- : unit = ()
- : unit = ()
h : heuristic = <heuristic>
- : unit = ()
APPLY CRITERIA (Marked dependency pairs)

TRS termination of:
[1] zeros -> cons(0,n__zeros)
[2] U11(tt,V1) -> U12(isNatIListKind(activate(V1)),activate(V1))
[3] U12(tt,V1) -> U13(isNatList(activate(V1)))
[4] U13(tt) -> tt
[5] U21(tt,V1) -> U22(isNatKind(activate(V1)),activate(V1))
[6] U22(tt,V1) -> U23(isNat(activate(V1)))
[7] U23(tt) -> tt
[8] U31(tt,V) -> U32(isNatIListKind(activate(V)),activate(V))
[9] U32(tt,V) -> U33(isNatList(activate(V)))
[10] U33(tt) -> tt
[11] U41(tt,V1,V2) -> U42(isNatKind(activate(V1)),activate(V1),activate(V2))
[12] U42(tt,V1,V2) ->
 U43(isNatIListKind(activate(V2)),activate(V1),activate(V2))
[13] U43(tt,V1,V2) ->
 U44(isNatIListKind(activate(V2)),activate(V1),activate(V2))
[14] U44(tt,V1,V2) -> U45(isNat(activate(V1)),activate(V2))
[15] U45(tt,V2) -> U46(isNatIList(activate(V2)))
[16] U46(tt) -> tt
[17] U51(tt,V2) -> U52(isNatIListKind(activate(V2)))
[18] U52(tt) -> tt
[19] U61(tt) -> tt
[20] U71(tt) -> tt
[21] U81(tt,V1,V2) -> U82(isNatKind(activate(V1)),activate(V1),activate(V2))
[22] U82(tt,V1,V2) ->
 U83(isNatIListKind(activate(V2)),activate(V1),activate(V2))
[23] U83(tt,V1,V2) ->
 U84(isNatIListKind(activate(V2)),activate(V1),activate(V2))
[24] U84(tt,V1,V2) -> U85(isNat(activate(V1)),activate(V2))
[25] U85(tt,V2) -> U86(isNatList(activate(V2)))
[26] U86(tt) -> tt
[27] U91(tt,L,N) -> U92(isNatIListKind(activate(L)),activate(L),activate(N))
[28] U92(tt,L,N) -> U93(isNat(activate(N)),activate(L),activate(N))
[29] U93(tt,L,N) -> U94(isNatKind(activate(N)),activate(L))
[30] U94(tt,L) -> s(length(activate(L)))
[31] isNat(n__0) -> tt
[32] isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)),activate(V1))
[33] isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1))
[34] isNatIList(V) -> U31(isNatIListKind(activate(V)),activate(V))
[35] isNatIList(n__zeros) -> tt
[36] isNatIList(n__cons(V1,V2)) ->
 U41(isNatKind(activate(V1)),activate(V1),activate(V2))
[37] isNatIListKind(n__nil) -> tt
[38] isNatIListKind(n__zeros) -> tt
[39] isNatIListKind(n__cons(V1,V2)) ->
 U51(isNatKind(activate(V1)),activate(V2))
[40] isNatKind(n__0) -> tt
[41] isNatKind(n__length(V1)) -> U61(isNatIListKind(activate(V1)))
[42] isNatKind(n__s(V1)) -> U71(isNatKind(activate(V1)))
[43] isNatList(n__nil) -> tt
[44] isNatList(n__cons(V1,V2)) ->
 U81(isNatKind(activate(V1)),activate(V1),activate(V2))
[45] length(nil) -> 0
[46] length(cons(N,L)) -> U91(isNatList(activate(L)),activate(L),N)
[47] zeros -> n__zeros
[48] 0 -> n__0
[49] length(X) -> n__length(X)
[50] s(X) -> n__s(X)
[51] cons(X1,X2) -> n__cons(X1,X2)
[52] nil -> n__nil
[53] activate(n__zeros) -> zeros
[54] activate(n__0) -> 0
[55] activate(n__length(X)) -> length(X)
[56] activate(n__s(X)) -> s(X)
[57] activate(n__cons(X1,X2)) -> cons(X1,X2)
[58] activate(n__nil) -> nil
[59] activate(X) -> X


Sub problem: 
guided: 

DP termination of:
<Marked_zeros , Marked_cons(0,n__zeros)>
<Marked_zeros , Marked_0>
<Marked_U11(tt,V1) , Marked_U12(isNatIListKind(activate(V1)),activate(V1))>
<Marked_U11(tt,V1) , Marked_isNatIListKind(activate(V1))>
<Marked_U11(tt,V1) , Marked_activate(V1)>
<Marked_U11(tt,V1) , Marked_activate(V1)>
<Marked_U12(tt,V1) , Marked_U13(isNatList(activate(V1)))>
<Marked_U12(tt,V1) , Marked_isNatList(activate(V1))>
<Marked_U12(tt,V1) , Marked_activate(V1)>
<Marked_U21(tt,V1) , Marked_U22(isNatKind(activate(V1)),activate(V1))>
<Marked_U21(tt,V1) , Marked_isNatKind(activate(V1))>
<Marked_U21(tt,V1) , Marked_activate(V1)>
<Marked_U21(tt,V1) , Marked_activate(V1)>
<Marked_U22(tt,V1) , Marked_U23(isNat(activate(V1)))>
<Marked_U22(tt,V1) , Marked_isNat(activate(V1))>
<Marked_U22(tt,V1) , Marked_activate(V1)>
<Marked_U31(tt,V) , Marked_U32(isNatIListKind(activate(V)),activate(V))>
<Marked_U31(tt,V) , Marked_isNatIListKind(activate(V))>
<Marked_U31(tt,V) , Marked_activate(V)>
<Marked_U31(tt,V) , Marked_activate(V)>
<Marked_U32(tt,V) , Marked_U33(isNatList(activate(V)))>
<Marked_U32(tt,V) , Marked_isNatList(activate(V))>
<Marked_U32(tt,V) , Marked_activate(V)>
<Marked_U41(tt,V1,V2) , Marked_U42(isNatKind(activate(V1)),activate(V1),
                         activate(V2))>
<Marked_U41(tt,V1,V2) , Marked_isNatKind(activate(V1))>
<Marked_U41(tt,V1,V2) , Marked_activate(V1)>
<Marked_U41(tt,V1,V2) , Marked_activate(V1)>
<Marked_U41(tt,V1,V2) , Marked_activate(V2)>
<Marked_U42(tt,V1,V2) , Marked_U43(isNatIListKind(activate(V2)),activate(V1),
                         activate(V2))>
<Marked_U42(tt,V1,V2) , Marked_isNatIListKind(activate(V2))>
<Marked_U42(tt,V1,V2) , Marked_activate(V2)>
<Marked_U42(tt,V1,V2) , Marked_activate(V1)>
<Marked_U42(tt,V1,V2) , Marked_activate(V2)>
<Marked_U43(tt,V1,V2) , Marked_U44(isNatIListKind(activate(V2)),activate(V1),
                         activate(V2))>
<Marked_U43(tt,V1,V2) , Marked_isNatIListKind(activate(V2))>
<Marked_U43(tt,V1,V2) , Marked_activate(V2)>
<Marked_U43(tt,V1,V2) , Marked_activate(V1)>
<Marked_U43(tt,V1,V2) , Marked_activate(V2)>
<Marked_U44(tt,V1,V2) , Marked_U45(isNat(activate(V1)),activate(V2))>
<Marked_U44(tt,V1,V2) , Marked_isNat(activate(V1))>
<Marked_U44(tt,V1,V2) , Marked_activate(V1)>
<Marked_U44(tt,V1,V2) , Marked_activate(V2)>
<Marked_U45(tt,V2) , Marked_U46(isNatIList(activate(V2)))>
<Marked_U45(tt,V2) , Marked_isNatIList(activate(V2))>
<Marked_U45(tt,V2) , Marked_activate(V2)>
<Marked_U51(tt,V2) , Marked_U52(isNatIListKind(activate(V2)))>
<Marked_U51(tt,V2) , Marked_isNatIListKind(activate(V2))>
<Marked_U51(tt,V2) , Marked_activate(V2)>
<Marked_U81(tt,V1,V2) , Marked_U82(isNatKind(activate(V1)),activate(V1),
                         activate(V2))>
<Marked_U81(tt,V1,V2) , Marked_isNatKind(activate(V1))>
<Marked_U81(tt,V1,V2) , Marked_activate(V1)>
<Marked_U81(tt,V1,V2) , Marked_activate(V1)>
<Marked_U81(tt,V1,V2) , Marked_activate(V2)>
<Marked_U82(tt,V1,V2) , Marked_U83(isNatIListKind(activate(V2)),activate(V1),
                         activate(V2))>
<Marked_U82(tt,V1,V2) , Marked_isNatIListKind(activate(V2))>
<Marked_U82(tt,V1,V2) , Marked_activate(V2)>
<Marked_U82(tt,V1,V2) , Marked_activate(V1)>
<Marked_U82(tt,V1,V2) , Marked_activate(V2)>
<Marked_U83(tt,V1,V2) , Marked_U84(isNatIListKind(activate(V2)),activate(V1),
                         activate(V2))>
<Marked_U83(tt,V1,V2) , Marked_isNatIListKind(activate(V2))>
<Marked_U83(tt,V1,V2) , Marked_activate(V2)>
<Marked_U83(tt,V1,V2) , Marked_activate(V1)>
<Marked_U83(tt,V1,V2) , Marked_activate(V2)>
<Marked_U84(tt,V1,V2) , Marked_U85(isNat(activate(V1)),activate(V2))>
<Marked_U84(tt,V1,V2) , Marked_isNat(activate(V1))>
<Marked_U84(tt,V1,V2) , Marked_activate(V1)>
<Marked_U84(tt,V1,V2) , Marked_activate(V2)>
<Marked_U85(tt,V2) , Marked_U86(isNatList(activate(V2)))>
<Marked_U85(tt,V2) , Marked_isNatList(activate(V2))>
<Marked_U85(tt,V2) , Marked_activate(V2)>
<Marked_U91(tt,L,N) , Marked_U92(isNatIListKind(activate(L)),activate(L),
                       activate(N))>
<Marked_U91(tt,L,N) , Marked_isNatIListKind(activate(L))>
<Marked_U91(tt,L,N) , Marked_activate(L)>
<Marked_U91(tt,L,N) , Marked_activate(L)>
<Marked_U91(tt,L,N) , Marked_activate(N)>
<Marked_U92(tt,L,N) , Marked_U93(isNat(activate(N)),activate(L),activate(N))>
<Marked_U92(tt,L,N) , Marked_isNat(activate(N))>
<Marked_U92(tt,L,N) , Marked_activate(N)>
<Marked_U92(tt,L,N) , Marked_activate(L)>
<Marked_U92(tt,L,N) , Marked_activate(N)>
<Marked_U93(tt,L,N) , Marked_U94(isNatKind(activate(N)),activate(L))>
<Marked_U93(tt,L,N) , Marked_isNatKind(activate(N))>
<Marked_U93(tt,L,N) , Marked_activate(N)>
<Marked_U93(tt,L,N) , Marked_activate(L)>
<Marked_U94(tt,L) , Marked_s(length(activate(L)))>
<Marked_U94(tt,L) , Marked_length(activate(L))>
<Marked_U94(tt,L) , Marked_activate(L)>
<Marked_isNat(n__length(V1)) , Marked_U11(isNatIListKind(activate(V1)),
                                activate(V1))>
<Marked_isNat(n__length(V1)) , Marked_isNatIListKind(activate(V1))>
<Marked_isNat(n__length(V1)) , Marked_activate(V1)>
<Marked_isNat(n__length(V1)) , Marked_activate(V1)>
<Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),activate(V1))>
<Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))>
<Marked_isNat(n__s(V1)) , Marked_activate(V1)>
<Marked_isNat(n__s(V1)) , Marked_activate(V1)>
<Marked_isNatIList(V) , Marked_U31(isNatIListKind(activate(V)),activate(V))>
<Marked_isNatIList(V) , Marked_isNatIListKind(activate(V))>
<Marked_isNatIList(V) , Marked_activate(V)>
<Marked_isNatIList(V) , Marked_activate(V)>
<Marked_isNatIList(n__cons(V1,V2)) , Marked_U41(isNatKind(activate(V1)),
                                      activate(V1),activate(V2))>
<Marked_isNatIList(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))>
<Marked_isNatIList(n__cons(V1,V2)) , Marked_activate(V1)>
<Marked_isNatIList(n__cons(V1,V2)) , Marked_activate(V1)>
<Marked_isNatIList(n__cons(V1,V2)) , Marked_activate(V2)>
<Marked_isNatIListKind(n__cons(V1,V2)) , Marked_U51(isNatKind(activate(V1)),
                                          activate(V2))>
<Marked_isNatIListKind(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))>
<Marked_isNatIListKind(n__cons(V1,V2)) , Marked_activate(V1)>
<Marked_isNatIListKind(n__cons(V1,V2)) , Marked_activate(V2)>
<Marked_isNatKind(n__length(V1)) , Marked_U61(isNatIListKind(activate(V1)))>
<Marked_isNatKind(n__length(V1)) , Marked_isNatIListKind(activate(V1))>
<Marked_isNatKind(n__length(V1)) , Marked_activate(V1)>
<Marked_isNatKind(n__s(V1)) , Marked_U71(isNatKind(activate(V1)))>
<Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))>
<Marked_isNatKind(n__s(V1)) , Marked_activate(V1)>
<Marked_isNatList(n__cons(V1,V2)) , Marked_U81(isNatKind(activate(V1)),
                                     activate(V1),activate(V2))>
<Marked_isNatList(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))>
<Marked_isNatList(n__cons(V1,V2)) , Marked_activate(V1)>
<Marked_isNatList(n__cons(V1,V2)) , Marked_activate(V1)>
<Marked_isNatList(n__cons(V1,V2)) , Marked_activate(V2)>
<Marked_length(nil) , Marked_0>
<Marked_length(cons(N,L)) , Marked_U91(isNatList(activate(L)),activate(L),N)>
<Marked_length(cons(N,L)) , Marked_isNatList(activate(L))>
<Marked_length(cons(N,L)) , Marked_activate(L)>
<Marked_length(cons(N,L)) , Marked_activate(L)>
<Marked_activate(n__zeros) , Marked_zeros>
<Marked_activate(n__0) , Marked_0>
<Marked_activate(n__length(X)) , Marked_length(X)>
<Marked_activate(n__s(X)) , Marked_s(X)>
<Marked_activate(n__cons(X1,X2)) , Marked_cons(X1,X2)>
<Marked_activate(n__nil) , Marked_nil>
 
END GUIDED
APPLY CRITERIA (Graph splitting)
Found 2 components:

{  <Marked_isNatIList(n__cons(V1,V2)) , Marked_U41(isNatKind(activate(V1)),
                                         activate(V1),activate(V2))> 
      --> <Marked_U41(tt,V1,V2) , Marked_U42(isNatKind(activate(V1)),
                                   activate(V1),activate(V2))>
  <Marked_U45(tt,V2) , Marked_isNatIList(activate(V2))> 
     --> <Marked_isNatIList(n__cons(V1,V2)) , Marked_U41(isNatKind(activate(V1)),
                                               activate(V1),activate(V2))>
  <Marked_U44(tt,V1,V2) , Marked_U45(isNat(activate(V1)),activate(V2))> 
     --> <Marked_U45(tt,V2) , Marked_isNatIList(activate(V2))>
  <Marked_U43(tt,V1,V2) , Marked_U44(isNatIListKind(activate(V2)),activate(V1),
                           activate(V2))> 
     --> <Marked_U44(tt,V1,V2) , Marked_U45(isNat(activate(V1)),activate(V2))>
  <Marked_U42(tt,V1,V2) , Marked_U43(isNatIListKind(activate(V2)),activate(V1),
                           activate(V2))> 
     --> <Marked_U43(tt,V1,V2) , Marked_U44(isNatIListKind(activate(V2)),
                                  activate(V1),activate(V2))>
  <Marked_U41(tt,V1,V2) , Marked_U42(isNatKind(activate(V1)),activate(V1),
                           activate(V2))> 
     --> <Marked_U42(tt,V1,V2) , Marked_U43(isNatIListKind(activate(V2)),
                                  activate(V1),activate(V2))>
}

{  <Marked_activate(n__length(X)) , Marked_length(X)> 
      --> <Marked_length(cons(N,L)) , Marked_activate(L)>
  <Marked_activate(n__length(X)) , Marked_length(X)> 
     --> <Marked_length(cons(N,L)) , Marked_activate(L)>
  <Marked_activate(n__length(X)) , Marked_length(X)> 
     --> <Marked_length(cons(N,L)) , Marked_isNatList(activate(L))>
  <Marked_activate(n__length(X)) , Marked_length(X)> 
     --> <Marked_length(cons(N,L)) , Marked_U91(isNatList(activate(L)),
                                      activate(L),N)>
  <Marked_length(cons(N,L)) , Marked_activate(L)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_length(cons(N,L)) , Marked_activate(L)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_length(cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(V1,V2)) , Marked_activate(V2)>
  <Marked_length(cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(V1,V2)) , Marked_activate(V1)>
  <Marked_length(cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(V1,V2)) , Marked_activate(V1)>
  <Marked_length(cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_length(cons(N,L)) , Marked_isNatList(activate(L))> 
     --> <Marked_isNatList(n__cons(V1,V2)) , Marked_U81(isNatKind(activate(V1)),
                                              activate(V1),activate(V2))>
  <Marked_length(cons(N,L)) , Marked_U91(isNatList(activate(L)),activate(L),N)> 
     --> <Marked_U91(tt,L,N) , Marked_activate(N)>
  <Marked_length(cons(N,L)) , Marked_U91(isNatList(activate(L)),activate(L),N)> 
     --> <Marked_U91(tt,L,N) , Marked_activate(L)>
  <Marked_length(cons(N,L)) , Marked_U91(isNatList(activate(L)),activate(L),N)> 
     --> <Marked_U91(tt,L,N) , Marked_activate(L)>
  <Marked_length(cons(N,L)) , Marked_U91(isNatList(activate(L)),activate(L),N)> 
     --> <Marked_U91(tt,L,N) , Marked_isNatIListKind(activate(L))>
  <Marked_length(cons(N,L)) , Marked_U91(isNatList(activate(L)),activate(L),N)> 
     --> <Marked_U91(tt,L,N) , Marked_U92(isNatIListKind(activate(L)),
                                activate(L),activate(N))>
  <Marked_isNatList(n__cons(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNatList(n__cons(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNatList(n__cons(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNatList(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)>
  <Marked_isNatList(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_isNatList(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__length(V1)) , Marked_activate(V1)>
  <Marked_isNatList(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__length(V1)) , Marked_isNatIListKind(activate(V1))>
  <Marked_isNatList(n__cons(V1,V2)) , Marked_U81(isNatKind(activate(V1)),
                                       activate(V1),activate(V2))> 
     --> <Marked_U81(tt,V1,V2) , Marked_activate(V2)>
  <Marked_isNatList(n__cons(V1,V2)) , Marked_U81(isNatKind(activate(V1)),
                                       activate(V1),activate(V2))> 
     --> <Marked_U81(tt,V1,V2) , Marked_activate(V1)>
  <Marked_isNatList(n__cons(V1,V2)) , Marked_U81(isNatKind(activate(V1)),
                                       activate(V1),activate(V2))> 
     --> <Marked_U81(tt,V1,V2) , Marked_activate(V1)>
  <Marked_isNatList(n__cons(V1,V2)) , Marked_U81(isNatKind(activate(V1)),
                                       activate(V1),activate(V2))> 
     --> <Marked_U81(tt,V1,V2) , Marked_isNatKind(activate(V1))>
  <Marked_isNatList(n__cons(V1,V2)) , Marked_U81(isNatKind(activate(V1)),
                                       activate(V1),activate(V2))> 
     --> <Marked_U81(tt,V1,V2) , Marked_U82(isNatKind(activate(V1)),
                                  activate(V1),activate(V2))>
  <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)>
  <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__length(V1)) , Marked_activate(V1)>
  <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__length(V1)) , Marked_isNatIListKind(activate(V1))>
  <Marked_isNatKind(n__length(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNatKind(n__length(V1)) , Marked_isNatIListKind(activate(V1))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_activate(V2)>
  <Marked_isNatKind(n__length(V1)) , Marked_isNatIListKind(activate(V1))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_activate(V1)>
  <Marked_isNatKind(n__length(V1)) , Marked_isNatIListKind(activate(V1))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_isNatKind(n__length(V1)) , Marked_isNatIListKind(activate(V1))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_U51(isNatKind(
                                                              activate(
                                                               V1)),
                                                   activate(V2))>
  <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_activate(V2)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)>
  <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__length(V1)) , Marked_activate(V1)>
  <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__length(V1)) , Marked_isNatIListKind(activate(V1))>
  <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_U51(isNatKind(activate(V1)),
                                            activate(V2))> 
     --> <Marked_U51(tt,V2) , Marked_activate(V2)>
  <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_U51(isNatKind(activate(V1)),
                                            activate(V2))> 
     --> <Marked_U51(tt,V2) , Marked_isNatIListKind(activate(V2))>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNat(n__s(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)>
  <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__length(V1)) , Marked_activate(V1)>
  <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__length(V1)) , Marked_isNatIListKind(activate(V1))>
  <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),activate(V1))> 
     --> <Marked_U21(tt,V1) , Marked_activate(V1)>
  <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),activate(V1))> 
     --> <Marked_U21(tt,V1) , Marked_activate(V1)>
  <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),activate(V1))> 
     --> <Marked_U21(tt,V1) , Marked_isNatKind(activate(V1))>
  <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),activate(V1))> 
     --> <Marked_U21(tt,V1) , Marked_U22(isNatKind(activate(V1)),activate(V1))>
  <Marked_isNat(n__length(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNat(n__length(V1)) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_isNat(n__length(V1)) , Marked_isNatIListKind(activate(V1))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_activate(V2)>
  <Marked_isNat(n__length(V1)) , Marked_isNatIListKind(activate(V1))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_activate(V1)>
  <Marked_isNat(n__length(V1)) , Marked_isNatIListKind(activate(V1))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_isNat(n__length(V1)) , Marked_isNatIListKind(activate(V1))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_U51(isNatKind(
                                                              activate(
                                                               V1)),
                                                   activate(V2))>
  <Marked_isNat(n__length(V1)) , Marked_U11(isNatIListKind(activate(V1)),
                                  activate(V1))> 
     --> <Marked_U11(tt,V1) , Marked_activate(V1)>
  <Marked_isNat(n__length(V1)) , Marked_U11(isNatIListKind(activate(V1)),
                                  activate(V1))> 
     --> <Marked_U11(tt,V1) , Marked_activate(V1)>
  <Marked_isNat(n__length(V1)) , Marked_U11(isNatIListKind(activate(V1)),
                                  activate(V1))> 
     --> <Marked_U11(tt,V1) , Marked_isNatIListKind(activate(V1))>
  <Marked_isNat(n__length(V1)) , Marked_U11(isNatIListKind(activate(V1)),
                                  activate(V1))> 
     --> <Marked_U11(tt,V1) , Marked_U12(isNatIListKind(activate(V1)),
                               activate(V1))>
  <Marked_U94(tt,L) , Marked_activate(L)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U94(tt,L) , Marked_length(activate(L))> 
     --> <Marked_length(cons(N,L)) , Marked_activate(L)>
  <Marked_U94(tt,L) , Marked_length(activate(L))> 
     --> <Marked_length(cons(N,L)) , Marked_activate(L)>
  <Marked_U94(tt,L) , Marked_length(activate(L))> 
     --> <Marked_length(cons(N,L)) , Marked_isNatList(activate(L))>
  <Marked_U94(tt,L) , Marked_length(activate(L))> 
     --> <Marked_length(cons(N,L)) , Marked_U91(isNatList(activate(L)),
                                      activate(L),N)>
  <Marked_U93(tt,L,N) , Marked_activate(L)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U93(tt,L,N) , Marked_activate(N)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U93(tt,L,N) , Marked_isNatKind(activate(N))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)>
  <Marked_U93(tt,L,N) , Marked_isNatKind(activate(N))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_U93(tt,L,N) , Marked_isNatKind(activate(N))> 
     --> <Marked_isNatKind(n__length(V1)) , Marked_activate(V1)>
  <Marked_U93(tt,L,N) , Marked_isNatKind(activate(N))> 
     --> <Marked_isNatKind(n__length(V1)) , Marked_isNatIListKind(activate(V1))>
  <Marked_U93(tt,L,N) , Marked_U94(isNatKind(activate(N)),activate(L))> 
     --> <Marked_U94(tt,L) , Marked_activate(L)>
  <Marked_U93(tt,L,N) , Marked_U94(isNatKind(activate(N)),activate(L))> 
     --> <Marked_U94(tt,L) , Marked_length(activate(L))>
  <Marked_U92(tt,L,N) , Marked_activate(N)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U92(tt,L,N) , Marked_activate(L)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U92(tt,L,N) , Marked_activate(N)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U92(tt,L,N) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_U92(tt,L,N) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_U92(tt,L,N) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_U92(tt,L,N) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),
                                    activate(V1))>
  <Marked_U92(tt,L,N) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__length(V1)) , Marked_activate(V1)>
  <Marked_U92(tt,L,N) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__length(V1)) , Marked_activate(V1)>
  <Marked_U92(tt,L,N) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__length(V1)) , Marked_isNatIListKind(activate(V1))>
  <Marked_U92(tt,L,N) , Marked_isNat(activate(N))> 
     --> <Marked_isNat(n__length(V1)) , Marked_U11(isNatIListKind(activate(V1)),
                                         activate(V1))>
  <Marked_U92(tt,L,N) , Marked_U93(isNat(activate(N)),activate(L),activate(N))> 
     --> <Marked_U93(tt,L,N) , Marked_activate(L)>
  <Marked_U92(tt,L,N) , Marked_U93(isNat(activate(N)),activate(L),activate(N))> 
     --> <Marked_U93(tt,L,N) , Marked_activate(N)>
  <Marked_U92(tt,L,N) , Marked_U93(isNat(activate(N)),activate(L),activate(N))> 
     --> <Marked_U93(tt,L,N) , Marked_isNatKind(activate(N))>
  <Marked_U92(tt,L,N) , Marked_U93(isNat(activate(N)),activate(L),activate(N))> 
     --> <Marked_U93(tt,L,N) , Marked_U94(isNatKind(activate(N)),activate(L))>
  <Marked_U91(tt,L,N) , Marked_activate(N)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U91(tt,L,N) , Marked_activate(L)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U91(tt,L,N) , Marked_activate(L)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U91(tt,L,N) , Marked_isNatIListKind(activate(L))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_activate(V2)>
  <Marked_U91(tt,L,N) , Marked_isNatIListKind(activate(L))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_activate(V1)>
  <Marked_U91(tt,L,N) , Marked_isNatIListKind(activate(L))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_U91(tt,L,N) , Marked_isNatIListKind(activate(L))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_U51(isNatKind(
                                                              activate(
                                                               V1)),
                                                   activate(V2))>
  <Marked_U91(tt,L,N) , Marked_U92(isNatIListKind(activate(L)),activate(L),
                         activate(N))> 
     --> <Marked_U92(tt,L,N) , Marked_activate(N)>
  <Marked_U91(tt,L,N) , Marked_U92(isNatIListKind(activate(L)),activate(L),
                         activate(N))> 
     --> <Marked_U92(tt,L,N) , Marked_activate(L)>
  <Marked_U91(tt,L,N) , Marked_U92(isNatIListKind(activate(L)),activate(L),
                         activate(N))> 
     --> <Marked_U92(tt,L,N) , Marked_activate(N)>
  <Marked_U91(tt,L,N) , Marked_U92(isNatIListKind(activate(L)),activate(L),
                         activate(N))> 
     --> <Marked_U92(tt,L,N) , Marked_isNat(activate(N))>
  <Marked_U91(tt,L,N) , Marked_U92(isNatIListKind(activate(L)),activate(L),
                         activate(N))> 
     --> <Marked_U92(tt,L,N) , Marked_U93(isNat(activate(N)),activate(L),
                                activate(N))>
  <Marked_U85(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U85(tt,V2) , Marked_isNatList(activate(V2))> 
     --> <Marked_isNatList(n__cons(V1,V2)) , Marked_activate(V2)>
  <Marked_U85(tt,V2) , Marked_isNatList(activate(V2))> 
     --> <Marked_isNatList(n__cons(V1,V2)) , Marked_activate(V1)>
  <Marked_U85(tt,V2) , Marked_isNatList(activate(V2))> 
     --> <Marked_isNatList(n__cons(V1,V2)) , Marked_activate(V1)>
  <Marked_U85(tt,V2) , Marked_isNatList(activate(V2))> 
     --> <Marked_isNatList(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_U85(tt,V2) , Marked_isNatList(activate(V2))> 
     --> <Marked_isNatList(n__cons(V1,V2)) , Marked_U81(isNatKind(activate(V1)),
                                              activate(V1),activate(V2))>
  <Marked_U84(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U84(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U84(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_U84(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_U84(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_U84(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),
                                    activate(V1))>
  <Marked_U84(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__length(V1)) , Marked_activate(V1)>
  <Marked_U84(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__length(V1)) , Marked_activate(V1)>
  <Marked_U84(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__length(V1)) , Marked_isNatIListKind(activate(V1))>
  <Marked_U84(tt,V1,V2) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__length(V1)) , Marked_U11(isNatIListKind(activate(V1)),
                                         activate(V1))>
  <Marked_U84(tt,V1,V2) , Marked_U85(isNat(activate(V1)),activate(V2))> 
     --> <Marked_U85(tt,V2) , Marked_activate(V2)>
  <Marked_U84(tt,V1,V2) , Marked_U85(isNat(activate(V1)),activate(V2))> 
     --> <Marked_U85(tt,V2) , Marked_isNatList(activate(V2))>
  <Marked_U83(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U83(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U83(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U83(tt,V1,V2) , Marked_isNatIListKind(activate(V2))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_activate(V2)>
  <Marked_U83(tt,V1,V2) , Marked_isNatIListKind(activate(V2))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_activate(V1)>
  <Marked_U83(tt,V1,V2) , Marked_isNatIListKind(activate(V2))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_U83(tt,V1,V2) , Marked_isNatIListKind(activate(V2))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_U51(isNatKind(
                                                              activate(
                                                               V1)),
                                                   activate(V2))>
  <Marked_U83(tt,V1,V2) , Marked_U84(isNatIListKind(activate(V2)),activate(V1),
                           activate(V2))> 
     --> <Marked_U84(tt,V1,V2) , Marked_activate(V2)>
  <Marked_U83(tt,V1,V2) , Marked_U84(isNatIListKind(activate(V2)),activate(V1),
                           activate(V2))> 
     --> <Marked_U84(tt,V1,V2) , Marked_activate(V1)>
  <Marked_U83(tt,V1,V2) , Marked_U84(isNatIListKind(activate(V2)),activate(V1),
                           activate(V2))> 
     --> <Marked_U84(tt,V1,V2) , Marked_isNat(activate(V1))>
  <Marked_U83(tt,V1,V2) , Marked_U84(isNatIListKind(activate(V2)),activate(V1),
                           activate(V2))> 
     --> <Marked_U84(tt,V1,V2) , Marked_U85(isNat(activate(V1)),activate(V2))>
  <Marked_U82(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U82(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U82(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U82(tt,V1,V2) , Marked_isNatIListKind(activate(V2))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_activate(V2)>
  <Marked_U82(tt,V1,V2) , Marked_isNatIListKind(activate(V2))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_activate(V1)>
  <Marked_U82(tt,V1,V2) , Marked_isNatIListKind(activate(V2))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_U82(tt,V1,V2) , Marked_isNatIListKind(activate(V2))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_U51(isNatKind(
                                                              activate(
                                                               V1)),
                                                   activate(V2))>
  <Marked_U82(tt,V1,V2) , Marked_U83(isNatIListKind(activate(V2)),activate(V1),
                           activate(V2))> 
     --> <Marked_U83(tt,V1,V2) , Marked_activate(V2)>
  <Marked_U82(tt,V1,V2) , Marked_U83(isNatIListKind(activate(V2)),activate(V1),
                           activate(V2))> 
     --> <Marked_U83(tt,V1,V2) , Marked_activate(V1)>
  <Marked_U82(tt,V1,V2) , Marked_U83(isNatIListKind(activate(V2)),activate(V1),
                           activate(V2))> 
     --> <Marked_U83(tt,V1,V2) , Marked_activate(V2)>
  <Marked_U82(tt,V1,V2) , Marked_U83(isNatIListKind(activate(V2)),activate(V1),
                           activate(V2))> 
     --> <Marked_U83(tt,V1,V2) , Marked_isNatIListKind(activate(V2))>
  <Marked_U82(tt,V1,V2) , Marked_U83(isNatIListKind(activate(V2)),activate(V1),
                           activate(V2))> 
     --> <Marked_U83(tt,V1,V2) , Marked_U84(isNatIListKind(activate(V2)),
                                  activate(V1),activate(V2))>
  <Marked_U81(tt,V1,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U81(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U81(tt,V1,V2) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U81(tt,V1,V2) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)>
  <Marked_U81(tt,V1,V2) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_U81(tt,V1,V2) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__length(V1)) , Marked_activate(V1)>
  <Marked_U81(tt,V1,V2) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__length(V1)) , Marked_isNatIListKind(activate(V1))>
  <Marked_U81(tt,V1,V2) , Marked_U82(isNatKind(activate(V1)),activate(V1),
                           activate(V2))> 
     --> <Marked_U82(tt,V1,V2) , Marked_activate(V2)>
  <Marked_U81(tt,V1,V2) , Marked_U82(isNatKind(activate(V1)),activate(V1),
                           activate(V2))> 
     --> <Marked_U82(tt,V1,V2) , Marked_activate(V1)>
  <Marked_U81(tt,V1,V2) , Marked_U82(isNatKind(activate(V1)),activate(V1),
                           activate(V2))> 
     --> <Marked_U82(tt,V1,V2) , Marked_activate(V2)>
  <Marked_U81(tt,V1,V2) , Marked_U82(isNatKind(activate(V1)),activate(V1),
                           activate(V2))> 
     --> <Marked_U82(tt,V1,V2) , Marked_isNatIListKind(activate(V2))>
  <Marked_U81(tt,V1,V2) , Marked_U82(isNatKind(activate(V1)),activate(V1),
                           activate(V2))> 
     --> <Marked_U82(tt,V1,V2) , Marked_U83(isNatIListKind(activate(V2)),
                                  activate(V1),activate(V2))>
  <Marked_U51(tt,V2) , Marked_activate(V2)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U51(tt,V2) , Marked_isNatIListKind(activate(V2))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_activate(V2)>
  <Marked_U51(tt,V2) , Marked_isNatIListKind(activate(V2))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_activate(V1)>
  <Marked_U51(tt,V2) , Marked_isNatIListKind(activate(V2))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_U51(tt,V2) , Marked_isNatIListKind(activate(V2))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_U51(isNatKind(
                                                              activate(
                                                               V1)),
                                                   activate(V2))>
  <Marked_U22(tt,V1) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U22(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_U22(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_activate(V1)>
  <Marked_U22(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_U22(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__s(V1)) , Marked_U21(isNatKind(activate(V1)),
                                    activate(V1))>
  <Marked_U22(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__length(V1)) , Marked_activate(V1)>
  <Marked_U22(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__length(V1)) , Marked_activate(V1)>
  <Marked_U22(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__length(V1)) , Marked_isNatIListKind(activate(V1))>
  <Marked_U22(tt,V1) , Marked_isNat(activate(V1))> 
     --> <Marked_isNat(n__length(V1)) , Marked_U11(isNatIListKind(activate(V1)),
                                         activate(V1))>
  <Marked_U21(tt,V1) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U21(tt,V1) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U21(tt,V1) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_activate(V1)>
  <Marked_U21(tt,V1) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__s(V1)) , Marked_isNatKind(activate(V1))>
  <Marked_U21(tt,V1) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__length(V1)) , Marked_activate(V1)>
  <Marked_U21(tt,V1) , Marked_isNatKind(activate(V1))> 
     --> <Marked_isNatKind(n__length(V1)) , Marked_isNatIListKind(activate(V1))>
  <Marked_U21(tt,V1) , Marked_U22(isNatKind(activate(V1)),activate(V1))> 
     --> <Marked_U22(tt,V1) , Marked_activate(V1)>
  <Marked_U21(tt,V1) , Marked_U22(isNatKind(activate(V1)),activate(V1))> 
     --> <Marked_U22(tt,V1) , Marked_isNat(activate(V1))>
  <Marked_U12(tt,V1) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U12(tt,V1) , Marked_isNatList(activate(V1))> 
     --> <Marked_isNatList(n__cons(V1,V2)) , Marked_activate(V2)>
  <Marked_U12(tt,V1) , Marked_isNatList(activate(V1))> 
     --> <Marked_isNatList(n__cons(V1,V2)) , Marked_activate(V1)>
  <Marked_U12(tt,V1) , Marked_isNatList(activate(V1))> 
     --> <Marked_isNatList(n__cons(V1,V2)) , Marked_activate(V1)>
  <Marked_U12(tt,V1) , Marked_isNatList(activate(V1))> 
     --> <Marked_isNatList(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_U12(tt,V1) , Marked_isNatList(activate(V1))> 
     --> <Marked_isNatList(n__cons(V1,V2)) , Marked_U81(isNatKind(activate(V1)),
                                              activate(V1),activate(V2))>
  <Marked_U11(tt,V1) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U11(tt,V1) , Marked_activate(V1)> 
     --> <Marked_activate(n__length(X)) , Marked_length(X)>
  <Marked_U11(tt,V1) , Marked_isNatIListKind(activate(V1))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_activate(V2)>
  <Marked_U11(tt,V1) , Marked_isNatIListKind(activate(V1))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_activate(V1)>
  <Marked_U11(tt,V1) , Marked_isNatIListKind(activate(V1))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_isNatKind(activate(V1))>
  <Marked_U11(tt,V1) , Marked_isNatIListKind(activate(V1))> 
     --> <Marked_isNatIListKind(n__cons(V1,V2)) , Marked_U51(isNatKind(
                                                              activate(
                                                               V1)),
                                                   activate(V2))>
  <Marked_U11(tt,V1) , Marked_U12(isNatIListKind(activate(V1)),activate(V1))> 
     --> <Marked_U12(tt,V1) , Marked_activate(V1)>
  <Marked_U11(tt,V1) , Marked_U12(isNatIListKind(activate(V1)),activate(V1))> 
     --> <Marked_U12(tt,V1) , Marked_isNatList(activate(V1))>
}
APPLY CRITERIA (Subterm criterion)
APPLY CRITERIA (Choosing graph)
Trying to solve the following constraints:
{
  cons(X1,X2) >= n__cons(X1,X2) ;
  0 >= n__0 ;
  zeros >= cons(0,n__zeros) ;
  zeros >= n__zeros ;
  U12(tt,V1) >= U13(isNatList(activate(V1))) ;
  isNatIListKind(n__zeros) >= tt ;
  isNatIListKind(n__cons(V1,V2)) >= U51(isNatKind(activate(V1)),activate(V2)) ;
  isNatIListKind(n__nil) >= tt ;
  activate(n__zeros) >= zeros ;
  activate(n__0) >= 0 ;
  activate(n__length(X)) >= length(X) ;
  activate(n__s(X)) >= s(X) ;
  activate(n__cons(X1,X2)) >= cons(X1,X2) ;
  activate(n__nil) >= nil ;
  activate(X) >= X ;
  U11(tt,V1) >= U12(isNatIListKind(activate(V1)),activate(V1)) ;
  U13(tt) >= tt ;
  isNatList(n__cons(V1,V2)) >= U81(isNatKind(activate(V1)),activate(V1),
                                activate(V2)) ;
  isNatList(n__nil) >= tt ;
  U22(tt,V1) >= U23(isNat(activate(V1))) ;
  isNatKind(n__0) >= tt ;
  isNatKind(n__length(V1)) >= U61(isNatIListKind(activate(V1))) ;
  isNatKind(n__s(V1)) >= U71(isNatKind(activate(V1))) ;
  U21(tt,V1) >= U22(isNatKind(activate(V1)),activate(V1)) ;
  U23(tt) >= tt ;
  isNat(n__0) >= tt ;
  isNat(n__length(V1)) >= U11(isNatIListKind(activate(V1)),activate(V1)) ;
  isNat(n__s(V1)) >= U21(isNatKind(activate(V1)),activate(V1)) ;
  U32(tt,V) >= U33(isNatList(activate(V))) ;
  U31(tt,V) >= U32(isNatIListKind(activate(V)),activate(V)) ;
  U33(tt) >= tt ;
  U42(tt,V1,V2) >= U43(isNatIListKind(activate(V2)),activate(V1),activate(V2)) ;
  U41(tt,V1,V2) >= U42(isNatKind(activate(V1)),activate(V1),activate(V2)) ;
  U43(tt,V1,V2) >= U44(isNatIListKind(activate(V2)),activate(V1),activate(V2)) ;
  U44(tt,V1,V2) >= U45(isNat(activate(V1)),activate(V2)) ;
  U45(tt,V2) >= U46(isNatIList(activate(V2))) ;
  U46(tt) >= tt ;
  isNatIList(n__zeros) >= tt ;
  isNatIList(n__cons(V1,V2)) >= U41(isNatKind(activate(V1)),activate(V1),
                                 activate(V2)) ;
  isNatIList(V) >= U31(isNatIListKind(activate(V)),activate(V)) ;
  U52(tt) >= tt ;
  U51(tt,V2) >= U52(isNatIListKind(activate(V2))) ;
  U61(tt) >= tt ;
  U71(tt) >= tt ;
  U82(tt,V1,V2) >= U83(isNatIListKind(activate(V2)),activate(V1),activate(V2)) ;
  U81(tt,V1,V2) >= U82(isNatKind(activate(V1)),activate(V1),activate(V2)) ;
  U83(tt,V1,V2) >= U84(isNatIListKind(activate(V2)),activate(V1),activate(V2)) ;
  U84(tt,V1,V2) >= U85(isNat(activate(V1)),activate(V2)) ;
  U85(tt,V2) >= U86(isNatList(activate(V2))) ;
  U86(tt) >= tt ;
  U92(tt,L,N) >= U93(isNat(activate(N)),activate(L),activate(N)) ;
  U91(tt,L,N) >= U92(isNatIListKind(activate(L)),activate(L),activate(N)) ;
  U93(tt,L,N) >= U94(isNatKind(activate(N)),activate(L)) ;
  U94(tt,L) >= s(length(activate(L))) ;
  s(X) >= n__s(X) ;
  length(cons(N,L)) >= U91(isNatList(activate(L)),activate(L),N) ;
  length(nil) >= 0 ;
  length(X) >= n__length(X) ;
  nil >= n__nil ;
  Marked_isNatIList(n__cons(V1,V2)) >= Marked_U41(isNatKind(activate(V1)),
                                        activate(V1),activate(V2)) ;
  Marked_U41(tt,V1,V2) >= Marked_U42(isNatKind(activate(V1)),activate(V1),
                           activate(V2)) ;
  Marked_U45(tt,V2) >= Marked_isNatIList(activate(V2)) ;
  Marked_U44(tt,V1,V2) >= Marked_U45(isNat(activate(V1)),activate(V2)) ;
  Marked_U43(tt,V1,V2) >= Marked_U44(isNatIListKind(activate(V2)),activate(V1),
                           activate(V2)) ;
  Marked_U42(tt,V1,V2) >= Marked_U43(isNatIListKind(activate(V2)),activate(V1),
                           activate(V2)) ;
 }
 + Disjunctions:{ 
{
  Marked_isNatIList(n__cons(V1,V2)) > Marked_U41(isNatKind(activate(V1)),
                                       activate(V1),activate(V2)) ;
 }
{
  Marked_U41(tt,V1,V2) > Marked_U42(isNatKind(activate(V1)),activate(V1),
                          activate(V2)) ;
 }
{
  Marked_U45(tt,V2) > Marked_isNatIList(activate(V2)) ;
 }
{
  Marked_U44(tt,V1,V2) > Marked_U45(isNat(activate(V1)),activate(V2)) ;
 }
{
  Marked_U43(tt,V1,V2) > Marked_U44(isNatIListKind(activate(V2)),activate(V1),
                          activate(V2)) ;
 }
{
  Marked_U42(tt,V1,V2) > Marked_U43(isNatIListKind(activate(V2)),activate(V1),
                          activate(V2)) ;
 }
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat timeout reached
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (Simple graph)
Found the following constraints:
{
  cons(X1,X2) >= n__cons(X1,X2) ;
  0 >= n__0 ;
  zeros >= cons(0,n__zeros) ;
  zeros >= n__zeros ;
  U12(tt,V1) >= U13(isNatList(activate(V1))) ;
  isNatIListKind(n__zeros) >= tt ;
  isNatIListKind(n__cons(V1,V2)) >= U51(isNatKind(activate(V1)),activate(V2)) ;
  isNatIListKind(n__nil) >= tt ;
  activate(n__zeros) >= zeros ;
  activate(n__0) >= 0 ;
  activate(n__length(X)) >= length(X) ;
  activate(n__s(X)) >= s(X) ;
  activate(n__cons(X1,X2)) >= cons(X1,X2) ;
  activate(n__nil) >= nil ;
  activate(X) >= X ;
  U11(tt,V1) >= U12(isNatIListKind(activate(V1)),activate(V1)) ;
  U13(tt) >= tt ;
  isNatList(n__cons(V1,V2)) >= U81(isNatKind(activate(V1)),activate(V1),
                                activate(V2)) ;
  isNatList(n__nil) >= tt ;
  U22(tt,V1) >= U23(isNat(activate(V1))) ;
  isNatKind(n__0) >= tt ;
  isNatKind(n__length(V1)) >= U61(isNatIListKind(activate(V1))) ;
  isNatKind(n__s(V1)) >= U71(isNatKind(activate(V1))) ;
  U21(tt,V1) >= U22(isNatKind(activate(V1)),activate(V1)) ;
  U23(tt) >= tt ;
  isNat(n__0) >= tt ;
  isNat(n__length(V1)) >= U11(isNatIListKind(activate(V1)),activate(V1)) ;
  isNat(n__s(V1)) >= U21(isNatKind(activate(V1)),activate(V1)) ;
  U32(tt,V) >= U33(isNatList(activate(V))) ;
  U31(tt,V) >= U32(isNatIListKind(activate(V)),activate(V)) ;
  U33(tt) >= tt ;
  U42(tt,V1,V2) >= U43(isNatIListKind(activate(V2)),activate(V1),activate(V2)) ;
  U41(tt,V1,V2) >= U42(isNatKind(activate(V1)),activate(V1),activate(V2)) ;
  U43(tt,V1,V2) >= U44(isNatIListKind(activate(V2)),activate(V1),activate(V2)) ;
  U44(tt,V1,V2) >= U45(isNat(activate(V1)),activate(V2)) ;
  U45(tt,V2) >= U46(isNatIList(activate(V2))) ;
  U46(tt) >= tt ;
  isNatIList(n__zeros) >= tt ;
  isNatIList(n__cons(V1,V2)) >= U41(isNatKind(activate(V1)),activate(V1),
                                 activate(V2)) ;
  isNatIList(V) >= U31(isNatIListKind(activate(V)),activate(V)) ;
  U52(tt) >= tt ;
  U51(tt,V2) >= U52(isNatIListKind(activate(V2))) ;
  U61(tt) >= tt ;
  U71(tt) >= tt ;
  U82(tt,V1,V2) >= U83(isNatIListKind(activate(V2)),activate(V1),activate(V2)) ;
  U81(tt,V1,V2) >= U82(isNatKind(activate(V1)),activate(V1),activate(V2)) ;
  U83(tt,V1,V2) >= U84(isNatIListKind(activate(V2)),activate(V1),activate(V2)) ;
  U84(tt,V1,V2) >= U85(isNat(activate(V1)),activate(V2)) ;
  U85(tt,V2) >= U86(isNatList(activate(V2))) ;
  U86(tt) >= tt ;
  U92(tt,L,N) >= U93(isNat(activate(N)),activate(L),activate(N)) ;
  U91(tt,L,N) >= U92(isNatIListKind(activate(L)),activate(L),activate(N)) ;
  U93(tt,L,N) >= U94(isNatKind(activate(N)),activate(L)) ;
  U94(tt,L) >= s(length(activate(L))) ;
  s(X) >= n__s(X) ;
  length(cons(N,L)) >= U91(isNatList(activate(L)),activate(L),N) ;
  length(nil) >= 0 ;
  length(X) >= n__length(X) ;
  nil >= n__nil ;
  Marked_isNatIList(n__cons(V1,V2)) >= Marked_U41(isNatKind(activate(V1)),
                                        activate(V1),activate(V2)) ;
  Marked_U41(tt,V1,V2) >= Marked_U42(isNatKind(activate(V1)),activate(V1),
                           activate(V2)) ;
  Marked_U45(tt,V2) > Marked_isNatIList(activate(V2)) ;
  Marked_U44(tt,V1,V2) >= Marked_U45(isNat(activate(V1)),activate(V2)) ;
  Marked_U43(tt,V1,V2) >= Marked_U44(isNatIListKind(activate(V2)),activate(V1),
                           activate(V2)) ;
  Marked_U42(tt,V1,V2) >= Marked_U43(isNatIListKind(activate(V2)),activate(V1),
                           activate(V2)) ;
 }

APPLY CRITERIA (SOLVE_ORD)
Trying to solve the following constraints:
{
  cons(X1,X2) >= n__cons(X1,X2) ;
  0 >= n__0 ;
  zeros >= cons(0,n__zeros) ;
  zeros >= n__zeros ;
  U12(tt,V1) >= U13(isNatList(activate(V1))) ;
  isNatIListKind(n__zeros) >= tt ;
  isNatIListKind(n__cons(V1,V2)) >= U51(isNatKind(activate(V1)),activate(V2)) ;
  isNatIListKind(n__nil) >= tt ;
  activate(n__zeros) >= zeros ;
  activate(n__0) >= 0 ;
  activate(n__length(X)) >= length(X) ;
  activate(n__s(X)) >= s(X) ;
  activate(n__cons(X1,X2)) >= cons(X1,X2) ;
  activate(n__nil) >= nil ;
  activate(X) >= X ;
  U11(tt,V1) >= U12(isNatIListKind(activate(V1)),activate(V1)) ;
  U13(tt) >= tt ;
  isNatList(n__cons(V1,V2)) >= U81(isNatKind(activate(V1)),activate(V1),
                                activate(V2)) ;
  isNatList(n__nil) >= tt ;
  U22(tt,V1) >= U23(isNat(activate(V1))) ;
  isNatKind(n__0) >= tt ;
  isNatKind(n__length(V1)) >= U61(isNatIListKind(activate(V1))) ;
  isNatKind(n__s(V1)) >= U71(isNatKind(activate(V1))) ;
  U21(tt,V1) >= U22(isNatKind(activate(V1)),activate(V1)) ;
  U23(tt) >= tt ;
  isNat(n__0) >= tt ;
  isNat(n__length(V1)) >= U11(isNatIListKind(activate(V1)),activate(V1)) ;
  isNat(n__s(V1)) >= U21(isNatKind(activate(V1)),activate(V1)) ;
  U32(tt,V) >= U33(isNatList(activate(V))) ;
  U31(tt,V) >= U32(isNatIListKind(activate(V)),activate(V)) ;
  U33(tt) >= tt ;
  U42(tt,V1,V2) >= U43(isNatIListKind(activate(V2)),activate(V1),activate(V2)) ;
  U41(tt,V1,V2) >= U42(isNatKind(activate(V1)),activate(V1),activate(V2)) ;
  U43(tt,V1,V2) >= U44(isNatIListKind(activate(V2)),activate(V1),activate(V2)) ;
  U44(tt,V1,V2) >= U45(isNat(activate(V1)),activate(V2)) ;
  U45(tt,V2) >= U46(isNatIList(activate(V2))) ;
  U46(tt) >= tt ;
  isNatIList(n__zeros) >= tt ;
  isNatIList(n__cons(V1,V2)) >= U41(isNatKind(activate(V1)),activate(V1),
                                 activate(V2)) ;
  isNatIList(V) >= U31(isNatIListKind(activate(V)),activate(V)) ;
  U52(tt) >= tt ;
  U51(tt,V2) >= U52(isNatIListKind(activate(V2))) ;
  U61(tt) >= tt ;
  U71(tt) >= tt ;
  U82(tt,V1,V2) >= U83(isNatIListKind(activate(V2)),activate(V1),activate(V2)) ;
  U81(tt,V1,V2) >= U82(isNatKind(activate(V1)),activate(V1),activate(V2)) ;
  U83(tt,V1,V2) >= U84(isNatIListKind(activate(V2)),activate(V1),activate(V2)) ;
  U84(tt,V1,V2) >= U85(isNat(activate(V1)),activate(V2)) ;
  U85(tt,V2) >= U86(isNatList(activate(V2))) ;
  U86(tt) >= tt ;
  U92(tt,L,N) >= U93(isNat(activate(N)),activate(L),activate(N)) ;
  U91(tt,L,N) >= U92(isNatIListKind(activate(L)),activate(L),activate(N)) ;
  U93(tt,L,N) >= U94(isNatKind(activate(N)),activate(L)) ;
  U94(tt,L) >= s(length(activate(L))) ;
  s(X) >= n__s(X) ;
  length(cons(N,L)) >= U91(isNatList(activate(L)),activate(L),N) ;
  length(nil) >= 0 ;
  length(X) >= n__length(X) ;
  nil >= n__nil ;
  Marked_isNatIList(n__cons(V1,V2)) >= Marked_U41(isNatKind(activate(V1)),
                                        activate(V1),activate(V2)) ;
  Marked_U41(tt,V1,V2) >= Marked_U42(isNatKind(activate(V1)),activate(V1),
                           activate(V2)) ;
  Marked_U45(tt,V2) > Marked_isNatIList(activate(V2)) ;
  Marked_U44(tt,V1,V2) >= Marked_U45(isNat(activate(V1)),activate(V2)) ;
  Marked_U43(tt,V1,V2) >= Marked_U44(isNatIListKind(activate(V2)),activate(V1),
                           activate(V2)) ;
  Marked_U42(tt,V1,V2) >= Marked_U43(isNatIListKind(activate(V2)),activate(V1),
                           activate(V2)) ;
 }
 + Disjunctions:{ 
 } 
=== TIMER virtual : 10.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 10.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
Entering rpo_solver
=== TIMER virtual : 25.000000 ===
Search parameters: AFS type: 2 ; time limit: 25.. 
=== STOPING TIMER virtual ===
Time out for these parameters.
=== TIMER virtual : 15.000000 ===
Entering poly_solver
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 15.000000 ===
=== STOPING TIMER real ===
Sat solver returned
=== STOPING TIMER real ===
=== STOPING TIMER virtual ===
No solution found for these parameters.
=== TIMER virtual : 50.000000 ===
trying sub matrices of size: 1
Matrix interpretation constraints generated.
Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. 
Termination constraints generated.
Starting Sat solver initialization
Calling Sat solver...
=== STOPING TIMER virtual ===
=== TIMER real : 50.000000 ===
=== STOPING TIMER real ===
Sat timeout reached
=== STOPING TIMER virtual ===
No solution found for these parameters.
No solution found for these constraints.
APPLY CRITERIA (ID_CRIT)
NOT SOLVED
No proof found
Cime worked for 166.233005 seconds (real time)
Cime Exit Status: 0