MAYBE

Problem:
 zeros() -> cons(0(),n__zeros())
 U11(tt()) -> tt()
 U21(tt()) -> tt()
 U31(tt()) -> tt()
 U41(tt(),V2) -> U42(isNatIList(activate(V2)))
 U42(tt()) -> tt()
 U51(tt(),V2) -> U52(isNatList(activate(V2)))
 U52(tt()) -> tt()
 U61(tt(),L,N) -> U62(isNat(activate(N)),activate(L))
 U62(tt(),L) -> s(length(activate(L)))
 isNat(n__0()) -> tt()
 isNat(n__length(V1)) -> U11(isNatList(activate(V1)))
 isNat(n__s(V1)) -> U21(isNat(activate(V1)))
 isNatIList(V) -> U31(isNatList(activate(V)))
 isNatIList(n__zeros()) -> tt()
 isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2))
 isNatList(n__nil()) -> tt()
 isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2))
 length(nil()) -> 0()
 length(cons(N,L)) -> U61(isNatList(activate(L)),activate(L),N)
 zeros() -> n__zeros()
 0() -> n__0()
 length(X) -> n__length(X)
 s(X) -> n__s(X)
 cons(X1,X2) -> n__cons(X1,X2)
 nil() -> n__nil()
 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

Proof:
 DP Processor:
  DPs:
   zeros#() -> 0#()
   zeros#() -> cons#(0(),n__zeros())
   U41#(tt(),V2) -> activate#(V2)
   U41#(tt(),V2) -> isNatIList#(activate(V2))
   U41#(tt(),V2) -> U42#(isNatIList(activate(V2)))
   U51#(tt(),V2) -> activate#(V2)
   U51#(tt(),V2) -> isNatList#(activate(V2))
   U51#(tt(),V2) -> U52#(isNatList(activate(V2)))
   U61#(tt(),L,N) -> activate#(L)
   U61#(tt(),L,N) -> activate#(N)
   U61#(tt(),L,N) -> isNat#(activate(N))
   U61#(tt(),L,N) -> U62#(isNat(activate(N)),activate(L))
   U62#(tt(),L) -> activate#(L)
   U62#(tt(),L) -> length#(activate(L))
   U62#(tt(),L) -> s#(length(activate(L)))
   isNat#(n__length(V1)) -> activate#(V1)
   isNat#(n__length(V1)) -> isNatList#(activate(V1))
   isNat#(n__length(V1)) -> U11#(isNatList(activate(V1)))
   isNat#(n__s(V1)) -> activate#(V1)
   isNat#(n__s(V1)) -> isNat#(activate(V1))
   isNat#(n__s(V1)) -> U21#(isNat(activate(V1)))
   isNatIList#(V) -> activate#(V)
   isNatIList#(V) -> isNatList#(activate(V))
   isNatIList#(V) -> U31#(isNatList(activate(V)))
   isNatIList#(n__cons(V1,V2)) -> activate#(V2)
   isNatIList#(n__cons(V1,V2)) -> activate#(V1)
   isNatIList#(n__cons(V1,V2)) -> isNat#(activate(V1))
   isNatIList#(n__cons(V1,V2)) -> U41#(isNat(activate(V1)),activate(V2))
   isNatList#(n__cons(V1,V2)) -> activate#(V2)
   isNatList#(n__cons(V1,V2)) -> activate#(V1)
   isNatList#(n__cons(V1,V2)) -> isNat#(activate(V1))
   isNatList#(n__cons(V1,V2)) -> U51#(isNat(activate(V1)),activate(V2))
   length#(nil()) -> 0#()
   length#(cons(N,L)) -> activate#(L)
   length#(cons(N,L)) -> isNatList#(activate(L))
   length#(cons(N,L)) -> U61#(isNatList(activate(L)),activate(L),N)
   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#()
  TRS:
   zeros() -> cons(0(),n__zeros())
   U11(tt()) -> tt()
   U21(tt()) -> tt()
   U31(tt()) -> tt()
   U41(tt(),V2) -> U42(isNatIList(activate(V2)))
   U42(tt()) -> tt()
   U51(tt(),V2) -> U52(isNatList(activate(V2)))
   U52(tt()) -> tt()
   U61(tt(),L,N) -> U62(isNat(activate(N)),activate(L))
   U62(tt(),L) -> s(length(activate(L)))
   isNat(n__0()) -> tt()
   isNat(n__length(V1)) -> U11(isNatList(activate(V1)))
   isNat(n__s(V1)) -> U21(isNat(activate(V1)))
   isNatIList(V) -> U31(isNatList(activate(V)))
   isNatIList(n__zeros()) -> tt()
   isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2))
   isNatList(n__nil()) -> tt()
   isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2))
   length(nil()) -> 0()
   length(cons(N,L)) -> U61(isNatList(activate(L)),activate(L),N)
   zeros() -> n__zeros()
   0() -> n__0()
   length(X) -> n__length(X)
   s(X) -> n__s(X)
   cons(X1,X2) -> n__cons(X1,X2)
   nil() -> n__nil()
   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
  CDG Processor:
   DPs:
    zeros#() -> 0#()
    zeros#() -> cons#(0(),n__zeros())
    U41#(tt(),V2) -> activate#(V2)
    U41#(tt(),V2) -> isNatIList#(activate(V2))
    U41#(tt(),V2) -> U42#(isNatIList(activate(V2)))
    U51#(tt(),V2) -> activate#(V2)
    U51#(tt(),V2) -> isNatList#(activate(V2))
    U51#(tt(),V2) -> U52#(isNatList(activate(V2)))
    U61#(tt(),L,N) -> activate#(L)
    U61#(tt(),L,N) -> activate#(N)
    U61#(tt(),L,N) -> isNat#(activate(N))
    U61#(tt(),L,N) -> U62#(isNat(activate(N)),activate(L))
    U62#(tt(),L) -> activate#(L)
    U62#(tt(),L) -> length#(activate(L))
    U62#(tt(),L) -> s#(length(activate(L)))
    isNat#(n__length(V1)) -> activate#(V1)
    isNat#(n__length(V1)) -> isNatList#(activate(V1))
    isNat#(n__length(V1)) -> U11#(isNatList(activate(V1)))
    isNat#(n__s(V1)) -> activate#(V1)
    isNat#(n__s(V1)) -> isNat#(activate(V1))
    isNat#(n__s(V1)) -> U21#(isNat(activate(V1)))
    isNatIList#(V) -> activate#(V)
    isNatIList#(V) -> isNatList#(activate(V))
    isNatIList#(V) -> U31#(isNatList(activate(V)))
    isNatIList#(n__cons(V1,V2)) -> activate#(V2)
    isNatIList#(n__cons(V1,V2)) -> activate#(V1)
    isNatIList#(n__cons(V1,V2)) -> isNat#(activate(V1))
    isNatIList#(n__cons(V1,V2)) -> U41#(isNat(activate(V1)),activate(V2))
    isNatList#(n__cons(V1,V2)) -> activate#(V2)
    isNatList#(n__cons(V1,V2)) -> activate#(V1)
    isNatList#(n__cons(V1,V2)) -> isNat#(activate(V1))
    isNatList#(n__cons(V1,V2)) -> U51#(isNat(activate(V1)),activate(V2))
    length#(nil()) -> 0#()
    length#(cons(N,L)) -> activate#(L)
    length#(cons(N,L)) -> isNatList#(activate(L))
    length#(cons(N,L)) -> U61#(isNatList(activate(L)),activate(L),N)
    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#()
   TRS:
    zeros() -> cons(0(),n__zeros())
    U11(tt()) -> tt()
    U21(tt()) -> tt()
    U31(tt()) -> tt()
    U41(tt(),V2) -> U42(isNatIList(activate(V2)))
    U42(tt()) -> tt()
    U51(tt(),V2) -> U52(isNatList(activate(V2)))
    U52(tt()) -> tt()
    U61(tt(),L,N) -> U62(isNat(activate(N)),activate(L))
    U62(tt(),L) -> s(length(activate(L)))
    isNat(n__0()) -> tt()
    isNat(n__length(V1)) -> U11(isNatList(activate(V1)))
    isNat(n__s(V1)) -> U21(isNat(activate(V1)))
    isNatIList(V) -> U31(isNatList(activate(V)))
    isNatIList(n__zeros()) -> tt()
    isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2))
    isNatList(n__nil()) -> tt()
    isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2))
    length(nil()) -> 0()
    length(cons(N,L)) -> U61(isNatList(activate(L)),activate(L),N)
    zeros() -> n__zeros()
    0() -> n__0()
    length(X) -> n__length(X)
    s(X) -> n__s(X)
    cons(X1,X2) -> n__cons(X1,X2)
    nil() -> n__nil()
    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
   graph:
    length#(cons(N,L)) -> U61#(isNatList(activate(L)),activate(L),N) ->
    U61#(tt(),L,N) -> activate#(L)
    length#(cons(N,L)) -> U61#(isNatList(activate(L)),activate(L),N) ->
    U61#(tt(),L,N) -> activate#(N)
    length#(cons(N,L)) -> U61#(isNatList(activate(L)),activate(L),N) ->
    U61#(tt(),L,N) -> isNat#(activate(N))
    length#(cons(N,L)) -> U61#(isNatList(activate(L)),activate(L),N) ->
    U61#(tt(),L,N) -> U62#(isNat(activate(N)),activate(L))
    length#(cons(N,L)) -> isNatList#(activate(L)) ->
    isNatList#(n__cons(V1,V2)) -> activate#(V2)
    length#(cons(N,L)) -> isNatList#(activate(L)) ->
    isNatList#(n__cons(V1,V2)) -> activate#(V1)
    length#(cons(N,L)) -> isNatList#(activate(L)) ->
    isNatList#(n__cons(V1,V2)) -> isNat#(activate(V1))
    length#(cons(N,L)) -> isNatList#(activate(L)) ->
    isNatList#(n__cons(V1,V2)) -> U51#(isNat(activate(V1)),activate(V2))
    length#(cons(N,L)) -> activate#(L) ->
    activate#(n__zeros()) -> zeros#()
    length#(cons(N,L)) -> activate#(L) ->
    activate#(n__0()) -> 0#()
    length#(cons(N,L)) -> activate#(L) ->
    activate#(n__length(X)) -> length#(X)
    length#(cons(N,L)) -> activate#(L) ->
    activate#(n__s(X)) -> s#(X)
    length#(cons(N,L)) -> activate#(L) ->
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    length#(cons(N,L)) -> activate#(L) ->
    activate#(n__nil()) -> nil#()
    U62#(tt(),L) -> length#(activate(L)) ->
    length#(nil()) -> 0#()
    U62#(tt(),L) -> length#(activate(L)) ->
    length#(cons(N,L)) -> activate#(L)
    U62#(tt(),L) -> length#(activate(L)) ->
    length#(cons(N,L)) -> isNatList#(activate(L))
    U62#(tt(),L) -> length#(activate(L)) ->
    length#(cons(N,L)) -> U61#(isNatList(activate(L)),activate(L),N)
    U62#(tt(),L) -> activate#(L) -> activate#(n__zeros()) -> zeros#()
    U62#(tt(),L) -> activate#(L) -> activate#(n__0()) -> 0#()
    U62#(tt(),L) -> activate#(L) ->
    activate#(n__length(X)) -> length#(X)
    U62#(tt(),L) -> activate#(L) -> activate#(n__s(X)) -> s#(X)
    U62#(tt(),L) -> activate#(L) ->
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    U62#(tt(),L) -> activate#(L) ->
    activate#(n__nil()) -> nil#()
    isNat#(n__s(V1)) -> isNat#(activate(V1)) ->
    isNat#(n__length(V1)) -> activate#(V1)
    isNat#(n__s(V1)) -> isNat#(activate(V1)) ->
    isNat#(n__length(V1)) -> isNatList#(activate(V1))
    isNat#(n__s(V1)) -> isNat#(activate(V1)) ->
    isNat#(n__length(V1)) -> U11#(isNatList(activate(V1)))
    isNat#(n__s(V1)) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> activate#(V1)
    isNat#(n__s(V1)) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> isNat#(activate(V1))
    isNat#(n__s(V1)) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> U21#(isNat(activate(V1)))
    isNat#(n__s(V1)) -> activate#(V1) ->
    activate#(n__zeros()) -> zeros#()
    isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__0()) -> 0#()
    isNat#(n__s(V1)) -> activate#(V1) ->
    activate#(n__length(X)) -> length#(X)
    isNat#(n__s(V1)) -> activate#(V1) ->
    activate#(n__s(X)) -> s#(X)
    isNat#(n__s(V1)) -> activate#(V1) ->
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    isNat#(n__s(V1)) -> activate#(V1) ->
    activate#(n__nil()) -> nil#()
    isNat#(n__length(V1)) -> isNatList#(activate(V1)) ->
    isNatList#(n__cons(V1,V2)) -> activate#(V2)
    isNat#(n__length(V1)) -> isNatList#(activate(V1)) ->
    isNatList#(n__cons(V1,V2)) -> activate#(V1)
    isNat#(n__length(V1)) -> isNatList#(activate(V1)) ->
    isNatList#(n__cons(V1,V2)) -> isNat#(activate(V1))
    isNat#(n__length(V1)) -> isNatList#(activate(V1)) ->
    isNatList#(n__cons(V1,V2)) -> U51#(isNat(activate(V1)),activate(V2))
    isNat#(n__length(V1)) -> activate#(V1) ->
    activate#(n__zeros()) -> zeros#()
    isNat#(n__length(V1)) -> activate#(V1) ->
    activate#(n__0()) -> 0#()
    isNat#(n__length(V1)) -> activate#(V1) ->
    activate#(n__length(X)) -> length#(X)
    isNat#(n__length(V1)) -> activate#(V1) ->
    activate#(n__s(X)) -> s#(X)
    isNat#(n__length(V1)) -> activate#(V1) ->
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    isNat#(n__length(V1)) -> activate#(V1) ->
    activate#(n__nil()) -> nil#()
    U61#(tt(),L,N) -> U62#(isNat(activate(N)),activate(L)) ->
    U62#(tt(),L) -> activate#(L)
    U61#(tt(),L,N) -> U62#(isNat(activate(N)),activate(L)) ->
    U62#(tt(),L) -> length#(activate(L))
    U61#(tt(),L,N) -> U62#(isNat(activate(N)),activate(L)) ->
    U62#(tt(),L) -> s#(length(activate(L)))
    U61#(tt(),L,N) -> isNat#(activate(N)) ->
    isNat#(n__length(V1)) -> activate#(V1)
    U61#(tt(),L,N) -> isNat#(activate(N)) ->
    isNat#(n__length(V1)) -> isNatList#(activate(V1))
    U61#(tt(),L,N) -> isNat#(activate(N)) ->
    isNat#(n__length(V1)) -> U11#(isNatList(activate(V1)))
    U61#(tt(),L,N) -> isNat#(activate(N)) ->
    isNat#(n__s(V1)) -> activate#(V1)
    U61#(tt(),L,N) -> isNat#(activate(N)) ->
    isNat#(n__s(V1)) -> isNat#(activate(V1))
    U61#(tt(),L,N) -> isNat#(activate(N)) ->
    isNat#(n__s(V1)) -> U21#(isNat(activate(V1)))
    U61#(tt(),L,N) -> activate#(N) ->
    activate#(n__zeros()) -> zeros#()
    U61#(tt(),L,N) -> activate#(N) -> activate#(n__0()) -> 0#()
    U61#(tt(),L,N) -> activate#(N) ->
    activate#(n__length(X)) -> length#(X)
    U61#(tt(),L,N) -> activate#(N) -> activate#(n__s(X)) -> s#(X)
    U61#(tt(),L,N) -> activate#(N) ->
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    U61#(tt(),L,N) -> activate#(N) -> activate#(n__nil()) -> nil#()
    U61#(tt(),L,N) -> activate#(L) ->
    activate#(n__zeros()) -> zeros#()
    U61#(tt(),L,N) -> activate#(L) -> activate#(n__0()) -> 0#()
    U61#(tt(),L,N) -> activate#(L) ->
    activate#(n__length(X)) -> length#(X)
    U61#(tt(),L,N) -> activate#(L) -> activate#(n__s(X)) -> s#(X)
    U61#(tt(),L,N) -> activate#(L) ->
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    U61#(tt(),L,N) -> activate#(L) ->
    activate#(n__nil()) -> nil#()
    isNatList#(n__cons(V1,V2)) -> isNat#(activate(V1)) ->
    isNat#(n__length(V1)) -> activate#(V1)
    isNatList#(n__cons(V1,V2)) -> isNat#(activate(V1)) ->
    isNat#(n__length(V1)) -> isNatList#(activate(V1))
    isNatList#(n__cons(V1,V2)) -> isNat#(activate(V1)) ->
    isNat#(n__length(V1)) -> U11#(isNatList(activate(V1)))
    isNatList#(n__cons(V1,V2)) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> activate#(V1)
    isNatList#(n__cons(V1,V2)) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> isNat#(activate(V1))
    isNatList#(n__cons(V1,V2)) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> U21#(isNat(activate(V1)))
    isNatList#(n__cons(V1,V2)) -> U51#(isNat(activate(V1)),activate(V2)) ->
    U51#(tt(),V2) -> activate#(V2)
    isNatList#(n__cons(V1,V2)) -> U51#(isNat(activate(V1)),activate(V2)) ->
    U51#(tt(),V2) -> isNatList#(activate(V2))
    isNatList#(n__cons(V1,V2)) -> U51#(isNat(activate(V1)),activate(V2)) ->
    U51#(tt(),V2) -> U52#(isNatList(activate(V2)))
    isNatList#(n__cons(V1,V2)) -> activate#(V1) ->
    activate#(n__zeros()) -> zeros#()
    isNatList#(n__cons(V1,V2)) -> activate#(V1) ->
    activate#(n__0()) -> 0#()
    isNatList#(n__cons(V1,V2)) -> activate#(V1) ->
    activate#(n__length(X)) -> length#(X)
    isNatList#(n__cons(V1,V2)) -> activate#(V1) ->
    activate#(n__s(X)) -> s#(X)
    isNatList#(n__cons(V1,V2)) -> activate#(V1) ->
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    isNatList#(n__cons(V1,V2)) -> activate#(V1) ->
    activate#(n__nil()) -> nil#()
    isNatList#(n__cons(V1,V2)) -> activate#(V2) ->
    activate#(n__zeros()) -> zeros#()
    isNatList#(n__cons(V1,V2)) -> activate#(V2) ->
    activate#(n__0()) -> 0#()
    isNatList#(n__cons(V1,V2)) -> activate#(V2) ->
    activate#(n__length(X)) -> length#(X)
    isNatList#(n__cons(V1,V2)) -> activate#(V2) ->
    activate#(n__s(X)) -> s#(X)
    isNatList#(n__cons(V1,V2)) -> activate#(V2) ->
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    isNatList#(n__cons(V1,V2)) -> activate#(V2) ->
    activate#(n__nil()) -> nil#()
    U51#(tt(),V2) -> isNatList#(activate(V2)) ->
    isNatList#(n__cons(V1,V2)) -> activate#(V2)
    U51#(tt(),V2) -> isNatList#(activate(V2)) ->
    isNatList#(n__cons(V1,V2)) -> activate#(V1)
    U51#(tt(),V2) -> isNatList#(activate(V2)) ->
    isNatList#(n__cons(V1,V2)) -> isNat#(activate(V1))
    U51#(tt(),V2) -> isNatList#(activate(V2)) ->
    isNatList#(n__cons(V1,V2)) -> U51#(isNat(activate(V1)),activate(V2))
    U51#(tt(),V2) -> activate#(V2) ->
    activate#(n__zeros()) -> zeros#()
    U51#(tt(),V2) -> activate#(V2) -> activate#(n__0()) -> 0#()
    U51#(tt(),V2) -> activate#(V2) ->
    activate#(n__length(X)) -> length#(X)
    U51#(tt(),V2) -> activate#(V2) -> activate#(n__s(X)) -> s#(X)
    U51#(tt(),V2) -> activate#(V2) ->
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    U51#(tt(),V2) -> activate#(V2) ->
    activate#(n__nil()) -> nil#()
    isNatIList#(n__cons(V1,V2)) -> isNat#(activate(V1)) ->
    isNat#(n__length(V1)) -> activate#(V1)
    isNatIList#(n__cons(V1,V2)) -> isNat#(activate(V1)) ->
    isNat#(n__length(V1)) -> isNatList#(activate(V1))
    isNatIList#(n__cons(V1,V2)) -> isNat#(activate(V1)) ->
    isNat#(n__length(V1)) -> U11#(isNatList(activate(V1)))
    isNatIList#(n__cons(V1,V2)) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> activate#(V1)
    isNatIList#(n__cons(V1,V2)) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> isNat#(activate(V1))
    isNatIList#(n__cons(V1,V2)) -> isNat#(activate(V1)) ->
    isNat#(n__s(V1)) -> U21#(isNat(activate(V1)))
    isNatIList#(n__cons(V1,V2)) -> activate#(V1) ->
    activate#(n__zeros()) -> zeros#()
    isNatIList#(n__cons(V1,V2)) -> activate#(V1) ->
    activate#(n__0()) -> 0#()
    isNatIList#(n__cons(V1,V2)) -> activate#(V1) ->
    activate#(n__length(X)) -> length#(X)
    isNatIList#(n__cons(V1,V2)) -> activate#(V1) ->
    activate#(n__s(X)) -> s#(X)
    isNatIList#(n__cons(V1,V2)) -> activate#(V1) ->
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    isNatIList#(n__cons(V1,V2)) -> activate#(V1) ->
    activate#(n__nil()) -> nil#()
    isNatIList#(n__cons(V1,V2)) -> activate#(V2) ->
    activate#(n__zeros()) -> zeros#()
    isNatIList#(n__cons(V1,V2)) -> activate#(V2) ->
    activate#(n__0()) -> 0#()
    isNatIList#(n__cons(V1,V2)) -> activate#(V2) ->
    activate#(n__length(X)) -> length#(X)
    isNatIList#(n__cons(V1,V2)) -> activate#(V2) ->
    activate#(n__s(X)) -> s#(X)
    isNatIList#(n__cons(V1,V2)) -> activate#(V2) ->
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    isNatIList#(n__cons(V1,V2)) -> activate#(V2) ->
    activate#(n__nil()) -> nil#()
    isNatIList#(n__cons(V1,V2)) -> U41#(isNat(activate(V1)),activate(V2)) ->
    U41#(tt(),V2) -> activate#(V2)
    isNatIList#(n__cons(V1,V2)) -> U41#(isNat(activate(V1)),activate(V2)) ->
    U41#(tt(),V2) -> isNatIList#(activate(V2))
    isNatIList#(n__cons(V1,V2)) -> U41#(isNat(activate(V1)),activate(V2)) ->
    U41#(tt(),V2) -> U42#(isNatIList(activate(V2)))
    isNatIList#(V) -> isNatList#(activate(V)) ->
    isNatList#(n__cons(V1,V2)) -> activate#(V2)
    isNatIList#(V) -> isNatList#(activate(V)) ->
    isNatList#(n__cons(V1,V2)) -> activate#(V1)
    isNatIList#(V) -> isNatList#(activate(V)) ->
    isNatList#(n__cons(V1,V2)) -> isNat#(activate(V1))
    isNatIList#(V) -> isNatList#(activate(V)) ->
    isNatList#(n__cons(V1,V2)) -> U51#(isNat(activate(V1)),activate(V2))
    isNatIList#(V) -> activate#(V) ->
    activate#(n__zeros()) -> zeros#()
    isNatIList#(V) -> activate#(V) -> activate#(n__0()) -> 0#()
    isNatIList#(V) -> activate#(V) ->
    activate#(n__length(X)) -> length#(X)
    isNatIList#(V) -> activate#(V) -> activate#(n__s(X)) -> s#(X)
    isNatIList#(V) -> activate#(V) ->
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    isNatIList#(V) -> activate#(V) ->
    activate#(n__nil()) -> nil#()
    activate#(n__length(X)) -> length#(X) ->
    length#(nil()) -> 0#()
    activate#(n__length(X)) -> length#(X) ->
    length#(cons(N,L)) -> activate#(L)
    activate#(n__length(X)) -> length#(X) ->
    length#(cons(N,L)) -> isNatList#(activate(L))
    activate#(n__length(X)) -> length#(X) ->
    length#(cons(N,L)) -> U61#(isNatList(activate(L)),activate(L),N)
    activate#(n__zeros()) -> zeros#() -> zeros#() -> 0#()
    activate#(n__zeros()) -> zeros#() ->
    zeros#() -> cons#(0(),n__zeros())
    U41#(tt(),V2) -> isNatIList#(activate(V2)) ->
    isNatIList#(V) -> activate#(V)
    U41#(tt(),V2) -> isNatIList#(activate(V2)) ->
    isNatIList#(V) -> isNatList#(activate(V))
    U41#(tt(),V2) -> isNatIList#(activate(V2)) ->
    isNatIList#(V) -> U31#(isNatList(activate(V)))
    U41#(tt(),V2) -> isNatIList#(activate(V2)) ->
    isNatIList#(n__cons(V1,V2)) -> activate#(V2)
    U41#(tt(),V2) -> isNatIList#(activate(V2)) ->
    isNatIList#(n__cons(V1,V2)) -> activate#(V1)
    U41#(tt(),V2) -> isNatIList#(activate(V2)) ->
    isNatIList#(n__cons(V1,V2)) -> isNat#(activate(V1))
    U41#(tt(),V2) -> isNatIList#(activate(V2)) ->
    isNatIList#(n__cons(V1,V2)) -> U41#(isNat(activate(V1)),activate(V2))
    U41#(tt(),V2) -> activate#(V2) ->
    activate#(n__zeros()) -> zeros#()
    U41#(tt(),V2) -> activate#(V2) -> activate#(n__0()) -> 0#()
    U41#(tt(),V2) -> activate#(V2) ->
    activate#(n__length(X)) -> length#(X)
    U41#(tt(),V2) -> activate#(V2) -> activate#(n__s(X)) -> s#(X)
    U41#(tt(),V2) -> activate#(V2) ->
    activate#(n__cons(X1,X2)) -> cons#(X1,X2)
    U41#(tt(),V2) -> activate#(V2) -> activate#(n__nil()) -> nil#()
   Restore Modifier:
    DPs:
     zeros#() -> 0#()
     zeros#() -> cons#(0(),n__zeros())
     U41#(tt(),V2) -> activate#(V2)
     U41#(tt(),V2) -> isNatIList#(activate(V2))
     U41#(tt(),V2) -> U42#(isNatIList(activate(V2)))
     U51#(tt(),V2) -> activate#(V2)
     U51#(tt(),V2) -> isNatList#(activate(V2))
     U51#(tt(),V2) -> U52#(isNatList(activate(V2)))
     U61#(tt(),L,N) -> activate#(L)
     U61#(tt(),L,N) -> activate#(N)
     U61#(tt(),L,N) -> isNat#(activate(N))
     U61#(tt(),L,N) -> U62#(isNat(activate(N)),activate(L))
     U62#(tt(),L) -> activate#(L)
     U62#(tt(),L) -> length#(activate(L))
     U62#(tt(),L) -> s#(length(activate(L)))
     isNat#(n__length(V1)) -> activate#(V1)
     isNat#(n__length(V1)) -> isNatList#(activate(V1))
     isNat#(n__length(V1)) -> U11#(isNatList(activate(V1)))
     isNat#(n__s(V1)) -> activate#(V1)
     isNat#(n__s(V1)) -> isNat#(activate(V1))
     isNat#(n__s(V1)) -> U21#(isNat(activate(V1)))
     isNatIList#(V) -> activate#(V)
     isNatIList#(V) -> isNatList#(activate(V))
     isNatIList#(V) -> U31#(isNatList(activate(V)))
     isNatIList#(n__cons(V1,V2)) -> activate#(V2)
     isNatIList#(n__cons(V1,V2)) -> activate#(V1)
     isNatIList#(n__cons(V1,V2)) -> isNat#(activate(V1))
     isNatIList#(n__cons(V1,V2)) -> U41#(isNat(activate(V1)),activate(V2))
     isNatList#(n__cons(V1,V2)) -> activate#(V2)
     isNatList#(n__cons(V1,V2)) -> activate#(V1)
     isNatList#(n__cons(V1,V2)) -> isNat#(activate(V1))
     isNatList#(n__cons(V1,V2)) -> U51#(isNat(activate(V1)),activate(V2))
     length#(nil()) -> 0#()
     length#(cons(N,L)) -> activate#(L)
     length#(cons(N,L)) -> isNatList#(activate(L))
     length#(cons(N,L)) -> U61#(isNatList(activate(L)),activate(L),N)
     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#()
    TRS:
     zeros() -> cons(0(),n__zeros())
     U11(tt()) -> tt()
     U21(tt()) -> tt()
     U31(tt()) -> tt()
     U41(tt(),V2) -> U42(isNatIList(activate(V2)))
     U42(tt()) -> tt()
     U51(tt(),V2) -> U52(isNatList(activate(V2)))
     U52(tt()) -> tt()
     U61(tt(),L,N) -> U62(isNat(activate(N)),activate(L))
     U62(tt(),L) -> s(length(activate(L)))
     isNat(n__0()) -> tt()
     isNat(n__length(V1)) -> U11(isNatList(activate(V1)))
     isNat(n__s(V1)) -> U21(isNat(activate(V1)))
     isNatIList(V) -> U31(isNatList(activate(V)))
     isNatIList(n__zeros()) -> tt()
     isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2))
     isNatList(n__nil()) -> tt()
     isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2))
     length(nil()) -> 0()
     length(cons(N,L)) -> U61(isNatList(activate(L)),activate(L),N)
     zeros() -> n__zeros()
     0() -> n__0()
     length(X) -> n__length(X)
     s(X) -> n__s(X)
     cons(X1,X2) -> n__cons(X1,X2)
     nil() -> n__nil()
     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
    SCC Processor:
     #sccs: 2
     #rules: 22
     #arcs: 148/1764
     DPs:
      isNatIList#(n__cons(V1,V2)) -> U41#(isNat(activate(V1)),activate(V2))
      U41#(tt(),V2) -> isNatIList#(activate(V2))
     TRS:
      zeros() -> cons(0(),n__zeros())
      U11(tt()) -> tt()
      U21(tt()) -> tt()
      U31(tt()) -> tt()
      U41(tt(),V2) -> U42(isNatIList(activate(V2)))
      U42(tt()) -> tt()
      U51(tt(),V2) -> U52(isNatList(activate(V2)))
      U52(tt()) -> tt()
      U61(tt(),L,N) -> U62(isNat(activate(N)),activate(L))
      U62(tt(),L) -> s(length(activate(L)))
      isNat(n__0()) -> tt()
      isNat(n__length(V1)) -> U11(isNatList(activate(V1)))
      isNat(n__s(V1)) -> U21(isNat(activate(V1)))
      isNatIList(V) -> U31(isNatList(activate(V)))
      isNatIList(n__zeros()) -> tt()
      isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2))
      isNatList(n__nil()) -> tt()
      isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2))
      length(nil()) -> 0()
      length(cons(N,L)) -> U61(isNatList(activate(L)),activate(L),N)
      zeros() -> n__zeros()
      0() -> n__0()
      length(X) -> n__length(X)
      s(X) -> n__s(X)
      cons(X1,X2) -> n__cons(X1,X2)
      nil() -> n__nil()
      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
     Open
     
     DPs:
      length#(cons(N,L)) -> U61#(isNatList(activate(L)),activate(L),N)
      U61#(tt(),L,N) -> U62#(isNat(activate(N)),activate(L))
      U62#(tt(),L) -> length#(activate(L))
      length#(cons(N,L)) -> isNatList#(activate(L))
      isNatList#(n__cons(V1,V2)) -> U51#(isNat(activate(V1)),activate(V2))
      U51#(tt(),V2) -> isNatList#(activate(V2))
      isNatList#(n__cons(V1,V2)) -> isNat#(activate(V1))
      isNat#(n__s(V1)) -> isNat#(activate(V1))
      isNat#(n__s(V1)) -> activate#(V1)
      activate#(n__length(X)) -> length#(X)
      length#(cons(N,L)) -> activate#(L)
      isNat#(n__length(V1)) -> isNatList#(activate(V1))
      isNatList#(n__cons(V1,V2)) -> activate#(V1)
      isNatList#(n__cons(V1,V2)) -> activate#(V2)
      isNat#(n__length(V1)) -> activate#(V1)
      U51#(tt(),V2) -> activate#(V2)
      U62#(tt(),L) -> activate#(L)
      U61#(tt(),L,N) -> isNat#(activate(N))
      U61#(tt(),L,N) -> activate#(N)
      U61#(tt(),L,N) -> activate#(L)
     TRS:
      zeros() -> cons(0(),n__zeros())
      U11(tt()) -> tt()
      U21(tt()) -> tt()
      U31(tt()) -> tt()
      U41(tt(),V2) -> U42(isNatIList(activate(V2)))
      U42(tt()) -> tt()
      U51(tt(),V2) -> U52(isNatList(activate(V2)))
      U52(tt()) -> tt()
      U61(tt(),L,N) -> U62(isNat(activate(N)),activate(L))
      U62(tt(),L) -> s(length(activate(L)))
      isNat(n__0()) -> tt()
      isNat(n__length(V1)) -> U11(isNatList(activate(V1)))
      isNat(n__s(V1)) -> U21(isNat(activate(V1)))
      isNatIList(V) -> U31(isNatList(activate(V)))
      isNatIList(n__zeros()) -> tt()
      isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2))
      isNatList(n__nil()) -> tt()
      isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2))
      length(nil()) -> 0()
      length(cons(N,L)) -> U61(isNatList(activate(L)),activate(L),N)
      zeros() -> n__zeros()
      0() -> n__0()
      length(X) -> n__length(X)
      s(X) -> n__s(X)
      cons(X1,X2) -> n__cons(X1,X2)
      nil() -> n__nil()
      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
     Open