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(isPalListKind(activate(V)),activate(V)) |
(4) |
U12(tt,V) |
→ |
U13(isNeList(activate(V))) |
(5) |
U13(tt) |
→ |
tt |
(6) |
U21(tt,V1,V2) |
→ |
U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) |
(7) |
U22(tt,V1,V2) |
→ |
U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) |
(8) |
U23(tt,V1,V2) |
→ |
U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) |
(9) |
U24(tt,V1,V2) |
→ |
U25(isList(activate(V1)),activate(V2)) |
(10) |
U25(tt,V2) |
→ |
U26(isList(activate(V2))) |
(11) |
U26(tt) |
→ |
tt |
(12) |
U31(tt,V) |
→ |
U32(isPalListKind(activate(V)),activate(V)) |
(13) |
U32(tt,V) |
→ |
U33(isQid(activate(V))) |
(14) |
U33(tt) |
→ |
tt |
(15) |
U41(tt,V1,V2) |
→ |
U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) |
(16) |
U42(tt,V1,V2) |
→ |
U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) |
(17) |
U43(tt,V1,V2) |
→ |
U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) |
(18) |
U44(tt,V1,V2) |
→ |
U45(isList(activate(V1)),activate(V2)) |
(19) |
U45(tt,V2) |
→ |
U46(isNeList(activate(V2))) |
(20) |
U46(tt) |
→ |
tt |
(21) |
U51(tt,V1,V2) |
→ |
U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) |
(22) |
U52(tt,V1,V2) |
→ |
U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) |
(23) |
U53(tt,V1,V2) |
→ |
U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) |
(24) |
U54(tt,V1,V2) |
→ |
U55(isNeList(activate(V1)),activate(V2)) |
(25) |
U55(tt,V2) |
→ |
U56(isList(activate(V2))) |
(26) |
U56(tt) |
→ |
tt |
(27) |
U61(tt,V) |
→ |
U62(isPalListKind(activate(V)),activate(V)) |
(28) |
U62(tt,V) |
→ |
U63(isQid(activate(V))) |
(29) |
U63(tt) |
→ |
tt |
(30) |
U71(tt,I,P) |
→ |
U72(isPalListKind(activate(I)),activate(P)) |
(31) |
U72(tt,P) |
→ |
U73(isPal(activate(P)),activate(P)) |
(32) |
U73(tt,P) |
→ |
U74(isPalListKind(activate(P))) |
(33) |
U74(tt) |
→ |
tt |
(34) |
U81(tt,V) |
→ |
U82(isPalListKind(activate(V)),activate(V)) |
(35) |
U82(tt,V) |
→ |
U83(isNePal(activate(V))) |
(36) |
U83(tt) |
→ |
tt |
(37) |
U91(tt,V2) |
→ |
U92(isPalListKind(activate(V2))) |
(38) |
U92(tt) |
→ |
tt |
(39) |
isList(V) |
→ |
U11(isPalListKind(activate(V)),activate(V)) |
(40) |
isList(n__nil) |
→ |
tt |
(41) |
isList(n____(V1,V2)) |
→ |
U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) |
(42) |
isNeList(V) |
→ |
U31(isPalListKind(activate(V)),activate(V)) |
(43) |
isNeList(n____(V1,V2)) |
→ |
U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) |
(44) |
isNeList(n____(V1,V2)) |
→ |
U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) |
(45) |
isNePal(V) |
→ |
U61(isPalListKind(activate(V)),activate(V)) |
(46) |
isNePal(n____(I,__(P,I))) |
→ |
U71(isQid(activate(I)),activate(I),activate(P)) |
(47) |
isPal(V) |
→ |
U81(isPalListKind(activate(V)),activate(V)) |
(48) |
isPal(n__nil) |
→ |
tt |
(49) |
isPalListKind(n__a) |
→ |
tt |
(50) |
isPalListKind(n__e) |
→ |
tt |
(51) |
isPalListKind(n__i) |
→ |
tt |
(52) |
isPalListKind(n__nil) |
→ |
tt |
(53) |
isPalListKind(n__o) |
→ |
tt |
(54) |
isPalListKind(n__u) |
→ |
tt |
(55) |
isPalListKind(n____(V1,V2)) |
→ |
U91(isPalListKind(activate(V1)),activate(V2)) |
(56) |
isQid(n__a) |
→ |
tt |
(57) |
isQid(n__e) |
→ |
tt |
(58) |
isQid(n__i) |
→ |
tt |
(59) |
isQid(n__o) |
→ |
tt |
(60) |
isQid(n__u) |
→ |
tt |
(61) |
nil |
→ |
n__nil |
(62) |
__(X1,X2) |
→ |
n____(X1,X2) |
(63) |
a |
→ |
n__a |
(64) |
e |
→ |
n__e |
(65) |
i |
→ |
n__i |
(66) |
o |
→ |
n__o |
(67) |
u |
→ |
n__u |
(68) |
activate(n__nil) |
→ |
nil |
(69) |
activate(n____(X1,X2)) |
→ |
__(X1,X2) |
(70) |
activate(n__a) |
→ |
a |
(71) |
activate(n__e) |
→ |
e |
(72) |
activate(n__i) |
→ |
i |
(73) |
activate(n__o) |
→ |
o |
(74) |
activate(n__u) |
→ |
u |
(75) |
activate(X) |
→ |
X |
(76) |
__(__(X,Y),Z) |
→ |
__(X,__(Y,Z)) |
(1) |
__(X,nil) |
→ |
X |
(2) |
__(nil,X) |
→ |
X |
(3) |
U11(tt,V) |
→ |
U12(isPalListKind(activate(V)),activate(V)) |
(4) |
U12(tt,V) |
→ |
U13(isNeList(activate(V))) |
(5) |
U13(tt) |
→ |
tt |
(6) |
U21(tt,V1,V2) |
→ |
U22(isPalListKind(activate(V1)),activate(V1),activate(V2)) |
(7) |
U22(tt,V1,V2) |
→ |
U23(isPalListKind(activate(V2)),activate(V1),activate(V2)) |
(8) |
U23(tt,V1,V2) |
→ |
U24(isPalListKind(activate(V2)),activate(V1),activate(V2)) |
(9) |
U24(tt,V1,V2) |
→ |
U25(isList(activate(V1)),activate(V2)) |
(10) |
U25(tt,V2) |
→ |
U26(isList(activate(V2))) |
(11) |
U26(tt) |
→ |
tt |
(12) |
U31(tt,V) |
→ |
U32(isPalListKind(activate(V)),activate(V)) |
(13) |
U32(tt,V) |
→ |
U33(isQid(activate(V))) |
(14) |
U33(tt) |
→ |
tt |
(15) |
U41(tt,V1,V2) |
→ |
U42(isPalListKind(activate(V1)),activate(V1),activate(V2)) |
(16) |
U42(tt,V1,V2) |
→ |
U43(isPalListKind(activate(V2)),activate(V1),activate(V2)) |
(17) |
U43(tt,V1,V2) |
→ |
U44(isPalListKind(activate(V2)),activate(V1),activate(V2)) |
(18) |
U44(tt,V1,V2) |
→ |
U45(isList(activate(V1)),activate(V2)) |
(19) |
U45(tt,V2) |
→ |
U46(isNeList(activate(V2))) |
(20) |
U46(tt) |
→ |
tt |
(21) |
U51(tt,V1,V2) |
→ |
U52(isPalListKind(activate(V1)),activate(V1),activate(V2)) |
(22) |
U52(tt,V1,V2) |
→ |
U53(isPalListKind(activate(V2)),activate(V1),activate(V2)) |
(23) |
U53(tt,V1,V2) |
→ |
U54(isPalListKind(activate(V2)),activate(V1),activate(V2)) |
(24) |
U54(tt,V1,V2) |
→ |
U55(isNeList(activate(V1)),activate(V2)) |
(25) |
U55(tt,V2) |
→ |
U56(isList(activate(V2))) |
(26) |
U56(tt) |
→ |
tt |
(27) |
U61(tt,V) |
→ |
U62(isPalListKind(activate(V)),activate(V)) |
(28) |
U62(tt,V) |
→ |
U63(isQid(activate(V))) |
(29) |
U63(tt) |
→ |
tt |
(30) |
U71(tt,I,P) |
→ |
U72(isPalListKind(activate(I)),activate(P)) |
(31) |
U72(tt,P) |
→ |
U73(isPal(activate(P)),activate(P)) |
(32) |
U73(tt,P) |
→ |
U74(isPalListKind(activate(P))) |
(33) |
U81(tt,V) |
→ |
U82(isPalListKind(activate(V)),activate(V)) |
(35) |
U82(tt,V) |
→ |
U83(isNePal(activate(V))) |
(36) |
U83(tt) |
→ |
tt |
(37) |
U91(tt,V2) |
→ |
U92(isPalListKind(activate(V2))) |
(38) |
U92(tt) |
→ |
tt |
(39) |
isList(V) |
→ |
U11(isPalListKind(activate(V)),activate(V)) |
(40) |
isList(n__nil) |
→ |
tt |
(41) |
isList(n____(V1,V2)) |
→ |
U21(isPalListKind(activate(V1)),activate(V1),activate(V2)) |
(42) |
isNeList(V) |
→ |
U31(isPalListKind(activate(V)),activate(V)) |
(43) |
isNeList(n____(V1,V2)) |
→ |
U41(isPalListKind(activate(V1)),activate(V1),activate(V2)) |
(44) |
isNeList(n____(V1,V2)) |
→ |
U51(isPalListKind(activate(V1)),activate(V1),activate(V2)) |
(45) |
isNePal(V) |
→ |
U61(isPalListKind(activate(V)),activate(V)) |
(46) |
isNePal(n____(I,__(P,I))) |
→ |
U71(isQid(activate(I)),activate(I),activate(P)) |
(47) |
isPal(V) |
→ |
U81(isPalListKind(activate(V)),activate(V)) |
(48) |
isPal(n__nil) |
→ |
tt |
(49) |
isPalListKind(n__a) |
→ |
tt |
(50) |
isPalListKind(n__e) |
→ |
tt |
(51) |
isPalListKind(n__i) |
→ |
tt |
(52) |
isPalListKind(n__nil) |
→ |
tt |
(53) |
isPalListKind(n__o) |
→ |
tt |
(54) |
isPalListKind(n__u) |
→ |
tt |
(55) |
isPalListKind(n____(V1,V2)) |
→ |
U91(isPalListKind(activate(V1)),activate(V2)) |
(56) |
isQid(n__a) |
→ |
tt |
(57) |
isQid(n__e) |
→ |
tt |
(58) |
isQid(n__i) |
→ |
tt |
(59) |
isQid(n__o) |
→ |
tt |
(60) |
isQid(n__u) |
→ |
tt |
(61) |
a |
→ |
n__a |
(64) |
e |
→ |
n__e |
(65) |
o |
→ |
n__o |
(67) |
u |
→ |
n__u |
(68) |
activate(n__nil) |
→ |
nil |
(69) |
activate(n____(X1,X2)) |
→ |
__(X1,X2) |
(70) |
activate(n__a) |
→ |
a |
(71) |
activate(n__e) |
→ |
e |
(72) |
activate(n__i) |
→ |
i |
(73) |
activate(n__o) |
→ |
o |
(74) |
activate(n__u) |
→ |
u |
(75) |
activate(X) |
→ |
X |
(76) |
There are no rules in the TRS. Hence, it is terminating.