/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


Termination of the given CSR could be proven:

(0) CSR
(1) CSRRRRProof [EQUIVALENT, 167 ms]
(2) CSR
(3) CSRRRRProof [EQUIVALENT, 0 ms]
(4) CSR
(5) CSRRRRProof [EQUIVALENT, 18 ms]
(6) CSR
(7) CSRRRRProof [EQUIVALENT, 15 ms]
(8) CSR
(9) CSRRRRProof [EQUIVALENT, 0 ms]
(10) CSR
(11) CSRRRRProof [EQUIVALENT, 0 ms]
(12) CSR
(13) CSRRRRProof [EQUIVALENT, 11 ms]
(14) CSR
(15) CSRRRRProof [EQUIVALENT, 9 ms]
(16) CSR
(17) CSRRRRProof [EQUIVALENT, 15 ms]
(18) CSR
(19) CSRRRRProof [EQUIVALENT, 14 ms]
(20) CSR
(21) CSRRRRProof [EQUIVALENT, 0 ms]
(22) CSR
(23) CSRRRRProof [EQUIVALENT, 0 ms]
(24) CSR
(25) CSRRRRProof [EQUIVALENT, 3 ms]
(26) CSR
(27) CSRRRRProof [EQUIVALENT, 0 ms]
(28) CSR
(29) CSRRRRProof [EQUIVALENT, 0 ms]
(30) CSR
(31) CSRRRRProof [EQUIVALENT, 0 ms]
(32) CSR
(33) CSRRRRProof [EQUIVALENT, 0 ms]
(34) CSR
(35) RisEmptyProof [EQUIVALENT, 0 ms]
(36) YES


----------------------------------------

(0)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   __(X, nil) -> X
   __(nil, X) -> X
   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U23(tt) -> tt
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U42(tt, V2) -> U43(isNeList(V2))
   U43(tt) -> tt
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   U52(tt, V2) -> U53(isList(V2))
   U53(tt) -> tt
   U61(tt, V) -> U62(isQid(V))
   U62(tt) -> tt
   U71(tt, V) -> U72(isNePal(V))
   U72(tt) -> tt
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(nil) -> tt
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNePal(V) -> U61(isPalListKind(V), V)
   isNePal(__(I, __(P, I))) -> and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P)))
   isPal(V) -> U71(isPalListKind(V), V)
   isPal(nil) -> tt
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
   isQid(a) -> tt
   isQid(e) -> tt
   isQid(i) -> tt
   isQid(o) -> tt
   isQid(u) -> tt

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U43: {1}
U51: {1}
U52: {1}
U53: {1}
U61: {1}
U62: {1}
U71: {1}
U72: {1}
isNePal: empty set
and: {1}
isPalListKind: empty set
isPal: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set

----------------------------------------

(1) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   __(X, nil) -> X
   __(nil, X) -> X
   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U23(tt) -> tt
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U42(tt, V2) -> U43(isNeList(V2))
   U43(tt) -> tt
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   U52(tt, V2) -> U53(isList(V2))
   U53(tt) -> tt
   U61(tt, V) -> U62(isQid(V))
   U62(tt) -> tt
   U71(tt, V) -> U72(isNePal(V))
   U72(tt) -> tt
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(nil) -> tt
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNePal(V) -> U61(isPalListKind(V), V)
   isNePal(__(I, __(P, I))) -> and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P)))
   isPal(V) -> U71(isPalListKind(V), V)
   isPal(nil) -> tt
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))
   isQid(a) -> tt
   isQid(e) -> tt
   isQid(i) -> tt
   isQid(o) -> tt
   isQid(u) -> tt

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U43: {1}
U51: {1}
U52: {1}
U53: {1}
U61: {1}
U62: {1}
U71: {1}
U72: {1}
isNePal: empty set
and: {1}
isPalListKind: empty set
isPal: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set
Used ordering:
Polynomial interpretation [POLO]:

   POL(U11(x_1, x_2)) = x_1 + x_2
   POL(U12(x_1)) = x_1
   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
   POL(U23(x_1)) = 1 + x_1
   POL(U31(x_1, x_2)) = x_1 + x_2
   POL(U32(x_1)) = x_1
   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
   POL(U43(x_1)) = 1 + x_1
   POL(U51(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U52(x_1, x_2)) = 1 + x_1 + x_2
   POL(U53(x_1)) = 1 + x_1
   POL(U61(x_1, x_2)) = 1 + x_1 + x_2
   POL(U62(x_1)) = 1 + x_1
   POL(U71(x_1, x_2)) = 1 + x_1 + x_2
   POL(U72(x_1)) = x_1
   POL(__(x_1, x_2)) = 1 + x_1 + x_2
   POL(a) = 1
   POL(and(x_1, x_2)) = x_1 + x_2
   POL(e) = 1
   POL(i) = 1
   POL(isList(x_1)) = x_1
   POL(isNeList(x_1)) = x_1
   POL(isNePal(x_1)) = 1 + x_1
   POL(isPal(x_1)) = 1 + x_1
   POL(isPalListKind(x_1)) = 0
   POL(isQid(x_1)) = x_1
   POL(nil) = 1
   POL(o) = 1
   POL(tt) = 0
   POL(u) = 1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   __(X, nil) -> X
   __(nil, X) -> X
   U23(tt) -> tt
   U43(tt) -> tt
   U53(tt) -> tt
   U62(tt) -> tt
   isList(nil) -> tt
   isNePal(__(I, __(P, I))) -> and(and(isQid(I), isPalListKind(I)), and(isPal(P), isPalListKind(P)))
   isPal(nil) -> tt
   isQid(a) -> tt
   isQid(e) -> tt
   isQid(i) -> tt
   isQid(o) -> tt
   isQid(u) -> tt




----------------------------------------

(2)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U42(tt, V2) -> U43(isNeList(V2))
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   U52(tt, V2) -> U53(isList(V2))
   U61(tt, V) -> U62(isQid(V))
   U71(tt, V) -> U72(isNePal(V))
   U72(tt) -> tt
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNePal(V) -> U61(isPalListKind(V), V)
   isPal(V) -> U71(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U43: {1}
U51: {1}
U52: {1}
U53: {1}
U61: {1}
U62: {1}
U71: {1}
U72: {1}
isNePal: empty set
and: {1}
isPalListKind: empty set
isPal: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set

----------------------------------------

(3) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U42(tt, V2) -> U43(isNeList(V2))
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   U52(tt, V2) -> U53(isList(V2))
   U61(tt, V) -> U62(isQid(V))
   U71(tt, V) -> U72(isNePal(V))
   U72(tt) -> tt
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNePal(V) -> U61(isPalListKind(V), V)
   isPal(V) -> U71(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U43: {1}
U51: {1}
U52: {1}
U53: {1}
U61: {1}
U62: {1}
U71: {1}
U72: {1}
isNePal: empty set
and: {1}
isPalListKind: empty set
isPal: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set
Used ordering:
Polynomial interpretation [POLO]:

   POL(U11(x_1, x_2)) = x_1 + x_2
   POL(U12(x_1)) = x_1
   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
   POL(U23(x_1)) = 1 + x_1
   POL(U31(x_1, x_2)) = x_1 + x_2
   POL(U32(x_1)) = x_1
   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
   POL(U43(x_1)) = x_1
   POL(U51(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U52(x_1, x_2)) = 1 + x_1 + x_2
   POL(U53(x_1)) = 1 + x_1
   POL(U61(x_1, x_2)) = 1 + x_1 + x_2
   POL(U62(x_1)) = 1 + x_1
   POL(U71(x_1, x_2)) = 1 + x_1 + x_2
   POL(U72(x_1)) = x_1
   POL(__(x_1, x_2)) = 1 + x_1 + x_2
   POL(a) = 1
   POL(and(x_1, x_2)) = x_1 + x_2
   POL(e) = 1
   POL(i) = 1
   POL(isList(x_1)) = x_1
   POL(isNeList(x_1)) = x_1
   POL(isNePal(x_1)) = 1 + x_1
   POL(isPal(x_1)) = 1 + x_1
   POL(isPalListKind(x_1)) = 0
   POL(isQid(x_1)) = x_1
   POL(nil) = 1
   POL(o) = 1
   POL(tt) = 0
   POL(u) = 1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   U42(tt, V2) -> U43(isNeList(V2))




----------------------------------------

(4)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   U52(tt, V2) -> U53(isList(V2))
   U61(tt, V) -> U62(isQid(V))
   U71(tt, V) -> U72(isNePal(V))
   U72(tt) -> tt
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNePal(V) -> U61(isPalListKind(V), V)
   isPal(V) -> U71(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U51: {1}
U52: {1}
U53: {1}
U61: {1}
U62: {1}
U71: {1}
U72: {1}
isNePal: empty set
and: {1}
isPalListKind: empty set
isPal: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set

----------------------------------------

(5) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   U52(tt, V2) -> U53(isList(V2))
   U61(tt, V) -> U62(isQid(V))
   U71(tt, V) -> U72(isNePal(V))
   U72(tt) -> tt
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNePal(V) -> U61(isPalListKind(V), V)
   isPal(V) -> U71(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U51: {1}
U52: {1}
U53: {1}
U61: {1}
U62: {1}
U71: {1}
U72: {1}
isNePal: empty set
and: {1}
isPalListKind: empty set
isPal: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set
Used ordering:
Polynomial interpretation [POLO]:

   POL(U11(x_1, x_2)) = x_1 + x_2
   POL(U12(x_1)) = x_1
   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
   POL(U23(x_1)) = 1 + x_1
   POL(U31(x_1, x_2)) = x_1 + x_2
   POL(U32(x_1)) = x_1
   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
   POL(U51(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U52(x_1, x_2)) = 1 + x_1 + x_2
   POL(U53(x_1)) = 1 + x_1
   POL(U61(x_1, x_2)) = 1 + x_1 + x_2
   POL(U62(x_1)) = x_1
   POL(U71(x_1, x_2)) = 1 + x_1 + x_2
   POL(U72(x_1)) = x_1
   POL(__(x_1, x_2)) = 1 + x_1 + x_2
   POL(a) = 1
   POL(and(x_1, x_2)) = x_1 + x_2
   POL(e) = 1
   POL(i) = 1
   POL(isList(x_1)) = x_1
   POL(isNeList(x_1)) = x_1
   POL(isNePal(x_1)) = 1 + x_1
   POL(isPal(x_1)) = 1 + x_1
   POL(isPalListKind(x_1)) = 0
   POL(isQid(x_1)) = x_1
   POL(nil) = 1
   POL(o) = 1
   POL(tt) = 0
   POL(u) = 1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   U61(tt, V) -> U62(isQid(V))




----------------------------------------

(6)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   U52(tt, V2) -> U53(isList(V2))
   U71(tt, V) -> U72(isNePal(V))
   U72(tt) -> tt
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNePal(V) -> U61(isPalListKind(V), V)
   isPal(V) -> U71(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U51: {1}
U52: {1}
U53: {1}
U61: {1}
U71: {1}
U72: {1}
isNePal: empty set
and: {1}
isPalListKind: empty set
isPal: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set

----------------------------------------

(7) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   U52(tt, V2) -> U53(isList(V2))
   U71(tt, V) -> U72(isNePal(V))
   U72(tt) -> tt
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNePal(V) -> U61(isPalListKind(V), V)
   isPal(V) -> U71(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U51: {1}
U52: {1}
U53: {1}
U61: {1}
U71: {1}
U72: {1}
isNePal: empty set
and: {1}
isPalListKind: empty set
isPal: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set
Used ordering:
Polynomial interpretation [POLO]:

   POL(U11(x_1, x_2)) = x_1 + x_2
   POL(U12(x_1)) = x_1
   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
   POL(U23(x_1)) = 1 + x_1
   POL(U31(x_1, x_2)) = x_1 + x_2
   POL(U32(x_1)) = x_1
   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
   POL(U51(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U52(x_1, x_2)) = 1 + x_1 + x_2
   POL(U53(x_1)) = 1 + x_1
   POL(U61(x_1, x_2)) = x_1 + x_2
   POL(U71(x_1, x_2)) = 1 + x_1 + x_2
   POL(U72(x_1)) = 1 + x_1
   POL(__(x_1, x_2)) = 1 + x_1 + x_2
   POL(a) = 1
   POL(and(x_1, x_2)) = x_1 + x_2
   POL(e) = 1
   POL(i) = 1
   POL(isList(x_1)) = x_1
   POL(isNeList(x_1)) = x_1
   POL(isNePal(x_1)) = x_1
   POL(isPal(x_1)) = 1 + x_1
   POL(isPalListKind(x_1)) = 0
   POL(isQid(x_1)) = x_1
   POL(nil) = 1
   POL(o) = 1
   POL(tt) = 0
   POL(u) = 1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   U72(tt) -> tt




----------------------------------------

(8)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   U52(tt, V2) -> U53(isList(V2))
   U71(tt, V) -> U72(isNePal(V))
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNePal(V) -> U61(isPalListKind(V), V)
   isPal(V) -> U71(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U51: {1}
U52: {1}
U53: {1}
U61: {1}
U71: {1}
U72: {1}
isNePal: empty set
and: {1}
isPalListKind: empty set
isPal: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set

----------------------------------------

(9) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   U52(tt, V2) -> U53(isList(V2))
   U71(tt, V) -> U72(isNePal(V))
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNePal(V) -> U61(isPalListKind(V), V)
   isPal(V) -> U71(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U51: {1}
U52: {1}
U53: {1}
U61: {1}
U71: {1}
U72: {1}
isNePal: empty set
and: {1}
isPalListKind: empty set
isPal: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set
Used ordering:
Polynomial interpretation [POLO]:

   POL(U11(x_1, x_2)) = x_1 + x_2
   POL(U12(x_1)) = x_1
   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
   POL(U23(x_1)) = 1 + x_1
   POL(U31(x_1, x_2)) = x_1 + x_2
   POL(U32(x_1)) = x_1
   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
   POL(U51(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U52(x_1, x_2)) = 1 + x_1 + x_2
   POL(U53(x_1)) = x_1
   POL(U61(x_1, x_2)) = 1 + x_1 + x_2
   POL(U71(x_1, x_2)) = 1 + x_1 + x_2
   POL(U72(x_1)) = x_1
   POL(__(x_1, x_2)) = 1 + x_1 + x_2
   POL(a) = 1
   POL(and(x_1, x_2)) = x_1 + x_2
   POL(e) = 1
   POL(i) = 1
   POL(isList(x_1)) = x_1
   POL(isNeList(x_1)) = x_1
   POL(isNePal(x_1)) = 1 + x_1
   POL(isPal(x_1)) = 1 + x_1
   POL(isPalListKind(x_1)) = 0
   POL(isQid(x_1)) = x_1
   POL(nil) = 1
   POL(o) = 1
   POL(tt) = 0
   POL(u) = 1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   U52(tt, V2) -> U53(isList(V2))




----------------------------------------

(10)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   U71(tt, V) -> U72(isNePal(V))
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNePal(V) -> U61(isPalListKind(V), V)
   isPal(V) -> U71(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U51: {1}
U52: {1}
U61: {1}
U71: {1}
U72: {1}
isNePal: empty set
and: {1}
isPalListKind: empty set
isPal: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set

----------------------------------------

(11) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   U71(tt, V) -> U72(isNePal(V))
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNePal(V) -> U61(isPalListKind(V), V)
   isPal(V) -> U71(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U51: {1}
U52: {1}
U61: {1}
U71: {1}
U72: {1}
isNePal: empty set
and: {1}
isPalListKind: empty set
isPal: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set
Used ordering:
Polynomial interpretation [POLO]:

   POL(U11(x_1, x_2)) = x_1 + x_2
   POL(U12(x_1)) = x_1
   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
   POL(U23(x_1)) = 1 + x_1
   POL(U31(x_1, x_2)) = x_1 + x_2
   POL(U32(x_1)) = x_1
   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
   POL(U51(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U52(x_1, x_2)) = 1 + x_1 + x_2
   POL(U61(x_1, x_2)) = x_1 + x_2
   POL(U71(x_1, x_2)) = 1 + x_1 + x_2
   POL(U72(x_1)) = x_1
   POL(__(x_1, x_2)) = 1 + x_1 + x_2
   POL(a) = 1
   POL(and(x_1, x_2)) = x_1 + x_2
   POL(e) = 1
   POL(i) = 1
   POL(isList(x_1)) = x_1
   POL(isNeList(x_1)) = x_1
   POL(isNePal(x_1)) = 1 + x_1
   POL(isPal(x_1)) = 1 + x_1
   POL(isPalListKind(x_1)) = 0
   POL(isQid(x_1)) = x_1
   POL(nil) = 1
   POL(o) = 1
   POL(tt) = 0
   POL(u) = 1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   isNePal(V) -> U61(isPalListKind(V), V)




----------------------------------------

(12)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   U71(tt, V) -> U72(isNePal(V))
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isPal(V) -> U71(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U51: {1}
U52: {1}
U71: {1}
U72: {1}
isNePal: empty set
and: {1}
isPalListKind: empty set
isPal: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set

----------------------------------------

(13) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   U71(tt, V) -> U72(isNePal(V))
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isPal(V) -> U71(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U51: {1}
U52: {1}
U71: {1}
U72: {1}
isNePal: empty set
and: {1}
isPalListKind: empty set
isPal: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set
Used ordering:
Polynomial interpretation [POLO]:

   POL(U11(x_1, x_2)) = x_1 + x_2
   POL(U12(x_1)) = x_1
   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
   POL(U23(x_1)) = 1 + x_1
   POL(U31(x_1, x_2)) = x_1 + x_2
   POL(U32(x_1)) = x_1
   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
   POL(U51(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U52(x_1, x_2)) = 1 + x_1 + x_2
   POL(U71(x_1, x_2)) = 1 + x_1 + x_2
   POL(U72(x_1)) = x_1
   POL(__(x_1, x_2)) = 1 + x_1 + x_2
   POL(a) = 1
   POL(and(x_1, x_2)) = x_1 + x_2
   POL(e) = 1
   POL(i) = 1
   POL(isList(x_1)) = x_1
   POL(isNeList(x_1)) = x_1
   POL(isNePal(x_1)) = x_1
   POL(isPal(x_1)) = 1 + x_1
   POL(isPalListKind(x_1)) = 0
   POL(isQid(x_1)) = x_1
   POL(nil) = 1
   POL(o) = 1
   POL(tt) = 0
   POL(u) = 1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   U71(tt, V) -> U72(isNePal(V))




----------------------------------------

(14)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isPal(V) -> U71(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U51: {1}
U52: {1}
U71: {1}
and: {1}
isPalListKind: empty set
isPal: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set

----------------------------------------

(15) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isPal(V) -> U71(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U51: {1}
U52: {1}
U71: {1}
and: {1}
isPalListKind: empty set
isPal: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set
Used ordering:
Polynomial interpretation [POLO]:

   POL(U11(x_1, x_2)) = x_1 + x_2
   POL(U12(x_1)) = x_1
   POL(U21(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U22(x_1, x_2)) = 1 + x_1 + x_2
   POL(U23(x_1)) = 1 + x_1
   POL(U31(x_1, x_2)) = x_1 + x_2
   POL(U32(x_1)) = x_1
   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U42(x_1, x_2)) = 1 + x_1 + x_2
   POL(U51(x_1, x_2, x_3)) = 1 + x_1 + x_2 + x_3
   POL(U52(x_1, x_2)) = 1 + x_1 + x_2
   POL(U71(x_1, x_2)) = x_1 + x_2
   POL(__(x_1, x_2)) = 1 + x_1 + x_2
   POL(a) = 1
   POL(and(x_1, x_2)) = x_1 + x_2
   POL(e) = 1
   POL(i) = 1
   POL(isList(x_1)) = x_1
   POL(isNeList(x_1)) = x_1
   POL(isPal(x_1)) = 1 + x_1
   POL(isPalListKind(x_1)) = 0
   POL(isQid(x_1)) = x_1
   POL(nil) = 1
   POL(o) = 1
   POL(tt) = 0
   POL(u) = 1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   isPal(V) -> U71(isPalListKind(V), V)




----------------------------------------

(16)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U51: {1}
U52: {1}
and: {1}
isPalListKind: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set

----------------------------------------

(17) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U51: {1}
U52: {1}
and: {1}
isPalListKind: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set
Used ordering:
Polynomial interpretation [POLO]:

   POL(U11(x_1, x_2)) = x_1
   POL(U12(x_1)) = 2*x_1
   POL(U21(x_1, x_2, x_3)) = 2*x_1
   POL(U22(x_1, x_2)) = 2*x_1
   POL(U23(x_1)) = 2*x_1
   POL(U31(x_1, x_2)) = x_1
   POL(U32(x_1)) = 2*x_1
   POL(U41(x_1, x_2, x_3)) = 2*x_1
   POL(U42(x_1, x_2)) = 2*x_1
   POL(U51(x_1, x_2, x_3)) = 2*x_1
   POL(U52(x_1, x_2)) = x_1
   POL(__(x_1, x_2)) = 1 + 2*x_1 + x_2
   POL(a) = 2
   POL(and(x_1, x_2)) = 2*x_1 + 2*x_2
   POL(e) = 2
   POL(i) = 2
   POL(isList(x_1)) = 0
   POL(isNeList(x_1)) = 0
   POL(isPalListKind(x_1)) = 0
   POL(isQid(x_1)) = 0
   POL(nil) = 2
   POL(o) = 2
   POL(tt) = 0
   POL(u) = 2
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   __(__(X, Y), Z) -> __(X, __(Y, Z))




----------------------------------------

(18)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U51: {1}
U52: {1}
and: {1}
isPalListKind: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set

----------------------------------------

(19) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U22(tt, V2) -> U23(isList(V2))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(V) -> U31(isPalListKind(V), V)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U23: {1}
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U51: {1}
U52: {1}
and: {1}
isPalListKind: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set
Used ordering:
Polynomial interpretation [POLO]:

   POL(U11(x_1, x_2)) = 2*x_1 + 2*x_2
   POL(U12(x_1)) = 2*x_1
   POL(U21(x_1, x_2, x_3)) = 1 + 2*x_1 + 2*x_2 + 2*x_3
   POL(U22(x_1, x_2)) = 1 + x_1 + 2*x_2
   POL(U23(x_1)) = x_1
   POL(U31(x_1, x_2)) = 2*x_1 + x_2
   POL(U32(x_1)) = x_1
   POL(U41(x_1, x_2, x_3)) = 2*x_1 + 2*x_2
   POL(U42(x_1, x_2)) = x_1
   POL(U51(x_1, x_2, x_3)) = 2*x_1 + 2*x_2
   POL(U52(x_1, x_2)) = 2*x_1
   POL(__(x_1, x_2)) = 1 + 2*x_1 + 2*x_2
   POL(a) = 2
   POL(and(x_1, x_2)) = 2*x_1 + 2*x_2
   POL(e) = 2
   POL(i) = 2
   POL(isList(x_1)) = 2*x_1
   POL(isNeList(x_1)) = x_1
   POL(isPalListKind(x_1)) = 0
   POL(isQid(x_1)) = 0
   POL(nil) = 2
   POL(o) = 2
   POL(tt) = 0
   POL(u) = 2
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   U22(tt, V2) -> U23(isList(V2))
   isList(__(V1, V2)) -> U21(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U41(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)
   isNeList(__(V1, V2)) -> U51(and(isPalListKind(V1), isPalListKind(V2)), V1, V2)




----------------------------------------

(20)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isNeList(V) -> U31(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U51: {1}
U52: {1}
and: {1}
isPalListKind: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set

----------------------------------------

(21) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isNeList(V) -> U31(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U21: {1}
U22: {1}
isList: empty set
U31: {1}
U32: {1}
isQid: empty set
U41: {1}
U42: {1}
U51: {1}
U52: {1}
and: {1}
isPalListKind: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set
Used ordering:
Polynomial interpretation [POLO]:

   POL(U11(x_1, x_2)) = 2*x_1
   POL(U12(x_1)) = 2*x_1
   POL(U21(x_1, x_2, x_3)) = 2 + 2*x_1 + 2*x_2 + 2*x_3
   POL(U22(x_1, x_2)) = 1 + 2*x_1 + 2*x_2
   POL(U31(x_1, x_2)) = 2*x_1
   POL(U32(x_1)) = x_1
   POL(U41(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3
   POL(U42(x_1, x_2)) = 2*x_1 + 2*x_2
   POL(U51(x_1, x_2, x_3)) = 1 + 2*x_1 + 2*x_2 + 2*x_3
   POL(U52(x_1, x_2)) = x_1 + 2*x_2
   POL(__(x_1, x_2)) = 2 + 2*x_1 + 2*x_2
   POL(a) = 2
   POL(and(x_1, x_2)) = x_1 + 2*x_2
   POL(e) = 2
   POL(i) = 2
   POL(isList(x_1)) = x_1
   POL(isNeList(x_1)) = 0
   POL(isPalListKind(x_1)) = 0
   POL(isQid(x_1)) = 0
   POL(nil) = 2
   POL(o) = 2
   POL(tt) = 0
   POL(u) = 2
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   U21(tt, V1, V2) -> U22(isList(V1), V2)
   U41(tt, V1, V2) -> U42(isList(V1), V2)
   U51(tt, V1, V2) -> U52(isNeList(V1), V2)




----------------------------------------

(22)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isNeList(V) -> U31(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
isList: empty set
U31: {1}
U32: {1}
isQid: empty set
and: {1}
isPalListKind: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set

----------------------------------------

(23) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   U11(tt, V) -> U12(isNeList(V))
   U12(tt) -> tt
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   and(tt, X) -> X
   isList(V) -> U11(isPalListKind(V), V)
   isNeList(V) -> U31(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
isList: empty set
U31: {1}
U32: {1}
isQid: empty set
and: {1}
isPalListKind: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set
Used ordering:
Polynomial interpretation [POLO]:

   POL(U11(x_1, x_2)) = 1 + x_1 + 2*x_2
   POL(U12(x_1)) = 1 + 2*x_1
   POL(U31(x_1, x_2)) = 2*x_1
   POL(U32(x_1)) = 2*x_1
   POL(__(x_1, x_2)) = 2 + x_1 + x_2
   POL(a) = 2
   POL(and(x_1, x_2)) = x_1 + 2*x_2
   POL(e) = 2
   POL(i) = 2
   POL(isList(x_1)) = 2 + 2*x_1
   POL(isNeList(x_1)) = 0
   POL(isPalListKind(x_1)) = 0
   POL(isQid(x_1)) = 0
   POL(nil) = 2
   POL(o) = 2
   POL(tt) = 0
   POL(u) = 2
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   U12(tt) -> tt
   isList(V) -> U11(isPalListKind(V), V)




----------------------------------------

(24)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   U11(tt, V) -> U12(isNeList(V))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   and(tt, X) -> X
   isNeList(V) -> U31(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U31: {1}
U32: {1}
isQid: empty set
and: {1}
isPalListKind: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set

----------------------------------------

(25) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   U11(tt, V) -> U12(isNeList(V))
   U31(tt, V) -> U32(isQid(V))
   U32(tt) -> tt
   and(tt, X) -> X
   isNeList(V) -> U31(isPalListKind(V), V)
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U31: {1}
U32: {1}
isQid: empty set
and: {1}
isPalListKind: empty set
a: empty set
e: empty set
i: empty set
o: empty set
u: empty set
Used ordering:
Polynomial interpretation [POLO]:

   POL(U11(x_1, x_2)) = 1 + x_1 + x_2
   POL(U12(x_1)) = 1 + x_1
   POL(U31(x_1, x_2)) = x_1
   POL(U32(x_1)) = 1 + x_1
   POL(__(x_1, x_2)) = 1 + x_1 + x_2
   POL(a) = 1
   POL(and(x_1, x_2)) = x_1 + x_2
   POL(e) = 1
   POL(i) = 1
   POL(isNeList(x_1)) = 1 + x_1
   POL(isPalListKind(x_1)) = 1 + x_1
   POL(isQid(x_1)) = 0
   POL(nil) = 1
   POL(o) = 1
   POL(tt) = 1
   POL(u) = 1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   U32(tt) -> tt
   and(tt, X) -> X
   isPalListKind(a) -> tt
   isPalListKind(e) -> tt
   isPalListKind(i) -> tt
   isPalListKind(nil) -> tt
   isPalListKind(o) -> tt
   isPalListKind(u) -> tt




----------------------------------------

(26)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   U11(tt, V) -> U12(isNeList(V))
   U31(tt, V) -> U32(isQid(V))
   isNeList(V) -> U31(isPalListKind(V), V)
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U31: {1}
U32: {1}
isQid: empty set
and: {1}
isPalListKind: empty set

----------------------------------------

(27) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   U11(tt, V) -> U12(isNeList(V))
   U31(tt, V) -> U32(isQid(V))
   isNeList(V) -> U31(isPalListKind(V), V)
   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))

The replacement map contains the following entries:

__: {1, 2}
U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U31: {1}
U32: {1}
isQid: empty set
and: {1}
isPalListKind: empty set
Used ordering:
Polynomial interpretation [POLO]:

   POL(U11(x_1, x_2)) = 1 + x_1 + x_2
   POL(U12(x_1)) = 1 + x_1
   POL(U31(x_1, x_2)) = 1 + x_1
   POL(U32(x_1)) = 1 + x_1
   POL(__(x_1, x_2)) = 1 + x_1 + x_2
   POL(and(x_1, x_2)) = x_1 + x_2
   POL(isNeList(x_1)) = 1 + x_1
   POL(isPalListKind(x_1)) = x_1
   POL(isQid(x_1)) = 1
   POL(tt) = 1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   isPalListKind(__(V1, V2)) -> and(isPalListKind(V1), isPalListKind(V2))




----------------------------------------

(28)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   U11(tt, V) -> U12(isNeList(V))
   U31(tt, V) -> U32(isQid(V))
   isNeList(V) -> U31(isPalListKind(V), V)

The replacement map contains the following entries:

U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U31: {1}
U32: {1}
isQid: empty set
isPalListKind: empty set

----------------------------------------

(29) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   U11(tt, V) -> U12(isNeList(V))
   U31(tt, V) -> U32(isQid(V))
   isNeList(V) -> U31(isPalListKind(V), V)

The replacement map contains the following entries:

U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U31: {1}
U32: {1}
isQid: empty set
isPalListKind: empty set
Used ordering:
Polynomial interpretation [POLO]:

   POL(U11(x_1, x_2)) = 1 + x_1 + x_2
   POL(U12(x_1)) = 1 + x_1
   POL(U31(x_1, x_2)) = 1 + x_1
   POL(U32(x_1)) = x_1
   POL(isNeList(x_1)) = 1 + x_1
   POL(isPalListKind(x_1)) = x_1
   POL(isQid(x_1)) = 0
   POL(tt) = 1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   U31(tt, V) -> U32(isQid(V))




----------------------------------------

(30)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   U11(tt, V) -> U12(isNeList(V))
   isNeList(V) -> U31(isPalListKind(V), V)

The replacement map contains the following entries:

U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U31: {1}
isPalListKind: empty set

----------------------------------------

(31) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   U11(tt, V) -> U12(isNeList(V))
   isNeList(V) -> U31(isPalListKind(V), V)

The replacement map contains the following entries:

U11: {1}
tt: empty set
U12: {1}
isNeList: empty set
U31: {1}
isPalListKind: empty set
Used ordering:
Polynomial interpretation [POLO]:

   POL(U11(x_1, x_2)) = 2 + 2*x_1 + 2*x_2
   POL(U12(x_1)) = 2*x_1
   POL(U31(x_1, x_2)) = x_1
   POL(isNeList(x_1)) = x_1
   POL(isPalListKind(x_1)) = x_1
   POL(tt) = 2
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   U11(tt, V) -> U12(isNeList(V))




----------------------------------------

(32)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   isNeList(V) -> U31(isPalListKind(V), V)

The replacement map contains the following entries:

isNeList: empty set
U31: {1}
isPalListKind: empty set

----------------------------------------

(33) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   isNeList(V) -> U31(isPalListKind(V), V)

The replacement map contains the following entries:

isNeList: empty set
U31: {1}
isPalListKind: empty set
Used ordering:
Polynomial interpretation [POLO]:

   POL(U31(x_1, x_2)) = 1 + 2*x_1
   POL(isNeList(x_1)) = 2 + 2*x_1
   POL(isPalListKind(x_1)) = x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   isNeList(V) -> U31(isPalListKind(V), V)




----------------------------------------

(34)
Obligation:
Context-sensitive rewrite system:
R is empty.

----------------------------------------

(35) RisEmptyProof (EQUIVALENT)
The CSR R is empty. Hence, termination is trivially proven.
----------------------------------------

(36)
YES