YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S)
(RULES
and(x:S,x:S) -> x:S
not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
not(not(x:S)) -> x:S
not(or(x:S,y:S)) -> and(not(x:S),not(y:S))
or(x:S,x:S) -> x:S
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 NOT(and(x:S,y:S)) -> NOT(x:S)
 NOT(and(x:S,y:S)) -> NOT(y:S)
 NOT(and(x:S,y:S)) -> OR(not(x:S),not(y:S))
 NOT(or(x:S,y:S)) -> AND(not(x:S),not(y:S))
 NOT(or(x:S,y:S)) -> NOT(x:S)
 NOT(or(x:S,y:S)) -> NOT(y:S)
-> Rules:
 and(x:S,x:S) -> x:S
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))
 or(x:S,x:S) -> x:S

Problem 1: 

SCC Processor:
-> Pairs:
 NOT(and(x:S,y:S)) -> NOT(x:S)
 NOT(and(x:S,y:S)) -> NOT(y:S)
 NOT(and(x:S,y:S)) -> OR(not(x:S),not(y:S))
 NOT(or(x:S,y:S)) -> AND(not(x:S),not(y:S))
 NOT(or(x:S,y:S)) -> NOT(x:S)
 NOT(or(x:S,y:S)) -> NOT(y:S)
-> Rules:
 and(x:S,x:S) -> x:S
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))
 or(x:S,x:S) -> x:S
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 NOT(and(x:S,y:S)) -> NOT(x:S)
 NOT(and(x:S,y:S)) -> NOT(y:S)
 NOT(or(x:S,y:S)) -> NOT(x:S)
 NOT(or(x:S,y:S)) -> NOT(y:S)
->->-> Rules:
 and(x:S,x:S) -> x:S
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))
 or(x:S,x:S) -> x:S

Problem 1: 

Subterm Processor:
-> Pairs:
 NOT(and(x:S,y:S)) -> NOT(x:S)
 NOT(and(x:S,y:S)) -> NOT(y:S)
 NOT(or(x:S,y:S)) -> NOT(x:S)
 NOT(or(x:S,y:S)) -> NOT(y:S)
-> Rules:
 and(x:S,x:S) -> x:S
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))
 or(x:S,x:S) -> x:S
->Projection:
 pi(NOT) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 and(x:S,x:S) -> x:S
 not(and(x:S,y:S)) -> or(not(x:S),not(y:S))
 not(not(x:S)) -> x:S
 not(or(x:S,y:S)) -> and(not(x:S),not(y:S))
 or(x:S,x:S) -> x:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.