(VAR L IL M N X V1 V V2 X1 X2 X3 X4) (RULES a__zeros -> cons(0,zeros) a__U11(tt,L) -> s(a__length(mark(L))) a__U21(tt) -> nil a__U31(tt,IL,M,N) -> cons(mark(N),take(M,IL)) a__and(tt,X) -> mark(X) a__isNat(0) -> tt a__isNat(length(V1)) -> a__isNatList(V1) a__isNat(s(V1)) -> a__isNat(V1) a__isNatIList(V) -> a__isNatList(V) a__isNatIList(zeros) -> tt a__isNatIList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__isNatList(nil) -> tt a__isNatList(cons(V1,V2)) -> a__and(a__isNat(V1),isNatList(V2)) a__isNatList(take(V1,V2)) -> a__and(a__isNat(V1),isNatIList(V2)) a__length(nil) -> 0 a__length(cons(N,L)) -> a__U11(a__and(a__isNatList(L),isNat(N)),L) a__take(0,IL) -> a__U21(a__isNatIList(IL)) a__take(s(M),cons(N,IL)) -> a__U31(a__and(a__isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N) mark(zeros) -> a__zeros mark(U11(X1,X2)) -> a__U11(mark(X1),X2) mark(length(X)) -> a__length(mark(X)) mark(U21(X)) -> a__U21(mark(X)) mark(U31(X1,X2,X3,X4)) -> a__U31(mark(X1),X2,X3,X4) mark(take(X1,X2)) -> a__take(mark(X1),mark(X2)) mark(and(X1,X2)) -> a__and(mark(X1),X2) mark(isNat(X)) -> a__isNat(X) mark(isNatList(X)) -> a__isNatList(X) mark(isNatIList(X)) -> a__isNatIList(X) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0) -> 0 mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(nil) -> nil a__zeros -> zeros a__U11(X1,X2) -> U11(X1,X2) a__length(X) -> length(X) a__U21(X) -> U21(X) a__U31(X1,X2,X3,X4) -> U31(X1,X2,X3,X4) a__take(X1,X2) -> take(X1,X2) a__and(X1,X2) -> and(X1,X2) a__isNat(X) -> isNat(X) a__isNatList(X) -> isNatList(X) a__isNatIList(X) -> isNatIList(X) )