MAYBE Problem: active(and(tt(),T)) -> mark(T) active(isNatIList(IL)) -> mark(isNatList(IL)) active(isNat(0())) -> mark(tt()) active(isNat(s(N))) -> mark(isNat(N)) active(isNat(length(L))) -> mark(isNatList(L)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L))) active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(zeros()) -> mark(cons(0(),zeros())) active(take(0(),IL)) -> mark(uTake1(isNatIList(IL))) active(uTake1(tt())) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL))) active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L)) active(uLength(tt(),L)) -> mark(s(length(L))) mark(and(X1,X2)) -> active(and(mark(X1),mark(X2))) mark(tt()) -> active(tt()) mark(isNatIList(X)) -> active(isNatIList(X)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(nil()) -> active(nil()) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(uTake1(X)) -> active(uTake1(mark(X))) mark(uTake2(X1,X2,X3,X4)) -> active(uTake2(mark(X1),X2,X3,X4)) mark(uLength(X1,X2)) -> active(uLength(mark(X1),X2)) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) 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) 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) uTake1(mark(X)) -> uTake1(X) uTake1(active(X)) -> uTake1(X) uTake2(mark(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,mark(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,mark(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,mark(X4)) -> uTake2(X1,X2,X3,X4) uTake2(active(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,active(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,active(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,active(X4)) -> uTake2(X1,X2,X3,X4) uLength(mark(X1),X2) -> uLength(X1,X2) uLength(X1,mark(X2)) -> uLength(X1,X2) uLength(active(X1),X2) -> uLength(X1,X2) uLength(X1,active(X2)) -> uLength(X1,X2) Proof: DP Processor: DPs: active#(and(tt(),T)) -> mark#(T) active#(isNatIList(IL)) -> isNatList#(IL) active#(isNatIList(IL)) -> mark#(isNatList(IL)) active#(isNat(0())) -> mark#(tt()) active#(isNat(s(N))) -> isNat#(N) active#(isNat(s(N))) -> mark#(isNat(N)) active#(isNat(length(L))) -> isNatList#(L) active#(isNat(length(L))) -> mark#(isNatList(L)) active#(isNatIList(zeros())) -> mark#(tt()) active#(isNatIList(cons(N,IL))) -> isNatIList#(IL) active#(isNatIList(cons(N,IL))) -> isNat#(N) active#(isNatIList(cons(N,IL))) -> and#(isNat(N),isNatIList(IL)) active#(isNatIList(cons(N,IL))) -> mark#(and(isNat(N),isNatIList(IL))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(N,L))) -> isNatList#(L) active#(isNatList(cons(N,L))) -> isNat#(N) active#(isNatList(cons(N,L))) -> and#(isNat(N),isNatList(L)) active#(isNatList(cons(N,L))) -> mark#(and(isNat(N),isNatList(L))) active#(isNatList(take(N,IL))) -> isNatIList#(IL) active#(isNatList(take(N,IL))) -> isNat#(N) active#(isNatList(take(N,IL))) -> and#(isNat(N),isNatIList(IL)) active#(isNatList(take(N,IL))) -> mark#(and(isNat(N),isNatIList(IL))) active#(zeros()) -> cons#(0(),zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) active#(take(0(),IL)) -> isNatIList#(IL) active#(take(0(),IL)) -> uTake1#(isNatIList(IL)) active#(take(0(),IL)) -> mark#(uTake1(isNatIList(IL))) active#(uTake1(tt())) -> mark#(nil()) active#(take(s(M),cons(N,IL))) -> isNatIList#(IL) active#(take(s(M),cons(N,IL))) -> isNat#(N) active#(take(s(M),cons(N,IL))) -> and#(isNat(N),isNatIList(IL)) active#(take(s(M),cons(N,IL))) -> isNat#(M) active#(take(s(M),cons(N,IL))) -> and#(isNat(M),and(isNat(N),isNatIList(IL))) active#(take(s(M),cons(N,IL))) -> uTake2#(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL) active#(take(s(M),cons(N,IL))) -> mark#(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active#(uTake2(tt(),M,N,IL)) -> take#(M,IL) active#(uTake2(tt(),M,N,IL)) -> cons#(N,take(M,IL)) active#(uTake2(tt(),M,N,IL)) -> mark#(cons(N,take(M,IL))) active#(length(cons(N,L))) -> isNatList#(L) active#(length(cons(N,L))) -> isNat#(N) active#(length(cons(N,L))) -> and#(isNat(N),isNatList(L)) active#(length(cons(N,L))) -> uLength#(and(isNat(N),isNatList(L)),L) active#(length(cons(N,L))) -> mark#(uLength(and(isNat(N),isNatList(L)),L)) active#(uLength(tt(),L)) -> length#(L) active#(uLength(tt(),L)) -> s#(length(L)) active#(uLength(tt(),L)) -> mark#(s(length(L))) mark#(and(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> and#(mark(X1),mark(X2)) mark#(and(X1,X2)) -> active#(and(mark(X1),mark(X2))) mark#(tt()) -> active#(tt()) mark#(isNatIList(X)) -> active#(isNatIList(X)) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(isNat(X)) -> active#(isNat(X)) mark#(0()) -> active#(0()) 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#(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#(nil()) -> active#(nil()) 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#(uTake1(X)) -> mark#(X) mark#(uTake1(X)) -> uTake1#(mark(X)) mark#(uTake1(X)) -> active#(uTake1(mark(X))) mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) mark#(uTake2(X1,X2,X3,X4)) -> uTake2#(mark(X1),X2,X3,X4) mark#(uTake2(X1,X2,X3,X4)) -> active#(uTake2(mark(X1),X2,X3,X4)) mark#(uLength(X1,X2)) -> mark#(X1) mark#(uLength(X1,X2)) -> uLength#(mark(X1),X2) mark#(uLength(X1,X2)) -> active#(uLength(mark(X1),X2)) and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) isNatIList#(mark(X)) -> isNatIList#(X) isNatIList#(active(X)) -> isNatIList#(X) isNatList#(mark(X)) -> isNatList#(X) isNatList#(active(X)) -> isNatList#(X) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) 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) 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) uTake1#(mark(X)) -> uTake1#(X) uTake1#(active(X)) -> uTake1#(X) uTake2#(mark(X1),X2,X3,X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,mark(X2),X3,X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,X2,mark(X3),X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,X2,X3,mark(X4)) -> uTake2#(X1,X2,X3,X4) uTake2#(active(X1),X2,X3,X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,active(X2),X3,X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,X2,active(X3),X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,X2,X3,active(X4)) -> uTake2#(X1,X2,X3,X4) uLength#(mark(X1),X2) -> uLength#(X1,X2) uLength#(X1,mark(X2)) -> uLength#(X1,X2) uLength#(active(X1),X2) -> uLength#(X1,X2) uLength#(X1,active(X2)) -> uLength#(X1,X2) TRS: active(and(tt(),T)) -> mark(T) active(isNatIList(IL)) -> mark(isNatList(IL)) active(isNat(0())) -> mark(tt()) active(isNat(s(N))) -> mark(isNat(N)) active(isNat(length(L))) -> mark(isNatList(L)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L))) active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(zeros()) -> mark(cons(0(),zeros())) active(take(0(),IL)) -> mark(uTake1(isNatIList(IL))) active(uTake1(tt())) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL))) active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L)) active(uLength(tt(),L)) -> mark(s(length(L))) mark(and(X1,X2)) -> active(and(mark(X1),mark(X2))) mark(tt()) -> active(tt()) mark(isNatIList(X)) -> active(isNatIList(X)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(nil()) -> active(nil()) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(uTake1(X)) -> active(uTake1(mark(X))) mark(uTake2(X1,X2,X3,X4)) -> active(uTake2(mark(X1),X2,X3,X4)) mark(uLength(X1,X2)) -> active(uLength(mark(X1),X2)) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) 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) 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) uTake1(mark(X)) -> uTake1(X) uTake1(active(X)) -> uTake1(X) uTake2(mark(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,mark(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,mark(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,mark(X4)) -> uTake2(X1,X2,X3,X4) uTake2(active(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,active(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,active(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,active(X4)) -> uTake2(X1,X2,X3,X4) uLength(mark(X1),X2) -> uLength(X1,X2) uLength(X1,mark(X2)) -> uLength(X1,X2) uLength(active(X1),X2) -> uLength(X1,X2) uLength(X1,active(X2)) -> uLength(X1,X2) TDG Processor: DPs: active#(and(tt(),T)) -> mark#(T) active#(isNatIList(IL)) -> isNatList#(IL) active#(isNatIList(IL)) -> mark#(isNatList(IL)) active#(isNat(0())) -> mark#(tt()) active#(isNat(s(N))) -> isNat#(N) active#(isNat(s(N))) -> mark#(isNat(N)) active#(isNat(length(L))) -> isNatList#(L) active#(isNat(length(L))) -> mark#(isNatList(L)) active#(isNatIList(zeros())) -> mark#(tt()) active#(isNatIList(cons(N,IL))) -> isNatIList#(IL) active#(isNatIList(cons(N,IL))) -> isNat#(N) active#(isNatIList(cons(N,IL))) -> and#(isNat(N),isNatIList(IL)) active#(isNatIList(cons(N,IL))) -> mark#(and(isNat(N),isNatIList(IL))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(N,L))) -> isNatList#(L) active#(isNatList(cons(N,L))) -> isNat#(N) active#(isNatList(cons(N,L))) -> and#(isNat(N),isNatList(L)) active#(isNatList(cons(N,L))) -> mark#(and(isNat(N),isNatList(L))) active#(isNatList(take(N,IL))) -> isNatIList#(IL) active#(isNatList(take(N,IL))) -> isNat#(N) active#(isNatList(take(N,IL))) -> and#(isNat(N),isNatIList(IL)) active#(isNatList(take(N,IL))) -> mark#(and(isNat(N),isNatIList(IL))) active#(zeros()) -> cons#(0(),zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) active#(take(0(),IL)) -> isNatIList#(IL) active#(take(0(),IL)) -> uTake1#(isNatIList(IL)) active#(take(0(),IL)) -> mark#(uTake1(isNatIList(IL))) active#(uTake1(tt())) -> mark#(nil()) active#(take(s(M),cons(N,IL))) -> isNatIList#(IL) active#(take(s(M),cons(N,IL))) -> isNat#(N) active#(take(s(M),cons(N,IL))) -> and#(isNat(N),isNatIList(IL)) active#(take(s(M),cons(N,IL))) -> isNat#(M) active#(take(s(M),cons(N,IL))) -> and#(isNat(M),and(isNat(N),isNatIList(IL))) active#(take(s(M),cons(N,IL))) -> uTake2#(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL) active#(take(s(M),cons(N,IL))) -> mark#(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active#(uTake2(tt(),M,N,IL)) -> take#(M,IL) active#(uTake2(tt(),M,N,IL)) -> cons#(N,take(M,IL)) active#(uTake2(tt(),M,N,IL)) -> mark#(cons(N,take(M,IL))) active#(length(cons(N,L))) -> isNatList#(L) active#(length(cons(N,L))) -> isNat#(N) active#(length(cons(N,L))) -> and#(isNat(N),isNatList(L)) active#(length(cons(N,L))) -> uLength#(and(isNat(N),isNatList(L)),L) active#(length(cons(N,L))) -> mark#(uLength(and(isNat(N),isNatList(L)),L)) active#(uLength(tt(),L)) -> length#(L) active#(uLength(tt(),L)) -> s#(length(L)) active#(uLength(tt(),L)) -> mark#(s(length(L))) mark#(and(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> and#(mark(X1),mark(X2)) mark#(and(X1,X2)) -> active#(and(mark(X1),mark(X2))) mark#(tt()) -> active#(tt()) mark#(isNatIList(X)) -> active#(isNatIList(X)) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(isNat(X)) -> active#(isNat(X)) mark#(0()) -> active#(0()) 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#(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#(nil()) -> active#(nil()) 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#(uTake1(X)) -> mark#(X) mark#(uTake1(X)) -> uTake1#(mark(X)) mark#(uTake1(X)) -> active#(uTake1(mark(X))) mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) mark#(uTake2(X1,X2,X3,X4)) -> uTake2#(mark(X1),X2,X3,X4) mark#(uTake2(X1,X2,X3,X4)) -> active#(uTake2(mark(X1),X2,X3,X4)) mark#(uLength(X1,X2)) -> mark#(X1) mark#(uLength(X1,X2)) -> uLength#(mark(X1),X2) mark#(uLength(X1,X2)) -> active#(uLength(mark(X1),X2)) and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) isNatIList#(mark(X)) -> isNatIList#(X) isNatIList#(active(X)) -> isNatIList#(X) isNatList#(mark(X)) -> isNatList#(X) isNatList#(active(X)) -> isNatList#(X) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) 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) 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) uTake1#(mark(X)) -> uTake1#(X) uTake1#(active(X)) -> uTake1#(X) uTake2#(mark(X1),X2,X3,X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,mark(X2),X3,X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,X2,mark(X3),X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,X2,X3,mark(X4)) -> uTake2#(X1,X2,X3,X4) uTake2#(active(X1),X2,X3,X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,active(X2),X3,X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,X2,active(X3),X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,X2,X3,active(X4)) -> uTake2#(X1,X2,X3,X4) uLength#(mark(X1),X2) -> uLength#(X1,X2) uLength#(X1,mark(X2)) -> uLength#(X1,X2) uLength#(active(X1),X2) -> uLength#(X1,X2) uLength#(X1,active(X2)) -> uLength#(X1,X2) TRS: active(and(tt(),T)) -> mark(T) active(isNatIList(IL)) -> mark(isNatList(IL)) active(isNat(0())) -> mark(tt()) active(isNat(s(N))) -> mark(isNat(N)) active(isNat(length(L))) -> mark(isNatList(L)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L))) active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(zeros()) -> mark(cons(0(),zeros())) active(take(0(),IL)) -> mark(uTake1(isNatIList(IL))) active(uTake1(tt())) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL))) active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L)) active(uLength(tt(),L)) -> mark(s(length(L))) mark(and(X1,X2)) -> active(and(mark(X1),mark(X2))) mark(tt()) -> active(tt()) mark(isNatIList(X)) -> active(isNatIList(X)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(nil()) -> active(nil()) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(uTake1(X)) -> active(uTake1(mark(X))) mark(uTake2(X1,X2,X3,X4)) -> active(uTake2(mark(X1),X2,X3,X4)) mark(uLength(X1,X2)) -> active(uLength(mark(X1),X2)) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) 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) 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) uTake1(mark(X)) -> uTake1(X) uTake1(active(X)) -> uTake1(X) uTake2(mark(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,mark(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,mark(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,mark(X4)) -> uTake2(X1,X2,X3,X4) uTake2(active(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,active(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,active(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,active(X4)) -> uTake2(X1,X2,X3,X4) uLength(mark(X1),X2) -> uLength(X1,X2) uLength(X1,mark(X2)) -> uLength(X1,X2) uLength(active(X1),X2) -> uLength(X1,X2) uLength(X1,active(X2)) -> uLength(X1,X2) graph: ... Restore Modifier: DPs: active#(and(tt(),T)) -> mark#(T) active#(isNatIList(IL)) -> isNatList#(IL) active#(isNatIList(IL)) -> mark#(isNatList(IL)) active#(isNat(0())) -> mark#(tt()) active#(isNat(s(N))) -> isNat#(N) active#(isNat(s(N))) -> mark#(isNat(N)) active#(isNat(length(L))) -> isNatList#(L) active#(isNat(length(L))) -> mark#(isNatList(L)) active#(isNatIList(zeros())) -> mark#(tt()) active#(isNatIList(cons(N,IL))) -> isNatIList#(IL) active#(isNatIList(cons(N,IL))) -> isNat#(N) active#(isNatIList(cons(N,IL))) -> and#(isNat(N),isNatIList(IL)) active#(isNatIList(cons(N,IL))) -> mark#(and(isNat(N),isNatIList(IL))) active#(isNatList(nil())) -> mark#(tt()) active#(isNatList(cons(N,L))) -> isNatList#(L) active#(isNatList(cons(N,L))) -> isNat#(N) active#(isNatList(cons(N,L))) -> and#(isNat(N),isNatList(L)) active#(isNatList(cons(N,L))) -> mark#(and(isNat(N),isNatList(L))) active#(isNatList(take(N,IL))) -> isNatIList#(IL) active#(isNatList(take(N,IL))) -> isNat#(N) active#(isNatList(take(N,IL))) -> and#(isNat(N),isNatIList(IL)) active#(isNatList(take(N,IL))) -> mark#(and(isNat(N),isNatIList(IL))) active#(zeros()) -> cons#(0(),zeros()) active#(zeros()) -> mark#(cons(0(),zeros())) active#(take(0(),IL)) -> isNatIList#(IL) active#(take(0(),IL)) -> uTake1#(isNatIList(IL)) active#(take(0(),IL)) -> mark#(uTake1(isNatIList(IL))) active#(uTake1(tt())) -> mark#(nil()) active#(take(s(M),cons(N,IL))) -> isNatIList#(IL) active#(take(s(M),cons(N,IL))) -> isNat#(N) active#(take(s(M),cons(N,IL))) -> and#(isNat(N),isNatIList(IL)) active#(take(s(M),cons(N,IL))) -> isNat#(M) active#(take(s(M),cons(N,IL))) -> and#(isNat(M),and(isNat(N),isNatIList(IL))) active#(take(s(M),cons(N,IL))) -> uTake2#(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL) active#(take(s(M),cons(N,IL))) -> mark#(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active#(uTake2(tt(),M,N,IL)) -> take#(M,IL) active#(uTake2(tt(),M,N,IL)) -> cons#(N,take(M,IL)) active#(uTake2(tt(),M,N,IL)) -> mark#(cons(N,take(M,IL))) active#(length(cons(N,L))) -> isNatList#(L) active#(length(cons(N,L))) -> isNat#(N) active#(length(cons(N,L))) -> and#(isNat(N),isNatList(L)) active#(length(cons(N,L))) -> uLength#(and(isNat(N),isNatList(L)),L) active#(length(cons(N,L))) -> mark#(uLength(and(isNat(N),isNatList(L)),L)) active#(uLength(tt(),L)) -> length#(L) active#(uLength(tt(),L)) -> s#(length(L)) active#(uLength(tt(),L)) -> mark#(s(length(L))) mark#(and(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> and#(mark(X1),mark(X2)) mark#(and(X1,X2)) -> active#(and(mark(X1),mark(X2))) mark#(tt()) -> active#(tt()) mark#(isNatIList(X)) -> active#(isNatIList(X)) mark#(isNatList(X)) -> active#(isNatList(X)) mark#(isNat(X)) -> active#(isNat(X)) mark#(0()) -> active#(0()) 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#(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#(nil()) -> active#(nil()) 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#(uTake1(X)) -> mark#(X) mark#(uTake1(X)) -> uTake1#(mark(X)) mark#(uTake1(X)) -> active#(uTake1(mark(X))) mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) mark#(uTake2(X1,X2,X3,X4)) -> uTake2#(mark(X1),X2,X3,X4) mark#(uTake2(X1,X2,X3,X4)) -> active#(uTake2(mark(X1),X2,X3,X4)) mark#(uLength(X1,X2)) -> mark#(X1) mark#(uLength(X1,X2)) -> uLength#(mark(X1),X2) mark#(uLength(X1,X2)) -> active#(uLength(mark(X1),X2)) and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) isNatIList#(mark(X)) -> isNatIList#(X) isNatIList#(active(X)) -> isNatIList#(X) isNatList#(mark(X)) -> isNatList#(X) isNatList#(active(X)) -> isNatList#(X) isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) 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) 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) uTake1#(mark(X)) -> uTake1#(X) uTake1#(active(X)) -> uTake1#(X) uTake2#(mark(X1),X2,X3,X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,mark(X2),X3,X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,X2,mark(X3),X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,X2,X3,mark(X4)) -> uTake2#(X1,X2,X3,X4) uTake2#(active(X1),X2,X3,X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,active(X2),X3,X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,X2,active(X3),X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,X2,X3,active(X4)) -> uTake2#(X1,X2,X3,X4) uLength#(mark(X1),X2) -> uLength#(X1,X2) uLength#(X1,mark(X2)) -> uLength#(X1,X2) uLength#(active(X1),X2) -> uLength#(X1,X2) uLength#(X1,active(X2)) -> uLength#(X1,X2) TRS: active(and(tt(),T)) -> mark(T) active(isNatIList(IL)) -> mark(isNatList(IL)) active(isNat(0())) -> mark(tt()) active(isNat(s(N))) -> mark(isNat(N)) active(isNat(length(L))) -> mark(isNatList(L)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L))) active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(zeros()) -> mark(cons(0(),zeros())) active(take(0(),IL)) -> mark(uTake1(isNatIList(IL))) active(uTake1(tt())) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL))) active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L)) active(uLength(tt(),L)) -> mark(s(length(L))) mark(and(X1,X2)) -> active(and(mark(X1),mark(X2))) mark(tt()) -> active(tt()) mark(isNatIList(X)) -> active(isNatIList(X)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(nil()) -> active(nil()) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(uTake1(X)) -> active(uTake1(mark(X))) mark(uTake2(X1,X2,X3,X4)) -> active(uTake2(mark(X1),X2,X3,X4)) mark(uLength(X1,X2)) -> active(uLength(mark(X1),X2)) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) 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) 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) uTake1(mark(X)) -> uTake1(X) uTake1(active(X)) -> uTake1(X) uTake2(mark(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,mark(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,mark(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,mark(X4)) -> uTake2(X1,X2,X3,X4) uTake2(active(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,active(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,active(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,active(X4)) -> uTake2(X1,X2,X3,X4) uLength(mark(X1),X2) -> uLength(X1,X2) uLength(X1,mark(X2)) -> uLength(X1,X2) uLength(active(X1),X2) -> uLength(X1,X2) uLength(X1,active(X2)) -> uLength(X1,X2) SCC Processor: #sccs: 12 #rules: 78 #arcs: 1847/13225 DPs: mark#(uLength(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> mark#(X2) mark#(and(X1,X2)) -> mark#(X1) mark#(and(X1,X2)) -> active#(and(mark(X1),mark(X2))) active#(and(tt(),T)) -> mark#(T) mark#(tt()) -> active#(tt()) active#(isNatIList(IL)) -> mark#(isNatList(IL)) mark#(isNatIList(X)) -> active#(isNatIList(X)) active#(isNat(0())) -> mark#(tt()) mark#(isNatList(X)) -> active#(isNatList(X)) active#(isNat(s(N))) -> mark#(isNat(N)) mark#(isNat(X)) -> active#(isNat(X)) active#(isNat(length(L))) -> mark#(isNatList(L)) mark#(0()) -> active#(0()) active#(isNatIList(zeros())) -> mark#(tt()) mark#(s(X)) -> mark#(X) mark#(s(X)) -> active#(s(mark(X))) active#(isNatIList(cons(N,IL))) -> mark#(and(isNat(N),isNatIList(IL))) mark#(length(X)) -> mark#(X) mark#(length(X)) -> active#(length(mark(X))) active#(isNatList(nil())) -> mark#(tt()) mark#(zeros()) -> active#(zeros()) active#(isNatList(cons(N,L))) -> mark#(and(isNat(N),isNatList(L))) mark#(cons(X1,X2)) -> mark#(X1) mark#(cons(X1,X2)) -> active#(cons(mark(X1),X2)) active#(isNatList(take(N,IL))) -> mark#(and(isNat(N),isNatIList(IL))) mark#(nil()) -> active#(nil()) active#(zeros()) -> mark#(cons(0(),zeros())) mark#(take(X1,X2)) -> mark#(X2) mark#(take(X1,X2)) -> mark#(X1) mark#(take(X1,X2)) -> active#(take(mark(X1),mark(X2))) active#(take(0(),IL)) -> mark#(uTake1(isNatIList(IL))) mark#(uTake1(X)) -> mark#(X) mark#(uTake1(X)) -> active#(uTake1(mark(X))) active#(uTake1(tt())) -> mark#(nil()) mark#(uTake2(X1,X2,X3,X4)) -> mark#(X1) mark#(uTake2(X1,X2,X3,X4)) -> active#(uTake2(mark(X1),X2,X3,X4)) active#(take(s(M),cons(N,IL))) -> mark#(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) mark#(uLength(X1,X2)) -> active#(uLength(mark(X1),X2)) active#(uTake2(tt(),M,N,IL)) -> mark#(cons(N,take(M,IL))) active#(length(cons(N,L))) -> mark#(uLength(and(isNat(N),isNatList(L)),L)) active#(uLength(tt(),L)) -> mark#(s(length(L))) TRS: active(and(tt(),T)) -> mark(T) active(isNatIList(IL)) -> mark(isNatList(IL)) active(isNat(0())) -> mark(tt()) active(isNat(s(N))) -> mark(isNat(N)) active(isNat(length(L))) -> mark(isNatList(L)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L))) active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(zeros()) -> mark(cons(0(),zeros())) active(take(0(),IL)) -> mark(uTake1(isNatIList(IL))) active(uTake1(tt())) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL))) active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L)) active(uLength(tt(),L)) -> mark(s(length(L))) mark(and(X1,X2)) -> active(and(mark(X1),mark(X2))) mark(tt()) -> active(tt()) mark(isNatIList(X)) -> active(isNatIList(X)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(nil()) -> active(nil()) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(uTake1(X)) -> active(uTake1(mark(X))) mark(uTake2(X1,X2,X3,X4)) -> active(uTake2(mark(X1),X2,X3,X4)) mark(uLength(X1,X2)) -> active(uLength(mark(X1),X2)) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) 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) 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) uTake1(mark(X)) -> uTake1(X) uTake1(active(X)) -> uTake1(X) uTake2(mark(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,mark(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,mark(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,mark(X4)) -> uTake2(X1,X2,X3,X4) uTake2(active(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,active(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,active(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,active(X4)) -> uTake2(X1,X2,X3,X4) uLength(mark(X1),X2) -> uLength(X1,X2) uLength(X1,mark(X2)) -> uLength(X1,X2) uLength(active(X1),X2) -> uLength(X1,X2) uLength(X1,active(X2)) -> uLength(X1,X2) Open DPs: isNatList#(mark(X)) -> isNatList#(X) isNatList#(active(X)) -> isNatList#(X) TRS: active(and(tt(),T)) -> mark(T) active(isNatIList(IL)) -> mark(isNatList(IL)) active(isNat(0())) -> mark(tt()) active(isNat(s(N))) -> mark(isNat(N)) active(isNat(length(L))) -> mark(isNatList(L)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L))) active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(zeros()) -> mark(cons(0(),zeros())) active(take(0(),IL)) -> mark(uTake1(isNatIList(IL))) active(uTake1(tt())) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL))) active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L)) active(uLength(tt(),L)) -> mark(s(length(L))) mark(and(X1,X2)) -> active(and(mark(X1),mark(X2))) mark(tt()) -> active(tt()) mark(isNatIList(X)) -> active(isNatIList(X)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(nil()) -> active(nil()) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(uTake1(X)) -> active(uTake1(mark(X))) mark(uTake2(X1,X2,X3,X4)) -> active(uTake2(mark(X1),X2,X3,X4)) mark(uLength(X1,X2)) -> active(uLength(mark(X1),X2)) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) 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) 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) uTake1(mark(X)) -> uTake1(X) uTake1(active(X)) -> uTake1(X) uTake2(mark(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,mark(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,mark(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,mark(X4)) -> uTake2(X1,X2,X3,X4) uTake2(active(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,active(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,active(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,active(X4)) -> uTake2(X1,X2,X3,X4) uLength(mark(X1),X2) -> uLength(X1,X2) uLength(X1,mark(X2)) -> uLength(X1,X2) uLength(active(X1),X2) -> uLength(X1,X2) uLength(X1,active(X2)) -> uLength(X1,X2) Open DPs: isNat#(mark(X)) -> isNat#(X) isNat#(active(X)) -> isNat#(X) TRS: active(and(tt(),T)) -> mark(T) active(isNatIList(IL)) -> mark(isNatList(IL)) active(isNat(0())) -> mark(tt()) active(isNat(s(N))) -> mark(isNat(N)) active(isNat(length(L))) -> mark(isNatList(L)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L))) active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(zeros()) -> mark(cons(0(),zeros())) active(take(0(),IL)) -> mark(uTake1(isNatIList(IL))) active(uTake1(tt())) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL))) active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L)) active(uLength(tt(),L)) -> mark(s(length(L))) mark(and(X1,X2)) -> active(and(mark(X1),mark(X2))) mark(tt()) -> active(tt()) mark(isNatIList(X)) -> active(isNatIList(X)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(nil()) -> active(nil()) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(uTake1(X)) -> active(uTake1(mark(X))) mark(uTake2(X1,X2,X3,X4)) -> active(uTake2(mark(X1),X2,X3,X4)) mark(uLength(X1,X2)) -> active(uLength(mark(X1),X2)) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) 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) 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) uTake1(mark(X)) -> uTake1(X) uTake1(active(X)) -> uTake1(X) uTake2(mark(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,mark(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,mark(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,mark(X4)) -> uTake2(X1,X2,X3,X4) uTake2(active(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,active(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,active(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,active(X4)) -> uTake2(X1,X2,X3,X4) uLength(mark(X1),X2) -> uLength(X1,X2) uLength(X1,mark(X2)) -> uLength(X1,X2) uLength(active(X1),X2) -> uLength(X1,X2) uLength(X1,active(X2)) -> uLength(X1,X2) Open DPs: isNatIList#(mark(X)) -> isNatIList#(X) isNatIList#(active(X)) -> isNatIList#(X) TRS: active(and(tt(),T)) -> mark(T) active(isNatIList(IL)) -> mark(isNatList(IL)) active(isNat(0())) -> mark(tt()) active(isNat(s(N))) -> mark(isNat(N)) active(isNat(length(L))) -> mark(isNatList(L)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L))) active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(zeros()) -> mark(cons(0(),zeros())) active(take(0(),IL)) -> mark(uTake1(isNatIList(IL))) active(uTake1(tt())) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL))) active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L)) active(uLength(tt(),L)) -> mark(s(length(L))) mark(and(X1,X2)) -> active(and(mark(X1),mark(X2))) mark(tt()) -> active(tt()) mark(isNatIList(X)) -> active(isNatIList(X)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(nil()) -> active(nil()) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(uTake1(X)) -> active(uTake1(mark(X))) mark(uTake2(X1,X2,X3,X4)) -> active(uTake2(mark(X1),X2,X3,X4)) mark(uLength(X1,X2)) -> active(uLength(mark(X1),X2)) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) 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) 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) uTake1(mark(X)) -> uTake1(X) uTake1(active(X)) -> uTake1(X) uTake2(mark(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,mark(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,mark(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,mark(X4)) -> uTake2(X1,X2,X3,X4) uTake2(active(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,active(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,active(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,active(X4)) -> uTake2(X1,X2,X3,X4) uLength(mark(X1),X2) -> uLength(X1,X2) uLength(X1,mark(X2)) -> uLength(X1,X2) uLength(active(X1),X2) -> uLength(X1,X2) uLength(X1,active(X2)) -> uLength(X1,X2) Open DPs: and#(mark(X1),X2) -> and#(X1,X2) and#(X1,mark(X2)) -> and#(X1,X2) and#(active(X1),X2) -> and#(X1,X2) and#(X1,active(X2)) -> and#(X1,X2) TRS: active(and(tt(),T)) -> mark(T) active(isNatIList(IL)) -> mark(isNatList(IL)) active(isNat(0())) -> mark(tt()) active(isNat(s(N))) -> mark(isNat(N)) active(isNat(length(L))) -> mark(isNatList(L)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L))) active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(zeros()) -> mark(cons(0(),zeros())) active(take(0(),IL)) -> mark(uTake1(isNatIList(IL))) active(uTake1(tt())) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL))) active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L)) active(uLength(tt(),L)) -> mark(s(length(L))) mark(and(X1,X2)) -> active(and(mark(X1),mark(X2))) mark(tt()) -> active(tt()) mark(isNatIList(X)) -> active(isNatIList(X)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(nil()) -> active(nil()) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(uTake1(X)) -> active(uTake1(mark(X))) mark(uTake2(X1,X2,X3,X4)) -> active(uTake2(mark(X1),X2,X3,X4)) mark(uLength(X1,X2)) -> active(uLength(mark(X1),X2)) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) 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) 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) uTake1(mark(X)) -> uTake1(X) uTake1(active(X)) -> uTake1(X) uTake2(mark(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,mark(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,mark(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,mark(X4)) -> uTake2(X1,X2,X3,X4) uTake2(active(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,active(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,active(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,active(X4)) -> uTake2(X1,X2,X3,X4) uLength(mark(X1),X2) -> uLength(X1,X2) uLength(X1,mark(X2)) -> uLength(X1,X2) uLength(active(X1),X2) -> uLength(X1,X2) uLength(X1,active(X2)) -> uLength(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(and(tt(),T)) -> mark(T) active(isNatIList(IL)) -> mark(isNatList(IL)) active(isNat(0())) -> mark(tt()) active(isNat(s(N))) -> mark(isNat(N)) active(isNat(length(L))) -> mark(isNatList(L)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L))) active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(zeros()) -> mark(cons(0(),zeros())) active(take(0(),IL)) -> mark(uTake1(isNatIList(IL))) active(uTake1(tt())) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL))) active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L)) active(uLength(tt(),L)) -> mark(s(length(L))) mark(and(X1,X2)) -> active(and(mark(X1),mark(X2))) mark(tt()) -> active(tt()) mark(isNatIList(X)) -> active(isNatIList(X)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(nil()) -> active(nil()) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(uTake1(X)) -> active(uTake1(mark(X))) mark(uTake2(X1,X2,X3,X4)) -> active(uTake2(mark(X1),X2,X3,X4)) mark(uLength(X1,X2)) -> active(uLength(mark(X1),X2)) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) 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) 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) uTake1(mark(X)) -> uTake1(X) uTake1(active(X)) -> uTake1(X) uTake2(mark(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,mark(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,mark(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,mark(X4)) -> uTake2(X1,X2,X3,X4) uTake2(active(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,active(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,active(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,active(X4)) -> uTake2(X1,X2,X3,X4) uLength(mark(X1),X2) -> uLength(X1,X2) uLength(X1,mark(X2)) -> uLength(X1,X2) uLength(active(X1),X2) -> uLength(X1,X2) uLength(X1,active(X2)) -> uLength(X1,X2) Open DPs: uTake1#(mark(X)) -> uTake1#(X) uTake1#(active(X)) -> uTake1#(X) TRS: active(and(tt(),T)) -> mark(T) active(isNatIList(IL)) -> mark(isNatList(IL)) active(isNat(0())) -> mark(tt()) active(isNat(s(N))) -> mark(isNat(N)) active(isNat(length(L))) -> mark(isNatList(L)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L))) active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(zeros()) -> mark(cons(0(),zeros())) active(take(0(),IL)) -> mark(uTake1(isNatIList(IL))) active(uTake1(tt())) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL))) active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L)) active(uLength(tt(),L)) -> mark(s(length(L))) mark(and(X1,X2)) -> active(and(mark(X1),mark(X2))) mark(tt()) -> active(tt()) mark(isNatIList(X)) -> active(isNatIList(X)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(nil()) -> active(nil()) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(uTake1(X)) -> active(uTake1(mark(X))) mark(uTake2(X1,X2,X3,X4)) -> active(uTake2(mark(X1),X2,X3,X4)) mark(uLength(X1,X2)) -> active(uLength(mark(X1),X2)) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) 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) 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) uTake1(mark(X)) -> uTake1(X) uTake1(active(X)) -> uTake1(X) uTake2(mark(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,mark(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,mark(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,mark(X4)) -> uTake2(X1,X2,X3,X4) uTake2(active(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,active(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,active(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,active(X4)) -> uTake2(X1,X2,X3,X4) uLength(mark(X1),X2) -> uLength(X1,X2) uLength(X1,mark(X2)) -> uLength(X1,X2) uLength(active(X1),X2) -> uLength(X1,X2) uLength(X1,active(X2)) -> uLength(X1,X2) Open DPs: uTake2#(mark(X1),X2,X3,X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,mark(X2),X3,X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,X2,mark(X3),X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,X2,X3,mark(X4)) -> uTake2#(X1,X2,X3,X4) uTake2#(active(X1),X2,X3,X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,active(X2),X3,X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,X2,active(X3),X4) -> uTake2#(X1,X2,X3,X4) uTake2#(X1,X2,X3,active(X4)) -> uTake2#(X1,X2,X3,X4) TRS: active(and(tt(),T)) -> mark(T) active(isNatIList(IL)) -> mark(isNatList(IL)) active(isNat(0())) -> mark(tt()) active(isNat(s(N))) -> mark(isNat(N)) active(isNat(length(L))) -> mark(isNatList(L)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L))) active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(zeros()) -> mark(cons(0(),zeros())) active(take(0(),IL)) -> mark(uTake1(isNatIList(IL))) active(uTake1(tt())) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL))) active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L)) active(uLength(tt(),L)) -> mark(s(length(L))) mark(and(X1,X2)) -> active(and(mark(X1),mark(X2))) mark(tt()) -> active(tt()) mark(isNatIList(X)) -> active(isNatIList(X)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(nil()) -> active(nil()) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(uTake1(X)) -> active(uTake1(mark(X))) mark(uTake2(X1,X2,X3,X4)) -> active(uTake2(mark(X1),X2,X3,X4)) mark(uLength(X1,X2)) -> active(uLength(mark(X1),X2)) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) 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) 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) uTake1(mark(X)) -> uTake1(X) uTake1(active(X)) -> uTake1(X) uTake2(mark(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,mark(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,mark(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,mark(X4)) -> uTake2(X1,X2,X3,X4) uTake2(active(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,active(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,active(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,active(X4)) -> uTake2(X1,X2,X3,X4) uLength(mark(X1),X2) -> uLength(X1,X2) uLength(X1,mark(X2)) -> uLength(X1,X2) uLength(active(X1),X2) -> uLength(X1,X2) uLength(X1,active(X2)) -> uLength(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(and(tt(),T)) -> mark(T) active(isNatIList(IL)) -> mark(isNatList(IL)) active(isNat(0())) -> mark(tt()) active(isNat(s(N))) -> mark(isNat(N)) active(isNat(length(L))) -> mark(isNatList(L)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L))) active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(zeros()) -> mark(cons(0(),zeros())) active(take(0(),IL)) -> mark(uTake1(isNatIList(IL))) active(uTake1(tt())) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL))) active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L)) active(uLength(tt(),L)) -> mark(s(length(L))) mark(and(X1,X2)) -> active(and(mark(X1),mark(X2))) mark(tt()) -> active(tt()) mark(isNatIList(X)) -> active(isNatIList(X)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(nil()) -> active(nil()) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(uTake1(X)) -> active(uTake1(mark(X))) mark(uTake2(X1,X2,X3,X4)) -> active(uTake2(mark(X1),X2,X3,X4)) mark(uLength(X1,X2)) -> active(uLength(mark(X1),X2)) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) 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) 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) uTake1(mark(X)) -> uTake1(X) uTake1(active(X)) -> uTake1(X) uTake2(mark(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,mark(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,mark(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,mark(X4)) -> uTake2(X1,X2,X3,X4) uTake2(active(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,active(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,active(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,active(X4)) -> uTake2(X1,X2,X3,X4) uLength(mark(X1),X2) -> uLength(X1,X2) uLength(X1,mark(X2)) -> uLength(X1,X2) uLength(active(X1),X2) -> uLength(X1,X2) uLength(X1,active(X2)) -> uLength(X1,X2) Open DPs: uLength#(mark(X1),X2) -> uLength#(X1,X2) uLength#(X1,mark(X2)) -> uLength#(X1,X2) uLength#(active(X1),X2) -> uLength#(X1,X2) uLength#(X1,active(X2)) -> uLength#(X1,X2) TRS: active(and(tt(),T)) -> mark(T) active(isNatIList(IL)) -> mark(isNatList(IL)) active(isNat(0())) -> mark(tt()) active(isNat(s(N))) -> mark(isNat(N)) active(isNat(length(L))) -> mark(isNatList(L)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L))) active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(zeros()) -> mark(cons(0(),zeros())) active(take(0(),IL)) -> mark(uTake1(isNatIList(IL))) active(uTake1(tt())) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL))) active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L)) active(uLength(tt(),L)) -> mark(s(length(L))) mark(and(X1,X2)) -> active(and(mark(X1),mark(X2))) mark(tt()) -> active(tt()) mark(isNatIList(X)) -> active(isNatIList(X)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(nil()) -> active(nil()) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(uTake1(X)) -> active(uTake1(mark(X))) mark(uTake2(X1,X2,X3,X4)) -> active(uTake2(mark(X1),X2,X3,X4)) mark(uLength(X1,X2)) -> active(uLength(mark(X1),X2)) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) 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) 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) uTake1(mark(X)) -> uTake1(X) uTake1(active(X)) -> uTake1(X) uTake2(mark(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,mark(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,mark(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,mark(X4)) -> uTake2(X1,X2,X3,X4) uTake2(active(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,active(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,active(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,active(X4)) -> uTake2(X1,X2,X3,X4) uLength(mark(X1),X2) -> uLength(X1,X2) uLength(X1,mark(X2)) -> uLength(X1,X2) uLength(active(X1),X2) -> uLength(X1,X2) uLength(X1,active(X2)) -> uLength(X1,X2) Open DPs: length#(mark(X)) -> length#(X) length#(active(X)) -> length#(X) TRS: active(and(tt(),T)) -> mark(T) active(isNatIList(IL)) -> mark(isNatList(IL)) active(isNat(0())) -> mark(tt()) active(isNat(s(N))) -> mark(isNat(N)) active(isNat(length(L))) -> mark(isNatList(L)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L))) active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(zeros()) -> mark(cons(0(),zeros())) active(take(0(),IL)) -> mark(uTake1(isNatIList(IL))) active(uTake1(tt())) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL))) active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L)) active(uLength(tt(),L)) -> mark(s(length(L))) mark(and(X1,X2)) -> active(and(mark(X1),mark(X2))) mark(tt()) -> active(tt()) mark(isNatIList(X)) -> active(isNatIList(X)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(nil()) -> active(nil()) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(uTake1(X)) -> active(uTake1(mark(X))) mark(uTake2(X1,X2,X3,X4)) -> active(uTake2(mark(X1),X2,X3,X4)) mark(uLength(X1,X2)) -> active(uLength(mark(X1),X2)) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) 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) 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) uTake1(mark(X)) -> uTake1(X) uTake1(active(X)) -> uTake1(X) uTake2(mark(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,mark(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,mark(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,mark(X4)) -> uTake2(X1,X2,X3,X4) uTake2(active(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,active(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,active(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,active(X4)) -> uTake2(X1,X2,X3,X4) uLength(mark(X1),X2) -> uLength(X1,X2) uLength(X1,mark(X2)) -> uLength(X1,X2) uLength(active(X1),X2) -> uLength(X1,X2) uLength(X1,active(X2)) -> uLength(X1,X2) Open DPs: s#(mark(X)) -> s#(X) s#(active(X)) -> s#(X) TRS: active(and(tt(),T)) -> mark(T) active(isNatIList(IL)) -> mark(isNatList(IL)) active(isNat(0())) -> mark(tt()) active(isNat(s(N))) -> mark(isNat(N)) active(isNat(length(L))) -> mark(isNatList(L)) active(isNatIList(zeros())) -> mark(tt()) active(isNatIList(cons(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(isNatList(nil())) -> mark(tt()) active(isNatList(cons(N,L))) -> mark(and(isNat(N),isNatList(L))) active(isNatList(take(N,IL))) -> mark(and(isNat(N),isNatIList(IL))) active(zeros()) -> mark(cons(0(),zeros())) active(take(0(),IL)) -> mark(uTake1(isNatIList(IL))) active(uTake1(tt())) -> mark(nil()) active(take(s(M),cons(N,IL))) -> mark(uTake2(and(isNat(M),and(isNat(N),isNatIList(IL))),M,N,IL)) active(uTake2(tt(),M,N,IL)) -> mark(cons(N,take(M,IL))) active(length(cons(N,L))) -> mark(uLength(and(isNat(N),isNatList(L)),L)) active(uLength(tt(),L)) -> mark(s(length(L))) mark(and(X1,X2)) -> active(and(mark(X1),mark(X2))) mark(tt()) -> active(tt()) mark(isNatIList(X)) -> active(isNatIList(X)) mark(isNatList(X)) -> active(isNatList(X)) mark(isNat(X)) -> active(isNat(X)) mark(0()) -> active(0()) mark(s(X)) -> active(s(mark(X))) mark(length(X)) -> active(length(mark(X))) mark(zeros()) -> active(zeros()) mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) mark(nil()) -> active(nil()) mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) mark(uTake1(X)) -> active(uTake1(mark(X))) mark(uTake2(X1,X2,X3,X4)) -> active(uTake2(mark(X1),X2,X3,X4)) mark(uLength(X1,X2)) -> active(uLength(mark(X1),X2)) and(mark(X1),X2) -> and(X1,X2) and(X1,mark(X2)) -> and(X1,X2) and(active(X1),X2) -> and(X1,X2) and(X1,active(X2)) -> and(X1,X2) isNatIList(mark(X)) -> isNatIList(X) isNatIList(active(X)) -> isNatIList(X) isNatList(mark(X)) -> isNatList(X) isNatList(active(X)) -> isNatList(X) isNat(mark(X)) -> isNat(X) isNat(active(X)) -> isNat(X) s(mark(X)) -> s(X) s(active(X)) -> s(X) length(mark(X)) -> length(X) length(active(X)) -> length(X) 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) 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) uTake1(mark(X)) -> uTake1(X) uTake1(active(X)) -> uTake1(X) uTake2(mark(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,mark(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,mark(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,mark(X4)) -> uTake2(X1,X2,X3,X4) uTake2(active(X1),X2,X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,active(X2),X3,X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,active(X3),X4) -> uTake2(X1,X2,X3,X4) uTake2(X1,X2,X3,active(X4)) -> uTake2(X1,X2,X3,X4) uLength(mark(X1),X2) -> uLength(X1,X2) uLength(X1,mark(X2)) -> uLength(X1,X2) uLength(active(X1),X2) -> uLength(X1,X2) uLength(X1,active(X2)) -> uLength(X1,X2) Open