| a__length#(cons(N, L)) | → | a__uLength#(a__and(a__isNat(N), a__isNatList(L)), L) | | a__uLength#(tt, L) | → | mark#(L) |
| mark#(isNat(X)) | → | a__isNat#(X) | | mark#(take(X1, X2)) | → | mark#(X1) |
| a__take#(s(M), cons(N, IL)) | → | a__isNat#(M) | | mark#(isNatIList(X)) | → | a__isNatIList#(X) |
| a__isNat#(s(N)) | → | a__isNat#(N) | | mark#(zeros) | → | a__zeros# |
| a__isNatList#(cons(N, L)) | → | a__and#(a__isNat(N), a__isNatList(L)) | | mark#(uTake1(X)) | → | a__uTake1#(mark(X)) |
| a__isNatIList#(IL) | → | a__isNatList#(IL) | | mark#(and(X1, X2)) | → | mark#(X2) |
| mark#(length(X)) | → | a__length#(mark(X)) | | a__take#(s(M), cons(N, IL)) | → | a__isNat#(N) |
| a__take#(s(M), cons(N, IL)) | → | a__isNatIList#(IL) | | a__take#(0, IL) | → | a__uTake1#(a__isNatIList(IL)) |
| mark#(uLength(X1, X2)) | → | a__uLength#(mark(X1), X2) | | mark#(length(X)) | → | mark#(X) |
| mark#(and(X1, X2)) | → | a__and#(mark(X1), mark(X2)) | | a__take#(s(M), cons(N, IL)) | → | a__and#(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))) |
| mark#(s(X)) | → | mark#(X) | | mark#(uLength(X1, X2)) | → | mark#(X1) |
| a__take#(s(M), cons(N, IL)) | → | a__and#(a__isNat(N), a__isNatIList(IL)) | | a__length#(cons(N, L)) | → | a__isNatList#(L) |
| a__take#(0, IL) | → | a__isNatIList#(IL) | | a__isNatList#(cons(N, L)) | → | a__isNat#(N) |
| a__uLength#(tt, L) | → | a__length#(mark(L)) | | a__isNatList#(take(N, IL)) | → | a__isNat#(N) |
| a__uTake2#(tt, M, N, IL) | → | mark#(N) | | a__isNatList#(take(N, IL)) | → | a__isNatIList#(IL) |
| mark#(uTake2(X1, X2, X3, X4)) | → | a__uTake2#(mark(X1), X2, X3, X4) | | mark#(cons(X1, X2)) | → | mark#(X1) |
| mark#(uTake2(X1, X2, X3, X4)) | → | mark#(X1) | | a__isNatList#(take(N, IL)) | → | a__and#(a__isNat(N), a__isNatIList(IL)) |
| a__take#(s(M), cons(N, IL)) | → | a__uTake2#(a__and(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))), M, N, IL) | | a__length#(cons(N, L)) | → | a__isNat#(N) |
| a__isNat#(length(L)) | → | a__isNatList#(L) | | mark#(isNatList(X)) | → | a__isNatList#(X) |
| mark#(uTake1(X)) | → | mark#(X) | | mark#(and(X1, X2)) | → | mark#(X1) |
| a__isNatIList#(cons(N, IL)) | → | a__and#(a__isNat(N), a__isNatIList(IL)) | | a__isNatIList#(cons(N, IL)) | → | a__isNatIList#(IL) |
| mark#(take(X1, X2)) | → | a__take#(mark(X1), mark(X2)) | | mark#(take(X1, X2)) | → | mark#(X2) |
| a__isNatList#(cons(N, L)) | → | a__isNatList#(L) | | a__and#(tt, T) | → | mark#(T) |
| a__isNatIList#(cons(N, IL)) | → | a__isNat#(N) | | a__length#(cons(N, L)) | → | a__and#(a__isNat(N), a__isNatList(L)) |
| a__and(tt, T) | → | mark(T) | | a__isNatIList(IL) | → | a__isNatList(IL) |
| a__isNat(0) | → | tt | | a__isNat(s(N)) | → | a__isNat(N) |
| a__isNat(length(L)) | → | a__isNatList(L) | | a__isNatIList(zeros) | → | tt |
| a__isNatIList(cons(N, IL)) | → | a__and(a__isNat(N), a__isNatIList(IL)) | | a__isNatList(nil) | → | tt |
| a__isNatList(cons(N, L)) | → | a__and(a__isNat(N), a__isNatList(L)) | | a__isNatList(take(N, IL)) | → | a__and(a__isNat(N), a__isNatIList(IL)) |
| a__zeros | → | cons(0, zeros) | | a__take(0, IL) | → | a__uTake1(a__isNatIList(IL)) |
| a__uTake1(tt) | → | nil | | a__take(s(M), cons(N, IL)) | → | a__uTake2(a__and(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))), M, N, IL) |
| a__uTake2(tt, M, N, IL) | → | cons(mark(N), take(M, IL)) | | a__length(cons(N, L)) | → | a__uLength(a__and(a__isNat(N), a__isNatList(L)), L) |
| a__uLength(tt, L) | → | s(a__length(mark(L))) | | mark(and(X1, X2)) | → | a__and(mark(X1), mark(X2)) |
| mark(isNatIList(X)) | → | a__isNatIList(X) | | mark(isNatList(X)) | → | a__isNatList(X) |
| mark(isNat(X)) | → | a__isNat(X) | | mark(length(X)) | → | a__length(mark(X)) |
| mark(zeros) | → | a__zeros | | mark(take(X1, X2)) | → | a__take(mark(X1), mark(X2)) |
| mark(uTake1(X)) | → | a__uTake1(mark(X)) | | mark(uTake2(X1, X2, X3, X4)) | → | a__uTake2(mark(X1), X2, X3, X4) |
| mark(uLength(X1, X2)) | → | a__uLength(mark(X1), X2) | | mark(tt) | → | tt |
| mark(0) | → | 0 | | mark(s(X)) | → | s(mark(X)) |
| mark(cons(X1, X2)) | → | cons(mark(X1), X2) | | mark(nil) | → | nil |
| a__and(X1, X2) | → | and(X1, X2) | | a__isNatIList(X) | → | isNatIList(X) |
| a__isNatList(X) | → | isNatList(X) | | a__isNat(X) | → | isNat(X) |
| a__length(X) | → | length(X) | | a__zeros | → | zeros |
| a__take(X1, X2) | → | take(X1, X2) | | a__uTake1(X) | → | uTake1(X) |
| a__uTake2(X1, X2, X3, X4) | → | uTake2(X1, X2, X3, X4) | | a__uLength(X1, X2) | → | uLength(X1, X2) |
| mark#(isNat(X)) → a__isNat#(X) | mark#(take(X1, X2)) → mark#(X1) |
| a__uLength#(tt, L) → mark#(L) | a__length#(cons(N, L)) → a__uLength#(a__and(a__isNat(N), a__isNatList(L)), L) |
| mark#(isNatIList(X)) → a__isNatIList#(X) | a__take#(s(M), cons(N, IL)) → a__isNat#(M) |
| a__isNat#(s(N)) → a__isNat#(N) | a__isNatList#(cons(N, L)) → a__and#(a__isNat(N), a__isNatList(L)) |
| a__isNatIList#(IL) → a__isNatList#(IL) | mark#(and(X1, X2)) → mark#(X2) |
| mark#(length(X)) → a__length#(mark(X)) | a__take#(s(M), cons(N, IL)) → a__isNat#(N) |
| a__take#(s(M), cons(N, IL)) → a__isNatIList#(IL) | mark#(and(X1, X2)) → a__and#(mark(X1), mark(X2)) |
| mark#(uLength(X1, X2)) → a__uLength#(mark(X1), X2) | mark#(length(X)) → mark#(X) |
| a__take#(s(M), cons(N, IL)) → a__and#(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))) | mark#(s(X)) → mark#(X) |
| a__take#(s(M), cons(N, IL)) → a__and#(a__isNat(N), a__isNatIList(IL)) | mark#(uLength(X1, X2)) → mark#(X1) |
| a__length#(cons(N, L)) → a__isNatList#(L) | a__take#(0, IL) → a__isNatIList#(IL) |
| a__isNatList#(cons(N, L)) → a__isNat#(N) | a__uLength#(tt, L) → a__length#(mark(L)) |
| a__isNatList#(take(N, IL)) → a__isNat#(N) | a__isNatList#(take(N, IL)) → a__isNatIList#(IL) |
| a__uTake2#(tt, M, N, IL) → mark#(N) | mark#(uTake2(X1, X2, X3, X4)) → a__uTake2#(mark(X1), X2, X3, X4) |
| mark#(cons(X1, X2)) → mark#(X1) | mark#(uTake2(X1, X2, X3, X4)) → mark#(X1) |
| a__isNatList#(take(N, IL)) → a__and#(a__isNat(N), a__isNatIList(IL)) | a__take#(s(M), cons(N, IL)) → a__uTake2#(a__and(a__isNat(M), a__and(a__isNat(N), a__isNatIList(IL))), M, N, IL) |
| a__isNat#(length(L)) → a__isNatList#(L) | a__length#(cons(N, L)) → a__isNat#(N) |
| mark#(uTake1(X)) → mark#(X) | mark#(isNatList(X)) → a__isNatList#(X) |
| mark#(and(X1, X2)) → mark#(X1) | a__isNatIList#(cons(N, IL)) → a__and#(a__isNat(N), a__isNatIList(IL)) |
| a__isNatIList#(cons(N, IL)) → a__isNatIList#(IL) | mark#(take(X1, X2)) → a__take#(mark(X1), mark(X2)) |
| mark#(take(X1, X2)) → mark#(X2) | a__isNatList#(cons(N, L)) → a__isNatList#(L) |
| a__and#(tt, T) → mark#(T) | a__isNatIList#(cons(N, IL)) → a__isNat#(N) |
| a__length#(cons(N, L)) → a__and#(a__isNat(N), a__isNatList(L)) |