YES

Problem 1: 

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

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 IMPLIES(not(x:S),or(y:S,z:S)) -> IMPLIES(y:S,or(x:S,z:S))
 IMPLIES(x:S,or(y:S,z:S)) -> IMPLIES(x:S,z:S)
-> Rules:
 implies(not(x:S),or(y:S,z:S)) -> implies(y:S,or(x:S,z:S))
 implies(not(x:S),y:S) -> or(x:S,y:S)
 implies(x:S,or(y:S,z:S)) -> or(y:S,implies(x:S,z:S))

Problem 1: 

SCC Processor:
-> Pairs:
 IMPLIES(not(x:S),or(y:S,z:S)) -> IMPLIES(y:S,or(x:S,z:S))
 IMPLIES(x:S,or(y:S,z:S)) -> IMPLIES(x:S,z:S)
-> Rules:
 implies(not(x:S),or(y:S,z:S)) -> implies(y:S,or(x:S,z:S))
 implies(not(x:S),y:S) -> or(x:S,y:S)
 implies(x:S,or(y:S,z:S)) -> or(y:S,implies(x:S,z:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 IMPLIES(not(x:S),or(y:S,z:S)) -> IMPLIES(y:S,or(x:S,z:S))
 IMPLIES(x:S,or(y:S,z:S)) -> IMPLIES(x:S,z:S)
->->-> Rules:
 implies(not(x:S),or(y:S,z:S)) -> implies(y:S,or(x:S,z:S))
 implies(not(x:S),y:S) -> or(x:S,y:S)
 implies(x:S,or(y:S,z:S)) -> or(y:S,implies(x:S,z:S))

Problem 1: 

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

Problem 1: 

SCC Processor:
-> Pairs:
 IMPLIES(x:S,or(y:S,z:S)) -> IMPLIES(x:S,z:S)
-> Rules:
 implies(not(x:S),or(y:S,z:S)) -> implies(y:S,or(x:S,z:S))
 implies(not(x:S),y:S) -> or(x:S,y:S)
 implies(x:S,or(y:S,z:S)) -> or(y:S,implies(x:S,z:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 IMPLIES(x:S,or(y:S,z:S)) -> IMPLIES(x:S,z:S)
->->-> Rules:
 implies(not(x:S),or(y:S,z:S)) -> implies(y:S,or(x:S,z:S))
 implies(not(x:S),y:S) -> or(x:S,y:S)
 implies(x:S,or(y:S,z:S)) -> or(y:S,implies(x:S,z:S))

Problem 1: 

Subterm Processor:
-> Pairs:
 IMPLIES(x:S,or(y:S,z:S)) -> IMPLIES(x:S,z:S)
-> Rules:
 implies(not(x:S),or(y:S,z:S)) -> implies(y:S,or(x:S,z:S))
 implies(not(x:S),y:S) -> or(x:S,y:S)
 implies(x:S,or(y:S,z:S)) -> or(y:S,implies(x:S,z:S))
->Projection:
 pi(IMPLIES) = 2

Problem 1: 

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

The problem is finite.