MAYBE Problem: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),L)) -> mark(U12(tt(),L)) active(U12(tt(),L)) -> mark(s(length(L))) active(U21(tt(),IL,M,N)) -> mark(U22(tt(),IL,M,N)) active(U22(tt(),IL,M,N)) -> mark(U23(tt(),IL,M,N)) active(U23(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U11(tt(),L)) active(take(0(),IL)) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(U21(tt(),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U21(X1,X2,X3,X4)) -> active(U21(mark(X1),X2,X3,X4)) mark(U22(X1,X2,X3,X4)) -> active(U22(mark(X1),X2,X3,X4)) mark(U23(X1,X2,X3,X4)) -> active(U23(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U21(mark(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,mark(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,mark(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,mark(X4)) -> U21(X1,X2,X3,X4) U21(active(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,active(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,active(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,active(X4)) -> U21(X1,X2,X3,X4) U22(mark(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,mark(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,mark(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,mark(X4)) -> U22(X1,X2,X3,X4) U22(active(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,active(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,active(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,active(X4)) -> U22(X1,X2,X3,X4) U23(mark(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,mark(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,mark(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,mark(X4)) -> U23(X1,X2,X3,X4) U23(active(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,active(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,active(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,active(X4)) -> U23(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Proof: DP Processor: DPs: active#(zeros()) -> cons#(0(),zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) active#(U11(tt(),L)) -> U12#(tt(),L) active#(U11(tt(),L)) -> mark#(U12(tt(),L)) active#(U12(tt(),L)) -> length#(L) active#(U12(tt(),L)) -> s#(length(L)) active#(U12(tt(),L)) -> mark#(s(length(L))) active#(U21(tt(),IL,M,N)) -> U22#(tt(),IL,M,N) active#(U21(tt(),IL,M,N)) -> mark#(U22(tt(),IL,M,N)) active#(U22(tt(),IL,M,N)) -> U23#(tt(),IL,M,N) active#(U22(tt(),IL,M,N)) -> mark#(U23(tt(),IL,M,N)) active#(U23(tt(),IL,M,N)) -> take#(M,IL) active#(U23(tt(),IL,M,N)) -> cons#(N,take(M,IL)) active#(U23(tt(),IL,M,N)) -> mark#(cons(N,take(M,IL))) active#(length(nil())) -> mark#(0()) active#(length(cons(N,L))) -> U11#(tt(),L) active#(length(cons(N,L))) -> mark#(U11(tt(),L)) active#(take(0(),IL)) -> mark#(nil()) active#(take(s(M),cons(N,IL))) -> U21#(tt(),IL,M,N) active#(take(s(M),cons(N,IL))) -> mark#(U21(tt(),IL,M,N)) mark#(zeros()) -> active#(zeros()) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(0()) -> active#(0()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> U11#(mark(X1),X2) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> U12#(mark(X1),X2) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) mark#(length(X)) -> mark#(X) mark#(length(X)) -> length#(mark(X)) mark#(length(X)) -> active#(length(mark(X))) mark#(U21(X1,X2,X3,X4)) -> mark#(X1) mark#(U21(X1,X2,X3,X4)) -> U21#(mark(X1),X2,X3,X4) mark#(U21(X1,X2,X3,X4)) -> active#(U21(mark(X1),X2,X3,X4)) mark#(U22(X1,X2,X3,X4)) -> mark#(X1) mark#(U22(X1,X2,X3,X4)) -> U22#(mark(X1),X2,X3,X4) mark#(U22(X1,X2,X3,X4)) -> active#(U22(mark(X1),X2,X3,X4)) mark#(U23(X1,X2,X3,X4)) -> mark#(X1) mark#(U23(X1,X2,X3,X4)) -> U23#(mark(X1),X2,X3,X4) mark#(U23(X1,X2,X3,X4)) -> active#(U23(mark(X1),X2,X3,X4)) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) mark#(nil()) -> active#(nil()) cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) U12#(mark(X1),X2) -> U12#(X1,X2) U12#(X1,mark(X2)) -> U12#(X1,X2) U12#(active(X1),X2) -> U12#(X1,X2) U12#(X1,active(X2)) -> U12#(X1,X2) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) U21#(mark(X1),X2,X3,X4) -> U21#(X1,X2,X3,X4) U21#(X1,mark(X2),X3,X4) -> U21#(X1,X2,X3,X4) U21#(X1,X2,mark(X3),X4) -> U21#(X1,X2,X3,X4) U21#(X1,X2,X3,mark(X4)) -> U21#(X1,X2,X3,X4) U21#(active(X1),X2,X3,X4) -> U21#(X1,X2,X3,X4) U21#(X1,active(X2),X3,X4) -> U21#(X1,X2,X3,X4) U21#(X1,X2,active(X3),X4) -> U21#(X1,X2,X3,X4) U21#(X1,X2,X3,active(X4)) -> U21#(X1,X2,X3,X4) U22#(mark(X1),X2,X3,X4) -> U22#(X1,X2,X3,X4) U22#(X1,mark(X2),X3,X4) -> U22#(X1,X2,X3,X4) U22#(X1,X2,mark(X3),X4) -> U22#(X1,X2,X3,X4) U22#(X1,X2,X3,mark(X4)) -> U22#(X1,X2,X3,X4) U22#(active(X1),X2,X3,X4) -> U22#(X1,X2,X3,X4) U22#(X1,active(X2),X3,X4) -> U22#(X1,X2,X3,X4) U22#(X1,X2,active(X3),X4) -> U22#(X1,X2,X3,X4) U22#(X1,X2,X3,active(X4)) -> U22#(X1,X2,X3,X4) U23#(mark(X1),X2,X3,X4) -> U23#(X1,X2,X3,X4) U23#(X1,mark(X2),X3,X4) -> U23#(X1,X2,X3,X4) U23#(X1,X2,mark(X3),X4) -> U23#(X1,X2,X3,X4) U23#(X1,X2,X3,mark(X4)) -> U23#(X1,X2,X3,X4) U23#(active(X1),X2,X3,X4) -> U23#(X1,X2,X3,X4) U23#(X1,active(X2),X3,X4) -> U23#(X1,X2,X3,X4) U23#(X1,X2,active(X3),X4) -> U23#(X1,X2,X3,X4) U23#(X1,X2,X3,active(X4)) -> U23#(X1,X2,X3,X4) take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) take#(X1,active(X2)) -> take#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),L)) -> mark(U12(tt(),L)) active(U12(tt(),L)) -> mark(s(length(L))) active(U21(tt(),IL,M,N)) -> mark(U22(tt(),IL,M,N)) active(U22(tt(),IL,M,N)) -> mark(U23(tt(),IL,M,N)) active(U23(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U11(tt(),L)) active(take(0(),IL)) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(U21(tt(),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U21(X1,X2,X3,X4)) -> active(U21(mark(X1),X2,X3,X4)) mark(U22(X1,X2,X3,X4)) -> active(U22(mark(X1),X2,X3,X4)) mark(U23(X1,X2,X3,X4)) -> active(U23(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U21(mark(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,mark(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,mark(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,mark(X4)) -> U21(X1,X2,X3,X4) U21(active(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,active(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,active(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,active(X4)) -> U21(X1,X2,X3,X4) U22(mark(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,mark(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,mark(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,mark(X4)) -> U22(X1,X2,X3,X4) U22(active(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,active(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,active(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,active(X4)) -> U22(X1,X2,X3,X4) U23(mark(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,mark(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,mark(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,mark(X4)) -> U23(X1,X2,X3,X4) U23(active(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,active(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,active(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,active(X4)) -> U23(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) TDG Processor: DPs: active#(zeros()) -> cons#(0(),zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) active#(U11(tt(),L)) -> U12#(tt(),L) active#(U11(tt(),L)) -> mark#(U12(tt(),L)) active#(U12(tt(),L)) -> length#(L) active#(U12(tt(),L)) -> s#(length(L)) active#(U12(tt(),L)) -> mark#(s(length(L))) active#(U21(tt(),IL,M,N)) -> U22#(tt(),IL,M,N) active#(U21(tt(),IL,M,N)) -> mark#(U22(tt(),IL,M,N)) active#(U22(tt(),IL,M,N)) -> U23#(tt(),IL,M,N) active#(U22(tt(),IL,M,N)) -> mark#(U23(tt(),IL,M,N)) active#(U23(tt(),IL,M,N)) -> take#(M,IL) active#(U23(tt(),IL,M,N)) -> cons#(N,take(M,IL)) active#(U23(tt(),IL,M,N)) -> mark#(cons(N,take(M,IL))) active#(length(nil())) -> mark#(0()) active#(length(cons(N,L))) -> U11#(tt(),L) active#(length(cons(N,L))) -> mark#(U11(tt(),L)) active#(take(0(),IL)) -> mark#(nil()) active#(take(s(M),cons(N,IL))) -> U21#(tt(),IL,M,N) active#(take(s(M),cons(N,IL))) -> mark#(U21(tt(),IL,M,N)) mark#(zeros()) -> active#(zeros()) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> cons#(mark(X1),X2) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) mark#(0()) -> active#(0()) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> U11#(mark(X1),X2) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) mark#(tt()) -> active#(tt()) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> U12#(mark(X1),X2) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) mark#(s(X)) -> mark#(X) mark#(s(X)) -> s#(mark(X)) mark#(s(X)) -> active#(s(mark(X))) mark#(length(X)) -> mark#(X) mark#(length(X)) -> length#(mark(X)) mark#(length(X)) -> active#(length(mark(X))) mark#(U21(X1,X2,X3,X4)) -> mark#(X1) mark#(U21(X1,X2,X3,X4)) -> U21#(mark(X1),X2,X3,X4) mark#(U21(X1,X2,X3,X4)) -> active#(U21(mark(X1),X2,X3,X4)) mark#(U22(X1,X2,X3,X4)) -> mark#(X1) mark#(U22(X1,X2,X3,X4)) -> U22#(mark(X1),X2,X3,X4) mark#(U22(X1,X2,X3,X4)) -> active#(U22(mark(X1),X2,X3,X4)) mark#(U23(X1,X2,X3,X4)) -> mark#(X1) mark#(U23(X1,X2,X3,X4)) -> U23#(mark(X1),X2,X3,X4) mark#(U23(X1,X2,X3,X4)) -> active#(U23(mark(X1),X2,X3,X4)) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> take#(mark(X1),mark(X2)) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) mark#(nil()) -> active#(nil()) cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) U12#(mark(X1),X2) -> U12#(X1,X2) U12#(X1,mark(X2)) -> U12#(X1,X2) U12#(active(X1),X2) -> U12#(X1,X2) U12#(X1,active(X2)) -> U12#(X1,X2) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) U21#(mark(X1),X2,X3,X4) -> U21#(X1,X2,X3,X4) U21#(X1,mark(X2),X3,X4) -> U21#(X1,X2,X3,X4) U21#(X1,X2,mark(X3),X4) -> U21#(X1,X2,X3,X4) U21#(X1,X2,X3,mark(X4)) -> U21#(X1,X2,X3,X4) U21#(active(X1),X2,X3,X4) -> U21#(X1,X2,X3,X4) U21#(X1,active(X2),X3,X4) -> U21#(X1,X2,X3,X4) U21#(X1,X2,active(X3),X4) -> U21#(X1,X2,X3,X4) U21#(X1,X2,X3,active(X4)) -> U21#(X1,X2,X3,X4) U22#(mark(X1),X2,X3,X4) -> U22#(X1,X2,X3,X4) U22#(X1,mark(X2),X3,X4) -> U22#(X1,X2,X3,X4) U22#(X1,X2,mark(X3),X4) -> U22#(X1,X2,X3,X4) U22#(X1,X2,X3,mark(X4)) -> U22#(X1,X2,X3,X4) U22#(active(X1),X2,X3,X4) -> U22#(X1,X2,X3,X4) U22#(X1,active(X2),X3,X4) -> U22#(X1,X2,X3,X4) U22#(X1,X2,active(X3),X4) -> U22#(X1,X2,X3,X4) U22#(X1,X2,X3,active(X4)) -> U22#(X1,X2,X3,X4) U23#(mark(X1),X2,X3,X4) -> U23#(X1,X2,X3,X4) U23#(X1,mark(X2),X3,X4) -> U23#(X1,X2,X3,X4) U23#(X1,X2,mark(X3),X4) -> U23#(X1,X2,X3,X4) U23#(X1,X2,X3,mark(X4)) -> U23#(X1,X2,X3,X4) U23#(active(X1),X2,X3,X4) -> U23#(X1,X2,X3,X4) U23#(X1,active(X2),X3,X4) -> U23#(X1,X2,X3,X4) U23#(X1,X2,active(X3),X4) -> U23#(X1,X2,X3,X4) U23#(X1,X2,X3,active(X4)) -> U23#(X1,X2,X3,X4) take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) take#(X1,active(X2)) -> take#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),L)) -> mark(U12(tt(),L)) active(U12(tt(),L)) -> mark(s(length(L))) active(U21(tt(),IL,M,N)) -> mark(U22(tt(),IL,M,N)) active(U22(tt(),IL,M,N)) -> mark(U23(tt(),IL,M,N)) active(U23(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U11(tt(),L)) active(take(0(),IL)) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(U21(tt(),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U21(X1,X2,X3,X4)) -> active(U21(mark(X1),X2,X3,X4)) mark(U22(X1,X2,X3,X4)) -> active(U22(mark(X1),X2,X3,X4)) mark(U23(X1,X2,X3,X4)) -> active(U23(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U21(mark(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,mark(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,mark(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,mark(X4)) -> U21(X1,X2,X3,X4) U21(active(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,active(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,active(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,active(X4)) -> U21(X1,X2,X3,X4) U22(mark(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,mark(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,mark(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,mark(X4)) -> U22(X1,X2,X3,X4) U22(active(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,active(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,active(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,active(X4)) -> U22(X1,X2,X3,X4) U23(mark(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,mark(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,mark(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,mark(X4)) -> U23(X1,X2,X3,X4) U23(active(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,active(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,active(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,active(X4)) -> U23(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) graph: ... SCC Processor: #sccs: 10 #rules: 77 #arcs: 1256/9216 DPs: mark#(nil()) -> active#(nil()) active#(zeros()) -> mark#(cons(0(),zeros())) mark#(zeros()) -> active#(zeros()) active#(U11(tt(),L)) -> mark#(U12(tt(),L)) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(U12(tt(),L)) -> mark#(s(length(L))) mark#(0()) -> active#(0()) active#(U21(tt(),IL,M,N)) -> mark#(U22(tt(),IL,M,N)) mark#(U11(X1,X2)) -> mark#(X1) mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2)) active#(U22(tt(),IL,M,N)) -> mark#(U23(tt(),IL,M,N)) mark#(tt()) -> active#(tt()) active#(U23(tt(),IL,M,N)) -> mark#(cons(N,take(M,IL))) mark#(U12(X1,X2)) -> mark#(X1) mark#(U12(X1,X2)) -> active#(U12(mark(X1),X2)) active#(length(nil())) -> mark#(0()) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(length(cons(N,L))) -> mark#(U11(tt(),L)) mark#(length(X)) -> mark#(X) mark#(length(X)) -> active#(length(mark(X))) active#(take(0(),IL)) -> mark#(nil()) mark#(U21(X1,X2,X3,X4)) -> mark#(X1) mark#(U21(X1,X2,X3,X4)) -> active#(U21(mark(X1),X2,X3,X4)) active#(take(s(M),cons(N,IL))) -> mark#(U21(tt(),IL,M,N)) mark#(U22(X1,X2,X3,X4)) -> mark#(X1) mark#(U22(X1,X2,X3,X4)) -> active#(U22(mark(X1),X2,X3,X4)) mark#(U23(X1,X2,X3,X4)) -> mark#(X1) mark#(U23(X1,X2,X3,X4)) -> active#(U23(mark(X1),X2,X3,X4)) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),L)) -> mark(U12(tt(),L)) active(U12(tt(),L)) -> mark(s(length(L))) active(U21(tt(),IL,M,N)) -> mark(U22(tt(),IL,M,N)) active(U22(tt(),IL,M,N)) -> mark(U23(tt(),IL,M,N)) active(U23(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U11(tt(),L)) active(take(0(),IL)) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(U21(tt(),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U21(X1,X2,X3,X4)) -> active(U21(mark(X1),X2,X3,X4)) mark(U22(X1,X2,X3,X4)) -> active(U22(mark(X1),X2,X3,X4)) mark(U23(X1,X2,X3,X4)) -> active(U23(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U21(mark(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,mark(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,mark(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,mark(X4)) -> U21(X1,X2,X3,X4) U21(active(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,active(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,active(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,active(X4)) -> U21(X1,X2,X3,X4) U22(mark(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,mark(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,mark(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,mark(X4)) -> U22(X1,X2,X3,X4) U22(active(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,active(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,active(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,active(X4)) -> U22(X1,X2,X3,X4) U23(mark(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,mark(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,mark(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,mark(X4)) -> U23(X1,X2,X3,X4) U23(active(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,active(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,active(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,active(X4)) -> U23(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: cons#(mark(X1),X2) -> cons#(X1,X2) cons#(X1,mark(X2)) -> cons#(X1,X2) cons#(active(X1),X2) -> cons#(X1,X2) cons#(X1,active(X2)) -> cons#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),L)) -> mark(U12(tt(),L)) active(U12(tt(),L)) -> mark(s(length(L))) active(U21(tt(),IL,M,N)) -> mark(U22(tt(),IL,M,N)) active(U22(tt(),IL,M,N)) -> mark(U23(tt(),IL,M,N)) active(U23(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U11(tt(),L)) active(take(0(),IL)) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(U21(tt(),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U21(X1,X2,X3,X4)) -> active(U21(mark(X1),X2,X3,X4)) mark(U22(X1,X2,X3,X4)) -> active(U22(mark(X1),X2,X3,X4)) mark(U23(X1,X2,X3,X4)) -> active(U23(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U21(mark(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,mark(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,mark(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,mark(X4)) -> U21(X1,X2,X3,X4) U21(active(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,active(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,active(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,active(X4)) -> U21(X1,X2,X3,X4) U22(mark(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,mark(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,mark(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,mark(X4)) -> U22(X1,X2,X3,X4) U22(active(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,active(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,active(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,active(X4)) -> U22(X1,X2,X3,X4) U23(mark(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,mark(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,mark(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,mark(X4)) -> U23(X1,X2,X3,X4) U23(active(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,active(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,active(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,active(X4)) -> U23(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U12#(mark(X1),X2) -> U12#(X1,X2) U12#(X1,mark(X2)) -> U12#(X1,X2) U12#(active(X1),X2) -> U12#(X1,X2) U12#(X1,active(X2)) -> U12#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),L)) -> mark(U12(tt(),L)) active(U12(tt(),L)) -> mark(s(length(L))) active(U21(tt(),IL,M,N)) -> mark(U22(tt(),IL,M,N)) active(U22(tt(),IL,M,N)) -> mark(U23(tt(),IL,M,N)) active(U23(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U11(tt(),L)) active(take(0(),IL)) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(U21(tt(),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U21(X1,X2,X3,X4)) -> active(U21(mark(X1),X2,X3,X4)) mark(U22(X1,X2,X3,X4)) -> active(U22(mark(X1),X2,X3,X4)) mark(U23(X1,X2,X3,X4)) -> active(U23(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U21(mark(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,mark(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,mark(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,mark(X4)) -> U21(X1,X2,X3,X4) U21(active(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,active(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,active(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,active(X4)) -> U21(X1,X2,X3,X4) U22(mark(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,mark(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,mark(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,mark(X4)) -> U22(X1,X2,X3,X4) U22(active(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,active(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,active(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,active(X4)) -> U22(X1,X2,X3,X4) U23(mark(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,mark(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,mark(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,mark(X4)) -> U23(X1,X2,X3,X4) U23(active(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,active(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,active(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,active(X4)) -> U23(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),L)) -> mark(U12(tt(),L)) active(U12(tt(),L)) -> mark(s(length(L))) active(U21(tt(),IL,M,N)) -> mark(U22(tt(),IL,M,N)) active(U22(tt(),IL,M,N)) -> mark(U23(tt(),IL,M,N)) active(U23(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U11(tt(),L)) active(take(0(),IL)) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(U21(tt(),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U21(X1,X2,X3,X4)) -> active(U21(mark(X1),X2,X3,X4)) mark(U22(X1,X2,X3,X4)) -> active(U22(mark(X1),X2,X3,X4)) mark(U23(X1,X2,X3,X4)) -> active(U23(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U21(mark(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,mark(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,mark(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,mark(X4)) -> U21(X1,X2,X3,X4) U21(active(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,active(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,active(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,active(X4)) -> U21(X1,X2,X3,X4) U22(mark(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,mark(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,mark(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,mark(X4)) -> U22(X1,X2,X3,X4) U22(active(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,active(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,active(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,active(X4)) -> U22(X1,X2,X3,X4) U23(mark(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,mark(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,mark(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,mark(X4)) -> U23(X1,X2,X3,X4) U23(active(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,active(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,active(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,active(X4)) -> U23(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),L)) -> mark(U12(tt(),L)) active(U12(tt(),L)) -> mark(s(length(L))) active(U21(tt(),IL,M,N)) -> mark(U22(tt(),IL,M,N)) active(U22(tt(),IL,M,N)) -> mark(U23(tt(),IL,M,N)) active(U23(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U11(tt(),L)) active(take(0(),IL)) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(U21(tt(),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U21(X1,X2,X3,X4)) -> active(U21(mark(X1),X2,X3,X4)) mark(U22(X1,X2,X3,X4)) -> active(U22(mark(X1),X2,X3,X4)) mark(U23(X1,X2,X3,X4)) -> active(U23(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U21(mark(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,mark(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,mark(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,mark(X4)) -> U21(X1,X2,X3,X4) U21(active(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,active(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,active(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,active(X4)) -> U21(X1,X2,X3,X4) U22(mark(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,mark(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,mark(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,mark(X4)) -> U22(X1,X2,X3,X4) U22(active(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,active(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,active(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,active(X4)) -> U22(X1,X2,X3,X4) U23(mark(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,mark(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,mark(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,mark(X4)) -> U23(X1,X2,X3,X4) U23(active(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,active(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,active(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,active(X4)) -> U23(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U22#(mark(X1),X2,X3,X4) -> U22#(X1,X2,X3,X4) U22#(X1,mark(X2),X3,X4) -> U22#(X1,X2,X3,X4) U22#(X1,X2,mark(X3),X4) -> U22#(X1,X2,X3,X4) U22#(X1,X2,X3,mark(X4)) -> U22#(X1,X2,X3,X4) U22#(active(X1),X2,X3,X4) -> U22#(X1,X2,X3,X4) U22#(X1,active(X2),X3,X4) -> U22#(X1,X2,X3,X4) U22#(X1,X2,active(X3),X4) -> U22#(X1,X2,X3,X4) U22#(X1,X2,X3,active(X4)) -> U22#(X1,X2,X3,X4) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),L)) -> mark(U12(tt(),L)) active(U12(tt(),L)) -> mark(s(length(L))) active(U21(tt(),IL,M,N)) -> mark(U22(tt(),IL,M,N)) active(U22(tt(),IL,M,N)) -> mark(U23(tt(),IL,M,N)) active(U23(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U11(tt(),L)) active(take(0(),IL)) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(U21(tt(),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U21(X1,X2,X3,X4)) -> active(U21(mark(X1),X2,X3,X4)) mark(U22(X1,X2,X3,X4)) -> active(U22(mark(X1),X2,X3,X4)) mark(U23(X1,X2,X3,X4)) -> active(U23(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U21(mark(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,mark(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,mark(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,mark(X4)) -> U21(X1,X2,X3,X4) U21(active(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,active(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,active(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,active(X4)) -> U21(X1,X2,X3,X4) U22(mark(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,mark(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,mark(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,mark(X4)) -> U22(X1,X2,X3,X4) U22(active(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,active(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,active(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,active(X4)) -> U22(X1,X2,X3,X4) U23(mark(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,mark(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,mark(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,mark(X4)) -> U23(X1,X2,X3,X4) U23(active(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,active(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,active(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,active(X4)) -> U23(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U23#(mark(X1),X2,X3,X4) -> U23#(X1,X2,X3,X4) U23#(X1,mark(X2),X3,X4) -> U23#(X1,X2,X3,X4) U23#(X1,X2,mark(X3),X4) -> U23#(X1,X2,X3,X4) U23#(X1,X2,X3,mark(X4)) -> U23#(X1,X2,X3,X4) U23#(active(X1),X2,X3,X4) -> U23#(X1,X2,X3,X4) U23#(X1,active(X2),X3,X4) -> U23#(X1,X2,X3,X4) U23#(X1,X2,active(X3),X4) -> U23#(X1,X2,X3,X4) U23#(X1,X2,X3,active(X4)) -> U23#(X1,X2,X3,X4) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),L)) -> mark(U12(tt(),L)) active(U12(tt(),L)) -> mark(s(length(L))) active(U21(tt(),IL,M,N)) -> mark(U22(tt(),IL,M,N)) active(U22(tt(),IL,M,N)) -> mark(U23(tt(),IL,M,N)) active(U23(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U11(tt(),L)) active(take(0(),IL)) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(U21(tt(),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U21(X1,X2,X3,X4)) -> active(U21(mark(X1),X2,X3,X4)) mark(U22(X1,X2,X3,X4)) -> active(U22(mark(X1),X2,X3,X4)) mark(U23(X1,X2,X3,X4)) -> active(U23(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U21(mark(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,mark(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,mark(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,mark(X4)) -> U21(X1,X2,X3,X4) U21(active(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,active(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,active(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,active(X4)) -> U21(X1,X2,X3,X4) U22(mark(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,mark(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,mark(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,mark(X4)) -> U22(X1,X2,X3,X4) U22(active(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,active(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,active(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,active(X4)) -> U22(X1,X2,X3,X4) U23(mark(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,mark(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,mark(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,mark(X4)) -> U23(X1,X2,X3,X4) U23(active(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,active(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,active(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,active(X4)) -> U23(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: take#(mark(X1),X2) -> take#(X1,X2) take#(X1,mark(X2)) -> take#(X1,X2) take#(active(X1),X2) -> take#(X1,X2) take#(X1,active(X2)) -> take#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),L)) -> mark(U12(tt(),L)) active(U12(tt(),L)) -> mark(s(length(L))) active(U21(tt(),IL,M,N)) -> mark(U22(tt(),IL,M,N)) active(U22(tt(),IL,M,N)) -> mark(U23(tt(),IL,M,N)) active(U23(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U11(tt(),L)) active(take(0(),IL)) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(U21(tt(),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U21(X1,X2,X3,X4)) -> active(U21(mark(X1),X2,X3,X4)) mark(U22(X1,X2,X3,X4)) -> active(U22(mark(X1),X2,X3,X4)) mark(U23(X1,X2,X3,X4)) -> active(U23(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U21(mark(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,mark(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,mark(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,mark(X4)) -> U21(X1,X2,X3,X4) U21(active(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,active(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,active(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,active(X4)) -> U21(X1,X2,X3,X4) U22(mark(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,mark(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,mark(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,mark(X4)) -> U22(X1,X2,X3,X4) U22(active(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,active(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,active(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,active(X4)) -> U22(X1,X2,X3,X4) U23(mark(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,mark(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,mark(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,mark(X4)) -> U23(X1,X2,X3,X4) U23(active(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,active(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,active(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,active(X4)) -> U23(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U11#(mark(X1),X2) -> U11#(X1,X2) U11#(X1,mark(X2)) -> U11#(X1,X2) U11#(active(X1),X2) -> U11#(X1,X2) U11#(X1,active(X2)) -> U11#(X1,X2) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),L)) -> mark(U12(tt(),L)) active(U12(tt(),L)) -> mark(s(length(L))) active(U21(tt(),IL,M,N)) -> mark(U22(tt(),IL,M,N)) active(U22(tt(),IL,M,N)) -> mark(U23(tt(),IL,M,N)) active(U23(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U11(tt(),L)) active(take(0(),IL)) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(U21(tt(),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U21(X1,X2,X3,X4)) -> active(U21(mark(X1),X2,X3,X4)) mark(U22(X1,X2,X3,X4)) -> active(U22(mark(X1),X2,X3,X4)) mark(U23(X1,X2,X3,X4)) -> active(U23(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U21(mark(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,mark(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,mark(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,mark(X4)) -> U21(X1,X2,X3,X4) U21(active(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,active(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,active(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,active(X4)) -> U21(X1,X2,X3,X4) U22(mark(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,mark(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,mark(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,mark(X4)) -> U22(X1,X2,X3,X4) U22(active(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,active(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,active(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,active(X4)) -> U22(X1,X2,X3,X4) U23(mark(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,mark(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,mark(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,mark(X4)) -> U23(X1,X2,X3,X4) U23(active(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,active(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,active(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,active(X4)) -> U23(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open DPs: U21#(mark(X1),X2,X3,X4) -> U21#(X1,X2,X3,X4) U21#(X1,mark(X2),X3,X4) -> U21#(X1,X2,X3,X4) U21#(X1,X2,mark(X3),X4) -> U21#(X1,X2,X3,X4) U21#(X1,X2,X3,mark(X4)) -> U21#(X1,X2,X3,X4) U21#(active(X1),X2,X3,X4) -> U21#(X1,X2,X3,X4) U21#(X1,active(X2),X3,X4) -> U21#(X1,X2,X3,X4) U21#(X1,X2,active(X3),X4) -> U21#(X1,X2,X3,X4) U21#(X1,X2,X3,active(X4)) -> U21#(X1,X2,X3,X4) TRS: active(zeros()) -> mark(cons(0(),zeros())) active(U11(tt(),L)) -> mark(U12(tt(),L)) active(U12(tt(),L)) -> mark(s(length(L))) active(U21(tt(),IL,M,N)) -> mark(U22(tt(),IL,M,N)) active(U22(tt(),IL,M,N)) -> mark(U23(tt(),IL,M,N)) active(U23(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) active(length(nil())) -> mark(0()) active(length(cons(N,L))) -> mark(U11(tt(),L)) active(take(0(),IL)) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(U21(tt(),IL,M,N)) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(0()) -> active(0()) mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) mark(tt()) -> active(tt()) mark(U12(X1,X2)) -> active(U12(mark(X1),X2)) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(U21(X1,X2,X3,X4)) -> active(U21(mark(X1),X2,X3,X4)) mark(U22(X1,X2,X3,X4)) -> active(U22(mark(X1),X2,X3,X4)) mark(U23(X1,X2,X3,X4)) -> active(U23(mark(X1),X2,X3,X4)) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(nil()) -> active(nil()) cons(mark(X1),X2) -> cons(X1,X2) cons(X1,mark(X2)) -> cons(X1,X2) cons(active(X1),X2) -> cons(X1,X2) cons(X1,active(X2)) -> cons(X1,X2) U11(mark(X1),X2) -> U11(X1,X2) U11(X1,mark(X2)) -> U11(X1,X2) U11(active(X1),X2) -> U11(X1,X2) U11(X1,active(X2)) -> U11(X1,X2) U12(mark(X1),X2) -> U12(X1,X2) U12(X1,mark(X2)) -> U12(X1,X2) U12(active(X1),X2) -> U12(X1,X2) U12(X1,active(X2)) -> U12(X1,X2) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) U21(mark(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,mark(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,mark(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,mark(X4)) -> U21(X1,X2,X3,X4) U21(active(X1),X2,X3,X4) -> U21(X1,X2,X3,X4) U21(X1,active(X2),X3,X4) -> U21(X1,X2,X3,X4) U21(X1,X2,active(X3),X4) -> U21(X1,X2,X3,X4) U21(X1,X2,X3,active(X4)) -> U21(X1,X2,X3,X4) U22(mark(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,mark(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,mark(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,mark(X4)) -> U22(X1,X2,X3,X4) U22(active(X1),X2,X3,X4) -> U22(X1,X2,X3,X4) U22(X1,active(X2),X3,X4) -> U22(X1,X2,X3,X4) U22(X1,X2,active(X3),X4) -> U22(X1,X2,X3,X4) U22(X1,X2,X3,active(X4)) -> U22(X1,X2,X3,X4) U23(mark(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,mark(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,mark(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,mark(X4)) -> U23(X1,X2,X3,X4) U23(active(X1),X2,X3,X4) -> U23(X1,X2,X3,X4) U23(X1,active(X2),X3,X4) -> U23(X1,X2,X3,X4) U23(X1,X2,active(X3),X4) -> U23(X1,X2,X3,X4) U23(X1,X2,X3,active(X4)) -> U23(X1,X2,X3,X4) take(mark(X1),X2) -> take(X1,X2) take(X1,mark(X2)) -> take(X1,X2) take(active(X1),X2) -> take(X1,X2) take(X1,active(X2)) -> take(X1,X2) Open