MAYBE Problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatList(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(X) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) Proof: DP Processor: DPs: a__U11#(tt(),V1) -> a__isNatList#(V1) a__U11#(tt(),V1) -> a__U12#(a__isNatList(V1)) a__U21#(tt(),V1) -> a__isNat#(V1) a__U21#(tt(),V1) -> a__U22#(a__isNat(V1)) a__U31#(tt(),V) -> a__isNatList#(V) a__U31#(tt(),V) -> a__U32#(a__isNatList(V)) a__U41#(tt(),V1,V2) -> a__isNat#(V1) a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) a__U42#(tt(),V2) -> a__isNatIList#(V2) a__U42#(tt(),V2) -> a__U43#(a__isNatIList(V2)) a__U51#(tt(),V1,V2) -> a__isNat#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) a__U52#(tt(),V2) -> a__isNatList#(V2) a__U52#(tt(),V2) -> a__U53#(a__isNatList(V2)) a__U61#(tt(),L) -> mark#(L) a__U61#(tt(),L) -> a__length#(mark(L)) a__and#(tt(),X) -> mark#(X) a__isNat#(length(V1)) -> a__isNatIListKind#(V1) a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) a__isNat#(s(V1)) -> a__isNatKind#(V1) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__isNatIList#(V) -> a__isNatIListKind#(V) a__isNatIList#(V) -> a__U31#(a__isNatIListKind(V),V) a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length#(cons(N,L)) -> a__isNatList#(L) a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNatIListKind(L)) a__length#(cons(N,L)) -> a__and#(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))) a__length#(cons(N,L)) -> a__U61#(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark#(zeros()) -> a__zeros#() mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> a__U12#(mark(X)) mark#(isNatList(X)) -> a__isNatList#(X) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U22(X)) -> mark#(X) mark#(U22(X)) -> a__U22#(mark(X)) mark#(isNat(X)) -> a__isNat#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> a__U32#(mark(X)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> a__U43#(mark(X)) mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> a__U53#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatList(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(X) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) TDG Processor: DPs: a__U11#(tt(),V1) -> a__isNatList#(V1) a__U11#(tt(),V1) -> a__U12#(a__isNatList(V1)) a__U21#(tt(),V1) -> a__isNat#(V1) a__U21#(tt(),V1) -> a__U22#(a__isNat(V1)) a__U31#(tt(),V) -> a__isNatList#(V) a__U31#(tt(),V) -> a__U32#(a__isNatList(V)) a__U41#(tt(),V1,V2) -> a__isNat#(V1) a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) a__U42#(tt(),V2) -> a__isNatIList#(V2) a__U42#(tt(),V2) -> a__U43#(a__isNatIList(V2)) a__U51#(tt(),V1,V2) -> a__isNat#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) a__U52#(tt(),V2) -> a__isNatList#(V2) a__U52#(tt(),V2) -> a__U53#(a__isNatList(V2)) a__U61#(tt(),L) -> mark#(L) a__U61#(tt(),L) -> a__length#(mark(L)) a__and#(tt(),X) -> mark#(X) a__isNat#(length(V1)) -> a__isNatIListKind#(V1) a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) a__isNat#(s(V1)) -> a__isNatKind#(V1) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__isNatIList#(V) -> a__isNatIListKind#(V) a__isNatIList#(V) -> a__U31#(a__isNatIListKind(V),V) a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length#(cons(N,L)) -> a__isNatList#(L) a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNatIListKind(L)) a__length#(cons(N,L)) -> a__and#(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))) a__length#(cons(N,L)) -> a__U61#(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark#(zeros()) -> a__zeros#() mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> a__U12#(mark(X)) mark#(isNatList(X)) -> a__isNatList#(X) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U22(X)) -> mark#(X) mark#(U22(X)) -> a__U22#(mark(X)) mark#(isNat(X)) -> a__isNat#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> a__U32#(mark(X)) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> a__U43#(mark(X)) mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> a__U53#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatList(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(X) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) graph: a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) -> a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) -> a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) -> a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) -> a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) -> a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) -> a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) -> a__and#(tt(),X) -> mark#(X) a__and#(tt(),X) -> mark#(X) -> mark#(s(X)) -> mark#(X) a__and#(tt(),X) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(isNatKind(X)) -> a__isNatKind#(X) a__and#(tt(),X) -> mark#(X) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) a__and#(tt(),X) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) a__and#(tt(),X) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) a__and#(tt(),X) -> mark#(X) -> mark#(length(X)) -> mark#(X) a__and#(tt(),X) -> mark#(X) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) a__and#(tt(),X) -> mark#(X) -> mark#(U61(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(U53(X)) -> a__U53#(mark(X)) a__and#(tt(),X) -> mark#(X) -> mark#(U53(X)) -> mark#(X) a__and#(tt(),X) -> mark#(X) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) a__and#(tt(),X) -> mark#(X) -> mark#(U52(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) a__and#(tt(),X) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) a__and#(tt(),X) -> mark#(X) -> mark#(U43(X)) -> a__U43#(mark(X)) a__and#(tt(),X) -> mark#(X) -> mark#(U43(X)) -> mark#(X) a__and#(tt(),X) -> mark#(X) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) a__and#(tt(),X) -> mark#(X) -> mark#(U42(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) a__and#(tt(),X) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(U32(X)) -> a__U32#(mark(X)) a__and#(tt(),X) -> mark#(X) -> mark#(U32(X)) -> mark#(X) a__and#(tt(),X) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) a__and#(tt(),X) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) a__and#(tt(),X) -> mark#(X) -> mark#(U22(X)) -> a__U22#(mark(X)) a__and#(tt(),X) -> mark#(X) -> mark#(U22(X)) -> mark#(X) a__and#(tt(),X) -> mark#(X) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) a__and#(tt(),X) -> mark#(X) -> mark#(U21(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) a__and#(tt(),X) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) a__and#(tt(),X) -> mark#(X) -> mark#(U12(X)) -> mark#(X) a__and#(tt(),X) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__and#(tt(),X) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(zeros()) -> a__zeros#() a__length#(cons(N,L)) -> a__and#(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))) -> a__and#(tt(),X) -> mark#(X) a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNatIListKind(L)) -> a__and#(tt(),X) -> mark#(X) a__length#(cons(N,L)) -> a__U61#(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) -> a__U61#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__U61#(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) -> a__U61#(tt(),L) -> mark#(L) a__length#(cons(N,L)) -> a__isNatList#(L) -> a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length#(cons(N,L)) -> a__isNatList#(L) -> a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__length#(cons(N,L)) -> a__isNatList#(L) -> a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) -> a__U61#(tt(),L) -> a__length#(mark(L)) mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) -> a__U61#(tt(),L) -> mark#(L) mark#(U53(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(U53(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U53(X)) -> mark#(X) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U53(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U53(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U53(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(U53(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U53(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U53(X)) -> mark#(X) -> mark#(U53(X)) -> mark#(X) mark#(U53(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U53(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U53(X)) -> mark#(X) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U53(X)) -> mark#(X) -> mark#(U43(X)) -> mark#(X) mark#(U53(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U53(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U53(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U53(X)) -> mark#(X) -> mark#(U32(X)) -> mark#(X) mark#(U53(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U53(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U53(X)) -> mark#(X) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U53(X)) -> mark#(X) -> mark#(U22(X)) -> mark#(X) mark#(U53(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U53(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U53(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U53(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(U53(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U53(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U53(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#() mark#(U52(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) -> a__U52#(tt(),V2) -> a__U53#(a__isNatList(V2)) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) -> a__U52#(tt(),V2) -> a__isNatList#(V2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) -> a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) -> a__U51#(tt(),V1,V2) -> a__isNat#(V1) mark#(isNatIList(X)) -> a__isNatIList#(X) -> a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) mark#(isNatIList(X)) -> a__isNatIList#(X) -> a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) mark#(isNatIList(X)) -> a__isNatIList#(X) -> a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) mark#(isNatIList(X)) -> a__isNatIList#(X) -> a__isNatIList#(V) -> a__U31#(a__isNatIListKind(V),V) mark#(isNatIList(X)) -> a__isNatIList#(X) -> a__isNatIList#(V) -> a__isNatIListKind#(V) mark#(U43(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(U43(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U43(X)) -> mark#(X) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U43(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U43(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U43(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(U43(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U43(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U43(X)) -> mark#(X) -> mark#(U53(X)) -> mark#(X) mark#(U43(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U43(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U43(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U43(X)) -> mark#(X) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U43(X)) -> mark#(X) -> mark#(U43(X)) -> mark#(X) mark#(U43(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U43(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U43(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U43(X)) -> mark#(X) -> mark#(U32(X)) -> mark#(X) mark#(U43(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U43(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U43(X)) -> mark#(X) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U43(X)) -> mark#(X) -> mark#(U22(X)) -> mark#(X) mark#(U43(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U43(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U43(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U43(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(U43(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U43(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U43(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#() mark#(U42(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) -> a__U42#(tt(),V2) -> a__U43#(a__isNatIList(V2)) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) -> a__U42#(tt(),V2) -> a__isNatIList#(V2) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) -> a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) -> a__U41#(tt(),V1,V2) -> a__isNat#(V1) mark#(U32(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(U32(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U32(X)) -> mark#(X) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U32(X)) -> mark#(X) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U32(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U32(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U32(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U32(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(U32(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U32(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U32(X)) -> mark#(X) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U32(X)) -> mark#(X) -> mark#(U53(X)) -> mark#(X) mark#(U32(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U32(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U32(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U32(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U32(X)) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U32(X)) -> mark#(X) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U32(X)) -> mark#(X) -> mark#(U43(X)) -> mark#(X) mark#(U32(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U32(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U32(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U32(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U32(X)) -> mark#(X) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U32(X)) -> mark#(X) -> mark#(U32(X)) -> mark#(X) mark#(U32(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U32(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U32(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U32(X)) -> mark#(X) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U32(X)) -> mark#(X) -> mark#(U22(X)) -> mark#(X) mark#(U32(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U32(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U32(X)) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U32(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U32(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(U32(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U32(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U32(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#() mark#(U31(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) -> a__U31#(tt(),V) -> a__U32#(a__isNatList(V)) mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) -> a__U31#(tt(),V) -> a__isNatList#(V) mark#(U22(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(U22(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U22(X)) -> mark#(X) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U22(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U22(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U22(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(U22(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U22(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U22(X)) -> mark#(X) -> mark#(U53(X)) -> mark#(X) mark#(U22(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U22(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U22(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U22(X)) -> mark#(X) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U22(X)) -> mark#(X) -> mark#(U43(X)) -> mark#(X) mark#(U22(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U22(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U22(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U22(X)) -> mark#(X) -> mark#(U32(X)) -> mark#(X) mark#(U22(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U22(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U22(X)) -> mark#(X) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U22(X)) -> mark#(X) -> mark#(U22(X)) -> mark#(X) mark#(U22(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U22(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U22(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U22(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(U22(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U22(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U22(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#() mark#(U21(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) -> a__U21#(tt(),V1) -> a__U22#(a__isNat(V1)) mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) -> a__U21#(tt(),V1) -> a__isNat#(V1) mark#(isNatList(X)) -> a__isNatList#(X) -> a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) mark#(isNatList(X)) -> a__isNatList#(X) -> a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) mark#(isNatList(X)) -> a__isNatList#(X) -> a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) mark#(U12(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U12(X)) -> mark#(X) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U12(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U12(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U12(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U12(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U12(X)) -> mark#(X) -> mark#(U53(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U12(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U12(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U12(X)) -> mark#(X) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U12(X)) -> mark#(X) -> mark#(U43(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U12(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U12(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U12(X)) -> mark#(X) -> mark#(U32(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U12(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U12(X)) -> mark#(X) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U12(X)) -> mark#(X) -> mark#(U22(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U12(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U12(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U12(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(U12(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U12(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U12(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#() mark#(U11(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) -> a__U11#(tt(),V1) -> a__U12#(a__isNatList(V1)) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) -> a__U11#(tt(),V1) -> a__isNatList#(V1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) -> a__and#(tt(),X) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(isNatKind(X)) -> a__isNatKind#(X) -> a__isNatKind#(s(V1)) -> a__isNatKind#(V1) mark#(isNatKind(X)) -> a__isNatKind#(X) -> a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) mark#(isNat(X)) -> a__isNat#(X) -> a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) mark#(isNat(X)) -> a__isNat#(X) -> a__isNat#(s(V1)) -> a__isNatKind#(V1) mark#(isNat(X)) -> a__isNat#(X) -> a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) mark#(isNat(X)) -> a__isNat#(X) -> a__isNat#(length(V1)) -> a__isNatIListKind#(V1) mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) -> a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) -> a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) mark#(length(X)) -> a__length#(mark(X)) -> a__length#(cons(N,L)) -> a__U61#(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark#(length(X)) -> a__length#(mark(X)) -> a__length#(cons(N,L)) -> a__and#(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))) mark#(length(X)) -> a__length#(mark(X)) -> a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNatIListKind(L)) mark#(length(X)) -> a__length#(mark(X)) -> a__length#(cons(N,L)) -> a__isNatList#(L) mark#(length(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(length(X)) -> mark#(X) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(length(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(length(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(length(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(length(X)) -> mark#(X) -> mark#(U53(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(length(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(length(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(length(X)) -> mark#(X) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(length(X)) -> mark#(X) -> mark#(U43(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(length(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(length(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(length(X)) -> mark#(X) -> mark#(U32(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(length(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(length(X)) -> mark#(X) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(length(X)) -> mark#(X) -> mark#(U22(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(length(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(length(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(length(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(length(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#() mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(s(X)) -> mark#(X) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(U53(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(s(X)) -> mark#(X) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(U43(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(s(X)) -> mark#(X) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(U32(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(s(X)) -> mark#(X) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(U22(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(s(X)) -> mark#(X) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(U12(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#() mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U61(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> a__U53#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U53(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U52(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> a__U43#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U43(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U42(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> a__U32#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U32(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> a__U22#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U22(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U21(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> a__U12#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U12(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() a__U61#(tt(),L) -> a__length#(mark(L)) -> a__length#(cons(N,L)) -> a__U61#(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) a__U61#(tt(),L) -> a__length#(mark(L)) -> a__length#(cons(N,L)) -> a__and#(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))) a__U61#(tt(),L) -> a__length#(mark(L)) -> a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNatIListKind(L)) a__U61#(tt(),L) -> a__length#(mark(L)) -> a__length#(cons(N,L)) -> a__isNatList#(L) a__U61#(tt(),L) -> mark#(L) -> mark#(s(X)) -> mark#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(cons(X1,X2)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(isNatKind(X)) -> a__isNatKind#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) a__U61#(tt(),L) -> mark#(L) -> mark#(and(X1,X2)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(length(X)) -> a__length#(mark(X)) a__U61#(tt(),L) -> mark#(L) -> mark#(length(X)) -> mark#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) a__U61#(tt(),L) -> mark#(L) -> mark#(U61(X1,X2)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(U53(X)) -> a__U53#(mark(X)) a__U61#(tt(),L) -> mark#(L) -> mark#(U53(X)) -> mark#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) a__U61#(tt(),L) -> mark#(L) -> mark#(U52(X1,X2)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) a__U61#(tt(),L) -> mark#(L) -> mark#(U51(X1,X2,X3)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(isNatIList(X)) -> a__isNatIList#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(U43(X)) -> a__U43#(mark(X)) a__U61#(tt(),L) -> mark#(L) -> mark#(U43(X)) -> mark#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) a__U61#(tt(),L) -> mark#(L) -> mark#(U42(X1,X2)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) a__U61#(tt(),L) -> mark#(L) -> mark#(U41(X1,X2,X3)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(U32(X)) -> a__U32#(mark(X)) a__U61#(tt(),L) -> mark#(L) -> mark#(U32(X)) -> mark#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) a__U61#(tt(),L) -> mark#(L) -> mark#(U31(X1,X2)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(isNat(X)) -> a__isNat#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(U22(X)) -> a__U22#(mark(X)) a__U61#(tt(),L) -> mark#(L) -> mark#(U22(X)) -> mark#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) a__U61#(tt(),L) -> mark#(L) -> mark#(U21(X1,X2)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(isNatList(X)) -> a__isNatList#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(U12(X)) -> a__U12#(mark(X)) a__U61#(tt(),L) -> mark#(L) -> mark#(U12(X)) -> mark#(X) a__U61#(tt(),L) -> mark#(L) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__U61#(tt(),L) -> mark#(L) -> mark#(U11(X1,X2)) -> mark#(X1) a__U61#(tt(),L) -> mark#(L) -> mark#(zeros()) -> a__zeros#() a__U52#(tt(),V2) -> a__isNatList#(V2) -> a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__U52#(tt(),V2) -> a__isNatList#(V2) -> a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__U52#(tt(),V2) -> a__isNatList#(V2) -> a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) -> a__U52#(tt(),V2) -> a__U53#(a__isNatList(V2)) a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) -> a__U52#(tt(),V2) -> a__isNatList#(V2) a__U51#(tt(),V1,V2) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U51#(tt(),V1,V2) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__isNatKind#(V1) a__U51#(tt(),V1,V2) -> a__isNat#(V1) -> a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) a__U51#(tt(),V1,V2) -> a__isNat#(V1) -> a__isNat#(length(V1)) -> a__isNatIListKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) -> a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) -> a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) -> a__and#(tt(),X) -> mark#(X) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) -> a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) -> a__U41#(tt(),V1,V2) -> a__isNat#(V1) a__isNatIList#(V) -> a__isNatIListKind#(V) -> a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatIList#(V) -> a__isNatIListKind#(V) -> a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIList#(V) -> a__U31#(a__isNatIListKind(V),V) -> a__U31#(tt(),V) -> a__U32#(a__isNatList(V)) a__isNatIList#(V) -> a__U31#(a__isNatIListKind(V),V) -> a__U31#(tt(),V) -> a__isNatList#(V) a__U42#(tt(),V2) -> a__isNatIList#(V2) -> a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__U42#(tt(),V2) -> a__isNatIList#(V2) -> a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__U42#(tt(),V2) -> a__isNatIList#(V2) -> a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) a__U42#(tt(),V2) -> a__isNatIList#(V2) -> a__isNatIList#(V) -> a__U31#(a__isNatIListKind(V),V) a__U42#(tt(),V2) -> a__isNatIList#(V2) -> a__isNatIList#(V) -> a__isNatIListKind#(V) a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) -> a__U42#(tt(),V2) -> a__U43#(a__isNatIList(V2)) a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) -> a__U42#(tt(),V2) -> a__isNatIList#(V2) a__U41#(tt(),V1,V2) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U41#(tt(),V1,V2) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__isNatKind#(V1) a__U41#(tt(),V1,V2) -> a__isNat#(V1) -> a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) a__U41#(tt(),V1,V2) -> a__isNat#(V1) -> a__isNat#(length(V1)) -> a__isNatIListKind#(V1) a__U31#(tt(),V) -> a__isNatList#(V) -> a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__U31#(tt(),V) -> a__isNatList#(V) -> a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__U31#(tt(),V) -> a__isNatList#(V) -> a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNat#(length(V1)) -> a__isNatIListKind#(V1) -> a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNat#(length(V1)) -> a__isNatIListKind#(V1) -> a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) -> a__U11#(tt(),V1) -> a__U12#(a__isNatList(V1)) a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) -> a__U11#(tt(),V1) -> a__isNatList#(V1) a__isNat#(s(V1)) -> a__isNatKind#(V1) -> a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNat#(s(V1)) -> a__isNatKind#(V1) -> a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) -> a__U21#(tt(),V1) -> a__U22#(a__isNat(V1)) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) -> a__U21#(tt(),V1) -> a__isNat#(V1) a__U21#(tt(),V1) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__isNatKind#(V1) a__U21#(tt(),V1) -> a__isNat#(V1) -> a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) a__U21#(tt(),V1) -> a__isNat#(V1) -> a__isNat#(length(V1)) -> a__isNatIListKind#(V1) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) -> a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) -> a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) -> a__and#(tt(),X) -> mark#(X) a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) -> a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) -> a__U51#(tt(),V1,V2) -> a__isNat#(V1) a__U11#(tt(),V1) -> a__isNatList#(V1) -> a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__U11#(tt(),V1) -> a__isNatList#(V1) -> a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__U11#(tt(),V1) -> a__isNatList#(V1) -> a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) SCC Processor: #sccs: 1 #rules: 64 #arcs: 829/5625 DPs: a__isNatKind#(length(V1)) -> a__isNatIListKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatKind#(s(V1)) -> a__isNatKind#(V1) a__isNatIListKind#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__and#(tt(),X) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__U11#(tt(),V1) -> a__isNatList#(V1) a__isNatList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatList#(cons(V1,V2)) -> a__U51#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__U51#(tt(),V1,V2) -> a__isNat#(V1) a__isNat#(length(V1)) -> a__isNatIListKind#(V1) a__isNat#(length(V1)) -> a__U11#(a__isNatIListKind(V1),V1) a__isNat#(s(V1)) -> a__isNatKind#(V1) a__isNat#(s(V1)) -> a__U21#(a__isNatKind(V1),V1) a__U21#(tt(),V1) -> a__isNat#(V1) a__U51#(tt(),V1,V2) -> a__U52#(a__isNat(V1),V2) a__U52#(tt(),V2) -> a__isNatList#(V2) mark#(U12(X)) -> mark#(X) mark#(isNatList(X)) -> a__isNatList#(X) mark#(U21(X1,X2)) -> mark#(X1) mark#(U21(X1,X2)) -> a__U21#(mark(X1),X2) mark#(U22(X)) -> mark#(X) mark#(isNat(X)) -> a__isNat#(X) mark#(U31(X1,X2)) -> mark#(X1) mark#(U31(X1,X2)) -> a__U31#(mark(X1),X2) a__U31#(tt(),V) -> a__isNatList#(V) mark#(U32(X)) -> mark#(X) mark#(U41(X1,X2,X3)) -> mark#(X1) mark#(U41(X1,X2,X3)) -> a__U41#(mark(X1),X2,X3) a__U41#(tt(),V1,V2) -> a__isNat#(V1) a__U41#(tt(),V1,V2) -> a__U42#(a__isNat(V1),V2) a__U42#(tt(),V2) -> a__isNatIList#(V2) a__isNatIList#(V) -> a__isNatIListKind#(V) a__isNatIList#(V) -> a__U31#(a__isNatIListKind(V),V) a__isNatIList#(cons(V1,V2)) -> a__isNatKind#(V1) a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNatKind(V1),isNatIListKind(V2)) a__isNatIList#(cons(V1,V2)) -> a__U41#(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) mark#(U42(X1,X2)) -> mark#(X1) mark#(U42(X1,X2)) -> a__U42#(mark(X1),X2) mark#(U43(X)) -> mark#(X) mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U51(X1,X2,X3)) -> mark#(X1) mark#(U51(X1,X2,X3)) -> a__U51#(mark(X1),X2,X3) mark#(U52(X1,X2)) -> mark#(X1) mark#(U52(X1,X2)) -> a__U52#(mark(X1),X2) mark#(U53(X)) -> mark#(X) mark#(U61(X1,X2)) -> mark#(X1) mark#(U61(X1,X2)) -> a__U61#(mark(X1),X2) a__U61#(tt(),L) -> mark#(L) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) a__length#(cons(N,L)) -> a__isNatList#(L) a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNatIListKind(L)) a__length#(cons(N,L)) -> a__and#(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))) a__length#(cons(N,L)) -> a__U61#(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) a__U61#(tt(),L) -> a__length#(mark(L)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isNatIListKind(X)) -> a__isNatIListKind#(X) mark#(isNatKind(X)) -> a__isNatKind#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),V1) -> a__U12(a__isNatList(V1)) a__U12(tt()) -> tt() a__U21(tt(),V1) -> a__U22(a__isNat(V1)) a__U22(tt()) -> tt() a__U31(tt(),V) -> a__U32(a__isNatList(V)) a__U32(tt()) -> tt() a__U41(tt(),V1,V2) -> a__U42(a__isNat(V1),V2) a__U42(tt(),V2) -> a__U43(a__isNatIList(V2)) a__U43(tt()) -> tt() a__U51(tt(),V1,V2) -> a__U52(a__isNat(V1),V2) a__U52(tt(),V2) -> a__U53(a__isNatList(V2)) a__U53(tt()) -> tt() a__U61(tt(),L) -> s(a__length(mark(L))) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__U11(a__isNatIListKind(V1),V1) a__isNat(s(V1)) -> a__U21(a__isNatKind(V1),V1) a__isNatIList(V) -> a__U31(a__isNatIListKind(V),V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__U41(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__isNatIListKind(nil()) -> tt() a__isNatIListKind(zeros()) -> tt() a__isNatIListKind(cons(V1,V2)) -> a__and(a__isNatKind(V1),isNatIListKind(V2)) a__isNatKind(0()) -> tt() a__isNatKind(length(V1)) -> a__isNatIListKind(V1) a__isNatKind(s(V1)) -> a__isNatKind(V1) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__U51(a__and(a__isNatKind(V1),isNatIListKind(V2)),V1,V2) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U61(a__and(a__and(a__isNatList(L),isNatIListKind(L)),and(isNat(N),isNatKind(N))),L) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(U12(X)) -> a__U12(mark(X)) mark(isNatList(X)) -> a__isNatList(X) mark(U21(X1,X2)) -> a__U21(mark(X1),X2) mark(U22(X)) -> a__U22(mark(X)) mark(isNat(X)) -> a__isNat(X) mark(U31(X1,X2)) -> a__U31(mark(X1),X2) mark(U32(X)) -> a__U32(mark(X)) mark(U41(X1,X2,X3)) -> a__U41(mark(X1),X2,X3) mark(U42(X1,X2)) -> a__U42(mark(X1),X2) mark(U43(X)) -> a__U43(mark(X)) mark(isNatIList(X)) -> a__isNatIList(X) mark(U51(X1,X2,X3)) -> a__U51(mark(X1),X2,X3) mark(U52(X1,X2)) -> a__U52(mark(X1),X2) mark(U53(X)) -> a__U53(mark(X)) mark(U61(X1,X2)) -> a__U61(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNatIListKind(X)) -> a__isNatIListKind(X) mark(isNatKind(X)) -> a__isNatKind(X) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() mark(tt()) -> tt() mark(s(X)) -> s(mark(X)) mark(nil()) -> nil() a__zeros() -> zeros() a__U11(X1,X2) -> U11(X1,X2) a__U12(X) -> U12(X) a__isNatList(X) -> isNatList(X) a__U21(X1,X2) -> U21(X1,X2) a__U22(X) -> U22(X) a__isNat(X) -> isNat(X) a__U31(X1,X2) -> U31(X1,X2) a__U32(X) -> U32(X) a__U41(X1,X2,X3) -> U41(X1,X2,X3) a__U42(X1,X2) -> U42(X1,X2) a__U43(X) -> U43(X) a__isNatIList(X) -> isNatIList(X) a__U51(X1,X2,X3) -> U51(X1,X2,X3) a__U52(X1,X2) -> U52(X1,X2) a__U53(X) -> U53(X) a__U61(X1,X2) -> U61(X1,X2) a__length(X) -> length(X) a__and(X1,X2) -> and(X1,X2) a__isNatIListKind(X) -> isNatIListKind(X) a__isNatKind(X) -> isNatKind(X) Open