YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S z:S)
(RULES
and(xor(x:S,y:S),z:S) -> xor(and(x:S,z:S),and(y:S,z:S))
and(x:S,ffalse) -> ffalse
and(x:S,ttrue) -> x:S
and(x:S,x:S) -> x:S
implies(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,ttrue))
not(x:S) -> xor(x:S,ttrue)
or(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,y:S))
xor(x:S,ffalse) -> x:S
xor(x:S,x:S) -> ffalse
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 AND(xor(x:S,y:S),z:S) -> AND(x:S,z:S)
 AND(xor(x:S,y:S),z:S) -> AND(y:S,z:S)
 AND(xor(x:S,y:S),z:S) -> XOR(and(x:S,z:S),and(y:S,z:S))
 IMPLIES(x:S,y:S) -> AND(x:S,y:S)
 IMPLIES(x:S,y:S) -> XOR(and(x:S,y:S),xor(x:S,ttrue))
 IMPLIES(x:S,y:S) -> XOR(x:S,ttrue)
 NOT(x:S) -> XOR(x:S,ttrue)
 OR(x:S,y:S) -> AND(x:S,y:S)
 OR(x:S,y:S) -> XOR(and(x:S,y:S),xor(x:S,y:S))
 OR(x:S,y:S) -> XOR(x:S,y:S)
-> Rules:
 and(xor(x:S,y:S),z:S) -> xor(and(x:S,z:S),and(y:S,z:S))
 and(x:S,ffalse) -> ffalse
 and(x:S,ttrue) -> x:S
 and(x:S,x:S) -> x:S
 implies(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,ttrue))
 not(x:S) -> xor(x:S,ttrue)
 or(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,y:S))
 xor(x:S,ffalse) -> x:S
 xor(x:S,x:S) -> ffalse

Problem 1: 

SCC Processor:
-> Pairs:
 AND(xor(x:S,y:S),z:S) -> AND(x:S,z:S)
 AND(xor(x:S,y:S),z:S) -> AND(y:S,z:S)
 AND(xor(x:S,y:S),z:S) -> XOR(and(x:S,z:S),and(y:S,z:S))
 IMPLIES(x:S,y:S) -> AND(x:S,y:S)
 IMPLIES(x:S,y:S) -> XOR(and(x:S,y:S),xor(x:S,ttrue))
 IMPLIES(x:S,y:S) -> XOR(x:S,ttrue)
 NOT(x:S) -> XOR(x:S,ttrue)
 OR(x:S,y:S) -> AND(x:S,y:S)
 OR(x:S,y:S) -> XOR(and(x:S,y:S),xor(x:S,y:S))
 OR(x:S,y:S) -> XOR(x:S,y:S)
-> Rules:
 and(xor(x:S,y:S),z:S) -> xor(and(x:S,z:S),and(y:S,z:S))
 and(x:S,ffalse) -> ffalse
 and(x:S,ttrue) -> x:S
 and(x:S,x:S) -> x:S
 implies(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,ttrue))
 not(x:S) -> xor(x:S,ttrue)
 or(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,y:S))
 xor(x:S,ffalse) -> x:S
 xor(x:S,x:S) -> ffalse
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 AND(xor(x:S,y:S),z:S) -> AND(x:S,z:S)
 AND(xor(x:S,y:S),z:S) -> AND(y:S,z:S)
->->-> Rules:
 and(xor(x:S,y:S),z:S) -> xor(and(x:S,z:S),and(y:S,z:S))
 and(x:S,ffalse) -> ffalse
 and(x:S,ttrue) -> x:S
 and(x:S,x:S) -> x:S
 implies(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,ttrue))
 not(x:S) -> xor(x:S,ttrue)
 or(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,y:S))
 xor(x:S,ffalse) -> x:S
 xor(x:S,x:S) -> ffalse

Problem 1: 

Subterm Processor:
-> Pairs:
 AND(xor(x:S,y:S),z:S) -> AND(x:S,z:S)
 AND(xor(x:S,y:S),z:S) -> AND(y:S,z:S)
-> Rules:
 and(xor(x:S,y:S),z:S) -> xor(and(x:S,z:S),and(y:S,z:S))
 and(x:S,ffalse) -> ffalse
 and(x:S,ttrue) -> x:S
 and(x:S,x:S) -> x:S
 implies(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,ttrue))
 not(x:S) -> xor(x:S,ttrue)
 or(x:S,y:S) -> xor(and(x:S,y:S),xor(x:S,y:S))
 xor(x:S,ffalse) -> x:S
 xor(x:S,x:S) -> ffalse
->Projection:
 pi(AND) = 1

Problem 1: 

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

The problem is finite.