MAYBE Problem: zeros() -> cons(0(),n__zeros()) U11(tt(),V1) -> U12(isNatList(activate(V1))) U12(tt()) -> tt() U21(tt(),V1) -> U22(isNat(activate(V1))) U22(tt()) -> tt() U31(tt(),V) -> U32(isNatList(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isNat(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNatIList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNat(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isNatList(activate(V2))) U53(tt()) -> tt() U61(tt(),L) -> s(length(activate(L))) and(tt(),X) -> activate(X) isNat(n__0()) -> tt() isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)),activate(V1)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatIList(V) -> U31(isNatIListKind(activate(V)),activate(V)) isNatIList(n__zeros()) -> tt() isNatIList(n__cons(V1,V2)) -> U41(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) isNatIListKind(n__nil()) -> tt() isNatIListKind(n__zeros()) -> tt() isNatIListKind(n__cons(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) isNatKind(n__0()) -> tt() isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) isNatKind(n__s(V1)) -> isNatKind(activate(V1)) isNatList(n__nil()) -> tt() isNatList(n__cons(V1,V2)) -> U51(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) length(nil()) -> 0() length(cons(N,L)) -> U61(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))),n__and ( n__isNat(N),n__isNatKind(N))), activate(L)) zeros() -> n__zeros() 0() -> n__0() length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) isNatIListKind(X) -> n__isNatIListKind(X) nil() -> n__nil() and(X1,X2) -> n__and(X1,X2) isNat(X) -> n__isNat(X) isNatKind(X) -> n__isNatKind(X) activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__isNatIListKind(X)) -> isNatIListKind(X) activate(n__nil()) -> nil() activate(n__and(X1,X2)) -> and(activate(X1),X2) activate(n__isNat(X)) -> isNat(X) activate(n__isNatKind(X)) -> isNatKind(X) activate(X) -> X Proof: DP Processor: DPs: zeros#() -> 0#() zeros#() -> cons#(0(),n__zeros()) U11#(tt(),V1) -> activate#(V1) U11#(tt(),V1) -> isNatList#(activate(V1)) U11#(tt(),V1) -> U12#(isNatList(activate(V1))) U21#(tt(),V1) -> activate#(V1) U21#(tt(),V1) -> isNat#(activate(V1)) U21#(tt(),V1) -> U22#(isNat(activate(V1))) U31#(tt(),V) -> activate#(V) U31#(tt(),V) -> isNatList#(activate(V)) U31#(tt(),V) -> U32#(isNatList(activate(V))) U41#(tt(),V1,V2) -> activate#(V2) U41#(tt(),V1,V2) -> activate#(V1) U41#(tt(),V1,V2) -> isNat#(activate(V1)) U41#(tt(),V1,V2) -> U42#(isNat(activate(V1)),activate(V2)) U42#(tt(),V2) -> activate#(V2) U42#(tt(),V2) -> isNatIList#(activate(V2)) U42#(tt(),V2) -> U43#(isNatIList(activate(V2))) U51#(tt(),V1,V2) -> activate#(V2) U51#(tt(),V1,V2) -> activate#(V1) U51#(tt(),V1,V2) -> isNat#(activate(V1)) U51#(tt(),V1,V2) -> U52#(isNat(activate(V1)),activate(V2)) U52#(tt(),V2) -> activate#(V2) U52#(tt(),V2) -> isNatList#(activate(V2)) U52#(tt(),V2) -> U53#(isNatList(activate(V2))) U61#(tt(),L) -> activate#(L) U61#(tt(),L) -> length#(activate(L)) U61#(tt(),L) -> s#(length(activate(L))) and#(tt(),X) -> activate#(X) isNat#(n__length(V1)) -> activate#(V1) isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)) isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)),activate(V1)) isNat#(n__s(V1)) -> activate#(V1) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) isNatIList#(V) -> activate#(V) isNatIList#(V) -> isNatIListKind#(activate(V)) isNatIList#(V) -> U31#(isNatIListKind(activate(V)),activate(V)) isNatIList#(n__cons(V1,V2)) -> activate#(V2) isNatIList#(n__cons(V1,V2)) -> activate#(V1) isNatIList#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) isNatIList#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) isNatIList#(n__cons(V1,V2)) -> U41#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) isNatIListKind#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) isNatIListKind#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) isNatKind#(n__length(V1)) -> activate#(V1) isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)) isNatKind#(n__s(V1)) -> activate#(V1) isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) isNatList#(n__cons(V1,V2)) -> activate#(V2) isNatList#(n__cons(V1,V2)) -> activate#(V1) isNatList#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) isNatList#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) isNatList#(n__cons(V1,V2)) -> U51#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) length#(nil()) -> 0#() length#(cons(N,L)) -> activate#(L) length#(cons(N,L)) -> isNatList#(activate(L)) length#(cons(N,L)) -> and#(isNatList(activate(L)),n__isNatIListKind(activate(L))) length#(cons(N,L)) -> and#(and(isNatList(activate(L)),n__isNatIListKind(activate(L))),n__and (n__isNat(N),n__isNatKind(N))) length#(cons(N,L)) -> U61#(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))), n__and(n__isNat(N),n__isNatKind(N))),activate(L)) activate#(n__zeros()) -> zeros#() activate#(n__0()) -> 0#() activate#(n__length(X)) -> activate#(X) activate#(n__length(X)) -> length#(activate(X)) activate#(n__s(X)) -> activate#(X) activate#(n__s(X)) -> s#(activate(X)) activate#(n__cons(X1,X2)) -> activate#(X1) activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) activate#(n__nil()) -> nil#() activate#(n__and(X1,X2)) -> activate#(X1) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) activate#(n__isNat(X)) -> isNat#(X) activate#(n__isNatKind(X)) -> isNatKind#(X) TRS: zeros() -> cons(0(),n__zeros()) U11(tt(),V1) -> U12(isNatList(activate(V1))) U12(tt()) -> tt() U21(tt(),V1) -> U22(isNat(activate(V1))) U22(tt()) -> tt() U31(tt(),V) -> U32(isNatList(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isNat(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNatIList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNat(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isNatList(activate(V2))) U53(tt()) -> tt() U61(tt(),L) -> s(length(activate(L))) and(tt(),X) -> activate(X) isNat(n__0()) -> tt() isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)),activate(V1)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatIList(V) -> U31(isNatIListKind(activate(V)),activate(V)) isNatIList(n__zeros()) -> tt() isNatIList(n__cons(V1,V2)) -> U41(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) isNatIListKind(n__nil()) -> tt() isNatIListKind(n__zeros()) -> tt() isNatIListKind(n__cons(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) isNatKind(n__0()) -> tt() isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) isNatKind(n__s(V1)) -> isNatKind(activate(V1)) isNatList(n__nil()) -> tt() isNatList(n__cons(V1,V2)) -> U51(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) length(nil()) -> 0() length(cons(N,L)) -> U61(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))), n__and(n__isNat(N),n__isNatKind(N))),activate(L)) zeros() -> n__zeros() 0() -> n__0() length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) isNatIListKind(X) -> n__isNatIListKind(X) nil() -> n__nil() and(X1,X2) -> n__and(X1,X2) isNat(X) -> n__isNat(X) isNatKind(X) -> n__isNatKind(X) activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__isNatIListKind(X)) -> isNatIListKind(X) activate(n__nil()) -> nil() activate(n__and(X1,X2)) -> and(activate(X1),X2) activate(n__isNat(X)) -> isNat(X) activate(n__isNatKind(X)) -> isNatKind(X) activate(X) -> X CDG Processor: DPs: zeros#() -> 0#() zeros#() -> cons#(0(),n__zeros()) U11#(tt(),V1) -> activate#(V1) U11#(tt(),V1) -> isNatList#(activate(V1)) U11#(tt(),V1) -> U12#(isNatList(activate(V1))) U21#(tt(),V1) -> activate#(V1) U21#(tt(),V1) -> isNat#(activate(V1)) U21#(tt(),V1) -> U22#(isNat(activate(V1))) U31#(tt(),V) -> activate#(V) U31#(tt(),V) -> isNatList#(activate(V)) U31#(tt(),V) -> U32#(isNatList(activate(V))) U41#(tt(),V1,V2) -> activate#(V2) U41#(tt(),V1,V2) -> activate#(V1) U41#(tt(),V1,V2) -> isNat#(activate(V1)) U41#(tt(),V1,V2) -> U42#(isNat(activate(V1)),activate(V2)) U42#(tt(),V2) -> activate#(V2) U42#(tt(),V2) -> isNatIList#(activate(V2)) U42#(tt(),V2) -> U43#(isNatIList(activate(V2))) U51#(tt(),V1,V2) -> activate#(V2) U51#(tt(),V1,V2) -> activate#(V1) U51#(tt(),V1,V2) -> isNat#(activate(V1)) U51#(tt(),V1,V2) -> U52#(isNat(activate(V1)),activate(V2)) U52#(tt(),V2) -> activate#(V2) U52#(tt(),V2) -> isNatList#(activate(V2)) U52#(tt(),V2) -> U53#(isNatList(activate(V2))) U61#(tt(),L) -> activate#(L) U61#(tt(),L) -> length#(activate(L)) U61#(tt(),L) -> s#(length(activate(L))) and#(tt(),X) -> activate#(X) isNat#(n__length(V1)) -> activate#(V1) isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)) isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)),activate(V1)) isNat#(n__s(V1)) -> activate#(V1) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) isNatIList#(V) -> activate#(V) isNatIList#(V) -> isNatIListKind#(activate(V)) isNatIList#(V) -> U31#(isNatIListKind(activate(V)),activate(V)) isNatIList#(n__cons(V1,V2)) -> activate#(V2) isNatIList#(n__cons(V1,V2)) -> activate#(V1) isNatIList#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) isNatIList#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) isNatIList#(n__cons(V1,V2)) -> U41#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) isNatIListKind#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) isNatIListKind#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) isNatKind#(n__length(V1)) -> activate#(V1) isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)) isNatKind#(n__s(V1)) -> activate#(V1) isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) isNatList#(n__cons(V1,V2)) -> activate#(V2) isNatList#(n__cons(V1,V2)) -> activate#(V1) isNatList#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) isNatList#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) isNatList#(n__cons(V1,V2)) -> U51#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) length#(nil()) -> 0#() length#(cons(N,L)) -> activate#(L) length#(cons(N,L)) -> isNatList#(activate(L)) length#(cons(N,L)) -> and#(isNatList(activate(L)),n__isNatIListKind(activate(L))) length#(cons(N,L)) -> and#(and(isNatList(activate(L)),n__isNatIListKind(activate(L))),n__and ( n__isNat(N),n__isNatKind(N))) length#(cons(N,L)) -> U61#(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))), n__and(n__isNat(N),n__isNatKind(N))),activate(L)) activate#(n__zeros()) -> zeros#() activate#(n__0()) -> 0#() activate#(n__length(X)) -> activate#(X) activate#(n__length(X)) -> length#(activate(X)) activate#(n__s(X)) -> activate#(X) activate#(n__s(X)) -> s#(activate(X)) activate#(n__cons(X1,X2)) -> activate#(X1) activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) activate#(n__nil()) -> nil#() activate#(n__and(X1,X2)) -> activate#(X1) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) activate#(n__isNat(X)) -> isNat#(X) activate#(n__isNatKind(X)) -> isNatKind#(X) TRS: zeros() -> cons(0(),n__zeros()) U11(tt(),V1) -> U12(isNatList(activate(V1))) U12(tt()) -> tt() U21(tt(),V1) -> U22(isNat(activate(V1))) U22(tt()) -> tt() U31(tt(),V) -> U32(isNatList(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isNat(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNatIList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNat(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isNatList(activate(V2))) U53(tt()) -> tt() U61(tt(),L) -> s(length(activate(L))) and(tt(),X) -> activate(X) isNat(n__0()) -> tt() isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)),activate(V1)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatIList(V) -> U31(isNatIListKind(activate(V)),activate(V)) isNatIList(n__zeros()) -> tt() isNatIList(n__cons(V1,V2)) -> U41(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) isNatIListKind(n__nil()) -> tt() isNatIListKind(n__zeros()) -> tt() isNatIListKind(n__cons(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) isNatKind(n__0()) -> tt() isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) isNatKind(n__s(V1)) -> isNatKind(activate(V1)) isNatList(n__nil()) -> tt() isNatList(n__cons(V1,V2)) -> U51(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) length(nil()) -> 0() length(cons(N,L)) -> U61(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))), n__and(n__isNat(N),n__isNatKind(N))),activate(L)) zeros() -> n__zeros() 0() -> n__0() length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) isNatIListKind(X) -> n__isNatIListKind(X) nil() -> n__nil() and(X1,X2) -> n__and(X1,X2) isNat(X) -> n__isNat(X) isNatKind(X) -> n__isNatKind(X) activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__isNatIListKind(X)) -> isNatIListKind(X) activate(n__nil()) -> nil() activate(n__and(X1,X2)) -> and(activate(X1),X2) activate(n__isNat(X)) -> isNat(X) activate(n__isNatKind(X)) -> isNatKind(X) activate(X) -> X graph: isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__length(V1)) -> activate#(V1) isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)) isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> activate#(V1) isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__zeros()) -> zeros#() isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__0()) -> 0#() isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__length(X)) -> activate#(X) isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__length(X)) -> length#(activate(X)) isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__s(X)) -> activate#(X) isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__s(X)) -> s#(activate(X)) isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> activate#(X1) isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__nil()) -> nil#() isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> activate#(X1) isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__isNat(X)) -> isNat#(X) isNatKind#(n__s(V1)) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)) -> isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)) -> isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)) -> isNatIListKind#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)) -> isNatIListKind#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) isNatKind#(n__length(V1)) -> activate#(V1) -> activate#(n__zeros()) -> zeros#() isNatKind#(n__length(V1)) -> activate#(V1) -> activate#(n__0()) -> 0#() isNatKind#(n__length(V1)) -> activate#(V1) -> activate#(n__length(X)) -> activate#(X) isNatKind#(n__length(V1)) -> activate#(V1) -> activate#(n__length(X)) -> length#(activate(X)) isNatKind#(n__length(V1)) -> activate#(V1) -> activate#(n__s(X)) -> activate#(X) isNatKind#(n__length(V1)) -> activate#(V1) -> activate#(n__s(X)) -> s#(activate(X)) isNatKind#(n__length(V1)) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> activate#(X1) isNatKind#(n__length(V1)) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) isNatKind#(n__length(V1)) -> activate#(V1) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) isNatKind#(n__length(V1)) -> activate#(V1) -> activate#(n__nil()) -> nil#() isNatKind#(n__length(V1)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> activate#(X1) isNatKind#(n__length(V1)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isNatKind#(n__length(V1)) -> activate#(V1) -> activate#(n__isNat(X)) -> isNat#(X) isNatKind#(n__length(V1)) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNatIListKind#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__length(V1)) -> activate#(V1) isNatIListKind#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)) isNatIListKind#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> activate#(V1) isNatIListKind#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) isNatIListKind#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) -> and#(tt(),X) -> activate#(X) isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__zeros()) -> zeros#() isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__0()) -> 0#() isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__length(X)) -> activate#(X) isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__length(X)) -> length#(activate(X)) isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__s(X)) -> activate#(X) isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__s(X)) -> s#(activate(X)) isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__cons(X1,X2)) -> activate#(X1) isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__nil()) -> nil#() isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> activate#(X1) isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__isNat(X)) -> isNat#(X) isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__zeros()) -> zeros#() isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__0()) -> 0#() isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__length(X)) -> activate#(X) isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__length(X)) -> length#(activate(X)) isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__s(X)) -> activate#(X) isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__s(X)) -> s#(activate(X)) isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> activate#(X1) isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__nil()) -> nil#() isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> activate#(X1) isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__isNat(X)) -> isNat#(X) isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) and#(tt(),X) -> activate#(X) -> activate#(n__zeros()) -> zeros#() and#(tt(),X) -> activate#(X) -> activate#(n__0()) -> 0#() and#(tt(),X) -> activate#(X) -> activate#(n__length(X)) -> activate#(X) and#(tt(),X) -> activate#(X) -> activate#(n__length(X)) -> length#(activate(X)) and#(tt(),X) -> activate#(X) -> activate#(n__s(X)) -> activate#(X) and#(tt(),X) -> activate#(X) -> activate#(n__s(X)) -> s#(activate(X)) and#(tt(),X) -> activate#(X) -> activate#(n__cons(X1,X2)) -> activate#(X1) and#(tt(),X) -> activate#(X) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) and#(tt(),X) -> activate#(X) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) and#(tt(),X) -> activate#(X) -> activate#(n__nil()) -> nil#() and#(tt(),X) -> activate#(X) -> activate#(n__and(X1,X2)) -> activate#(X1) and#(tt(),X) -> activate#(X) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) and#(tt(),X) -> activate#(X) -> activate#(n__isNat(X)) -> isNat#(X) and#(tt(),X) -> activate#(X) -> activate#(n__isNatKind(X)) -> isNatKind#(X) length#(cons(N,L)) -> and#(and(isNatList(activate(L)),n__isNatIListKind(activate(L))),n__and ( n__isNat(N),n__isNatKind(N))) -> and#(tt(),X) -> activate#(X) length#(cons(N,L)) -> and#(isNatList(activate(L)),n__isNatIListKind(activate(L))) -> and#(tt(),X) -> activate#(X) length#(cons(N,L)) -> U61#(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))), n__and(n__isNat(N),n__isNatKind(N))),activate(L)) -> U61#(tt(),L) -> activate#(L) length#(cons(N,L)) -> U61#(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))), n__and(n__isNat(N),n__isNatKind(N))),activate(L)) -> U61#(tt(),L) -> length#(activate(L)) length#(cons(N,L)) -> U61#(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))), n__and(n__isNat(N),n__isNatKind(N))),activate(L)) -> U61#(tt(),L) -> s#(length(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)) -> isNatKind#(activate(V1)) length#(cons(N,L)) -> isNatList#(activate(L)) -> isNatList#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) length#(cons(N,L)) -> isNatList#(activate(L)) -> isNatList#(n__cons(V1,V2)) -> U51#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),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)) -> activate#(X) length#(cons(N,L)) -> activate#(L) -> activate#(n__length(X)) -> length#(activate(X)) length#(cons(N,L)) -> activate#(L) -> activate#(n__s(X)) -> activate#(X) length#(cons(N,L)) -> activate#(L) -> activate#(n__s(X)) -> s#(activate(X)) length#(cons(N,L)) -> activate#(L) -> activate#(n__cons(X1,X2)) -> activate#(X1) length#(cons(N,L)) -> activate#(L) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) length#(cons(N,L)) -> activate#(L) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) length#(cons(N,L)) -> activate#(L) -> activate#(n__nil()) -> nil#() length#(cons(N,L)) -> activate#(L) -> activate#(n__and(X1,X2)) -> activate#(X1) length#(cons(N,L)) -> activate#(L) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) length#(cons(N,L)) -> activate#(L) -> activate#(n__isNat(X)) -> isNat#(X) length#(cons(N,L)) -> activate#(L) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U61#(tt(),L) -> length#(activate(L)) -> length#(nil()) -> 0#() U61#(tt(),L) -> length#(activate(L)) -> length#(cons(N,L)) -> activate#(L) U61#(tt(),L) -> length#(activate(L)) -> length#(cons(N,L)) -> isNatList#(activate(L)) U61#(tt(),L) -> length#(activate(L)) -> length#(cons(N,L)) -> and#(isNatList(activate(L)),n__isNatIListKind(activate(L))) U61#(tt(),L) -> length#(activate(L)) -> length#(cons(N,L)) -> and#(and(isNatList(activate(L)),n__isNatIListKind(activate(L))),n__and ( n__isNat(N),n__isNatKind(N))) U61#(tt(),L) -> length#(activate(L)) -> length#(cons(N,L)) -> U61#(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))), n__and(n__isNat(N),n__isNatKind(N))),activate(L)) U61#(tt(),L) -> activate#(L) -> activate#(n__zeros()) -> zeros#() U61#(tt(),L) -> activate#(L) -> activate#(n__0()) -> 0#() U61#(tt(),L) -> activate#(L) -> activate#(n__length(X)) -> activate#(X) U61#(tt(),L) -> activate#(L) -> activate#(n__length(X)) -> length#(activate(X)) U61#(tt(),L) -> activate#(L) -> activate#(n__s(X)) -> activate#(X) U61#(tt(),L) -> activate#(L) -> activate#(n__s(X)) -> s#(activate(X)) U61#(tt(),L) -> activate#(L) -> activate#(n__cons(X1,X2)) -> activate#(X1) U61#(tt(),L) -> activate#(L) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) U61#(tt(),L) -> activate#(L) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) U61#(tt(),L) -> activate#(L) -> activate#(n__nil()) -> nil#() U61#(tt(),L) -> activate#(L) -> activate#(n__and(X1,X2)) -> activate#(X1) U61#(tt(),L) -> activate#(L) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U61#(tt(),L) -> activate#(L) -> activate#(n__isNat(X)) -> isNat#(X) U61#(tt(),L) -> activate#(L) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U52#(tt(),V2) -> isNatList#(activate(V2)) -> isNatList#(n__cons(V1,V2)) -> activate#(V2) U52#(tt(),V2) -> isNatList#(activate(V2)) -> isNatList#(n__cons(V1,V2)) -> activate#(V1) U52#(tt(),V2) -> isNatList#(activate(V2)) -> isNatList#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) U52#(tt(),V2) -> isNatList#(activate(V2)) -> isNatList#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) U52#(tt(),V2) -> isNatList#(activate(V2)) -> isNatList#(n__cons(V1,V2)) -> U51#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) U52#(tt(),V2) -> activate#(V2) -> activate#(n__zeros()) -> zeros#() U52#(tt(),V2) -> activate#(V2) -> activate#(n__0()) -> 0#() U52#(tt(),V2) -> activate#(V2) -> activate#(n__length(X)) -> activate#(X) U52#(tt(),V2) -> activate#(V2) -> activate#(n__length(X)) -> length#(activate(X)) U52#(tt(),V2) -> activate#(V2) -> activate#(n__s(X)) -> activate#(X) U52#(tt(),V2) -> activate#(V2) -> activate#(n__s(X)) -> s#(activate(X)) U52#(tt(),V2) -> activate#(V2) -> activate#(n__cons(X1,X2)) -> activate#(X1) U52#(tt(),V2) -> activate#(V2) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) U52#(tt(),V2) -> activate#(V2) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) U52#(tt(),V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() U52#(tt(),V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> activate#(X1) U52#(tt(),V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U52#(tt(),V2) -> activate#(V2) -> activate#(n__isNat(X)) -> isNat#(X) U52#(tt(),V2) -> activate#(V2) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U51#(tt(),V1,V2) -> U52#(isNat(activate(V1)),activate(V2)) -> U52#(tt(),V2) -> activate#(V2) U51#(tt(),V1,V2) -> U52#(isNat(activate(V1)),activate(V2)) -> U52#(tt(),V2) -> isNatList#(activate(V2)) U51#(tt(),V1,V2) -> U52#(isNat(activate(V1)),activate(V2)) -> U52#(tt(),V2) -> U53#(isNatList(activate(V2))) U51#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__length(V1)) -> activate#(V1) U51#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)) U51#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)),activate(V1)) U51#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__s(V1)) -> activate#(V1) U51#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__s(V1)) -> isNatKind#(activate(V1)) U51#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__zeros()) -> zeros#() U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__0()) -> 0#() U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__length(X)) -> activate#(X) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__length(X)) -> length#(activate(X)) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__s(X)) -> activate#(X) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__s(X)) -> s#(activate(X)) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__cons(X1,X2)) -> activate#(X1) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> activate#(X1) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__isNat(X)) -> isNat#(X) U51#(tt(),V1,V2) -> activate#(V2) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__zeros()) -> zeros#() U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__0()) -> 0#() U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__length(X)) -> activate#(X) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__length(X)) -> length#(activate(X)) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__s(X)) -> activate#(X) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__s(X)) -> s#(activate(X)) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> activate#(X1) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__nil()) -> nil#() U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__and(X1,X2)) -> activate#(X1) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__isNat(X)) -> isNat#(X) U51#(tt(),V1,V2) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNatIList#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__length(V1)) -> activate#(V1) isNatIList#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)) isNatIList#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> activate#(V1) isNatIList#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) isNatIList#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) -> and#(tt(),X) -> activate#(X) isNatIList#(n__cons(V1,V2)) -> U41#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) -> U41#(tt(),V1,V2) -> activate#(V2) isNatIList#(n__cons(V1,V2)) -> U41#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) -> U41#(tt(),V1,V2) -> activate#(V1) isNatIList#(n__cons(V1,V2)) -> U41#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) -> U41#(tt(),V1,V2) -> isNat#(activate(V1)) isNatIList#(n__cons(V1,V2)) -> U41#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) -> U41#(tt(),V1,V2) -> U42#(isNat(activate(V1)),activate(V2)) 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)) -> activate#(X) isNatIList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__length(X)) -> length#(activate(X)) isNatIList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__s(X)) -> activate#(X) isNatIList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__s(X)) -> s#(activate(X)) isNatIList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__cons(X1,X2)) -> activate#(X1) isNatIList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) isNatIList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) isNatIList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__nil()) -> nil#() isNatIList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> activate#(X1) isNatIList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isNatIList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__isNat(X)) -> isNat#(X) isNatIList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__isNatKind(X)) -> isNatKind#(X) 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)) -> activate#(X) isNatIList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__length(X)) -> length#(activate(X)) isNatIList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__s(X)) -> activate#(X) isNatIList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__s(X)) -> s#(activate(X)) isNatIList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> activate#(X1) isNatIList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) isNatIList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) isNatIList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__nil()) -> nil#() isNatIList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> activate#(X1) isNatIList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isNatIList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__isNat(X)) -> isNat#(X) isNatIList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNatIList#(V) -> isNatIListKind#(activate(V)) -> isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) isNatIList#(V) -> isNatIListKind#(activate(V)) -> isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) isNatIList#(V) -> isNatIListKind#(activate(V)) -> isNatIListKind#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) isNatIList#(V) -> isNatIListKind#(activate(V)) -> isNatIListKind#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) isNatIList#(V) -> U31#(isNatIListKind(activate(V)),activate(V)) -> U31#(tt(),V) -> activate#(V) isNatIList#(V) -> U31#(isNatIListKind(activate(V)),activate(V)) -> U31#(tt(),V) -> isNatList#(activate(V)) isNatIList#(V) -> U31#(isNatIListKind(activate(V)),activate(V)) -> U31#(tt(),V) -> U32#(isNatList(activate(V))) isNatIList#(V) -> activate#(V) -> activate#(n__zeros()) -> zeros#() isNatIList#(V) -> activate#(V) -> activate#(n__0()) -> 0#() isNatIList#(V) -> activate#(V) -> activate#(n__length(X)) -> activate#(X) isNatIList#(V) -> activate#(V) -> activate#(n__length(X)) -> length#(activate(X)) isNatIList#(V) -> activate#(V) -> activate#(n__s(X)) -> activate#(X) isNatIList#(V) -> activate#(V) -> activate#(n__s(X)) -> s#(activate(X)) isNatIList#(V) -> activate#(V) -> activate#(n__cons(X1,X2)) -> activate#(X1) isNatIList#(V) -> activate#(V) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) isNatIList#(V) -> activate#(V) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) isNatIList#(V) -> activate#(V) -> activate#(n__nil()) -> nil#() isNatIList#(V) -> activate#(V) -> activate#(n__and(X1,X2)) -> activate#(X1) isNatIList#(V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isNatIList#(V) -> activate#(V) -> activate#(n__isNat(X)) -> isNat#(X) isNatIList#(V) -> activate#(V) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U42#(tt(),V2) -> isNatIList#(activate(V2)) -> isNatIList#(V) -> activate#(V) U42#(tt(),V2) -> isNatIList#(activate(V2)) -> isNatIList#(V) -> isNatIListKind#(activate(V)) U42#(tt(),V2) -> isNatIList#(activate(V2)) -> isNatIList#(V) -> U31#(isNatIListKind(activate(V)),activate(V)) U42#(tt(),V2) -> isNatIList#(activate(V2)) -> isNatIList#(n__cons(V1,V2)) -> activate#(V2) U42#(tt(),V2) -> isNatIList#(activate(V2)) -> isNatIList#(n__cons(V1,V2)) -> activate#(V1) U42#(tt(),V2) -> isNatIList#(activate(V2)) -> isNatIList#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) U42#(tt(),V2) -> isNatIList#(activate(V2)) -> isNatIList#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) U42#(tt(),V2) -> isNatIList#(activate(V2)) -> isNatIList#(n__cons(V1,V2)) -> U41#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) U42#(tt(),V2) -> activate#(V2) -> activate#(n__zeros()) -> zeros#() U42#(tt(),V2) -> activate#(V2) -> activate#(n__0()) -> 0#() U42#(tt(),V2) -> activate#(V2) -> activate#(n__length(X)) -> activate#(X) U42#(tt(),V2) -> activate#(V2) -> activate#(n__length(X)) -> length#(activate(X)) U42#(tt(),V2) -> activate#(V2) -> activate#(n__s(X)) -> activate#(X) U42#(tt(),V2) -> activate#(V2) -> activate#(n__s(X)) -> s#(activate(X)) U42#(tt(),V2) -> activate#(V2) -> activate#(n__cons(X1,X2)) -> activate#(X1) U42#(tt(),V2) -> activate#(V2) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) U42#(tt(),V2) -> activate#(V2) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) U42#(tt(),V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() U42#(tt(),V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> activate#(X1) U42#(tt(),V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U42#(tt(),V2) -> activate#(V2) -> activate#(n__isNat(X)) -> isNat#(X) U42#(tt(),V2) -> activate#(V2) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U41#(tt(),V1,V2) -> U42#(isNat(activate(V1)),activate(V2)) -> U42#(tt(),V2) -> activate#(V2) U41#(tt(),V1,V2) -> U42#(isNat(activate(V1)),activate(V2)) -> U42#(tt(),V2) -> isNatIList#(activate(V2)) U41#(tt(),V1,V2) -> U42#(isNat(activate(V1)),activate(V2)) -> U42#(tt(),V2) -> U43#(isNatIList(activate(V2))) U41#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__length(V1)) -> activate#(V1) U41#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)) U41#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)),activate(V1)) U41#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__s(V1)) -> activate#(V1) U41#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__s(V1)) -> isNatKind#(activate(V1)) U41#(tt(),V1,V2) -> isNat#(activate(V1)) -> isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__zeros()) -> zeros#() U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__0()) -> 0#() U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__length(X)) -> activate#(X) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__length(X)) -> length#(activate(X)) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__s(X)) -> activate#(X) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__s(X)) -> s#(activate(X)) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__cons(X1,X2)) -> activate#(X1) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__nil()) -> nil#() U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> activate#(X1) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__isNat(X)) -> isNat#(X) U41#(tt(),V1,V2) -> activate#(V2) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__zeros()) -> zeros#() U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__0()) -> 0#() U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__length(X)) -> activate#(X) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__length(X)) -> length#(activate(X)) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__s(X)) -> activate#(X) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__s(X)) -> s#(activate(X)) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> activate#(X1) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__nil()) -> nil#() U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__and(X1,X2)) -> activate#(X1) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__isNat(X)) -> isNat#(X) U41#(tt(),V1,V2) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) U31#(tt(),V) -> isNatList#(activate(V)) -> isNatList#(n__cons(V1,V2)) -> activate#(V2) U31#(tt(),V) -> isNatList#(activate(V)) -> isNatList#(n__cons(V1,V2)) -> activate#(V1) U31#(tt(),V) -> isNatList#(activate(V)) -> isNatList#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) U31#(tt(),V) -> isNatList#(activate(V)) -> isNatList#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) U31#(tt(),V) -> isNatList#(activate(V)) -> isNatList#(n__cons(V1,V2)) -> U51#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) U31#(tt(),V) -> activate#(V) -> activate#(n__zeros()) -> zeros#() U31#(tt(),V) -> activate#(V) -> activate#(n__0()) -> 0#() U31#(tt(),V) -> activate#(V) -> activate#(n__length(X)) -> activate#(X) U31#(tt(),V) -> activate#(V) -> activate#(n__length(X)) -> length#(activate(X)) U31#(tt(),V) -> activate#(V) -> activate#(n__s(X)) -> activate#(X) U31#(tt(),V) -> activate#(V) -> activate#(n__s(X)) -> s#(activate(X)) U31#(tt(),V) -> activate#(V) -> activate#(n__cons(X1,X2)) -> activate#(X1) U31#(tt(),V) -> activate#(V) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) U31#(tt(),V) -> activate#(V) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) U31#(tt(),V) -> activate#(V) -> activate#(n__nil()) -> nil#() U31#(tt(),V) -> activate#(V) -> activate#(n__and(X1,X2)) -> activate#(X1) U31#(tt(),V) -> activate#(V) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U31#(tt(),V) -> activate#(V) -> activate#(n__isNat(X)) -> isNat#(X) U31#(tt(),V) -> activate#(V) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__length(V1)) -> activate#(V1) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> activate#(V1) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) -> U21#(tt(),V1) -> activate#(V1) isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) -> U21#(tt(),V1) -> isNat#(activate(V1)) isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) -> U21#(tt(),V1) -> U22#(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)) -> activate#(X) isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__length(X)) -> length#(activate(X)) isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__s(X)) -> activate#(X) isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__s(X)) -> s#(activate(X)) isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> activate#(X1) isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__nil()) -> nil#() isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> activate#(X1) isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__isNat(X)) -> isNat#(X) isNat#(n__s(V1)) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)) -> isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)) -> isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)) -> isNatIListKind#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)) -> isNatIListKind#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(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)) -> activate#(X) isNat#(n__length(V1)) -> activate#(V1) -> activate#(n__length(X)) -> length#(activate(X)) isNat#(n__length(V1)) -> activate#(V1) -> activate#(n__s(X)) -> activate#(X) isNat#(n__length(V1)) -> activate#(V1) -> activate#(n__s(X)) -> s#(activate(X)) isNat#(n__length(V1)) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> activate#(X1) isNat#(n__length(V1)) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) isNat#(n__length(V1)) -> activate#(V1) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) isNat#(n__length(V1)) -> activate#(V1) -> activate#(n__nil()) -> nil#() isNat#(n__length(V1)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> activate#(X1) isNat#(n__length(V1)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isNat#(n__length(V1)) -> activate#(V1) -> activate#(n__isNat(X)) -> isNat#(X) isNat#(n__length(V1)) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)),activate(V1)) -> U11#(tt(),V1) -> activate#(V1) isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)),activate(V1)) -> U11#(tt(),V1) -> isNatList#(activate(V1)) isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)),activate(V1)) -> U11#(tt(),V1) -> U12#(isNatList(activate(V1))) U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__length(V1)) -> activate#(V1) U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)) U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)),activate(V1)) U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__s(V1)) -> activate#(V1) U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__s(V1)) -> isNatKind#(activate(V1)) U21#(tt(),V1) -> isNat#(activate(V1)) -> isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) U21#(tt(),V1) -> activate#(V1) -> activate#(n__zeros()) -> zeros#() U21#(tt(),V1) -> activate#(V1) -> activate#(n__0()) -> 0#() U21#(tt(),V1) -> activate#(V1) -> activate#(n__length(X)) -> activate#(X) U21#(tt(),V1) -> activate#(V1) -> activate#(n__length(X)) -> length#(activate(X)) U21#(tt(),V1) -> activate#(V1) -> activate#(n__s(X)) -> activate#(X) U21#(tt(),V1) -> activate#(V1) -> activate#(n__s(X)) -> s#(activate(X)) U21#(tt(),V1) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> activate#(X1) U21#(tt(),V1) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) U21#(tt(),V1) -> activate#(V1) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) U21#(tt(),V1) -> activate#(V1) -> activate#(n__nil()) -> nil#() U21#(tt(),V1) -> activate#(V1) -> activate#(n__and(X1,X2)) -> activate#(X1) U21#(tt(),V1) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U21#(tt(),V1) -> activate#(V1) -> activate#(n__isNat(X)) -> isNat#(X) U21#(tt(),V1) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) isNatList#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__length(V1)) -> activate#(V1) isNatList#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)) isNatList#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> activate#(V1) isNatList#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) -> isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) isNatList#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) -> and#(tt(),X) -> activate#(X) isNatList#(n__cons(V1,V2)) -> U51#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) -> U51#(tt(),V1,V2) -> activate#(V2) isNatList#(n__cons(V1,V2)) -> U51#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) -> U51#(tt(),V1,V2) -> activate#(V1) isNatList#(n__cons(V1,V2)) -> U51#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) -> U51#(tt(),V1,V2) -> isNat#(activate(V1)) isNatList#(n__cons(V1,V2)) -> U51#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) -> U51#(tt(),V1,V2) -> U52#(isNat(activate(V1)),activate(V2)) 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)) -> activate#(X) isNatList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__length(X)) -> length#(activate(X)) isNatList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__s(X)) -> activate#(X) isNatList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__s(X)) -> s#(activate(X)) isNatList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__cons(X1,X2)) -> activate#(X1) isNatList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) isNatList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) isNatList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__nil()) -> nil#() isNatList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> activate#(X1) isNatList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isNatList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__isNat(X)) -> isNat#(X) isNatList#(n__cons(V1,V2)) -> activate#(V2) -> activate#(n__isNatKind(X)) -> isNatKind#(X) 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)) -> activate#(X) isNatList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__length(X)) -> length#(activate(X)) isNatList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__s(X)) -> activate#(X) isNatList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__s(X)) -> s#(activate(X)) isNatList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> activate#(X1) isNatList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) isNatList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) isNatList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__nil()) -> nil#() isNatList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> activate#(X1) isNatList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) isNatList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__isNat(X)) -> isNat#(X) isNatList#(n__cons(V1,V2)) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) -> and#(tt(),X) -> activate#(X) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__zeros()) -> zeros#() activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__0()) -> 0#() activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__length(X)) -> activate#(X) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__length(X)) -> length#(activate(X)) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__s(X)) -> activate#(X) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__s(X)) -> s#(activate(X)) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__cons(X1,X2)) -> activate#(X1) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__nil()) -> nil#() activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__and(X1,X2)) -> activate#(X1) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__isNat(X)) -> isNat#(X) activate#(n__and(X1,X2)) -> activate#(X1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) activate#(n__isNatKind(X)) -> isNatKind#(X) -> isNatKind#(n__length(V1)) -> activate#(V1) activate#(n__isNatKind(X)) -> isNatKind#(X) -> isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)) activate#(n__isNatKind(X)) -> isNatKind#(X) -> isNatKind#(n__s(V1)) -> activate#(V1) activate#(n__isNatKind(X)) -> isNatKind#(X) -> isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) activate#(n__isNat(X)) -> isNat#(X) -> isNat#(n__length(V1)) -> activate#(V1) activate#(n__isNat(X)) -> isNat#(X) -> isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)) activate#(n__isNat(X)) -> isNat#(X) -> isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)),activate(V1)) activate#(n__isNat(X)) -> isNat#(X) -> isNat#(n__s(V1)) -> activate#(V1) activate#(n__isNat(X)) -> isNat#(X) -> isNat#(n__s(V1)) -> isNatKind#(activate(V1)) activate#(n__isNat(X)) -> isNat#(X) -> isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) -> isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) -> isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) -> isNatIListKind#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) -> isNatIListKind#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) activate#(n__cons(X1,X2)) -> activate#(X1) -> activate#(n__zeros()) -> zeros#() activate#(n__cons(X1,X2)) -> activate#(X1) -> activate#(n__0()) -> 0#() activate#(n__cons(X1,X2)) -> activate#(X1) -> activate#(n__length(X)) -> activate#(X) activate#(n__cons(X1,X2)) -> activate#(X1) -> activate#(n__length(X)) -> length#(activate(X)) activate#(n__cons(X1,X2)) -> activate#(X1) -> activate#(n__s(X)) -> activate#(X) activate#(n__cons(X1,X2)) -> activate#(X1) -> activate#(n__s(X)) -> s#(activate(X)) activate#(n__cons(X1,X2)) -> activate#(X1) -> activate#(n__cons(X1,X2)) -> activate#(X1) activate#(n__cons(X1,X2)) -> activate#(X1) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) activate#(n__cons(X1,X2)) -> activate#(X1) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) activate#(n__cons(X1,X2)) -> activate#(X1) -> activate#(n__nil()) -> nil#() activate#(n__cons(X1,X2)) -> activate#(X1) -> activate#(n__and(X1,X2)) -> activate#(X1) activate#(n__cons(X1,X2)) -> activate#(X1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) activate#(n__cons(X1,X2)) -> activate#(X1) -> activate#(n__isNat(X)) -> isNat#(X) activate#(n__cons(X1,X2)) -> activate#(X1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) activate#(n__s(X)) -> activate#(X) -> activate#(n__zeros()) -> zeros#() activate#(n__s(X)) -> activate#(X) -> activate#(n__0()) -> 0#() activate#(n__s(X)) -> activate#(X) -> activate#(n__length(X)) -> activate#(X) activate#(n__s(X)) -> activate#(X) -> activate#(n__length(X)) -> length#(activate(X)) activate#(n__s(X)) -> activate#(X) -> activate#(n__s(X)) -> activate#(X) activate#(n__s(X)) -> activate#(X) -> activate#(n__s(X)) -> s#(activate(X)) activate#(n__s(X)) -> activate#(X) -> activate#(n__cons(X1,X2)) -> activate#(X1) activate#(n__s(X)) -> activate#(X) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) activate#(n__s(X)) -> activate#(X) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) activate#(n__s(X)) -> activate#(X) -> activate#(n__nil()) -> nil#() activate#(n__s(X)) -> activate#(X) -> activate#(n__and(X1,X2)) -> activate#(X1) activate#(n__s(X)) -> activate#(X) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) activate#(n__s(X)) -> activate#(X) -> activate#(n__isNat(X)) -> isNat#(X) activate#(n__s(X)) -> activate#(X) -> activate#(n__isNatKind(X)) -> isNatKind#(X) activate#(n__length(X)) -> length#(activate(X)) -> length#(nil()) -> 0#() activate#(n__length(X)) -> length#(activate(X)) -> length#(cons(N,L)) -> activate#(L) activate#(n__length(X)) -> length#(activate(X)) -> length#(cons(N,L)) -> isNatList#(activate(L)) activate#(n__length(X)) -> length#(activate(X)) -> length#(cons(N,L)) -> and#(isNatList(activate(L)),n__isNatIListKind(activate(L))) activate#(n__length(X)) -> length#(activate(X)) -> length#(cons(N,L)) -> and#(and(isNatList(activate(L)),n__isNatIListKind(activate(L))),n__and ( n__isNat(N),n__isNatKind(N))) activate#(n__length(X)) -> length#(activate(X)) -> length#(cons(N,L)) -> U61#(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))), n__and(n__isNat(N),n__isNatKind(N))),activate(L)) activate#(n__length(X)) -> activate#(X) -> activate#(n__zeros()) -> zeros#() activate#(n__length(X)) -> activate#(X) -> activate#(n__0()) -> 0#() activate#(n__length(X)) -> activate#(X) -> activate#(n__length(X)) -> activate#(X) activate#(n__length(X)) -> activate#(X) -> activate#(n__length(X)) -> length#(activate(X)) activate#(n__length(X)) -> activate#(X) -> activate#(n__s(X)) -> activate#(X) activate#(n__length(X)) -> activate#(X) -> activate#(n__s(X)) -> s#(activate(X)) activate#(n__length(X)) -> activate#(X) -> activate#(n__cons(X1,X2)) -> activate#(X1) activate#(n__length(X)) -> activate#(X) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) activate#(n__length(X)) -> activate#(X) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) activate#(n__length(X)) -> activate#(X) -> activate#(n__nil()) -> nil#() activate#(n__length(X)) -> activate#(X) -> activate#(n__and(X1,X2)) -> activate#(X1) activate#(n__length(X)) -> activate#(X) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) activate#(n__length(X)) -> activate#(X) -> activate#(n__isNat(X)) -> isNat#(X) activate#(n__length(X)) -> activate#(X) -> activate#(n__isNatKind(X)) -> isNatKind#(X) activate#(n__zeros()) -> zeros#() -> zeros#() -> 0#() activate#(n__zeros()) -> zeros#() -> zeros#() -> cons#(0(),n__zeros()) U11#(tt(),V1) -> isNatList#(activate(V1)) -> isNatList#(n__cons(V1,V2)) -> activate#(V2) U11#(tt(),V1) -> isNatList#(activate(V1)) -> isNatList#(n__cons(V1,V2)) -> activate#(V1) U11#(tt(),V1) -> isNatList#(activate(V1)) -> isNatList#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) U11#(tt(),V1) -> isNatList#(activate(V1)) -> isNatList#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) U11#(tt(),V1) -> isNatList#(activate(V1)) -> isNatList#(n__cons(V1,V2)) -> U51#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) U11#(tt(),V1) -> activate#(V1) -> activate#(n__zeros()) -> zeros#() U11#(tt(),V1) -> activate#(V1) -> activate#(n__0()) -> 0#() U11#(tt(),V1) -> activate#(V1) -> activate#(n__length(X)) -> activate#(X) U11#(tt(),V1) -> activate#(V1) -> activate#(n__length(X)) -> length#(activate(X)) U11#(tt(),V1) -> activate#(V1) -> activate#(n__s(X)) -> activate#(X) U11#(tt(),V1) -> activate#(V1) -> activate#(n__s(X)) -> s#(activate(X)) U11#(tt(),V1) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> activate#(X1) U11#(tt(),V1) -> activate#(V1) -> activate#(n__cons(X1,X2)) -> cons#(activate(X1),X2) U11#(tt(),V1) -> activate#(V1) -> activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) U11#(tt(),V1) -> activate#(V1) -> activate#(n__nil()) -> nil#() U11#(tt(),V1) -> activate#(V1) -> activate#(n__and(X1,X2)) -> activate#(X1) U11#(tt(),V1) -> activate#(V1) -> activate#(n__and(X1,X2)) -> and#(activate(X1),X2) U11#(tt(),V1) -> activate#(V1) -> activate#(n__isNat(X)) -> isNat#(X) U11#(tt(),V1) -> activate#(V1) -> activate#(n__isNatKind(X)) -> isNatKind#(X) SCC Processor: #sccs: 2 #rules: 49 #arcs: 516/5776 DPs: isNatIList#(n__cons(V1,V2)) -> U41#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) U41#(tt(),V1,V2) -> U42#(isNat(activate(V1)),activate(V2)) U42#(tt(),V2) -> isNatIList#(activate(V2)) TRS: zeros() -> cons(0(),n__zeros()) U11(tt(),V1) -> U12(isNatList(activate(V1))) U12(tt()) -> tt() U21(tt(),V1) -> U22(isNat(activate(V1))) U22(tt()) -> tt() U31(tt(),V) -> U32(isNatList(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isNat(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNatIList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNat(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isNatList(activate(V2))) U53(tt()) -> tt() U61(tt(),L) -> s(length(activate(L))) and(tt(),X) -> activate(X) isNat(n__0()) -> tt() isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)),activate(V1)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatIList(V) -> U31(isNatIListKind(activate(V)),activate(V)) isNatIList(n__zeros()) -> tt() isNatIList(n__cons(V1,V2)) -> U41(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) isNatIListKind(n__nil()) -> tt() isNatIListKind(n__zeros()) -> tt() isNatIListKind(n__cons(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) isNatKind(n__0()) -> tt() isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) isNatKind(n__s(V1)) -> isNatKind(activate(V1)) isNatList(n__nil()) -> tt() isNatList(n__cons(V1,V2)) -> U51(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) length(nil()) -> 0() length(cons(N,L)) -> U61(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))), n__and(n__isNat(N),n__isNatKind(N))),activate(L)) zeros() -> n__zeros() 0() -> n__0() length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) isNatIListKind(X) -> n__isNatIListKind(X) nil() -> n__nil() and(X1,X2) -> n__and(X1,X2) isNat(X) -> n__isNat(X) isNatKind(X) -> n__isNatKind(X) activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__isNatIListKind(X)) -> isNatIListKind(X) activate(n__nil()) -> nil() activate(n__and(X1,X2)) -> and(activate(X1),X2) activate(n__isNat(X)) -> isNat(X) activate(n__isNatKind(X)) -> isNatKind(X) activate(X) -> X Open DPs: isNatKind#(n__s(V1)) -> isNatKind#(activate(V1)) isNatKind#(n__s(V1)) -> activate#(V1) activate#(n__isNatKind(X)) -> isNatKind#(X) isNatKind#(n__length(V1)) -> isNatIListKind#(activate(V1)) isNatIListKind#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) and#(tt(),X) -> activate#(X) activate#(n__isNat(X)) -> isNat#(X) isNat#(n__s(V1)) -> U21#(isNatKind(activate(V1)),activate(V1)) U21#(tt(),V1) -> isNat#(activate(V1)) isNat#(n__s(V1)) -> isNatKind#(activate(V1)) isNatKind#(n__length(V1)) -> activate#(V1) activate#(n__and(X1,X2)) -> and#(activate(X1),X2) activate#(n__and(X1,X2)) -> activate#(X1) activate#(n__isNatIListKind(X)) -> isNatIListKind#(X) isNatIListKind#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) isNatIListKind#(n__cons(V1,V2)) -> activate#(V1) activate#(n__cons(X1,X2)) -> activate#(X1) activate#(n__s(X)) -> activate#(X) activate#(n__length(X)) -> length#(activate(X)) length#(cons(N,L)) -> U61#(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))), n__and(n__isNat(N),n__isNatKind(N))),activate(L)) U61#(tt(),L) -> length#(activate(L)) length#(cons(N,L)) -> and#(and(isNatList(activate(L)),n__isNatIListKind(activate(L))), n__and(n__isNat(N),n__isNatKind(N))) length#(cons(N,L)) -> and#(isNatList(activate(L)),n__isNatIListKind(activate(L))) length#(cons(N,L)) -> isNatList#(activate(L)) isNatList#(n__cons(V1,V2)) -> U51#(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) U51#(tt(),V1,V2) -> U52#(isNat(activate(V1)),activate(V2)) U52#(tt(),V2) -> isNatList#(activate(V2)) isNatList#(n__cons(V1,V2)) -> and#(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) isNatList#(n__cons(V1,V2)) -> isNatKind#(activate(V1)) isNatList#(n__cons(V1,V2)) -> activate#(V1) activate#(n__length(X)) -> activate#(X) isNatList#(n__cons(V1,V2)) -> activate#(V2) U52#(tt(),V2) -> activate#(V2) U51#(tt(),V1,V2) -> isNat#(activate(V1)) isNat#(n__s(V1)) -> activate#(V1) isNat#(n__length(V1)) -> U11#(isNatIListKind(activate(V1)),activate(V1)) U11#(tt(),V1) -> isNatList#(activate(V1)) U11#(tt(),V1) -> activate#(V1) isNat#(n__length(V1)) -> isNatIListKind#(activate(V1)) isNatIListKind#(n__cons(V1,V2)) -> activate#(V2) isNat#(n__length(V1)) -> activate#(V1) U51#(tt(),V1,V2) -> activate#(V1) U51#(tt(),V1,V2) -> activate#(V2) length#(cons(N,L)) -> activate#(L) U61#(tt(),L) -> activate#(L) U21#(tt(),V1) -> activate#(V1) TRS: zeros() -> cons(0(),n__zeros()) U11(tt(),V1) -> U12(isNatList(activate(V1))) U12(tt()) -> tt() U21(tt(),V1) -> U22(isNat(activate(V1))) U22(tt()) -> tt() U31(tt(),V) -> U32(isNatList(activate(V))) U32(tt()) -> tt() U41(tt(),V1,V2) -> U42(isNat(activate(V1)),activate(V2)) U42(tt(),V2) -> U43(isNatIList(activate(V2))) U43(tt()) -> tt() U51(tt(),V1,V2) -> U52(isNat(activate(V1)),activate(V2)) U52(tt(),V2) -> U53(isNatList(activate(V2))) U53(tt()) -> tt() U61(tt(),L) -> s(length(activate(L))) and(tt(),X) -> activate(X) isNat(n__0()) -> tt() isNat(n__length(V1)) -> U11(isNatIListKind(activate(V1)),activate(V1)) isNat(n__s(V1)) -> U21(isNatKind(activate(V1)),activate(V1)) isNatIList(V) -> U31(isNatIListKind(activate(V)),activate(V)) isNatIList(n__zeros()) -> tt() isNatIList(n__cons(V1,V2)) -> U41(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) isNatIListKind(n__nil()) -> tt() isNatIListKind(n__zeros()) -> tt() isNatIListKind(n__cons(V1,V2)) -> and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))) isNatKind(n__0()) -> tt() isNatKind(n__length(V1)) -> isNatIListKind(activate(V1)) isNatKind(n__s(V1)) -> isNatKind(activate(V1)) isNatList(n__nil()) -> tt() isNatList(n__cons(V1,V2)) -> U51(and(isNatKind(activate(V1)),n__isNatIListKind(activate(V2))),activate(V1),activate(V2)) length(nil()) -> 0() length(cons(N,L)) -> U61(and(and(isNatList(activate(L)),n__isNatIListKind(activate(L))), n__and(n__isNat(N),n__isNatKind(N))),activate(L)) zeros() -> n__zeros() 0() -> n__0() length(X) -> n__length(X) s(X) -> n__s(X) cons(X1,X2) -> n__cons(X1,X2) isNatIListKind(X) -> n__isNatIListKind(X) nil() -> n__nil() and(X1,X2) -> n__and(X1,X2) isNat(X) -> n__isNat(X) isNatKind(X) -> n__isNatKind(X) activate(n__zeros()) -> zeros() activate(n__0()) -> 0() activate(n__length(X)) -> length(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__cons(X1,X2)) -> cons(activate(X1),X2) activate(n__isNatIListKind(X)) -> isNatIListKind(X) activate(n__nil()) -> nil() activate(n__and(X1,X2)) -> and(activate(X1),X2) activate(n__isNat(X)) -> isNat(X) activate(n__isNatKind(X)) -> isNatKind(X) activate(X) -> X Open