YES Termination w.r.t. Q proof of Transformed_CSR_04_PALINDROME_complete_noand_GM.ari

(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U13(tt) → tt
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U26(tt) → tt
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U33(tt) → tt
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U46(tt) → tt
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U56(tt) → tt
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U63(tt) → tt
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U74(tt) → tt
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U83(tt) → tt
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__U92(tt) → tt
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Combined order from the following AFS and order.
a____(x1, x2)  =  a____(x1, x2)
__(x1, x2)  =  __(x1, x2)
mark(x1)  =  x1
nil  =  nil
a__U11(x1, x2)  =  a__U11(x1, x2)
tt  =  tt
a__U12(x1, x2)  =  a__U12(x1, x2)
a__isPalListKind(x1)  =  x1
a__U13(x1)  =  x1
a__isNeList(x1)  =  a__isNeList(x1)
a__U21(x1, x2, x3)  =  a__U21(x1, x2, x3)
a__U22(x1, x2, x3)  =  a__U22(x1, x2, x3)
a__U23(x1, x2, x3)  =  a__U23(x1, x2, x3)
a__U24(x1, x2, x3)  =  a__U24(x1, x2, x3)
a__U25(x1, x2)  =  a__U25(x1, x2)
a__isList(x1)  =  a__isList(x1)
a__U26(x1)  =  x1
a__U31(x1, x2)  =  a__U31(x1, x2)
a__U32(x1, x2)  =  a__U32(x1, x2)
a__U33(x1)  =  x1
a__isQid(x1)  =  a__isQid(x1)
a__U41(x1, x2, x3)  =  a__U41(x1, x2, x3)
a__U42(x1, x2, x3)  =  a__U42(x1, x2, x3)
a__U43(x1, x2, x3)  =  a__U43(x1, x2, x3)
a__U44(x1, x2, x3)  =  a__U44(x1, x2, x3)
a__U45(x1, x2)  =  a__U45(x1, x2)
a__U46(x1)  =  x1
a__U51(x1, x2, x3)  =  a__U51(x1, x2, x3)
a__U52(x1, x2, x3)  =  a__U52(x1, x2, x3)
a__U53(x1, x2, x3)  =  a__U53(x1, x2, x3)
a__U54(x1, x2, x3)  =  a__U54(x1, x2, x3)
a__U55(x1, x2)  =  a__U55(x1, x2)
a__U56(x1)  =  x1
a__U61(x1, x2)  =  a__U61(x1, x2)
a__U62(x1, x2)  =  a__U62(x1, x2)
a__U63(x1)  =  x1
a__U71(x1, x2, x3)  =  a__U71(x1, x2, x3)
a__U72(x1, x2)  =  a__U72(x1, x2)
a__U73(x1, x2)  =  a__U73(x1, x2)
a__isPal(x1)  =  a__isPal(x1)
a__U74(x1)  =  x1
a__U81(x1, x2)  =  a__U81(x1, x2)
a__U82(x1, x2)  =  a__U82(x1, x2)
a__U83(x1)  =  x1
a__isNePal(x1)  =  a__isNePal(x1)
a__U91(x1, x2)  =  a__U91(x1, x2)
a__U92(x1)  =  x1
a  =  a
e  =  e
i  =  i
o  =  o
u  =  u
U11(x1, x2)  =  U11(x1, x2)
U12(x1, x2)  =  U12(x1, x2)
isPalListKind(x1)  =  x1
U13(x1)  =  x1
isNeList(x1)  =  isNeList(x1)
U21(x1, x2, x3)  =  U21(x1, x2, x3)
U22(x1, x2, x3)  =  U22(x1, x2, x3)
U23(x1, x2, x3)  =  U23(x1, x2, x3)
U24(x1, x2, x3)  =  U24(x1, x2, x3)
U25(x1, x2)  =  U25(x1, x2)
isList(x1)  =  isList(x1)
U26(x1)  =  x1
U31(x1, x2)  =  U31(x1, x2)
U32(x1, x2)  =  U32(x1, x2)
U33(x1)  =  x1
isQid(x1)  =  isQid(x1)
U41(x1, x2, x3)  =  U41(x1, x2, x3)
U42(x1, x2, x3)  =  U42(x1, x2, x3)
U43(x1, x2, x3)  =  U43(x1, x2, x3)
U44(x1, x2, x3)  =  U44(x1, x2, x3)
U45(x1, x2)  =  U45(x1, x2)
U46(x1)  =  x1
U51(x1, x2, x3)  =  U51(x1, x2, x3)
U52(x1, x2, x3)  =  U52(x1, x2, x3)
U53(x1, x2, x3)  =  U53(x1, x2, x3)
U54(x1, x2, x3)  =  U54(x1, x2, x3)
U55(x1, x2)  =  U55(x1, x2)
U56(x1)  =  x1
U61(x1, x2)  =  U61(x1, x2)
U62(x1, x2)  =  U62(x1, x2)
U63(x1)  =  x1
U71(x1, x2, x3)  =  U71(x1, x2, x3)
U72(x1, x2)  =  U72(x1, x2)
U73(x1, x2)  =  U73(x1, x2)
isPal(x1)  =  isPal(x1)
U74(x1)  =  x1
U81(x1, x2)  =  U81(x1, x2)
U82(x1, x2)  =  U82(x1, x2)
U83(x1)  =  x1
isNePal(x1)  =  isNePal(x1)
U91(x1, x2)  =  U91(x1, x2)
U92(x1)  =  x1

Recursive path order with status [RPO].
Quasi-Precedence:
[a2, 2] > [aU213, U213] > [aU223, U223] > [aU233, U233] > [aU243, U243] > [aU252, U252] > [tt, aisList1, isList1] > [aU112, U112] > [aU122, U122] > [aisNeList1, isNeList1] > [aU312, U312] > [aU322, aisQid1, aU622, U322, isQid1, U622]
[a2, 2] > [aU213, U213] > [aU223, U223] > [aU233, U233] > [aU243, U243] > [aU252, U252] > [tt, aisList1, isList1] > [aisNePal1, isNePal1] > [aU612, U612] > [aU322, aisQid1, aU622, U322, isQid1, U622]
[a2, 2] > [aU413, U413] > [aU423, U423] > [aU433, U433] > [aU443, U443] > [tt, aisList1, isList1] > [aU112, U112] > [aU122, U122] > [aisNeList1, isNeList1] > [aU312, U312] > [aU322, aisQid1, aU622, U322, isQid1, U622]
[a2, 2] > [aU413, U413] > [aU423, U423] > [aU433, U433] > [aU443, U443] > [tt, aisList1, isList1] > [aisNePal1, isNePal1] > [aU612, U612] > [aU322, aisQid1, aU622, U322, isQid1, U622]
[a2, 2] > [aU413, U413] > [aU423, U423] > [aU433, U433] > [aU443, U443] > [aU452, U452] > [aisNeList1, isNeList1] > [aU312, U312] > [aU322, aisQid1, aU622, U322, isQid1, U622]
[a2, 2] > [aU513, U513] > [aU523, U523] > [aU533, U533] > [aU543, U543] > [aU552, U552] > [tt, aisList1, isList1] > [aU112, U112] > [aU122, U122] > [aisNeList1, isNeList1] > [aU312, U312] > [aU322, aisQid1, aU622, U322, isQid1, U622]
[a2, 2] > [aU513, U513] > [aU523, U523] > [aU533, U533] > [aU543, U543] > [aU552, U552] > [tt, aisList1, isList1] > [aisNePal1, isNePal1] > [aU612, U612] > [aU322, aisQid1, aU622, U322, isQid1, U622]
[a2, 2] > [aU713, aU722, U713, U722] > [aU732, U732] > [aU322, aisQid1, aU622, U322, isQid1, U622]
[a2, 2] > [aU713, aU722, U713, U722] > [aisPal1, isPal1] > [tt, aisList1, isList1] > [aU112, U112] > [aU122, U122] > [aisNeList1, isNeList1] > [aU312, U312] > [aU322, aisQid1, aU622, U322, isQid1, U622]
[a2, 2] > [aU713, aU722, U713, U722] > [aisPal1, isPal1] > [tt, aisList1, isList1] > [aisNePal1, isNePal1] > [aU612, U612] > [aU322, aisQid1, aU622, U322, isQid1, U622]
[a2, 2] > [aU713, aU722, U713, U722] > [aisPal1, isPal1] > [aU812, U812] > [aU822, U822] > [aisNePal1, isNePal1] > [aU612, U612] > [aU322, aisQid1, aU622, U322, isQid1, U622]
[a2, 2] > [aU912, U912] > [aU322, aisQid1, aU622, U322, isQid1, U622]
nil > [tt, aisList1, isList1] > [aU112, U112] > [aU122, U122] > [aisNeList1, isNeList1] > [aU312, U312] > [aU322, aisQid1, aU622, U322, isQid1, U622]
nil > [tt, aisList1, isList1] > [aisNePal1, isNePal1] > [aU612, U612] > [aU322, aisQid1, aU622, U322, isQid1, U622]
a > [tt, aisList1, isList1] > [aU112, U112] > [aU122, U122] > [aisNeList1, isNeList1] > [aU312, U312] > [aU322, aisQid1, aU622, U322, isQid1, U622]
a > [tt, aisList1, isList1] > [aisNePal1, isNePal1] > [aU612, U612] > [aU322, aisQid1, aU622, U322, isQid1, U622]
e > [tt, aisList1, isList1] > [aU112, U112] > [aU122, U122] > [aisNeList1, isNeList1] > [aU312, U312] > [aU322, aisQid1, aU622, U322, isQid1, U622]
e > [tt, aisList1, isList1] > [aisNePal1, isNePal1] > [aU612, U612] > [aU322, aisQid1, aU622, U322, isQid1, U622]
i > [tt, aisList1, isList1] > [aU112, U112] > [aU122, U122] > [aisNeList1, isNeList1] > [aU312, U312] > [aU322, aisQid1, aU622, U322, isQid1, U622]
i > [tt, aisList1, isList1] > [aisNePal1, isNePal1] > [aU612, U612] > [aU322, aisQid1, aU622, U322, isQid1, U622]
o > [tt, aisList1, isList1] > [aU112, U112] > [aU122, U122] > [aisNeList1, isNeList1] > [aU312, U312] > [aU322, aisQid1, aU622, U322, isQid1, U622]
o > [tt, aisList1, isList1] > [aisNePal1, isNePal1] > [aU612, U612] > [aU322, aisQid1, aU622, U322, isQid1, U622]
u > [tt, aisList1, isList1] > [aU112, U112] > [aU122, U122] > [aisNeList1, isNeList1] > [aU312, U312] > [aU322, aisQid1, aU622, U322, isQid1, U622]
u > [tt, aisList1, isList1] > [aisNePal1, isNePal1] > [aU612, U612] > [aU322, aisQid1, aU622, U322, isQid1, U622]

Status:
a2: [1,2]
_2: [1,2]
nil: multiset
aU112: [2,1]
tt: multiset
aU122: [2,1]
aisNeList1: [1]
aU213: multiset
aU223: multiset
aU233: [3,1,2]
aU243: [1,2,3]
aU252: [2,1]
aisList1: multiset
aU312: [2,1]
aU322: [2,1]
aisQid1: [1]
aU413: [2,3,1]
aU423: [2,3,1]
aU433: multiset
aU443: multiset
aU452: [1,2]
aU513: multiset
aU523: multiset
aU533: multiset
aU543: multiset
aU552: multiset
aU612: multiset
aU622: [2,1]
aU713: [3,2,1]
aU722: [2,1]
aU732: multiset
aisPal1: multiset
aU812: multiset
aU822: [2,1]
aisNePal1: [1]
aU912: multiset
a: multiset
e: multiset
i: multiset
o: multiset
u: multiset
U112: [2,1]
U122: [2,1]
isNeList1: [1]
U213: multiset
U223: multiset
U233: [3,1,2]
U243: [1,2,3]
U252: [2,1]
isList1: multiset
U312: [2,1]
U322: [2,1]
isQid1: [1]
U413: [2,3,1]
U423: [2,3,1]
U433: multiset
U443: multiset
U452: [1,2]
U513: multiset
U523: multiset
U533: multiset
U543: multiset
U552: multiset
U612: multiset
U622: [2,1]
U713: [3,2,1]
U722: [2,1]
U732: multiset
isPal1: multiset
U812: multiset
U822: [2,1]
isNePal1: [1]
U912: multiset

With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

a____(__(X, Y), Z) → a____(mark(X), a____(mark(Y), mark(Z)))
a____(X, nil) → mark(X)
a____(nil, X) → mark(X)
a__U11(tt, V) → a__U12(a__isPalListKind(V), V)
a__U12(tt, V) → a__U13(a__isNeList(V))
a__U21(tt, V1, V2) → a__U22(a__isPalListKind(V1), V1, V2)
a__U22(tt, V1, V2) → a__U23(a__isPalListKind(V2), V1, V2)
a__U23(tt, V1, V2) → a__U24(a__isPalListKind(V2), V1, V2)
a__U24(tt, V1, V2) → a__U25(a__isList(V1), V2)
a__U25(tt, V2) → a__U26(a__isList(V2))
a__U31(tt, V) → a__U32(a__isPalListKind(V), V)
a__U32(tt, V) → a__U33(a__isQid(V))
a__U41(tt, V1, V2) → a__U42(a__isPalListKind(V1), V1, V2)
a__U42(tt, V1, V2) → a__U43(a__isPalListKind(V2), V1, V2)
a__U43(tt, V1, V2) → a__U44(a__isPalListKind(V2), V1, V2)
a__U44(tt, V1, V2) → a__U45(a__isList(V1), V2)
a__U45(tt, V2) → a__U46(a__isNeList(V2))
a__U51(tt, V1, V2) → a__U52(a__isPalListKind(V1), V1, V2)
a__U52(tt, V1, V2) → a__U53(a__isPalListKind(V2), V1, V2)
a__U53(tt, V1, V2) → a__U54(a__isPalListKind(V2), V1, V2)
a__U54(tt, V1, V2) → a__U55(a__isNeList(V1), V2)
a__U55(tt, V2) → a__U56(a__isList(V2))
a__U61(tt, V) → a__U62(a__isPalListKind(V), V)
a__U62(tt, V) → a__U63(a__isQid(V))
a__U71(tt, I, P) → a__U72(a__isPalListKind(I), P)
a__U72(tt, P) → a__U73(a__isPal(P), P)
a__U73(tt, P) → a__U74(a__isPalListKind(P))
a__U81(tt, V) → a__U82(a__isPalListKind(V), V)
a__U82(tt, V) → a__U83(a__isNePal(V))
a__U91(tt, V2) → a__U92(a__isPalListKind(V2))
a__isList(V) → a__U11(a__isPalListKind(V), V)
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isPalListKind(V1), V1, V2)
a__isNeList(V) → a__U31(a__isPalListKind(V), V)
a__isNeList(__(V1, V2)) → a__U41(a__isPalListKind(V1), V1, V2)
a__isNeList(__(V1, V2)) → a__U51(a__isPalListKind(V1), V1, V2)
a__isNePal(V) → a__U61(a__isPalListKind(V), V)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), I, P)
a__isPal(V) → a__U81(a__isPalListKind(V), V)
a__isPal(nil) → tt
a__isPalListKind(a) → tt
a__isPalListKind(e) → tt
a__isPalListKind(i) → tt
a__isPalListKind(nil) → tt
a__isPalListKind(o) → tt
a__isPalListKind(u) → tt
a__isPalListKind(__(V1, V2)) → a__U91(a__isPalListKind(V1), V2)
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt


(2) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

a__U13(tt) → tt
a__U26(tt) → tt
a__U33(tt) → tt
a__U46(tt) → tt
a__U56(tt) → tt
a__U63(tt) → tt
a__U74(tt) → tt
a__U83(tt) → tt
a__U92(tt) → tt
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)

Q is empty.

(3) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Polynomial interpretation [POLO]:

POL(U11(x1, x2)) = 1 + x1 + x2   
POL(U12(x1, x2)) = 1 + x1 + x2   
POL(U13(x1)) = 1 + x1   
POL(U21(x1, x2, x3)) = 1 + x1 + x2 + x3   
POL(U22(x1, x2, x3)) = 1 + x1 + x2 + x3   
POL(U23(x1, x2, x3)) = 1 + x1 + x2 + x3   
POL(U24(x1, x2, x3)) = 1 + x1 + x2 + x3   
POL(U25(x1, x2)) = 1 + x1 + x2   
POL(U26(x1)) = 1 + x1   
POL(U31(x1, x2)) = 1 + x1 + x2   
POL(U32(x1, x2)) = 1 + x1 + x2   
POL(U33(x1)) = 1 + x1   
POL(U41(x1, x2, x3)) = 1 + x1 + x2 + x3   
POL(U42(x1, x2, x3)) = 1 + 2·x1 + x2 + x3   
POL(U43(x1, x2, x3)) = 1 + x1 + x2 + x3   
POL(U44(x1, x2, x3)) = 1 + x1 + x2 + x3   
POL(U45(x1, x2)) = 1 + x1 + x2   
POL(U46(x1)) = 1 + 2·x1   
POL(U51(x1, x2, x3)) = 1 + x1 + x2 + x3   
POL(U52(x1, x2, x3)) = 1 + x1 + x2 + x3   
POL(U53(x1, x2, x3)) = 1 + x1 + x2 + x3   
POL(U54(x1, x2, x3)) = 1 + x1 + x2 + x3   
POL(U55(x1, x2)) = 1 + x1 + x2   
POL(U56(x1)) = 1 + x1   
POL(U61(x1, x2)) = 1 + x1 + x2   
POL(U62(x1, x2)) = 1 + x1 + x2   
POL(U63(x1)) = 1 + x1   
POL(U71(x1, x2, x3)) = 1 + x1 + x2 + x3   
POL(U72(x1, x2)) = 1 + x1 + x2   
POL(U73(x1, x2)) = 1 + x1 + x2   
POL(U74(x1)) = 1 + 2·x1   
POL(U81(x1, x2)) = 1 + x1 + x2   
POL(U82(x1, x2)) = 1 + x1 + x2   
POL(U83(x1)) = 1 + x1   
POL(U91(x1, x2)) = 1 + x1 + x2   
POL(U92(x1)) = 1 + x1   
POL(__(x1, x2)) = 1 + x1 + x2   
POL(a) = 2   
POL(a__U11(x1, x2)) = 2 + x1 + x2   
POL(a__U12(x1, x2)) = 2 + x1 + 2·x2   
POL(a__U13(x1)) = 2 + x1   
POL(a__U21(x1, x2, x3)) = 2 + x1 + 2·x2 + 2·x3   
POL(a__U22(x1, x2, x3)) = 2 + x1 + 2·x2 + x3   
POL(a__U23(x1, x2, x3)) = 2 + x1 + 2·x2 + 2·x3   
POL(a__U24(x1, x2, x3)) = 2 + x1 + x2 + x3   
POL(a__U25(x1, x2)) = 2 + x1 + 2·x2   
POL(a__U26(x1)) = 2 + x1   
POL(a__U31(x1, x2)) = 2 + x1 + x2   
POL(a__U32(x1, x2)) = 2 + x1 + x2   
POL(a__U33(x1)) = 2 + x1   
POL(a__U41(x1, x2, x3)) = 2 + x1 + x2 + x3   
POL(a__U42(x1, x2, x3)) = 2 + 2·x1 + x2 + 2·x3   
POL(a__U43(x1, x2, x3)) = 2 + x1 + x2 + 2·x3   
POL(a__U44(x1, x2, x3)) = 2 + x1 + 2·x2 + 2·x3   
POL(a__U45(x1, x2)) = 2 + x1 + x2   
POL(a__U46(x1)) = 2 + 2·x1   
POL(a__U51(x1, x2, x3)) = 2 + x1 + 2·x2 + 2·x3   
POL(a__U52(x1, x2, x3)) = 2 + x1 + 2·x2 + x3   
POL(a__U53(x1, x2, x3)) = 2 + x1 + x2 + x3   
POL(a__U54(x1, x2, x3)) = 2 + x1 + x2 + x3   
POL(a__U55(x1, x2)) = 2 + x1 + x2   
POL(a__U56(x1)) = 2 + x1   
POL(a__U61(x1, x2)) = 2 + x1 + 2·x2   
POL(a__U62(x1, x2)) = 2 + x1 + x2   
POL(a__U63(x1)) = 2 + x1   
POL(a__U71(x1, x2, x3)) = 2 + x1 + 2·x2 + x3   
POL(a__U72(x1, x2)) = 2 + x1 + x2   
POL(a__U73(x1, x2)) = 2 + x1 + x2   
POL(a__U74(x1)) = 2 + 2·x1   
POL(a__U81(x1, x2)) = 2 + x1 + x2   
POL(a__U82(x1, x2)) = 2 + x1 + x2   
POL(a__U83(x1)) = 2 + x1   
POL(a__U91(x1, x2)) = 2 + x1 + x2   
POL(a__U92(x1)) = 2 + x1   
POL(a____(x1, x2)) = 2 + x1 + x2   
POL(a__isList(x1)) = 2 + x1   
POL(a__isNeList(x1)) = 2 + x1   
POL(a__isNePal(x1)) = 2 + x1   
POL(a__isPal(x1)) = 2 + 2·x1   
POL(a__isPalListKind(x1)) = 2 + 2·x1   
POL(a__isQid(x1)) = 2 + x1   
POL(e) = 0   
POL(i) = 1   
POL(isList(x1)) = 1 + x1   
POL(isNeList(x1)) = 1 + x1   
POL(isNePal(x1)) = 1 + x1   
POL(isPal(x1)) = 1 + x1   
POL(isPalListKind(x1)) = 1 + x1   
POL(isQid(x1)) = 1 + x1   
POL(mark(x1)) = 2·x1   
POL(nil) = 1   
POL(o) = 1   
POL(tt) = 1   
POL(u) = 2   
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

a__U13(tt) → tt
a__U26(tt) → tt
a__U33(tt) → tt
a__U46(tt) → tt
a__U56(tt) → tt
a__U63(tt) → tt
a__U74(tt) → tt
a__U83(tt) → tt
a__U92(tt) → tt
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(i) → i
mark(o) → o
mark(u) → u
a____(X1, X2) → __(X1, X2)
a__U11(X1, X2) → U11(X1, X2)
a__U12(X1, X2) → U12(X1, X2)
a__isPalListKind(X) → isPalListKind(X)
a__U13(X) → U13(X)
a__isNeList(X) → isNeList(X)
a__U21(X1, X2, X3) → U21(X1, X2, X3)
a__U22(X1, X2, X3) → U22(X1, X2, X3)
a__U23(X1, X2, X3) → U23(X1, X2, X3)
a__U24(X1, X2, X3) → U24(X1, X2, X3)
a__U25(X1, X2) → U25(X1, X2)
a__isList(X) → isList(X)
a__U26(X) → U26(X)
a__U31(X1, X2) → U31(X1, X2)
a__U32(X1, X2) → U32(X1, X2)
a__U33(X) → U33(X)
a__isQid(X) → isQid(X)
a__U41(X1, X2, X3) → U41(X1, X2, X3)
a__U42(X1, X2, X3) → U42(X1, X2, X3)
a__U43(X1, X2, X3) → U43(X1, X2, X3)
a__U44(X1, X2, X3) → U44(X1, X2, X3)
a__U45(X1, X2) → U45(X1, X2)
a__U46(X) → U46(X)
a__U51(X1, X2, X3) → U51(X1, X2, X3)
a__U52(X1, X2, X3) → U52(X1, X2, X3)
a__U53(X1, X2, X3) → U53(X1, X2, X3)
a__U54(X1, X2, X3) → U54(X1, X2, X3)
a__U55(X1, X2) → U55(X1, X2)
a__U56(X) → U56(X)
a__U61(X1, X2) → U61(X1, X2)
a__U62(X1, X2) → U62(X1, X2)
a__U63(X) → U63(X)
a__U71(X1, X2, X3) → U71(X1, X2, X3)
a__U72(X1, X2) → U72(X1, X2)
a__U73(X1, X2) → U73(X1, X2)
a__isPal(X) → isPal(X)
a__U74(X) → U74(X)
a__U81(X1, X2) → U81(X1, X2)
a__U82(X1, X2) → U82(X1, X2)
a__U83(X) → U83(X)
a__isNePal(X) → isNePal(X)
a__U91(X1, X2) → U91(X1, X2)
a__U92(X) → U92(X)


(4) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(e) → e

Q is empty.

(5) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Polynomial interpretation [POLO]:

POL(U11(x1, x2)) = 2 + 2·x1 + x2   
POL(U12(x1, x2)) = 1 + 2·x1 + x2   
POL(U13(x1)) = 2 + 2·x1   
POL(U21(x1, x2, x3)) = 2 + 2·x1 + x2 + x3   
POL(U22(x1, x2, x3)) = 2 + 2·x1 + x2 + x3   
POL(U23(x1, x2, x3)) = 2 + 2·x1 + x2 + x3   
POL(U24(x1, x2, x3)) = 2 + 2·x1 + x2 + x3   
POL(U25(x1, x2)) = 2 + 2·x1 + x2   
POL(U26(x1)) = 2 + 2·x1   
POL(U31(x1, x2)) = 2 + 2·x1 + x2   
POL(U32(x1, x2)) = 1 + 2·x1 + x2   
POL(U33(x1)) = 2 + 2·x1   
POL(U41(x1, x2, x3)) = 2 + 2·x1 + x2 + x3   
POL(U42(x1, x2, x3)) = 1 + 2·x1 + x2 + x3   
POL(U43(x1, x2, x3)) = 1 + 2·x1 + x2 + x3   
POL(U44(x1, x2, x3)) = 2 + 2·x1 + x2 + x3   
POL(U45(x1, x2)) = 2 + 2·x1 + x2   
POL(U46(x1)) = 2 + 2·x1   
POL(U51(x1, x2, x3)) = 2 + 2·x1 + x2 + x3   
POL(U52(x1, x2, x3)) = 2 + 2·x1 + x2 + x3   
POL(U53(x1, x2, x3)) = 2 + 2·x1 + x2 + x3   
POL(U54(x1, x2, x3)) = 2 + 2·x1 + x2 + x3   
POL(U55(x1, x2)) = 1 + 2·x1 + x2   
POL(U56(x1)) = 2 + 2·x1   
POL(U61(x1, x2)) = 2 + 2·x1 + x2   
POL(U62(x1, x2)) = 2 + 2·x1 + x2   
POL(U63(x1)) = 1 + 2·x1   
POL(U71(x1, x2, x3)) = 2 + 2·x1 + x2 + x3   
POL(U72(x1, x2)) = 1 + 2·x1 + x2   
POL(U73(x1, x2)) = 2 + 2·x1 + x2   
POL(U74(x1)) = 1 + 2·x1   
POL(U81(x1, x2)) = 2 + 2·x1 + x2   
POL(U82(x1, x2)) = 2 + 2·x1 + x2   
POL(U83(x1)) = 2 + 2·x1   
POL(U91(x1, x2)) = 1 + 2·x1 + x2   
POL(U92(x1)) = 2 + 2·x1   
POL(__(x1, x2)) = 2 + 2·x1 + 2·x2   
POL(a__U11(x1, x2)) = 1 + 2·x1 + x2   
POL(a__U12(x1, x2)) = 1 + x1 + x2   
POL(a__U13(x1)) = 1 + 2·x1   
POL(a__U21(x1, x2, x3)) = 1 + 2·x1 + x2 + x3   
POL(a__U22(x1, x2, x3)) = 1 + 2·x1 + x2 + x3   
POL(a__U23(x1, x2, x3)) = 1 + 2·x1 + x2 + x3   
POL(a__U24(x1, x2, x3)) = 1 + 2·x1 + x2 + x3   
POL(a__U25(x1, x2)) = 1 + 2·x1 + x2   
POL(a__U26(x1)) = 1 + 2·x1   
POL(a__U31(x1, x2)) = 1 + 2·x1 + x2   
POL(a__U32(x1, x2)) = 1 + x1 + x2   
POL(a__U33(x1)) = 1 + 2·x1   
POL(a__U41(x1, x2, x3)) = 1 + 2·x1 + x2 + x3   
POL(a__U42(x1, x2, x3)) = 1 + x1 + x2 + x3   
POL(a__U43(x1, x2, x3)) = 1 + x1 + x2 + x3   
POL(a__U44(x1, x2, x3)) = 1 + 2·x1 + x2 + x3   
POL(a__U45(x1, x2)) = 1 + 2·x1 + x2   
POL(a__U46(x1)) = 1 + 2·x1   
POL(a__U51(x1, x2, x3)) = 1 + 2·x1 + x2 + x3   
POL(a__U52(x1, x2, x3)) = 1 + 2·x1 + x2 + x3   
POL(a__U53(x1, x2, x3)) = 1 + 2·x1 + x2 + x3   
POL(a__U54(x1, x2, x3)) = 1 + 2·x1 + x2 + x3   
POL(a__U55(x1, x2)) = 1 + x1 + x2   
POL(a__U56(x1)) = 1 + 2·x1   
POL(a__U61(x1, x2)) = 1 + 2·x1 + x2   
POL(a__U62(x1, x2)) = 1 + 2·x1 + x2   
POL(a__U63(x1)) = 1 + x1   
POL(a__U71(x1, x2, x3)) = 1 + 2·x1 + x2 + x3   
POL(a__U72(x1, x2)) = 1 + x1 + x2   
POL(a__U73(x1, x2)) = 1 + 2·x1 + x2   
POL(a__U74(x1)) = 1 + x1   
POL(a__U81(x1, x2)) = 1 + 2·x1 + x2   
POL(a__U82(x1, x2)) = 1 + 2·x1 + x2   
POL(a__U83(x1)) = 1 + 2·x1   
POL(a__U91(x1, x2)) = 1 + x1 + x2   
POL(a__U92(x1)) = 1 + 2·x1   
POL(a____(x1, x2)) = 1 + x1 + x2   
POL(a__isList(x1)) = 1 + x1   
POL(a__isNeList(x1)) = 1 + x1   
POL(a__isNePal(x1)) = 1 + x1   
POL(a__isPal(x1)) = 1 + x1   
POL(a__isPalListKind(x1)) = 1 + x1   
POL(a__isQid(x1)) = 1 + x1   
POL(e) = 1   
POL(isList(x1)) = 2 + x1   
POL(isNeList(x1)) = 2 + x1   
POL(isNePal(x1)) = 2 + x1   
POL(isPal(x1)) = 2 + x1   
POL(isPalListKind(x1)) = 2 + x1   
POL(isQid(x1)) = 2 + x1   
POL(mark(x1)) = 2 + 2·x1   
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X1, X2)) → a__U11(mark(X1), X2)
mark(U12(X1, X2)) → a__U12(mark(X1), X2)
mark(isPalListKind(X)) → a__isPalListKind(X)
mark(U13(X)) → a__U13(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U21(X1, X2, X3)) → a__U21(mark(X1), X2, X3)
mark(U22(X1, X2, X3)) → a__U22(mark(X1), X2, X3)
mark(U23(X1, X2, X3)) → a__U23(mark(X1), X2, X3)
mark(U24(X1, X2, X3)) → a__U24(mark(X1), X2, X3)
mark(U25(X1, X2)) → a__U25(mark(X1), X2)
mark(isList(X)) → a__isList(X)
mark(U26(X)) → a__U26(mark(X))
mark(U31(X1, X2)) → a__U31(mark(X1), X2)
mark(U32(X1, X2)) → a__U32(mark(X1), X2)
mark(U33(X)) → a__U33(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(U41(X1, X2, X3)) → a__U41(mark(X1), X2, X3)
mark(U42(X1, X2, X3)) → a__U42(mark(X1), X2, X3)
mark(U43(X1, X2, X3)) → a__U43(mark(X1), X2, X3)
mark(U44(X1, X2, X3)) → a__U44(mark(X1), X2, X3)
mark(U45(X1, X2)) → a__U45(mark(X1), X2)
mark(U46(X)) → a__U46(mark(X))
mark(U51(X1, X2, X3)) → a__U51(mark(X1), X2, X3)
mark(U52(X1, X2, X3)) → a__U52(mark(X1), X2, X3)
mark(U53(X1, X2, X3)) → a__U53(mark(X1), X2, X3)
mark(U54(X1, X2, X3)) → a__U54(mark(X1), X2, X3)
mark(U55(X1, X2)) → a__U55(mark(X1), X2)
mark(U56(X)) → a__U56(mark(X))
mark(U61(X1, X2)) → a__U61(mark(X1), X2)
mark(U62(X1, X2)) → a__U62(mark(X1), X2)
mark(U63(X)) → a__U63(mark(X))
mark(U71(X1, X2, X3)) → a__U71(mark(X1), X2, X3)
mark(U72(X1, X2)) → a__U72(mark(X1), X2)
mark(U73(X1, X2)) → a__U73(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(U74(X)) → a__U74(mark(X))
mark(U81(X1, X2)) → a__U81(mark(X1), X2)
mark(U82(X1, X2)) → a__U82(mark(X1), X2)
mark(U83(X)) → a__U83(mark(X))
mark(isNePal(X)) → a__isNePal(X)
mark(U91(X1, X2)) → a__U91(mark(X1), X2)
mark(U92(X)) → a__U92(mark(X))
mark(e) → e


(6) Obligation:

Q restricted rewrite system:
R is empty.
Q is empty.

(7) RisEmptyProof (EQUIVALENT transformation)

The TRS R is empty. Hence, termination is trivially proven.

(8) YES