The rewrite relation of the following TRS is considered.
and(tt,T) |
→ |
T |
(1) |
isNatIList(IL) |
→ |
isNatList(activate(IL)) |
(2) |
isNat(n__0) |
→ |
tt |
(3) |
isNat(n__s(N)) |
→ |
isNat(activate(N)) |
(4) |
isNat(n__length(L)) |
→ |
isNatList(activate(L)) |
(5) |
isNatIList(n__zeros) |
→ |
tt |
(6) |
isNatIList(n__cons(N,IL)) |
→ |
and(isNat(activate(N)),isNatIList(activate(IL))) |
(7) |
isNatList(n__nil) |
→ |
tt |
(8) |
isNatList(n__cons(N,L)) |
→ |
and(isNat(activate(N)),isNatList(activate(L))) |
(9) |
isNatList(n__take(N,IL)) |
→ |
and(isNat(activate(N)),isNatIList(activate(IL))) |
(10) |
zeros |
→ |
cons(0,n__zeros) |
(11) |
take(0,IL) |
→ |
uTake1(isNatIList(IL)) |
(12) |
uTake1(tt) |
→ |
nil |
(13) |
take(s(M),cons(N,IL)) |
→ |
uTake2(and(isNat(M),and(isNat(N),isNatIList(activate(IL)))),M,N,activate(IL)) |
(14) |
uTake2(tt,M,N,IL) |
→ |
cons(activate(N),n__take(activate(M),activate(IL))) |
(15) |
length(cons(N,L)) |
→ |
uLength(and(isNat(N),isNatList(activate(L))),activate(L)) |
(16) |
uLength(tt,L) |
→ |
s(length(activate(L))) |
(17) |
0 |
→ |
n__0 |
(18) |
s(X) |
→ |
n__s(X) |
(19) |
length(X) |
→ |
n__length(X) |
(20) |
zeros |
→ |
n__zeros |
(21) |
cons(X1,X2) |
→ |
n__cons(X1,X2) |
(22) |
nil |
→ |
n__nil |
(23) |
take(X1,X2) |
→ |
n__take(X1,X2) |
(24) |
activate(n__0) |
→ |
0 |
(25) |
activate(n__s(X)) |
→ |
s(X) |
(26) |
activate(n__length(X)) |
→ |
length(X) |
(27) |
activate(n__zeros) |
→ |
zeros |
(28) |
activate(n__cons(X1,X2)) |
→ |
cons(X1,X2) |
(29) |
activate(n__nil) |
→ |
nil |
(30) |
activate(n__take(X1,X2)) |
→ |
take(X1,X2) |
(31) |
activate(X) |
→ |
X |
(32) |