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) |
→ |
tt |
(4) |
U21(tt,V2) |
→ |
U22(isList(activate(V2))) |
(5) |
U22(tt) |
→ |
tt |
(6) |
U31(tt) |
→ |
tt |
(7) |
U41(tt,V2) |
→ |
U42(isNeList(activate(V2))) |
(8) |
U42(tt) |
→ |
tt |
(9) |
U51(tt,V2) |
→ |
U52(isList(activate(V2))) |
(10) |
U52(tt) |
→ |
tt |
(11) |
U61(tt) |
→ |
tt |
(12) |
U71(tt,P) |
→ |
U72(isPal(activate(P))) |
(13) |
U72(tt) |
→ |
tt |
(14) |
U81(tt) |
→ |
tt |
(15) |
isList(V) |
→ |
U11(isNeList(activate(V))) |
(16) |
isList(n__nil) |
→ |
tt |
(17) |
isList(n____(V1,V2)) |
→ |
U21(isList(activate(V1)),activate(V2)) |
(18) |
isNeList(V) |
→ |
U31(isQid(activate(V))) |
(19) |
isNeList(n____(V1,V2)) |
→ |
U41(isList(activate(V1)),activate(V2)) |
(20) |
isNeList(n____(V1,V2)) |
→ |
U51(isNeList(activate(V1)),activate(V2)) |
(21) |
isNePal(V) |
→ |
U61(isQid(activate(V))) |
(22) |
isNePal(n____(I,__(P,I))) |
→ |
U71(isQid(activate(I)),activate(P)) |
(23) |
isPal(V) |
→ |
U81(isNePal(activate(V))) |
(24) |
isPal(n__nil) |
→ |
tt |
(25) |
isQid(n__a) |
→ |
tt |
(26) |
isQid(n__e) |
→ |
tt |
(27) |
isQid(n__i) |
→ |
tt |
(28) |
isQid(n__o) |
→ |
tt |
(29) |
isQid(n__u) |
→ |
tt |
(30) |
nil |
→ |
n__nil |
(31) |
__(X1,X2) |
→ |
n____(X1,X2) |
(32) |
a |
→ |
n__a |
(33) |
e |
→ |
n__e |
(34) |
i |
→ |
n__i |
(35) |
o |
→ |
n__o |
(36) |
u |
→ |
n__u |
(37) |
activate(n__nil) |
→ |
nil |
(38) |
activate(n____(X1,X2)) |
→ |
__(X1,X2) |
(39) |
activate(n__a) |
→ |
a |
(40) |
activate(n__e) |
→ |
e |
(41) |
activate(n__i) |
→ |
i |
(42) |
activate(n__o) |
→ |
o |
(43) |
activate(n__u) |
→ |
u |
(44) |
activate(X) |
→ |
X |
(45) |
[U81(x1)] |
= |
· x1 +
|
[U21(x1, x2)] |
= |
· x1 + · x2 +
|
[U71(x1, x2)] |
= |
· x1 + · x2 +
|
[U31(x1)] |
= |
· x1 +
|
[nil] |
= |
|
[U11(x1)] |
= |
· x1 +
|
[isPal(x1)] |
= |
· x1 +
|
[isQid(x1)] |
= |
· x1 +
|
[n__o] |
= |
|
[u] |
= |
|
[n__nil] |
= |
|
[U72(x1)] |
= |
· x1 +
|
[n__u] |
= |
|
[isNePal(x1)] |
= |
· x1 +
|
[a] |
= |
|
[activate(x1)] |
= |
· x1 +
|
[isNeList(x1)] |
= |
· x1 +
|
[__(x1, x2)] |
= |
· x1 + · x2 +
|
[U22(x1)] |
= |
· x1 +
|
[n____(x1, x2)] |
= |
· x1 + · x2 +
|
[n__i] |
= |
|
[i] |
= |
|
[U61(x1)] |
= |
· x1 +
|
[o] |
= |
|
[U51(x1, x2)] |
= |
· x1 + · x2 +
|
[n__a] |
= |
|
[n__e] |
= |
|
[U42(x1)] |
= |
· x1 +
|
[U41(x1, x2)] |
= |
· x1 + · x2 +
|
[U52(x1)] |
= |
· x1 +
|
[isList(x1)] |
= |
· x1 +
|
[e] |
= |
|
[tt] |
= |
|
all of the following rules can be deleted.
[U81(x1)] |
= |
· x1 +
|
[U21(x1, x2)] |
= |
· x1 + · x2 +
|
[U31(x1)] |
= |
· x1 +
|
[nil] |
= |
|
[U11(x1)] |
= |
· x1 +
|
[isPal(x1)] |
= |
· x1 +
|
[isQid(x1)] |
= |
· x1 +
|
[n__o] |
= |
|
[u] |
= |
|
[n__nil] |
= |
|
[U72(x1)] |
= |
· x1 +
|
[n__u] |
= |
|
[isNePal(x1)] |
= |
· x1 +
|
[a] |
= |
|
[activate(x1)] |
= |
· x1 +
|
[isNeList(x1)] |
= |
· x1 +
|
[__(x1, x2)] |
= |
· x1 + · x2 +
|
[U22(x1)] |
= |
· x1 +
|
[n____(x1, x2)] |
= |
· x1 + · x2 +
|
[n__i] |
= |
|
[i] |
= |
|
[U61(x1)] |
= |
· x1 +
|
[o] |
= |
|
[U51(x1, x2)] |
= |
· x1 + · x2 +
|
[n__a] |
= |
|
[n__e] |
= |
|
[U42(x1)] |
= |
· x1 +
|
[U41(x1, x2)] |
= |
· x1 + · x2 +
|
[U52(x1)] |
= |
· x1 +
|
[isList(x1)] |
= |
· x1 +
|
[e] |
= |
|
[tt] |
= |
|
all of the following rules can be deleted.
[U81(x1)] |
= |
· x1 +
|
[U21(x1, x2)] |
= |
· x1 + · x2 +
|
[U31(x1)] |
= |
· x1 +
|
[nil] |
= |
|
[U11(x1)] |
= |
· x1 +
|
[isPal(x1)] |
= |
· x1 +
|
[isQid(x1)] |
= |
· x1 +
|
[n__o] |
= |
|
[u] |
= |
|
[n__nil] |
= |
|
[U72(x1)] |
= |
· x1 +
|
[n__u] |
= |
|
[isNePal(x1)] |
= |
· x1 +
|
[a] |
= |
|
[activate(x1)] |
= |
· x1 +
|
[isNeList(x1)] |
= |
· x1 +
|
[__(x1, x2)] |
= |
· x1 + · x2 +
|
[n____(x1, x2)] |
= |
· x1 + · x2 +
|
[n__i] |
= |
|
[i] |
= |
|
[U61(x1)] |
= |
· x1 +
|
[o] |
= |
|
[U51(x1, x2)] |
= |
· x1 + · x2 +
|
[n__a] |
= |
|
[n__e] |
= |
|
[U42(x1)] |
= |
· x1 +
|
[U41(x1, x2)] |
= |
· x1 + · x2 +
|
[U52(x1)] |
= |
· x1 +
|
[isList(x1)] |
= |
· x1 +
|
[e] |
= |
|
[tt] |
= |
|
all of the following rules can be deleted.
[U81(x1)] |
= |
· x1 +
|
[U21(x1, x2)] |
= |
· x1 + · x2 +
|
[U31(x1)] |
= |
· x1 +
|
[nil] |
= |
|
[isPal(x1)] |
= |
· x1 +
|
[isQid(x1)] |
= |
· x1 +
|
[n__o] |
= |
|
[u] |
= |
|
[n__nil] |
= |
|
[U72(x1)] |
= |
· x1 +
|
[n__u] |
= |
|
[isNePal(x1)] |
= |
· x1 +
|
[a] |
= |
|
[activate(x1)] |
= |
· x1 +
|
[isNeList(x1)] |
= |
· x1 +
|
[__(x1, x2)] |
= |
· x1 + · x2 +
|
[n____(x1, x2)] |
= |
· x1 + · x2 +
|
[n__i] |
= |
|
[i] |
= |
|
[U61(x1)] |
= |
· x1 +
|
[o] |
= |
|
[U51(x1, x2)] |
= |
· x1 + · x2 +
|
[n__a] |
= |
|
[n__e] |
= |
|
[U42(x1)] |
= |
· x1 +
|
[U41(x1, x2)] |
= |
· x1 + · x2 +
|
[U52(x1)] |
= |
· x1 +
|
[isList(x1)] |
= |
· x1 +
|
[e] |
= |
|
[tt] |
= |
|
all of the following rules can be deleted.
[U81(x1)] |
= |
· x1 +
|
[U21(x1, x2)] |
= |
· x1 + · x2 +
|
[U31(x1)] |
= |
· x1 +
|
[nil] |
= |
|
[isQid(x1)] |
= |
· x1 +
|
[n__o] |
= |
|
[u] |
= |
|
[n__nil] |
= |
|
[U72(x1)] |
= |
· x1 +
|
[n__u] |
= |
|
[a] |
= |
|
[activate(x1)] |
= |
· x1 +
|
[isNeList(x1)] |
= |
· x1 +
|
[__(x1, x2)] |
= |
· x1 + · x2 +
|
[n____(x1, x2)] |
= |
· x1 + · x2 +
|
[n__i] |
= |
|
[i] |
= |
|
[U61(x1)] |
= |
· x1 +
|
[o] |
= |
|
[U51(x1, x2)] |
= |
· x1 + · x2 +
|
[n__a] |
= |
|
[n__e] |
= |
|
[U41(x1, x2)] |
= |
· x1 + · x2 +
|
[U52(x1)] |
= |
· x1 +
|
[isList(x1)] |
= |
· x1 +
|
[e] |
= |
|
[tt] |
= |
|
all of the following rules can be deleted.
[U21(x1, x2)] |
= |
· x1 + · x2 +
|
[U31(x1)] |
= |
· x1 +
|
[nil] |
= |
|
[isQid(x1)] |
= |
· x1 +
|
[n__o] |
= |
|
[u] |
= |
|
[n__nil] |
= |
|
[n__u] |
= |
|
[a] |
= |
|
[activate(x1)] |
= |
· x1 +
|
[isNeList(x1)] |
= |
· x1 +
|
[__(x1, x2)] |
= |
· x1 + · x2 +
|
[n____(x1, x2)] |
= |
· x1 + · x2 +
|
[n__i] |
= |
|
[i] |
= |
|
[o] |
= |
|
[n__a] |
= |
|
[n__e] |
= |
|
[isList(x1)] |
= |
· x1 +
|
[e] |
= |
|
[tt] |
= |
|
all of the following rules can be deleted.
[U21(x1, x2)] |
= |
· x1 + · x2 +
|
[U31(x1)] |
= |
· x1 +
|
[nil] |
= |
|
[isQid(x1)] |
= |
· x1 +
|
[n__o] |
= |
|
[u] |
= |
|
[n__nil] |
= |
|
[n__u] |
= |
|
[a] |
= |
|
[activate(x1)] |
= |
· x1 +
|
[isNeList(x1)] |
= |
· x1 +
|
[__(x1, x2)] |
= |
· x1 + · x2 +
|
[n____(x1, x2)] |
= |
· x1 + · x2 +
|
[n__i] |
= |
|
[i] |
= |
|
[o] |
= |
|
[n__a] |
= |
|
[n__e] |
= |
|
[isList(x1)] |
= |
· x1 +
|
[e] |
= |
|
[tt] |
= |
|
all of the following rules can be deleted.
The dependency pairs are split into 1
component.