MAYBE Problem: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> s(a__length(mark(L))) a__U21(tt()) -> nil() a__U31(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__isNatList(V1) a__isNat(s(V1)) -> a__isNat(V1) a__isNatIList(V) -> a__isNatList(V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2)) a__isNatList(take(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) a__take(0(),IL) -> a__U21(a__isNatIList(IL)) a__take(s(M),cons(N,IL)) -> a__U31(a__and(a__isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1,X2,X3,X4)) -> a__U31(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatList(X)) -> a__isNatList(X) mark(isNatIList(X)) -> a__isNatIList(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__length(X) -> length(X) a__U21(X) -> U21(X) a__U31(X1,X2,X3,X4) -> U31(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__and(X1,X2) -> and(X1,X2) a__isNat(X) -> isNat(X) a__isNatList(X) -> isNatList(X) a__isNatIList(X) -> isNatIList(X) Proof: DP Processor: DPs: a__U11#(tt(),L) -> mark#(L) a__U11#(tt(),L) -> a__length#(mark(L)) a__U31#(tt(),IL,M,N) -> mark#(N) a__and#(tt(),X) -> mark#(X) a__isNat#(length(V1)) -> a__isNatList#(V1) a__isNat#(s(V1)) -> a__isNat#(V1) a__isNatIList#(V) -> a__isNatList#(V) a__isNatIList#(cons(V1,V2)) -> a__isNat#(V1) a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatIList(V2)) a__isNatList#(cons(V1,V2)) -> a__isNat#(V1) a__isNatList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatList(V2)) a__isNatList#(take(V1,V2)) -> a__isNat#(V1) a__isNatList#(take(V1,V2)) -> a__and#(a__isNat(V1),isNatIList(V2)) a__length#(cons(N,L)) -> a__isNatList#(L) a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNat(N)) a__length#(cons(N,L)) -> a__U11#(a__and(a__isNatList(L),isNat(N)),L) a__take#(0(),IL) -> a__isNatIList#(IL) a__take#(0(),IL) -> a__U21#(a__isNatIList(IL)) a__take#(s(M),cons(N,IL)) -> a__isNatIList#(IL) a__take#(s(M),cons(N,IL)) -> a__and#(a__isNatIList(IL),and(isNat(M),isNat(N))) a__take#(s(M),cons(N,IL)) -> a__U31#(a__and(a__isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N) mark#(zeros()) -> a__zeros#() mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(U21(X)) -> mark#(X) mark#(U21(X)) -> a__U21#(mark(X)) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) mark#(U31(X1,X2,X3,X4)) -> a__U31#(mark(X1),X2,X3,X4) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isNat(X)) -> a__isNat#(X) mark#(isNatList(X)) -> a__isNatList#(X) mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> s(a__length(mark(L))) a__U21(tt()) -> nil() a__U31(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__isNatList(V1) a__isNat(s(V1)) -> a__isNat(V1) a__isNatIList(V) -> a__isNatList(V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2)) a__isNatList(take(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) a__take(0(),IL) -> a__U21(a__isNatIList(IL)) a__take(s(M),cons(N,IL)) -> a__U31(a__and(a__isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1,X2,X3,X4)) -> a__U31(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatList(X)) -> a__isNatList(X) mark(isNatIList(X)) -> a__isNatIList(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__length(X) -> length(X) a__U21(X) -> U21(X) a__U31(X1,X2,X3,X4) -> U31(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__and(X1,X2) -> and(X1,X2) a__isNat(X) -> isNat(X) a__isNatList(X) -> isNatList(X) a__isNatIList(X) -> isNatIList(X) EDG Processor: DPs: a__U11#(tt(),L) -> mark#(L) a__U11#(tt(),L) -> a__length#(mark(L)) a__U31#(tt(),IL,M,N) -> mark#(N) a__and#(tt(),X) -> mark#(X) a__isNat#(length(V1)) -> a__isNatList#(V1) a__isNat#(s(V1)) -> a__isNat#(V1) a__isNatIList#(V) -> a__isNatList#(V) a__isNatIList#(cons(V1,V2)) -> a__isNat#(V1) a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatIList(V2)) a__isNatList#(cons(V1,V2)) -> a__isNat#(V1) a__isNatList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatList(V2)) a__isNatList#(take(V1,V2)) -> a__isNat#(V1) a__isNatList#(take(V1,V2)) -> a__and#(a__isNat(V1),isNatIList(V2)) a__length#(cons(N,L)) -> a__isNatList#(L) a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNat(N)) a__length#(cons(N,L)) -> a__U11#(a__and(a__isNatList(L),isNat(N)),L) a__take#(0(),IL) -> a__isNatIList#(IL) a__take#(0(),IL) -> a__U21#(a__isNatIList(IL)) a__take#(s(M),cons(N,IL)) -> a__isNatIList#(IL) a__take#(s(M),cons(N,IL)) -> a__and#(a__isNatIList(IL),and(isNat(M),isNat(N))) a__take#(s(M),cons(N,IL)) -> a__U31#(a__and(a__isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N) mark#(zeros()) -> a__zeros#() mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(U21(X)) -> mark#(X) mark#(U21(X)) -> a__U21#(mark(X)) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) mark#(U31(X1,X2,X3,X4)) -> a__U31#(mark(X1),X2,X3,X4) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isNat(X)) -> a__isNat#(X) mark#(isNatList(X)) -> a__isNatList#(X) mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> s(a__length(mark(L))) a__U21(tt()) -> nil() a__U31(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__isNatList(V1) a__isNat(s(V1)) -> a__isNat(V1) a__isNatIList(V) -> a__isNatList(V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2)) a__isNatList(take(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) a__take(0(),IL) -> a__U21(a__isNatIList(IL)) a__take(s(M),cons(N,IL)) -> a__U31(a__and(a__isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1,X2,X3,X4)) -> a__U31(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatList(X)) -> a__isNatList(X) mark(isNatIList(X)) -> a__isNatIList(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__length(X) -> length(X) a__U21(X) -> U21(X) a__U31(X1,X2,X3,X4) -> U31(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__and(X1,X2) -> and(X1,X2) a__isNat(X) -> isNat(X) a__isNatList(X) -> isNatList(X) a__isNatIList(X) -> isNatIList(X) graph: a__take#(s(M),cons(N,IL)) -> a__isNatIList#(IL) -> a__isNatIList#(V) -> a__isNatList#(V) a__take#(s(M),cons(N,IL)) -> a__isNatIList#(IL) -> a__isNatIList#(cons(V1,V2)) -> a__isNat#(V1) a__take#(s(M),cons(N,IL)) -> a__isNatIList#(IL) -> a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatIList(V2)) a__take#(s(M),cons(N,IL)) -> a__and#(a__isNatIList(IL),and(isNat(M),isNat(N))) -> a__and#(tt(),X) -> mark#(X) a__take#(s(M),cons(N,IL)) -> a__U31#(a__and(a__isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N) -> a__U31#(tt(),IL,M,N) -> mark#(N) a__take#(0(),IL) -> a__isNatIList#(IL) -> a__isNatIList#(V) -> a__isNatList#(V) a__take#(0(),IL) -> a__isNatIList#(IL) -> a__isNatIList#(cons(V1,V2)) -> a__isNat#(V1) a__take#(0(),IL) -> a__isNatIList#(IL) -> a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatIList(V2)) a__isNatIList#(cons(V1,V2)) -> a__isNat#(V1) -> a__isNat#(length(V1)) -> a__isNatList#(V1) a__isNatIList#(cons(V1,V2)) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__isNat#(V1) a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatIList(V2)) -> a__and#(tt(),X) -> mark#(X) a__isNatIList#(V) -> a__isNatList#(V) -> a__isNatList#(cons(V1,V2)) -> a__isNat#(V1) a__isNatIList#(V) -> a__isNatList#(V) -> a__isNatList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatList(V2)) a__isNatIList#(V) -> a__isNatList#(V) -> a__isNatList#(take(V1,V2)) -> a__isNat#(V1) a__isNatIList#(V) -> a__isNatList#(V) -> a__isNatList#(take(V1,V2)) -> a__and#(a__isNat(V1),isNatIList(V2)) a__isNatList#(take(V1,V2)) -> a__isNat#(V1) -> a__isNat#(length(V1)) -> a__isNatList#(V1) a__isNatList#(take(V1,V2)) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__isNat#(V1) a__isNatList#(take(V1,V2)) -> a__and#(a__isNat(V1),isNatIList(V2)) -> a__and#(tt(),X) -> mark#(X) a__isNatList#(cons(V1,V2)) -> a__isNat#(V1) -> a__isNat#(length(V1)) -> a__isNatList#(V1) a__isNatList#(cons(V1,V2)) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__isNat#(V1) a__isNatList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatList(V2)) -> a__and#(tt(),X) -> mark#(X) a__isNat#(length(V1)) -> a__isNatList#(V1) -> a__isNatList#(cons(V1,V2)) -> a__isNat#(V1) a__isNat#(length(V1)) -> a__isNatList#(V1) -> a__isNatList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatList(V2)) a__isNat#(length(V1)) -> a__isNatList#(V1) -> a__isNatList#(take(V1,V2)) -> a__isNat#(V1) a__isNat#(length(V1)) -> a__isNatList#(V1) -> a__isNatList#(take(V1,V2)) -> a__and#(a__isNat(V1),isNatIList(V2)) a__isNat#(s(V1)) -> a__isNat#(V1) -> a__isNat#(length(V1)) -> a__isNatList#(V1) a__isNat#(s(V1)) -> a__isNat#(V1) -> a__isNat#(s(V1)) -> a__isNat#(V1) a__and#(tt(),X) -> mark#(X) -> mark#(zeros()) -> a__zeros#() a__and#(tt(),X) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__and#(tt(),X) -> mark#(X) -> mark#(length(X)) -> mark#(X) a__and#(tt(),X) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) a__and#(tt(),X) -> mark#(X) -> mark#(U21(X)) -> mark#(X) a__and#(tt(),X) -> mark#(X) -> mark#(U21(X)) -> a__U21#(mark(X)) a__and#(tt(),X) -> mark#(X) -> mark#(U31(X1,X2,X3,X4)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(U31(X1,X2,X3,X4)) -> a__U31#(mark(X1),X2,X3,X4) a__and#(tt(),X) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X2) a__and#(tt(),X) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) a__and#(tt(),X) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) a__and#(tt(),X) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) a__and#(tt(),X) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) a__and#(tt(),X) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) a__and#(tt(),X) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) a__and#(tt(),X) -> mark#(X) -> mark#(s(X)) -> mark#(X) a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(zeros()) -> a__zeros#() a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(U11(X1,X2)) -> mark#(X1) a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(length(X)) -> mark#(X) a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(length(X)) -> a__length#(mark(X)) a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(U21(X)) -> mark#(X) a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(U21(X)) -> a__U21#(mark(X)) a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(U31(X1,X2,X3,X4)) -> mark#(X1) a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(U31(X1,X2,X3,X4)) -> a__U31#(mark(X1),X2,X3,X4) a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(take(X1,X2)) -> mark#(X2) a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(take(X1,X2)) -> mark#(X1) a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(and(X1,X2)) -> mark#(X1) a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(isNat(X)) -> a__isNat#(X) a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(isNatList(X)) -> a__isNatList#(X) a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(isNatIList(X)) -> a__isNatIList#(X) a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(cons(X1,X2)) -> mark#(X1) a__U31#(tt(),IL,M,N) -> mark#(N) -> mark#(s(X)) -> mark#(X) a__length#(cons(N,L)) -> a__isNatList#(L) -> a__isNatList#(cons(V1,V2)) -> a__isNat#(V1) a__length#(cons(N,L)) -> a__isNatList#(L) -> a__isNatList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatList(V2)) a__length#(cons(N,L)) -> a__isNatList#(L) -> a__isNatList#(take(V1,V2)) -> a__isNat#(V1) a__length#(cons(N,L)) -> a__isNatList#(L) -> a__isNatList#(take(V1,V2)) -> a__and#(a__isNat(V1),isNatIList(V2)) a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNat(N)) -> a__and#(tt(),X) -> mark#(X) a__length#(cons(N,L)) -> a__U11#(a__and(a__isNatList(L),isNat(N)),L) -> a__U11#(tt(),L) -> mark#(L) a__length#(cons(N,L)) -> a__U11#(a__and(a__isNatList(L),isNat(N)),L) -> a__U11#(tt(),L) -> a__length#(mark(L)) mark#(U31(X1,X2,X3,X4)) -> a__U31#(mark(X1),X2,X3,X4) -> a__U31#(tt(),IL,M,N) -> mark#(N) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(U21(X)) -> mark#(X) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(U31(X1,X2,X3,X4)) -> mark#(X1) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(U31(X1,X2,X3,X4)) -> a__U31#(mark(X1),X2,X3,X4) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X2) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X1) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U21(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#() mark#(U21(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U21(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U21(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(U21(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U21(X)) -> mark#(X) -> mark#(U21(X)) -> mark#(X) mark#(U21(X)) -> mark#(X) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(U21(X)) -> mark#(X) -> mark#(U31(X1,X2,X3,X4)) -> mark#(X1) mark#(U21(X)) -> mark#(X) -> mark#(U31(X1,X2,X3,X4)) -> a__U31#(mark(X1),X2,X3,X4) mark#(U21(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X2) mark#(U21(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X1) mark#(U21(X)) -> mark#(X) -> mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) mark#(U21(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U21(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U21(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U21(X)) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U21(X)) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U21(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U21(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U21(X)) -> mark#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2,X3,X4)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2,X3,X4)) -> a__U31#(mark(X1),X2,X3,X4) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) -> a__U11#(tt(),L) -> mark#(L) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) -> a__U11#(tt(),L) -> a__length#(mark(L)) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) -> a__and#(tt(),X) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(and(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U21(X)) -> mark#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2,X3,X4)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2,X3,X4)) -> a__U31#(mark(X1),X2,X3,X4) mark#(and(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(and(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(isNat(X)) -> a__isNat#(X) -> a__isNat#(length(V1)) -> a__isNatList#(V1) mark#(isNat(X)) -> a__isNat#(X) -> a__isNat#(s(V1)) -> a__isNat#(V1) mark#(isNatList(X)) -> a__isNatList#(X) -> a__isNatList#(cons(V1,V2)) -> a__isNat#(V1) mark#(isNatList(X)) -> a__isNatList#(X) -> a__isNatList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatList(V2)) mark#(isNatList(X)) -> a__isNatList#(X) -> a__isNatList#(take(V1,V2)) -> a__isNat#(V1) mark#(isNatList(X)) -> a__isNatList#(X) -> a__isNatList#(take(V1,V2)) -> a__and#(a__isNat(V1),isNatIList(V2)) mark#(isNatIList(X)) -> a__isNatIList#(X) -> a__isNatIList#(V) -> a__isNatList#(V) mark#(isNatIList(X)) -> a__isNatIList#(X) -> a__isNatIList#(cons(V1,V2)) -> a__isNat#(V1) mark#(isNatIList(X)) -> a__isNatIList#(X) -> a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatIList(V2)) mark#(length(X)) -> a__length#(mark(X)) -> a__length#(cons(N,L)) -> a__isNatList#(L) mark#(length(X)) -> a__length#(mark(X)) -> a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNat(N)) mark#(length(X)) -> a__length#(mark(X)) -> a__length#(cons(N,L)) -> a__U11#(a__and(a__isNatList(L),isNat(N)),L) mark#(length(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#() mark#(length(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) mark#(length(X)) -> mark#(X) -> mark#(U21(X)) -> mark#(X) mark#(length(X)) -> mark#(X) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(length(X)) -> mark#(X) -> mark#(U31(X1,X2,X3,X4)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(U31(X1,X2,X3,X4)) -> a__U31#(mark(X1),X2,X3,X4) mark#(length(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X2) mark#(length(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) mark#(length(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(length(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(length(X)) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(length(X)) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(length(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(length(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) -> a__take#(0(),IL) -> a__isNatIList#(IL) mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) -> a__take#(0(),IL) -> a__U21#(a__isNatIList(IL)) mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) -> a__take#(s(M),cons(N,IL)) -> a__isNatIList#(IL) mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) -> a__take#(s(M),cons(N,IL)) -> a__and#(a__isNatIList(IL),and(isNat(M),isNat(N))) mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) -> a__take#(s(M),cons(N,IL)) -> a__U31#(a__and(a__isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N) mark#(take(X1,X2)) -> mark#(X2) -> mark#(zeros()) -> a__zeros#() mark#(take(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> mark#(X2) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(take(X1,X2)) -> mark#(X2) -> mark#(length(X)) -> mark#(X) mark#(take(X1,X2)) -> mark#(X2) -> mark#(length(X)) -> a__length#(mark(X)) mark#(take(X1,X2)) -> mark#(X2) -> mark#(U21(X)) -> mark#(X) mark#(take(X1,X2)) -> mark#(X2) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(take(X1,X2)) -> mark#(X2) -> mark#(U31(X1,X2,X3,X4)) -> mark#(X1) mark#(take(X1,X2)) -> mark#(X2) -> mark#(U31(X1,X2,X3,X4)) -> a__U31#(mark(X1),X2,X3,X4) mark#(take(X1,X2)) -> mark#(X2) -> mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X2) -> mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> mark#(X2) -> mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) mark#(take(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> mark#(X2) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(take(X1,X2)) -> mark#(X2) -> mark#(isNat(X)) -> a__isNat#(X) mark#(take(X1,X2)) -> mark#(X2) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(take(X1,X2)) -> mark#(X2) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(take(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X) mark#(take(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(take(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(take(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(take(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(take(X1,X2)) -> mark#(X1) -> mark#(U21(X)) -> mark#(X) mark#(take(X1,X2)) -> mark#(X1) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(take(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2,X3,X4)) -> mark#(X1) mark#(take(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2,X3,X4)) -> a__U31#(mark(X1),X2,X3,X4) mark#(take(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) mark#(take(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(take(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(take(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(take(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(take(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(zeros()) -> a__zeros#() mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(U21(X)) -> mark#(X) mark#(s(X)) -> mark#(X) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(s(X)) -> mark#(X) -> mark#(U31(X1,X2,X3,X4)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(U31(X1,X2,X3,X4)) -> a__U31#(mark(X1),X2,X3,X4) mark#(s(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X2) mark#(s(X)) -> mark#(X) -> mark#(take(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(s(X)) -> mark#(X) -> mark#(isNat(X)) -> a__isNat#(X) mark#(s(X)) -> mark#(X) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(s(X)) -> mark#(X) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(zeros()) -> a__zeros#() mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(length(X)) -> a__length#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U21(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U21(X)) -> a__U21#(mark(X)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2,X3,X4)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(U31(X1,X2,X3,X4)) -> a__U31#(mark(X1),X2,X3,X4) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(isNat(X)) -> a__isNat#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(isNatList(X)) -> a__isNatList#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X) a__U11#(tt(),L) -> a__length#(mark(L)) -> a__length#(cons(N,L)) -> a__isNatList#(L) a__U11#(tt(),L) -> a__length#(mark(L)) -> a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNat(N)) a__U11#(tt(),L) -> a__length#(mark(L)) -> a__length#(cons(N,L)) -> a__U11#(a__and(a__isNatList(L),isNat(N)),L) a__U11#(tt(),L) -> mark#(L) -> mark#(zeros()) -> a__zeros#() a__U11#(tt(),L) -> mark#(L) -> mark#(U11(X1,X2)) -> mark#(X1) a__U11#(tt(),L) -> mark#(L) -> mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) a__U11#(tt(),L) -> mark#(L) -> mark#(length(X)) -> mark#(X) a__U11#(tt(),L) -> mark#(L) -> mark#(length(X)) -> a__length#(mark(X)) a__U11#(tt(),L) -> mark#(L) -> mark#(U21(X)) -> mark#(X) a__U11#(tt(),L) -> mark#(L) -> mark#(U21(X)) -> a__U21#(mark(X)) a__U11#(tt(),L) -> mark#(L) -> mark#(U31(X1,X2,X3,X4)) -> mark#(X1) a__U11#(tt(),L) -> mark#(L) -> mark#(U31(X1,X2,X3,X4)) -> a__U31#(mark(X1),X2,X3,X4) a__U11#(tt(),L) -> mark#(L) -> mark#(take(X1,X2)) -> mark#(X2) a__U11#(tt(),L) -> mark#(L) -> mark#(take(X1,X2)) -> mark#(X1) a__U11#(tt(),L) -> mark#(L) -> mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) a__U11#(tt(),L) -> mark#(L) -> mark#(and(X1,X2)) -> mark#(X1) a__U11#(tt(),L) -> mark#(L) -> mark#(and(X1,X2)) -> a__and#(mark(X1),X2) a__U11#(tt(),L) -> mark#(L) -> mark#(isNat(X)) -> a__isNat#(X) a__U11#(tt(),L) -> mark#(L) -> mark#(isNatList(X)) -> a__isNatList#(X) a__U11#(tt(),L) -> mark#(L) -> mark#(isNatIList(X)) -> a__isNatIList#(X) a__U11#(tt(),L) -> mark#(L) -> mark#(cons(X1,X2)) -> mark#(X1) a__U11#(tt(),L) -> mark#(L) -> mark#(s(X)) -> mark#(X) Restore Modifier: DPs: a__U11#(tt(),L) -> mark#(L) a__U11#(tt(),L) -> a__length#(mark(L)) a__U31#(tt(),IL,M,N) -> mark#(N) a__and#(tt(),X) -> mark#(X) a__isNat#(length(V1)) -> a__isNatList#(V1) a__isNat#(s(V1)) -> a__isNat#(V1) a__isNatIList#(V) -> a__isNatList#(V) a__isNatIList#(cons(V1,V2)) -> a__isNat#(V1) a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatIList(V2)) a__isNatList#(cons(V1,V2)) -> a__isNat#(V1) a__isNatList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatList(V2)) a__isNatList#(take(V1,V2)) -> a__isNat#(V1) a__isNatList#(take(V1,V2)) -> a__and#(a__isNat(V1),isNatIList(V2)) a__length#(cons(N,L)) -> a__isNatList#(L) a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNat(N)) a__length#(cons(N,L)) -> a__U11#(a__and(a__isNatList(L),isNat(N)),L) a__take#(0(),IL) -> a__isNatIList#(IL) a__take#(0(),IL) -> a__U21#(a__isNatIList(IL)) a__take#(s(M),cons(N,IL)) -> a__isNatIList#(IL) a__take#(s(M),cons(N,IL)) -> a__and#(a__isNatIList(IL),and(isNat(M),isNat(N))) a__take#(s(M),cons(N,IL)) -> a__U31#(a__and(a__isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N) mark#(zeros()) -> a__zeros#() mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(length(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) mark#(U21(X)) -> mark#(X) mark#(U21(X)) -> a__U21#(mark(X)) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) mark#(U31(X1,X2,X3,X4)) -> a__U31#(mark(X1),X2,X3,X4) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(isNat(X)) -> a__isNat#(X) mark#(isNatList(X)) -> a__isNatList#(X) mark#(isNatIList(X)) -> a__isNatIList#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(s(X)) -> mark#(X) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> s(a__length(mark(L))) a__U21(tt()) -> nil() a__U31(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__isNatList(V1) a__isNat(s(V1)) -> a__isNat(V1) a__isNatIList(V) -> a__isNatList(V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2)) a__isNatList(take(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) a__take(0(),IL) -> a__U21(a__isNatIList(IL)) a__take(s(M),cons(N,IL)) -> a__U31(a__and(a__isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1,X2,X3,X4)) -> a__U31(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatList(X)) -> a__isNatList(X) mark(isNatIList(X)) -> a__isNatIList(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__length(X) -> length(X) a__U21(X) -> U21(X) a__U31(X1,X2,X3,X4) -> U31(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__and(X1,X2) -> and(X1,X2) a__isNat(X) -> isNat(X) a__isNatList(X) -> isNatList(X) a__isNatIList(X) -> isNatIList(X) SCC Processor: #sccs: 1 #rules: 37 #arcs: 286/1600 DPs: a__take#(s(M),cons(N,IL)) -> a__isNatIList#(IL) a__isNatIList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatIList(V2)) a__and#(tt(),X) -> mark#(X) mark#(s(X)) -> mark#(X) mark#(cons(X1,X2)) -> mark#(X1) mark#(isNatIList(X)) -> a__isNatIList#(X) a__isNatIList#(cons(V1,V2)) -> a__isNat#(V1) a__isNat#(s(V1)) -> a__isNat#(V1) a__isNat#(length(V1)) -> a__isNatList#(V1) a__isNatList#(take(V1,V2)) -> a__and#(a__isNat(V1),isNatIList(V2)) a__isNatList#(take(V1,V2)) -> a__isNat#(V1) a__isNatList#(cons(V1,V2)) -> a__and#(a__isNat(V1),isNatList(V2)) a__isNatList#(cons(V1,V2)) -> a__isNat#(V1) a__isNatIList#(V) -> a__isNatList#(V) mark#(isNatList(X)) -> a__isNatList#(X) mark#(isNat(X)) -> a__isNat#(X) mark#(and(X1,X2)) -> a__and#(mark(X1),X2) mark#(and(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> a__take#(mark(X1),mark(X2)) a__take#(s(M),cons(N,IL)) -> a__U31#(a__and(a__isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N) a__U31#(tt(),IL,M,N) -> mark#(N) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> mark#(X2) mark#(U31(X1,X2,X3,X4)) -> a__U31#(mark(X1),X2,X3,X4) mark#(U31(X1,X2,X3,X4)) -> mark#(X1) mark#(U21(X)) -> mark#(X) mark#(length(X)) -> a__length#(mark(X)) a__length#(cons(N,L)) -> a__U11#(a__and(a__isNatList(L),isNat(N)),L) a__U11#(tt(),L) -> a__length#(mark(L)) a__length#(cons(N,L)) -> a__and#(a__isNatList(L),isNat(N)) a__length#(cons(N,L)) -> a__isNatList#(L) a__U11#(tt(),L) -> mark#(L) mark#(length(X)) -> mark#(X) mark#(U11(X1,X2)) -> a__U11#(mark(X1),X2) mark#(U11(X1,X2)) -> mark#(X1) a__take#(s(M),cons(N,IL)) -> a__and#(a__isNatIList(IL),and(isNat(M),isNat(N))) a__take#(0(),IL) -> a__isNatIList#(IL) TRS: a__zeros() -> cons(0(),zeros()) a__U11(tt(),L) -> s(a__length(mark(L))) a__U21(tt()) -> nil() a__U31(tt(),IL,M,N) -> cons(mark(N),take(M,IL)) a__and(tt(),X) -> mark(X) a__isNat(0()) -> tt() a__isNat(length(V1)) -> a__isNatList(V1) a__isNat(s(V1)) -> a__isNat(V1) a__isNatIList(V) -> a__isNatList(V) a__isNatIList(zeros()) -> tt() a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(nil()) -> tt() a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2)) a__isNatList(take(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__length(nil()) -> 0() a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) a__take(0(),IL) -> a__U21(a__isNatIList(IL)) a__take(s(M),cons(N,IL)) -> a__U31(a__and(a__isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N) mark(zeros()) -> a__zeros() mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1,X2,X3,X4)) -> a__U31(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatList(X)) -> a__isNatList(X) mark(isNatIList(X)) -> a__isNatIList(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__length(X) -> length(X) a__U21(X) -> U21(X) a__U31(X1,X2,X3,X4) -> U31(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__and(X1,X2) -> and(X1,X2) a__isNat(X) -> isNat(X) a__isNatList(X) -> isNatList(X) a__isNatIList(X) -> isNatIList(X) Open