YES

Problem 1: 

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

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 IMPLIES(not(x:S),not(y:S)) -> AND(x:S,y:S)
 IMPLIES(not(x:S),not(y:S)) -> IMPLIES(y:S,and(x:S,y:S))
 IMPLIES(x:S,ffalse) -> NOT(x:S)
-> Rules:
 and(x:S,not(ffalse)) -> x:S
 and(x:S,ffalse) -> ffalse
 implies(not(x:S),not(y:S)) -> implies(y:S,and(x:S,y:S))
 implies(ffalse,y:S) -> not(ffalse)
 implies(x:S,ffalse) -> not(x:S)
 not(not(x:S)) -> x:S

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 IMPLIES(not(x:S),not(y:S)) -> IMPLIES(y:S,and(x:S,y:S))
-> Rules:
 and(x:S,not(ffalse)) -> x:S
 and(x:S,ffalse) -> ffalse
 implies(not(x:S),not(y:S)) -> implies(y:S,and(x:S,y:S))
 implies(ffalse,y:S) -> not(ffalse)
 implies(x:S,ffalse) -> not(x:S)
 not(not(x:S)) -> x:S
-> Usable rules:
 and(x:S,not(ffalse)) -> x:S
 and(x:S,ffalse) -> ffalse
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[and](X1,X2) = 2.X1 + 2
[not](X) = 2.X + 2
[false] = 0
[IMPLIES](X1,X2) = 2.X1 + 2.X2

Problem 1: 

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

The problem is finite.