Termination w.r.t. Q proof of Transformed_CSR_04_PALINDROME_nokinds_noand

Termination w.r.t. Q of the given QTRS could be proven:

0 QTRS

↳1 QTRSRRRProof (⇔, 85 ms)

↳2 QTRS

↳3 QTRSRRRProof (⇔, 2 ms)

↳4 QTRS

↳5 QTRSRRRProof (⇔, 14 ms)

↳6 QTRS

↳7 QTRSRRRProof (⇔, 0 ms)

↳8 QTRS

↳9 QTRSRRRProof (⇔, 0 ms)

↳10 QTRS

↳11 QTRSRRRProof (⇔, 0 ms)

↳12 QTRS

↳13 RisEmptyProof (⇔, 0 ms)

↳14 YES

(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) → tt
a__U21(tt, V2) → a__U22(a__isList(V2))
a__U22(tt) → tt
a__U31(tt) → tt
a__U41(tt, V2) → a__U42(a__isNeList(V2))
a__U42(tt) → tt
a__U51(tt, V2) → a__U52(a__isList(V2))
a__U52(tt) → tt
a__U61(tt) → tt
a__U71(tt, P) → a__U72(a__isPal(P))
a__U72(tt) → tt
a__U81(tt) → tt
a__isList(V) → a__U11(a__isNeList(V))
a__isList(nil) → tt
a__isList(__(V1, V2)) → a__U21(a__isList(V1), V2)
a__isNeList(V) → a__U31(a__isQid(V))
a__isNeList(__(V1, V2)) → a__U41(a__isList(V1), V2)
a__isNeList(__(V1, V2)) → a__U51(a__isNeList(V1), V2)
a__isNePal(V) → a__U61(a__isQid(V))
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), P)
a__isPal(V) → a__U81(a__isNePal(V))
a__isPal(nil) → tt
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(X)) → a__U11(mark(X))
mark(U21(X1, X2)) → a__U21(mark(X1), X2)
mark(U22(X)) → a__U22(mark(X))
mark(isList(X)) → a__isList(X)
mark(U31(X)) → a__U31(mark(X))
mark(U41(X1, X2)) → a__U41(mark(X1), X2)
mark(U42(X)) → a__U42(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U51(X1, X2)) → a__U51(mark(X1), X2)
mark(U52(X)) → a__U52(mark(X))
mark(U61(X)) → a__U61(mark(X))
mark(U71(X1, X2)) → a__U71(mark(X1), X2)
mark(U72(X)) → a__U72(mark(X))
mark(isPal(X)) → a__isPal(X)
mark(U81(X)) → a__U81(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(isNePal(X)) → a__isNePal(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(X) → U11(X)
a__U21(X1, X2) → U21(X1, X2)
a__U22(X) → U22(X)
a__isList(X) → isList(X)
a__U31(X) → U31(X)
a__U41(X1, X2) → U41(X1, X2)
a__U42(X) → U42(X)
a__isNeList(X) → isNeList(X)
a__U51(X1, X2) → U51(X1, X2)
a__U52(X) → U52(X)
a__U61(X) → U61(X)
a__U71(X1, X2) → U71(X1, X2)
a__U72(X) → U72(X)
a__isPal(X) → isPal(X)
a__U81(X) → U81(X)
a__isQid(X) → isQid(X)
a__isNePal(X) → isNePal(X)

Q is empty.

(1) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Polynomial interpretation [POLO]:

POL(U11(x₁)) = x₁
POL(U21(x₁, x₂)) = 2·x₁ + 2·x₂
POL(U22(x₁)) = 2 + x₁
POL(U31(x₁)) = 2·x₁
POL(U41(x₁, x₂)) = 2·x₁ + 2·x₂
POL(U42(x₁)) = 2 + x₁
POL(U51(x₁, x₂)) = x₁ + 2·x₂
POL(U52(x₁)) = x₁
POL(U61(x₁)) = x₁
POL(U71(x₁, x₂)) = x₁ + 2·x₂
POL(U72(x₁)) = x₁
POL(U81(x₁)) = 2 + x₁
POL(__(x₁, x₂)) = 2 + 2·x₁ + x₂
POL(a) = 2
POL(a__U11(x₁)) = x₁
POL(a__U21(x₁, x₂)) = 2·x₁ + 2·x₂
POL(a__U22(x₁)) = 2 + x₁
POL(a__U31(x₁)) = 2·x₁
POL(a__U41(x₁, x₂)) = 2·x₁ + 2·x₂
POL(a__U42(x₁)) = 2 + x₁
POL(a__U51(x₁, x₂)) = x₁ + 2·x₂
POL(a__U52(x₁)) = x₁
POL(a__U61(x₁)) = x₁
POL(a__U71(x₁, x₂)) = x₁ + 2·x₂
POL(a__U72(x₁)) = x₁
POL(a__U81(x₁)) = 2 + x₁
POL(a____(x₁, x₂)) = 2 + 2·x₁ + x₂
POL(a__isList(x₁)) = 2 + 2·x₁
POL(a__isNeList(x₁)) = 1 + 2·x₁
POL(a__isNePal(x₁)) = x₁
POL(a__isPal(x₁)) = 2 + 2·x₁
POL(a__isQid(x₁)) = x₁
POL(e) = 2
POL(i) = 2
POL(isList(x₁)) = 2 + 2·x₁
POL(isNeList(x₁)) = 1 + 2·x₁
POL(isNePal(x₁)) = x₁
POL(isPal(x₁)) = 2 + 2·x₁
POL(isQid(x₁)) = x₁
POL(mark(x₁)) = x₁
POL(nil) = 0
POL(o) = 2
POL(tt) = 2
POL(u) = 2

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__U22(tt) → tt
a__U31(tt) → tt
a__U41(tt, V2) → a__U42(a__isNeList(V2))
a__U42(tt) → tt
a__U81(tt) → tt
a__isList(V) → a__U11(a__isNeList(V))
a__isList(__(V1, V2)) → a__U21(a__isList(V1), V2)
a__isNeList(V) → a__U31(a__isQid(V))
a__isNeList(__(V1, V2)) → a__U41(a__isList(V1), V2)
a__isNeList(__(V1, V2)) → a__U51(a__isNeList(V1), V2)
a__isNePal(__(I, __(P, I))) → a__U71(a__isQid(I), P)

(2) Obligation:

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

a__U11(tt) → tt
a__U21(tt, V2) → a__U22(a__isList(V2))
a__U51(tt, V2) → a__U52(a__isList(V2))
a__U52(tt) → tt
a__U61(tt) → tt
a__U71(tt, P) → a__U72(a__isPal(P))
a__U72(tt) → tt
a__isList(nil) → tt
a__isNePal(V) → a__U61(a__isQid(V))
a__isPal(V) → a__U81(a__isNePal(V))
a__isPal(nil) → tt
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(X)) → a__U11(mark(X))
mark(U21(X1, X2)) → a__U21(mark(X1), X2)
mark(U22(X)) → a__U22(mark(X))
mark(isList(X)) → a__isList(X)
mark(U31(X)) → a__U31(mark(X))
mark(U41(X1, X2)) → a__U41(mark(X1), X2)
mark(U42(X)) → a__U42(mark(X))
mark(isNeList(X)) → a__isNeList(X)
mark(U51(X1, X2)) → a__U51(mark(X1), X2)
mark(U52(X)) → a__U52(mark(X))
mark(U61(X)) → a__U61(mark(X))
mark(U71(X1, X2)) → a__U71(mark(X1), X2)
mark(U72(X)) → a__U72(mark(X))
mark(isPal(X)) → a__isPal(X)
mark(U81(X)) → a__U81(mark(X))
mark(isQid(X)) → a__isQid(X)
mark(isNePal(X)) → a__isNePal(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(X) → U11(X)
a__U21(X1, X2) → U21(X1, X2)
a__U22(X) → U22(X)
a__isList(X) → isList(X)
a__U31(X) → U31(X)
a__U41(X1, X2) → U41(X1, X2)
a__U42(X) → U42(X)
a__isNeList(X) → isNeList(X)
a__U51(X1, X2) → U51(X1, X2)
a__U52(X) → U52(X)
a__U61(X) → U61(X)
a__U71(X1, X2) → U71(X1, X2)
a__U72(X) → U72(X)
a__isPal(X) → isPal(X)
a__U81(X) → U81(X)
a__isQid(X) → isQid(X)
a__isNePal(X) → isNePal(X)

Q is empty.

(3) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Polynomial interpretation [POLO]:

POL(U11(x₁)) = 2 + 2·x₁
POL(U21(x₁, x₂)) = 1 + x₁ + 2·x₂
POL(U22(x₁)) = 1 + x₁
POL(U31(x₁)) = 2 + x₁
POL(U41(x₁, x₂)) = 2 + x₁ + x₂
POL(U42(x₁)) = 2 + 2·x₁
POL(U51(x₁, x₂)) = 2 + x₁ + 2·x₂
POL(U52(x₁)) = 1 + x₁
POL(U61(x₁)) = x₁
POL(U71(x₁, x₂)) = 2 + x₁ + 2·x₂
POL(U72(x₁)) = x₁
POL(U81(x₁)) = x₁
POL(__(x₁, x₂)) = 2 + x₁ + x₂
POL(a) = 0
POL(a__U11(x₁)) = 2 + 2·x₁
POL(a__U21(x₁, x₂)) = 2 + x₁ + 2·x₂
POL(a__U22(x₁)) = 2 + x₁
POL(a__U31(x₁)) = 2 + x₁
POL(a__U41(x₁, x₂)) = 2 + x₁ + 2·x₂
POL(a__U42(x₁)) = 2 + 2·x₁
POL(a__U51(x₁, x₂)) = 2 + x₁ + 2·x₂
POL(a__U52(x₁)) = 2 + x₁
POL(a__U61(x₁)) = x₁
POL(a__U71(x₁, x₂)) = 2 + x₁ + 2·x₂
POL(a__U72(x₁)) = x₁
POL(a__U81(x₁)) = 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 + 2·x₁
POL(a__isPal(x₁)) = 2 + 2·x₁
POL(a__isQid(x₁)) = 2 + x₁
POL(e) = 1
POL(i) = 0
POL(isList(x₁)) = x₁
POL(isNeList(x₁)) = 1 + x₁
POL(isNePal(x₁)) = 1 + x₁
POL(isPal(x₁)) = 1 + x₁
POL(isQid(x₁)) = 1 + x₁
POL(mark(x₁)) = 2 + 2·x₁
POL(nil) = 2
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:

a__U11(tt) → tt
a__U52(tt) → tt
a__isList(nil) → tt
a__isPal(nil) → tt
a__isQid(a) → tt
a__isQid(e) → tt
a__isQid(i) → tt
a__isQid(o) → tt
a__isQid(u) → tt
mark(isList(X)) → a__isList(X)
mark(U31(X)) → a__U31(mark(X))
mark(U41(X1, X2)) → a__U41(mark(X1), X2)
mark(isNeList(X)) → a__isNeList(X)
mark(U51(X1, X2)) → a__U51(mark(X1), X2)
mark(U71(X1, X2)) → a__U71(mark(X1), X2)
mark(isPal(X)) → a__isPal(X)
mark(isQid(X)) → a__isQid(X)
mark(isNePal(X)) → a__isNePal(X)
mark(nil) → nil
mark(tt) → tt
mark(a) → a
mark(e) → e
mark(i) → i
mark(o) → o
mark(u) → u
a__U21(X1, X2) → U21(X1, X2)
a__U22(X) → U22(X)
a__isNeList(X) → isNeList(X)
a__U52(X) → U52(X)
a__isPal(X) → isPal(X)
a__isQid(X) → isQid(X)
a__isNePal(X) → isNePal(X)

(4) Obligation:

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

a__U21(tt, V2) → a__U22(a__isList(V2))
a__U51(tt, V2) → a__U52(a__isList(V2))
a__U61(tt) → tt
a__U71(tt, P) → a__U72(a__isPal(P))
a__U72(tt) → tt
a__isNePal(V) → a__U61(a__isQid(V))
a__isPal(V) → a__U81(a__isNePal(V))
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X)) → a__U11(mark(X))
mark(U21(X1, X2)) → a__U21(mark(X1), X2)
mark(U22(X)) → a__U22(mark(X))
mark(U42(X)) → a__U42(mark(X))
mark(U52(X)) → a__U52(mark(X))
mark(U61(X)) → a__U61(mark(X))
mark(U72(X)) → a__U72(mark(X))
mark(U81(X)) → a__U81(mark(X))
a____(X1, X2) → __(X1, X2)
a__U11(X) → U11(X)
a__isList(X) → isList(X)
a__U31(X) → U31(X)
a__U41(X1, X2) → U41(X1, X2)
a__U42(X) → U42(X)
a__U51(X1, X2) → U51(X1, X2)
a__U61(X) → U61(X)
a__U71(X1, X2) → U71(X1, X2)
a__U72(X) → U72(X)
a__U81(X) → U81(X)

Q is empty.

(5) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Polynomial interpretation [POLO]:

POL(U11(x₁)) = x₁
POL(U21(x₁, x₂)) = x₁ + 2·x₂
POL(U22(x₁)) = 2·x₁
POL(U31(x₁)) = x₁
POL(U41(x₁, x₂)) = 1 + x₁ + x₂
POL(U42(x₁)) = x₁
POL(U51(x₁, x₂)) = x₁ + x₂
POL(U52(x₁)) = 2·x₁
POL(U61(x₁)) = x₁
POL(U71(x₁, x₂)) = x₁ + 2·x₂
POL(U72(x₁)) = x₁
POL(U81(x₁)) = x₁
POL(__(x₁, x₂)) = x₁ + x₂
POL(a__U11(x₁)) = x₁
POL(a__U21(x₁, x₂)) = x₁ + 2·x₂
POL(a__U22(x₁)) = 2·x₁
POL(a__U31(x₁)) = 2 + 2·x₁
POL(a__U41(x₁, x₂)) = 2 + 2·x₁ + 2·x₂
POL(a__U42(x₁)) = x₁
POL(a__U51(x₁, x₂)) = 2·x₁ + 2·x₂
POL(a__U52(x₁)) = x₁
POL(a__U61(x₁)) = x₁
POL(a__U71(x₁, x₂)) = 2·x₁ + 2·x₂
POL(a__U72(x₁)) = x₁
POL(a__U81(x₁)) = x₁
POL(a____(x₁, x₂)) = x₁ + x₂
POL(a__isList(x₁)) = x₁
POL(a__isNePal(x₁)) = x₁
POL(a__isPal(x₁)) = x₁
POL(a__isQid(x₁)) = x₁
POL(isList(x₁)) = x₁
POL(mark(x₁)) = x₁
POL(tt) = 0

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

a__U31(X) → U31(X)
a__U41(X1, X2) → U41(X1, X2)

(6) Obligation:

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

a__U21(tt, V2) → a__U22(a__isList(V2))
a__U51(tt, V2) → a__U52(a__isList(V2))
a__U61(tt) → tt
a__U71(tt, P) → a__U72(a__isPal(P))
a__U72(tt) → tt
a__isNePal(V) → a__U61(a__isQid(V))
a__isPal(V) → a__U81(a__isNePal(V))
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U11(X)) → a__U11(mark(X))
mark(U21(X1, X2)) → a__U21(mark(X1), X2)
mark(U22(X)) → a__U22(mark(X))
mark(U42(X)) → a__U42(mark(X))
mark(U52(X)) → a__U52(mark(X))
mark(U61(X)) → a__U61(mark(X))
mark(U72(X)) → a__U72(mark(X))
mark(U81(X)) → a__U81(mark(X))
a____(X1, X2) → __(X1, X2)
a__U11(X) → U11(X)
a__isList(X) → isList(X)
a__U42(X) → U42(X)
a__U51(X1, X2) → U51(X1, X2)
a__U61(X) → U61(X)
a__U71(X1, X2) → U71(X1, X2)
a__U72(X) → U72(X)
a__U81(X) → U81(X)

Q is empty.

(7) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Polynomial interpretation [POLO]:

POL(U11(x₁)) = 1 + x₁
POL(U21(x₁, x₂)) = 2 + 2·x₁ + 2·x₂
POL(U22(x₁)) = 2 + 2·x₁
POL(U42(x₁)) = 2 + x₁
POL(U51(x₁, x₂)) = 1 + 2·x₁ + x₂
POL(U52(x₁)) = 2 + 2·x₁
POL(U61(x₁)) = x₁
POL(U71(x₁, x₂)) = 1 + x₁ + 2·x₂
POL(U72(x₁)) = x₁
POL(U81(x₁)) = 1 + x₁
POL(__(x₁, x₂)) = 2 + x₁ + x₂
POL(a__U11(x₁)) = 1 + x₁
POL(a__U21(x₁, x₂)) = 1 + 2·x₁ + 2·x₂
POL(a__U22(x₁)) = 1 + 2·x₁
POL(a__U42(x₁)) = 2 + x₁
POL(a__U51(x₁, x₂)) = 2 + 2·x₁ + 2·x₂
POL(a__U52(x₁)) = 1 + 2·x₁
POL(a__U61(x₁)) = x₁
POL(a__U71(x₁, x₂)) = 2 + 2·x₁ + 2·x₂
POL(a__U72(x₁)) = x₁
POL(a__U81(x₁)) = 2 + x₁
POL(a____(x₁, x₂)) = 2 + x₁ + x₂
POL(a__isList(x₁)) = x₁
POL(a__isNePal(x₁)) = x₁
POL(a__isPal(x₁)) = 2 + x₁
POL(a__isQid(x₁)) = x₁
POL(isList(x₁)) = x₁
POL(mark(x₁)) = 2 + 2·x₁
POL(tt) = 0

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

a__U51(tt, V2) → a__U52(a__isList(V2))
mark(U11(X)) → a__U11(mark(X))
mark(U21(X1, X2)) → a__U21(mark(X1), X2)
mark(U22(X)) → a__U22(mark(X))
mark(U42(X)) → a__U42(mark(X))
mark(U52(X)) → a__U52(mark(X))
a__U51(X1, X2) → U51(X1, X2)
a__U71(X1, X2) → U71(X1, X2)
a__U81(X) → U81(X)

(8) Obligation:

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

a__U21(tt, V2) → a__U22(a__isList(V2))
a__U61(tt) → tt
a__U71(tt, P) → a__U72(a__isPal(P))
a__U72(tt) → tt
a__isNePal(V) → a__U61(a__isQid(V))
a__isPal(V) → a__U81(a__isNePal(V))
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U61(X)) → a__U61(mark(X))
mark(U72(X)) → a__U72(mark(X))
mark(U81(X)) → a__U81(mark(X))
a____(X1, X2) → __(X1, X2)
a__U11(X) → U11(X)
a__isList(X) → isList(X)
a__U42(X) → U42(X)
a__U61(X) → U61(X)
a__U72(X) → U72(X)

Q is empty.

(9) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Polynomial interpretation [POLO]:

POL(U11(x₁)) = 1 + x₁
POL(U42(x₁)) = 1 + x₁
POL(U61(x₁)) = x₁
POL(U72(x₁)) = x₁
POL(U81(x₁)) = 2·x₁
POL(__(x₁, x₂)) = x₁ + x₂
POL(a__U11(x₁)) = 2 + 2·x₁
POL(a__U21(x₁, x₂)) = x₁ + 2·x₂
POL(a__U22(x₁)) = 2·x₁
POL(a__U42(x₁)) = 1 + 2·x₁
POL(a__U61(x₁)) = x₁
POL(a__U71(x₁, x₂)) = x₁ + 2·x₂
POL(a__U72(x₁)) = x₁
POL(a__U81(x₁)) = x₁
POL(a____(x₁, x₂)) = x₁ + x₂
POL(a__isList(x₁)) = x₁
POL(a__isNePal(x₁)) = x₁
POL(a__isPal(x₁)) = x₁
POL(a__isQid(x₁)) = x₁
POL(isList(x₁)) = x₁
POL(mark(x₁)) = x₁
POL(tt) = 0

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

a__U11(X) → U11(X)

(10) Obligation:

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

a__U21(tt, V2) → a__U22(a__isList(V2))
a__U61(tt) → tt
a__U71(tt, P) → a__U72(a__isPal(P))
a__U72(tt) → tt
a__isNePal(V) → a__U61(a__isQid(V))
a__isPal(V) → a__U81(a__isNePal(V))
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U61(X)) → a__U61(mark(X))
mark(U72(X)) → a__U72(mark(X))
mark(U81(X)) → a__U81(mark(X))
a____(X1, X2) → __(X1, X2)
a__isList(X) → isList(X)
a__U42(X) → U42(X)
a__U61(X) → U61(X)
a__U72(X) → U72(X)

Q is empty.

(11) QTRSRRRProof (EQUIVALENT transformation)

Used ordering:
Knuth-Bendix order [KBO] with precedence:

mark₁ > tt > a_{_isQid₁} > a_{_U61₁} > U61₁ > a_{_{_{_₂}}} > __₂ > a_{_U21₂} > a_{_U81₁} > a_{_U71₂} > a_{_isList₁} > a_{_isNePal₁} > U42₁ > a_{_U42₁} > isList₁ > a_{_U22₁} > U81₁ > a_{_U72₁} > U72₁ > a_{_isPal₁}

and weight map:

tt=1
a__U22_1=1
a__isList_1=2
a__U61_1=1
a__U72_1=2
a__isPal_1=5
a__isNePal_1=3
a__isQid_1=1
a__U81_1=1
mark_1=0
U61_1=1
U72_1=2
U81_1=2
isList_1=1
a__U42_1=2
U42_1=1
a__U21_2=2
a__U71_2=6
___2=0
a_____2=0

The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

a__U21(tt, V2) → a__U22(a__isList(V2))
a__U61(tt) → tt
a__U71(tt, P) → a__U72(a__isPal(P))
a__U72(tt) → tt
a__isNePal(V) → a__U61(a__isQid(V))
a__isPal(V) → a__U81(a__isNePal(V))
mark(__(X1, X2)) → a____(mark(X1), mark(X2))
mark(U61(X)) → a__U61(mark(X))
mark(U72(X)) → a__U72(mark(X))
mark(U81(X)) → a__U81(mark(X))
a____(X1, X2) → __(X1, X2)
a__isList(X) → isList(X)
a__U42(X) → U42(X)
a__U61(X) → U61(X)
a__U72(X) → U72(X)

(0) Obligation:

(1) QTRSRRRProof (EQUIVALENT transformation)

(2) Obligation:

(3) QTRSRRRProof (EQUIVALENT transformation)

(4) Obligation:

(5) QTRSRRRProof (EQUIVALENT transformation)

(6) Obligation:

(7) QTRSRRRProof (EQUIVALENT transformation)

(8) Obligation:

(9) QTRSRRRProof (EQUIVALENT transformation)

(10) Obligation:

(11) QTRSRRRProof (EQUIVALENT transformation)

(12) Obligation:

(13) RisEmptyProof (EQUIVALENT transformation)

(14) YES