2
      #U52	w: 0
      n__s	w: x1
      #U42	w: 0
      #U62	w: 0
      0 	w: 0
      #zeros	w: 0
      n__take	w: x1 + x2 + 24326
      #isNatList	w: x1
      #s 	w: 0
      n__cons	w: x1 + x2
      nil	w: 2
      U62	w: 3
      #nil	w: 0
      n__0	w: 0
      n__length	w: x1 + 32539
      isNat	w: 1
      U52	w: 3
      U61	w: x1 + x2 + 1
      #U51	w: x2
      #U11	w: 0
      U31	w: 2
      U92	w: x2 + x3 + x4 + 24326
      #U41	w: x2 + 1
      cons	w: x1 + x2
      #isNatIList	w: x1 + 1
      #U21	w: 0
      U81	w: 2
      tt	w: 4
      #U71	w: x2 + x3
      U51	w: 2
      length	w: x1 + 32539
      #length	w: x1
      U41	w: 2
      #U31	w: 0
      #U91	w: x2 + x3 + x4
      #U61	w: x2 + 2
    USABLE RULES: { 1 11..16 26..44 }
    Removed DPs: #2..5 #11..15 #18 #19 #37..40 #42 #43 #50 #52 #54..56 #78 #79
Number of SCCs: 5, DPs: 10
  SCC { #62 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded.
      #0 	w: [0;0]
      #U72	w: [0;0]
      U21	w: [0,0;0,1] * x1 + [39557;37784]
      isNatList	w: x1 + [0;13908]
      U11	w: [0,0;1,0] * x1 + [37781;36008]
      #cons	w: [0;0]
      s 	w: [1,0;0,0] * x1 + [37782;1]
      #isNat	w: [1,0;1,0] * x1
      #take	w: [0;0]
      U42	w: [37782;73791]
      U91	w: [0,0;1,0] * x1 + [0,0;1,0] * x3 + [37782;59883]
      activate	w: x1
      take	w: [0,0;1,0] * x1 + [37782;59883]
      U71	w: [1,0;1,1] * x1 + [1,1;1,0] * x2 + [1;0]
      #U81	w: [0;0]
      #U92	w: [0;0]
      n__zeros	w: [0;1]
      isNatIList	w: [0,0;1,1] * x1 + [37782;73791]
      #U93	w: [0;0]
      #activate	w: [0;0]
      U93	w: [0,0;1,0] * x3 + [37782;97665]
      U72	w: [1,1;1,0] * x2 + [37783;111573]
      zeros	w: [0;1]
      n__nil	w: [37782;59883]
      #U52	w: [0;0]
      n__s	w: [1,0;0,0] * x1 + [37782;1]
      #U42	w: [0;0]
      #U62	w: [0;0]
      0 	w: [1;1]
      #zeros	w: [0;0]
      n__take	w: [0,0;1,0] * x1 + [37782;59883]
      #isNatList	w: [0;0]
      #s 	w: [0;0]
      n__cons	w: [1,0;1,1] * x2
      nil	w: [37782;59883]
      U62	w: [37782;73791]
      #nil	w: [0;0]
      n__0	w: [1;1]
      n__length	w: [1,1;1,1] * x1 + [1;36006]
      isNat	w: [1,1;1,1] * x1 + [1773;0]
      U52	w: [1,0;1,1] * x1
      U61	w: [37782;73791]
      #U51	w: [0;0]
      #U11	w: [0;0]
      U31	w: [37782;73791]
      U92	w: [0,0;1,0] * x3 + [37782;97665]
      #U41	w: [0;0]
      cons	w: [1,0;1,1] * x2
      #isNatIList	w: [0;0]
      #U21	w: [0;0]
      U81	w: [1,0;1,0] * x1 + [0;22102]
      tt	w: [37782;73791]
      #U71	w: [0;0]
      U51	w: [1,0;1,1] * x2 + [0;13908]
      length	w: [1,1;1,1] * x1 + [1;36006]
      #length	w: [0;0]
      U41	w: [0,0;0,1] * x2 + [37782;73791]
      #U31	w: [0;0]
      #U91	w: [0;0]
      #U61	w: [0;0]
    USABLE RULES: { 1 4..16 20..44 }
    Removed DPs: #62
Number of SCCs: 4, DPs: 9
  SCC { #7 #9 }
POLO(Sum)... succeeded.
      #0 	w: 0
      #U72	w: 0
      U21	w: x1 + 1
      isNatList	w: 1
      U11	w: 3
      #cons	w: 0
      s 	w: 38050
      #isNat	w: 0
      #take	w: 2
      U42	w: x1 + 2
      U91	w: x2 + x3 + 3
      activate	w: 1
      take	w: 2
      U71	w: 38048
      #U81	w: 0
      #U92	w: 0
      n__zeros	w: 3
      isNatIList	w: 0
      #U93	w: 0
      #activate	w: x1
      U93	w: x1 + x3 + x4 + 38047
      U72	w: 38049
      zeros	w: 2
      n__nil	w: 9
      #U52	w: 0
      n__s	w: x1 + 38051
      #U42	w: 0
      #U62	w: 0
      0 	w: 10
      #zeros	w: 0
      n__take	w: x1 + x2 + 3
      #isNatList	w: 0
      #s 	w: 0
      n__cons	w: x1 + 38047
      nil	w: 8
      U62	w: 2
      #nil	w: 0
      n__0	w: 11
      n__length	w: 2
      isNat	w: 1
      U52	w: 3
      U61	w: x2 + 1
      #U51	w: 0
      #U11	w: 0
      U31	w: 1
      U92	w: x3 + x4 + 2
      #U41	w: 1
      cons	w: x1 + x2 + 38046
      #isNatIList	w: 1
      #U21	w: 0
      U81	w: x1 + 3
      tt	w: 4
      #U71	w: 0
      U51	w: 2
      length	w: x1 + 1
      #length	w: 0
      U41	w: x2 + 1
      #U31	w: 0
      #U91	w: 0
      #U61	w: 2
    USABLE RULES: { }
    Removed DPs: #7 #9
Number of SCCs: 3, DPs: 7
  SCC { #49 #53 }
POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
Finding a loop...  failed.