YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S z:S)
(RULES
and(ffalse,y:S) -> ffalse
and(x:S,and(y:S,y:S)) -> and(x:S,y:S)
and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
and(x:S,ttrue) -> x:S
and(x:S,x:S) -> x:S
or(or(x:S,y:S),and(y:S,z:S)) -> or(x:S,y:S)
or(ttrue,y:S) -> ttrue
or(x:S,and(x:S,y:S)) -> x:S
or(x:S,or(y:S,y:S)) -> or(x:S,y:S)
or(x:S,ffalse) -> x:S
or(x:S,x:S) -> x:S
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 AND(x:S,and(y:S,y:S)) -> AND(x:S,y:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,y:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,z:S)
 AND(x:S,or(y:S,z:S)) -> OR(and(x:S,y:S),and(x:S,z:S))
 OR(x:S,or(y:S,y:S)) -> OR(x:S,y:S)
-> Rules:
 and(ffalse,y:S) -> ffalse
 and(x:S,and(y:S,y:S)) -> and(x:S,y:S)
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,ttrue) -> x:S
 and(x:S,x:S) -> x:S
 or(or(x:S,y:S),and(y:S,z:S)) -> or(x:S,y:S)
 or(ttrue,y:S) -> ttrue
 or(x:S,and(x:S,y:S)) -> x:S
 or(x:S,or(y:S,y:S)) -> or(x:S,y:S)
 or(x:S,ffalse) -> x:S
 or(x:S,x:S) -> x:S

Problem 1: 

SCC Processor:
-> Pairs:
 AND(x:S,and(y:S,y:S)) -> AND(x:S,y:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,y:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,z:S)
 AND(x:S,or(y:S,z:S)) -> OR(and(x:S,y:S),and(x:S,z:S))
 OR(x:S,or(y:S,y:S)) -> OR(x:S,y:S)
-> Rules:
 and(ffalse,y:S) -> ffalse
 and(x:S,and(y:S,y:S)) -> and(x:S,y:S)
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,ttrue) -> x:S
 and(x:S,x:S) -> x:S
 or(or(x:S,y:S),and(y:S,z:S)) -> or(x:S,y:S)
 or(ttrue,y:S) -> ttrue
 or(x:S,and(x:S,y:S)) -> x:S
 or(x:S,or(y:S,y:S)) -> or(x:S,y:S)
 or(x:S,ffalse) -> x:S
 or(x:S,x:S) -> x:S
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 OR(x:S,or(y:S,y:S)) -> OR(x:S,y:S)
->->-> Rules:
 and(ffalse,y:S) -> ffalse
 and(x:S,and(y:S,y:S)) -> and(x:S,y:S)
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,ttrue) -> x:S
 and(x:S,x:S) -> x:S
 or(or(x:S,y:S),and(y:S,z:S)) -> or(x:S,y:S)
 or(ttrue,y:S) -> ttrue
 or(x:S,and(x:S,y:S)) -> x:S
 or(x:S,or(y:S,y:S)) -> or(x:S,y:S)
 or(x:S,ffalse) -> x:S
 or(x:S,x:S) -> x:S
->->Cycle:
->->-> Pairs:
 AND(x:S,and(y:S,y:S)) -> AND(x:S,y:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,y:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,z:S)
->->-> Rules:
 and(ffalse,y:S) -> ffalse
 and(x:S,and(y:S,y:S)) -> and(x:S,y:S)
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,ttrue) -> x:S
 and(x:S,x:S) -> x:S
 or(or(x:S,y:S),and(y:S,z:S)) -> or(x:S,y:S)
 or(ttrue,y:S) -> ttrue
 or(x:S,and(x:S,y:S)) -> x:S
 or(x:S,or(y:S,y:S)) -> or(x:S,y:S)
 or(x:S,ffalse) -> x:S
 or(x:S,x:S) -> x:S


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 OR(x:S,or(y:S,y:S)) -> OR(x:S,y:S)
-> Rules:
 and(ffalse,y:S) -> ffalse
 and(x:S,and(y:S,y:S)) -> and(x:S,y:S)
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,ttrue) -> x:S
 and(x:S,x:S) -> x:S
 or(or(x:S,y:S),and(y:S,z:S)) -> or(x:S,y:S)
 or(ttrue,y:S) -> ttrue
 or(x:S,and(x:S,y:S)) -> x:S
 or(x:S,or(y:S,y:S)) -> or(x:S,y:S)
 or(x:S,ffalse) -> x:S
 or(x:S,x:S) -> x:S
->Projection:
 pi(OR) = 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 and(ffalse,y:S) -> ffalse
 and(x:S,and(y:S,y:S)) -> and(x:S,y:S)
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,ttrue) -> x:S
 and(x:S,x:S) -> x:S
 or(or(x:S,y:S),and(y:S,z:S)) -> or(x:S,y:S)
 or(ttrue,y:S) -> ttrue
 or(x:S,and(x:S,y:S)) -> x:S
 or(x:S,or(y:S,y:S)) -> or(x:S,y:S)
 or(x:S,ffalse) -> x:S
 or(x:S,x:S) -> x:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 AND(x:S,and(y:S,y:S)) -> AND(x:S,y:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,y:S)
 AND(x:S,or(y:S,z:S)) -> AND(x:S,z:S)
-> Rules:
 and(ffalse,y:S) -> ffalse
 and(x:S,and(y:S,y:S)) -> and(x:S,y:S)
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,ttrue) -> x:S
 and(x:S,x:S) -> x:S
 or(or(x:S,y:S),and(y:S,z:S)) -> or(x:S,y:S)
 or(ttrue,y:S) -> ttrue
 or(x:S,and(x:S,y:S)) -> x:S
 or(x:S,or(y:S,y:S)) -> or(x:S,y:S)
 or(x:S,ffalse) -> x:S
 or(x:S,x:S) -> x:S
->Projection:
 pi(AND) = 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 and(ffalse,y:S) -> ffalse
 and(x:S,and(y:S,y:S)) -> and(x:S,y:S)
 and(x:S,or(y:S,z:S)) -> or(and(x:S,y:S),and(x:S,z:S))
 and(x:S,ttrue) -> x:S
 and(x:S,x:S) -> x:S
 or(or(x:S,y:S),and(y:S,z:S)) -> or(x:S,y:S)
 or(ttrue,y:S) -> ttrue
 or(x:S,and(x:S,y:S)) -> x:S
 or(x:S,or(y:S,y:S)) -> or(x:S,y:S)
 or(x:S,ffalse) -> x:S
 or(x:S,x:S) -> x:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.