(0) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
U11(tt) → U12(tt)
U12(tt) → tt
isNePal(__(I, __(P, I))) → U11(tt)
Q is empty.
(1) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Polynomial interpretation [POLO]:
POL(U11(x1)) = 2 + x1
POL(U12(x1)) = 1 + x1
POL(__(x1, x2)) = x1 + x2
POL(isNePal(x1)) = 3 + x1
POL(nil) = 0
POL(tt) = 0
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
U11(tt) → U12(tt)
U12(tt) → tt
isNePal(__(I, __(P, I))) → U11(tt)
(2) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
Q is empty.
(3) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Polynomial interpretation [POLO]:
POL(__(x1, x2)) = 1 + x1 + x2
POL(nil) = 0
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
(4) Obligation:
Q restricted rewrite system:
The TRS R consists of the following rules:
__(__(X, Y), Z) → __(X, __(Y, Z))
Q is empty.
(5) QTRSRRRProof (EQUIVALENT transformation)
Used ordering:
Polynomial interpretation [POLO]:
POL(__(x1, x2)) = 2 + 2·x1 + x2
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))
(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) TRUE
(9) RisEmptyProof (EQUIVALENT transformation)
The TRS R is empty. Hence, termination is trivially proven.
(10) TRUE