YES
(VAR X Y Z I P)
(RULES 
__(nil,X) -> X
__(X,nil) -> X
__(__(X,Y),Z) -> __(X,__(Y,Z))
U11(tt) -> U12(tt)
U12(tt) -> tt
isNePal(__(I,__(P,I))) -> U11(tt)
)

Proving termination of rewriting for PALINDROME_nosorts_noand_Z_1:

-> Dependency pairs:
nF___(__(X,Y),Z) -> nF___(X,__(Y,Z))
nF___(__(X,Y),Z) -> nF___(Y,Z)
nF_U11(tt) -> nF_U12(tt)
nF_isNePal(__(I,__(P,I))) -> nF_U11(tt)

-> Proof of termination for PALINDROME_nosorts_noand_Z_1:
-> -> Dependency pairs in cycle:
nF___(__(X,Y),Z) -> nF___(X,__(Y,Z))
nF___(__(X,Y),Z) -> nF___(Y,Z)

Termination proved: Cycles verify subterm criterion.

SETTINGS:
Base ordering: Polynomial ordering
Proof mode: SCCs in DG + base ordering
Upper bound for coeffs: 1
Rationals below 1 for all non-replacing args: No
Polynomial interpretation: Linear
Coeffs in polynomials: No rationals
Delta: automatic

(VAR X)
(RULES 
activate(X) -> X
)

The TRS is an overlay system and all critical pairs are trivial, thus termination of innermost rewriting is equivalent to termination of rewriting.

Proving termination of innermost rewriting for PALINDROME_nosorts_noand_Z_2:

-> Dependency pairs:
No dependency pairs found.

-> Proof of termination for PALINDROME_nosorts_noand_Z_2:
Termination proved: No cycles in dependency graph.

SETTINGS:
Base ordering: Polynomial ordering
Proof mode: SCCs in DG + base ordering
Upper bound for coeffs: 1
Rationals below 1 for all non-replacing args: No
Polynomial interpretation: Linear
Coeffs in polynomials: No rationals
Delta: automatic



Termination was proved succesfully.