The rewrite relation of the following TRS is considered.
__(__(X,Y),Z) |
→ |
__(X,__(Y,Z)) |
(1) |
__(X,nil) |
→ |
X |
(2) |
__(nil,X) |
→ |
X |
(3) |
U11(tt,V) |
→ |
U12(isNeList(activate(V))) |
(4) |
U12(tt) |
→ |
tt |
(5) |
U21(tt,V1,V2) |
→ |
U22(isList(activate(V1)),activate(V2)) |
(6) |
U22(tt,V2) |
→ |
U23(isList(activate(V2))) |
(7) |
U23(tt) |
→ |
tt |
(8) |
U31(tt,V) |
→ |
U32(isQid(activate(V))) |
(9) |
U32(tt) |
→ |
tt |
(10) |
U41(tt,V1,V2) |
→ |
U42(isList(activate(V1)),activate(V2)) |
(11) |
U42(tt,V2) |
→ |
U43(isNeList(activate(V2))) |
(12) |
U43(tt) |
→ |
tt |
(13) |
U51(tt,V1,V2) |
→ |
U52(isNeList(activate(V1)),activate(V2)) |
(14) |
U52(tt,V2) |
→ |
U53(isList(activate(V2))) |
(15) |
U53(tt) |
→ |
tt |
(16) |
U61(tt,V) |
→ |
U62(isQid(activate(V))) |
(17) |
U62(tt) |
→ |
tt |
(18) |
U71(tt,V) |
→ |
U72(isNePal(activate(V))) |
(19) |
U72(tt) |
→ |
tt |
(20) |
and(tt,X) |
→ |
activate(X) |
(21) |
isList(V) |
→ |
U11(isPalListKind(activate(V)),activate(V)) |
(22) |
isList(n__nil) |
→ |
tt |
(23) |
isList(n____(V1,V2)) |
→ |
U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) |
(24) |
isNeList(V) |
→ |
U31(isPalListKind(activate(V)),activate(V)) |
(25) |
isNeList(n____(V1,V2)) |
→ |
U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) |
(26) |
isNeList(n____(V1,V2)) |
→ |
U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) |
(27) |
isNePal(V) |
→ |
U61(isPalListKind(activate(V)),activate(V)) |
(28) |
isNePal(n____(I,__(P,I))) |
→ |
and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(isPal(activate(P)),n__isPalListKind(activate(P)))) |
(29) |
isPal(V) |
→ |
U71(isPalListKind(activate(V)),activate(V)) |
(30) |
isPal(n__nil) |
→ |
tt |
(31) |
isPalListKind(n__a) |
→ |
tt |
(32) |
isPalListKind(n__e) |
→ |
tt |
(33) |
isPalListKind(n__i) |
→ |
tt |
(34) |
isPalListKind(n__nil) |
→ |
tt |
(35) |
isPalListKind(n__o) |
→ |
tt |
(36) |
isPalListKind(n__u) |
→ |
tt |
(37) |
isPalListKind(n____(V1,V2)) |
→ |
and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) |
(38) |
isQid(n__a) |
→ |
tt |
(39) |
isQid(n__e) |
→ |
tt |
(40) |
isQid(n__i) |
→ |
tt |
(41) |
isQid(n__o) |
→ |
tt |
(42) |
isQid(n__u) |
→ |
tt |
(43) |
nil |
→ |
n__nil |
(44) |
__(X1,X2) |
→ |
n____(X1,X2) |
(45) |
isPalListKind(X) |
→ |
n__isPalListKind(X) |
(46) |
and(X1,X2) |
→ |
n__and(X1,X2) |
(47) |
a |
→ |
n__a |
(48) |
e |
→ |
n__e |
(49) |
i |
→ |
n__i |
(50) |
o |
→ |
n__o |
(51) |
u |
→ |
n__u |
(52) |
activate(n__nil) |
→ |
nil |
(53) |
activate(n____(X1,X2)) |
→ |
__(X1,X2) |
(54) |
activate(n__isPalListKind(X)) |
→ |
isPalListKind(X) |
(55) |
activate(n__and(X1,X2)) |
→ |
and(X1,X2) |
(56) |
activate(n__a) |
→ |
a |
(57) |
activate(n__e) |
→ |
e |
(58) |
activate(n__i) |
→ |
i |
(59) |
activate(n__o) |
→ |
o |
(60) |
activate(n__u) |
→ |
u |
(61) |
activate(X) |
→ |
X |
(62) |
__(__(X,Y),Z) |
→ |
__(X,__(Y,Z)) |
(1) |
__(X,nil) |
→ |
X |
(2) |
__(nil,X) |
→ |
X |
(3) |
U11(tt,V) |
→ |
U12(isNeList(activate(V))) |
(4) |
U21(tt,V1,V2) |
→ |
U22(isList(activate(V1)),activate(V2)) |
(6) |
U22(tt,V2) |
→ |
U23(isList(activate(V2))) |
(7) |
U31(tt,V) |
→ |
U32(isQid(activate(V))) |
(9) |
U41(tt,V1,V2) |
→ |
U42(isList(activate(V1)),activate(V2)) |
(11) |
U42(tt,V2) |
→ |
U43(isNeList(activate(V2))) |
(12) |
U51(tt,V1,V2) |
→ |
U52(isNeList(activate(V1)),activate(V2)) |
(14) |
U52(tt,V2) |
→ |
U53(isList(activate(V2))) |
(15) |
U61(tt,V) |
→ |
U62(isQid(activate(V))) |
(17) |
U62(tt) |
→ |
tt |
(18) |
U71(tt,V) |
→ |
U72(isNePal(activate(V))) |
(19) |
and(tt,X) |
→ |
activate(X) |
(21) |
isList(V) |
→ |
U11(isPalListKind(activate(V)),activate(V)) |
(22) |
isList(n__nil) |
→ |
tt |
(23) |
isList(n____(V1,V2)) |
→ |
U21(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) |
(24) |
isNeList(V) |
→ |
U31(isPalListKind(activate(V)),activate(V)) |
(25) |
isNeList(n____(V1,V2)) |
→ |
U41(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) |
(26) |
isNeList(n____(V1,V2)) |
→ |
U51(and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))),activate(V1),activate(V2)) |
(27) |
isNePal(V) |
→ |
U61(isPalListKind(activate(V)),activate(V)) |
(28) |
isNePal(n____(I,__(P,I))) |
→ |
and(and(isQid(activate(I)),n__isPalListKind(activate(I))),n__and(isPal(activate(P)),n__isPalListKind(activate(P)))) |
(29) |
isPal(V) |
→ |
U71(isPalListKind(activate(V)),activate(V)) |
(30) |
isPal(n__nil) |
→ |
tt |
(31) |
isPalListKind(n__a) |
→ |
tt |
(32) |
isPalListKind(n__e) |
→ |
tt |
(33) |
isPalListKind(n__i) |
→ |
tt |
(34) |
isPalListKind(n__nil) |
→ |
tt |
(35) |
isPalListKind(n__o) |
→ |
tt |
(36) |
isPalListKind(n__u) |
→ |
tt |
(37) |
isPalListKind(n____(V1,V2)) |
→ |
and(isPalListKind(activate(V1)),n__isPalListKind(activate(V2))) |
(38) |
isQid(n__e) |
→ |
tt |
(40) |
isQid(n__o) |
→ |
tt |
(42) |
isQid(n__u) |
→ |
tt |
(43) |
isPalListKind(X) |
→ |
n__isPalListKind(X) |
(46) |
a |
→ |
n__a |
(48) |
e |
→ |
n__e |
(49) |
i |
→ |
n__i |
(50) |
activate(n__nil) |
→ |
nil |
(53) |
activate(n____(X1,X2)) |
→ |
__(X1,X2) |
(54) |
activate(n__isPalListKind(X)) |
→ |
isPalListKind(X) |
(55) |
activate(n__and(X1,X2)) |
→ |
and(X1,X2) |
(56) |
activate(n__a) |
→ |
a |
(57) |
activate(n__e) |
→ |
e |
(58) |
activate(n__i) |
→ |
i |
(59) |
activate(n__o) |
→ |
o |
(60) |
activate(n__u) |
→ |
u |
(61) |
activate(X) |
→ |
X |
(62) |
There are no rules in the TRS. Hence, it is terminating.