The rewrite relation of the following TRS is considered.
__(__(X,Y),Z) |
→ |
__(X,__(Y,Z)) |
(1) |
__(X,nil) |
→ |
X |
(2) |
__(nil,X) |
→ |
X |
(3) |
and(tt,X) |
→ |
activate(X) |
(4) |
isList(V) |
→ |
isNeList(activate(V)) |
(5) |
isList(n__nil) |
→ |
tt |
(6) |
isList(n____(V1,V2)) |
→ |
and(isList(activate(V1)),n__isList(activate(V2))) |
(7) |
isNeList(V) |
→ |
isQid(activate(V)) |
(8) |
isNeList(n____(V1,V2)) |
→ |
and(isList(activate(V1)),n__isNeList(activate(V2))) |
(9) |
isNeList(n____(V1,V2)) |
→ |
and(isNeList(activate(V1)),n__isList(activate(V2))) |
(10) |
isNePal(V) |
→ |
isQid(activate(V)) |
(11) |
isNePal(n____(I,n____(P,I))) |
→ |
and(isQid(activate(I)),n__isPal(activate(P))) |
(12) |
isPal(V) |
→ |
isNePal(activate(V)) |
(13) |
isPal(n__nil) |
→ |
tt |
(14) |
isQid(n__a) |
→ |
tt |
(15) |
isQid(n__e) |
→ |
tt |
(16) |
isQid(n__i) |
→ |
tt |
(17) |
isQid(n__o) |
→ |
tt |
(18) |
isQid(n__u) |
→ |
tt |
(19) |
nil |
→ |
n__nil |
(20) |
__(X1,X2) |
→ |
n____(X1,X2) |
(21) |
isList(X) |
→ |
n__isList(X) |
(22) |
isNeList(X) |
→ |
n__isNeList(X) |
(23) |
isPal(X) |
→ |
n__isPal(X) |
(24) |
a |
→ |
n__a |
(25) |
e |
→ |
n__e |
(26) |
i |
→ |
n__i |
(27) |
o |
→ |
n__o |
(28) |
u |
→ |
n__u |
(29) |
activate(n__nil) |
→ |
nil |
(30) |
activate(n____(X1,X2)) |
→ |
__(activate(X1),activate(X2)) |
(31) |
activate(n__isList(X)) |
→ |
isList(X) |
(32) |
activate(n__isNeList(X)) |
→ |
isNeList(X) |
(33) |
activate(n__isPal(X)) |
→ |
isPal(X) |
(34) |
activate(n__a) |
→ |
a |
(35) |
activate(n__e) |
→ |
e |
(36) |
activate(n__i) |
→ |
i |
(37) |
activate(n__o) |
→ |
o |
(38) |
activate(n__u) |
→ |
u |
(39) |
activate(X) |
→ |
X |
(40) |
__(__(X,Y),Z) |
→ |
__(X,__(Y,Z)) |
(1) |
__(X,nil) |
→ |
X |
(2) |
__(nil,X) |
→ |
X |
(3) |
and(tt,X) |
→ |
activate(X) |
(4) |
isList(V) |
→ |
isNeList(activate(V)) |
(5) |
isList(n__nil) |
→ |
tt |
(6) |
isList(n____(V1,V2)) |
→ |
and(isList(activate(V1)),n__isList(activate(V2))) |
(7) |
isNeList(V) |
→ |
isQid(activate(V)) |
(8) |
isNeList(n____(V1,V2)) |
→ |
and(isList(activate(V1)),n__isNeList(activate(V2))) |
(9) |
isNeList(n____(V1,V2)) |
→ |
and(isNeList(activate(V1)),n__isList(activate(V2))) |
(10) |
isNePal(V) |
→ |
isQid(activate(V)) |
(11) |
isNePal(n____(I,n____(P,I))) |
→ |
and(isQid(activate(I)),n__isPal(activate(P))) |
(12) |
isPal(V) |
→ |
isNePal(activate(V)) |
(13) |
isPal(n__nil) |
→ |
tt |
(14) |
isQid(n__a) |
→ |
tt |
(15) |
isQid(n__e) |
→ |
tt |
(16) |
isQid(n__i) |
→ |
tt |
(17) |
isQid(n__o) |
→ |
tt |
(18) |
isQid(n__u) |
→ |
tt |
(19) |
nil |
→ |
n__nil |
(20) |
__(X1,X2) |
→ |
n____(X1,X2) |
(21) |
isList(X) |
→ |
n__isList(X) |
(22) |
isNeList(X) |
→ |
n__isNeList(X) |
(23) |
isPal(X) |
→ |
n__isPal(X) |
(24) |
a |
→ |
n__a |
(25) |
e |
→ |
n__e |
(26) |
i |
→ |
n__i |
(27) |
o |
→ |
n__o |
(28) |
u |
→ |
n__u |
(29) |
activate(n__nil) |
→ |
nil |
(30) |
activate(n____(X1,X2)) |
→ |
__(activate(X1),activate(X2)) |
(31) |
activate(n__isList(X)) |
→ |
isList(X) |
(32) |
activate(n__isNeList(X)) |
→ |
isNeList(X) |
(33) |
activate(n__isPal(X)) |
→ |
isPal(X) |
(34) |
activate(n__a) |
→ |
a |
(35) |
activate(n__e) |
→ |
e |
(36) |
activate(n__i) |
→ |
i |
(37) |
activate(n__o) |
→ |
o |
(38) |
activate(n__u) |
→ |
u |
(39) |
activate(X) |
→ |
X |
(40) |
There are no rules in the TRS. Hence, it is terminating.