YES
0 QTRS
↳1 QTRSRRRProof (⇔, 174 ms)
↳2 QTRS
↳3 QTRSRRRProof (⇔, 13 ms)
↳4 QTRS
↳5 RisEmptyProof (⇔, 0 ms)
↳6 YES
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
U11(tt, V) → U12(isNeList(activate(V)))
U12(tt) → tt
U21(tt, V1, V2) → U22(isList(activate(V1)), activate(V2))
U22(tt, V2) → U23(isList(activate(V2)))
U23(tt) → tt
U31(tt, V) → U32(isQid(activate(V)))
U32(tt) → tt
U41(tt, V1, V2) → U42(isList(activate(V1)), activate(V2))
U42(tt, V2) → U43(isNeList(activate(V2)))
U43(tt) → tt
U51(tt, V1, V2) → U52(isNeList(activate(V1)), activate(V2))
U52(tt, V2) → U53(isList(activate(V2)))
U53(tt) → tt
U61(tt, V) → U62(isQid(activate(V)))
U62(tt) → tt
U71(tt, V) → U72(isNePal(activate(V)))
U72(tt) → tt
and(tt, X) → activate(X)
isList(V) → U11(isPalListKind(activate(V)), activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → U21(and(isPalListKind(activate(V1)), n__isPalListKind(activate(V2))), activate(V1), activate(V2))
isNeList(V) → U31(isPalListKind(activate(V)), activate(V))
isNeList(n____(V1, V2)) → U41(and(isPalListKind(activate(V1)), n__isPalListKind(activate(V2))), activate(V1), activate(V2))
isNeList(n____(V1, V2)) → U51(and(isPalListKind(activate(V1)), n__isPalListKind(activate(V2))), activate(V1), activate(V2))
isNePal(V) → U61(isPalListKind(activate(V)), activate(V))
isNePal(n____(I, __(P, I))) → and(and(isQid(activate(I)), n__isPalListKind(activate(I))), n__and(isPal(activate(P)), n__isPalListKind(activate(P))))
isPal(V) → U71(isPalListKind(activate(V)), activate(V))
isPal(n__nil) → tt
isPalListKind(n__a) → tt
isPalListKind(n__e) → tt
isPalListKind(n__i) → tt
isPalListKind(n__nil) → tt
isPalListKind(n__o) → tt
isPalListKind(n__u) → tt
isPalListKind(n____(V1, V2)) → and(isPalListKind(activate(V1)), n__isPalListKind(activate(V2)))
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isPalListKind(X) → n__isPalListKind(X)
and(X1, X2) → n__and(X1, X2)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__isPalListKind(X)) → isPalListKind(X)
activate(n__and(X1, X2)) → and(X1, X2)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
[2, n2] > U213 > [U222, isList1, U522] > U112 > isNeList1 > [U312, isQid1, U612] > [tt, na, a]
[2, n2] > U213 > [U222, isList1, U522] > U112 > isNeList1 > [and2, nand2]
[2, n2] > U213 > [U222, isList1, U522] > U231 > [tt, na, a]
[2, n2] > U413 > [U222, isList1, U522] > U112 > isNeList1 > [U312, isQid1, U612] > [tt, na, a]
[2, n2] > U413 > [U222, isList1, U522] > U112 > isNeList1 > [and2, nand2]
[2, n2] > U413 > [U222, isList1, U522] > U231 > [tt, na, a]
[2, n2] > U413 > U422 > isNeList1 > [U312, isQid1, U612] > [tt, na, a]
[2, n2] > U413 > U422 > isNeList1 > [and2, nand2]
[2, n2] > U513 > [U222, isList1, U522] > U112 > isNeList1 > [U312, isQid1, U612] > [tt, na, a]
[2, n2] > U513 > [U222, isList1, U522] > U112 > isNeList1 > [and2, nand2]
[2, n2] > U513 > [U222, isList1, U522] > U231 > [tt, na, a]
[2, n2] > isPal1 > U712 > isNePal1 > [U312, isQid1, U612] > [tt, na, a]
[2, n2] > isPal1 > U712 > isNePal1 > [and2, nand2]
[nil, nnil] > [tt, na, a]
[ne, e] > [tt, na, a]
[ni, i] > [tt, na, a]
[no, o] > [tt, na, a]
[nu, u] > [tt, na, a]
_2: [1,2]
nil: multiset
U112: multiset
tt: multiset
isNeList1: [1]
U213: [2,1,3]
U222: multiset
isList1: multiset
U231: [1]
U312: multiset
isQid1: multiset
U413: [2,3,1]
U422: [2,1]
U513: multiset
U522: multiset
U612: multiset
U712: multiset
isNePal1: [1]
and2: [2,1]
nnil: multiset
n2: [1,2]
nand2: [2,1]
isPal1: multiset
na: multiset
ne: multiset
ni: multiset
no: multiset
nu: multiset
a: multiset
e: multiset
i: multiset
o: multiset
u: multiset
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
U11(tt, V) → U12(isNeList(activate(V)))
U21(tt, V1, V2) → U22(isList(activate(V1)), activate(V2))
U22(tt, V2) → U23(isList(activate(V2)))
U23(tt) → tt
U31(tt, V) → U32(isQid(activate(V)))
U41(tt, V1, V2) → U42(isList(activate(V1)), activate(V2))
U42(tt, V2) → U43(isNeList(activate(V2)))
U51(tt, V1, V2) → U52(isNeList(activate(V1)), activate(V2))
U52(tt, V2) → U53(isList(activate(V2)))
U61(tt, V) → U62(isQid(activate(V)))
U71(tt, V) → U72(isNePal(activate(V)))
and(tt, X) → activate(X)
isList(V) → U11(isPalListKind(activate(V)), activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → U21(and(isPalListKind(activate(V1)), n__isPalListKind(activate(V2))), activate(V1), activate(V2))
isNeList(V) → U31(isPalListKind(activate(V)), activate(V))
isNeList(n____(V1, V2)) → U41(and(isPalListKind(activate(V1)), n__isPalListKind(activate(V2))), activate(V1), activate(V2))
isNeList(n____(V1, V2)) → U51(and(isPalListKind(activate(V1)), n__isPalListKind(activate(V2))), activate(V1), activate(V2))
isNePal(V) → U61(isPalListKind(activate(V)), activate(V))
isNePal(n____(I, __(P, I))) → and(and(isQid(activate(I)), n__isPalListKind(activate(I))), n__and(isPal(activate(P)), n__isPalListKind(activate(P))))
isPal(V) → U71(isPalListKind(activate(V)), activate(V))
isPal(n__nil) → tt
isPalListKind(n__e) → tt
isPalListKind(n__i) → tt
isPalListKind(n__nil) → tt
isPalListKind(n__o) → tt
isPalListKind(n__u) → tt
isPalListKind(n____(V1, V2)) → and(isPalListKind(activate(V1)), n__isPalListKind(activate(V2)))
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
U12(tt) → tt
U32(tt) → tt
U43(tt) → tt
U53(tt) → tt
U62(tt) → tt
U72(tt) → tt
isPalListKind(n__a) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isPalListKind(X) → n__isPalListKind(X)
and(X1, X2) → n__and(X1, X2)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__isPalListKind(X)) → isPalListKind(X)
activate(n__and(X1, X2)) → and(X1, X2)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
activate1 > u > nu > isPalListKind1 > o > no > i > ni > U431 > e > ne > a > and2 > nand2 > nisPalListKind1 > tt > _2 > n2 > nil > nnil > na > U721 > U621 > U531 > U321 > U121
tt=2
n__a=1
nil=1
n__nil=1
a=1
e=1
n__e=1
i=1
n__i=1
o=1
n__o=1
u=1
n__u=1
U12_1=1
U32_1=1
U43_1=1
U53_1=1
U62_1=1
U72_1=1
isPalListKind_1=1
n__isPalListKind_1=1
activate_1=0
___2=0
n_____2=0
and_2=0
n__and_2=0
U12(tt) → tt
U32(tt) → tt
U43(tt) → tt
U53(tt) → tt
U62(tt) → tt
U72(tt) → tt
isPalListKind(n__a) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isPalListKind(X) → n__isPalListKind(X)
and(X1, X2) → n__and(X1, X2)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(X1, X2)
activate(n__isPalListKind(X)) → isPalListKind(X)
activate(n__and(X1, X2)) → and(X1, X2)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X