YES

Problem 1: 

(VAR v_NonEmpty:S p:S x:S xs:S)
(RULES
app(app(and,ffalse),ffalse) -> ffalse
app(app(and,ffalse),ttrue) -> ffalse
app(app(and,ttrue),ffalse) -> ffalse
app(app(and,ttrue),ttrue) -> ttrue
app(app(forall,p:S),app(app(cons,x:S),xs:S)) -> app(app(and,app(p:S,x:S)),app(app(forall,p:S),xs:S))
app(app(forall,p:S),nil) -> ttrue
app(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> app(app(or,app(p:S,x:S)),app(app(forsome,p:S),xs:S))
app(app(forsome,p:S),nil) -> ffalse
app(app(or,ffalse),ffalse) -> ffalse
app(app(or,ffalse),ttrue) -> ttrue
app(app(or,ttrue),ffalse) -> ttrue
app(app(or,ttrue),ttrue) -> ttrue
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 app(app(and,ffalse),ffalse) -> ffalse
 app(app(and,ffalse),ttrue) -> ffalse
 app(app(and,ttrue),ffalse) -> ffalse
 app(app(and,ttrue),ttrue) -> ttrue
 app(app(forall,p:S),app(app(cons,x:S),xs:S)) -> app(app(and,app(p:S,x:S)),app(app(forall,p:S),xs:S))
 app(app(forall,p:S),nil) -> ttrue
 app(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> app(app(or,app(p:S,x:S)),app(app(forsome,p:S),xs:S))
 app(app(forsome,p:S),nil) -> ffalse
 app(app(or,ffalse),ffalse) -> ffalse
 app(app(or,ffalse),ttrue) -> ttrue
 app(app(or,ttrue),ffalse) -> ttrue
 app(app(or,ttrue),ttrue) -> ttrue
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 APP(app(forall,p:S),app(app(cons,x:S),xs:S)) -> APP(app(and,app(p:S,x:S)),app(app(forall,p:S),xs:S))
 APP(app(forall,p:S),app(app(cons,x:S),xs:S)) -> APP(app(forall,p:S),xs:S)
 APP(app(forall,p:S),app(app(cons,x:S),xs:S)) -> APP(and,app(p:S,x:S))
 APP(app(forall,p:S),app(app(cons,x:S),xs:S)) -> APP(p:S,x:S)
 APP(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> APP(app(forsome,p:S),xs:S)
 APP(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> APP(app(or,app(p:S,x:S)),app(app(forsome,p:S),xs:S))
 APP(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> APP(or,app(p:S,x:S))
 APP(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> APP(p:S,x:S)
-> Rules:
 app(app(and,ffalse),ffalse) -> ffalse
 app(app(and,ffalse),ttrue) -> ffalse
 app(app(and,ttrue),ffalse) -> ffalse
 app(app(and,ttrue),ttrue) -> ttrue
 app(app(forall,p:S),app(app(cons,x:S),xs:S)) -> app(app(and,app(p:S,x:S)),app(app(forall,p:S),xs:S))
 app(app(forall,p:S),nil) -> ttrue
 app(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> app(app(or,app(p:S,x:S)),app(app(forsome,p:S),xs:S))
 app(app(forsome,p:S),nil) -> ffalse
 app(app(or,ffalse),ffalse) -> ffalse
 app(app(or,ffalse),ttrue) -> ttrue
 app(app(or,ttrue),ffalse) -> ttrue
 app(app(or,ttrue),ttrue) -> ttrue

Problem 1: 

SCC Processor:
-> Pairs:
 APP(app(forall,p:S),app(app(cons,x:S),xs:S)) -> APP(app(and,app(p:S,x:S)),app(app(forall,p:S),xs:S))
 APP(app(forall,p:S),app(app(cons,x:S),xs:S)) -> APP(app(forall,p:S),xs:S)
 APP(app(forall,p:S),app(app(cons,x:S),xs:S)) -> APP(and,app(p:S,x:S))
 APP(app(forall,p:S),app(app(cons,x:S),xs:S)) -> APP(p:S,x:S)
 APP(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> APP(app(forsome,p:S),xs:S)
 APP(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> APP(app(or,app(p:S,x:S)),app(app(forsome,p:S),xs:S))
 APP(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> APP(or,app(p:S,x:S))
 APP(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> APP(p:S,x:S)
-> Rules:
 app(app(and,ffalse),ffalse) -> ffalse
 app(app(and,ffalse),ttrue) -> ffalse
 app(app(and,ttrue),ffalse) -> ffalse
 app(app(and,ttrue),ttrue) -> ttrue
 app(app(forall,p:S),app(app(cons,x:S),xs:S)) -> app(app(and,app(p:S,x:S)),app(app(forall,p:S),xs:S))
 app(app(forall,p:S),nil) -> ttrue
 app(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> app(app(or,app(p:S,x:S)),app(app(forsome,p:S),xs:S))
 app(app(forsome,p:S),nil) -> ffalse
 app(app(or,ffalse),ffalse) -> ffalse
 app(app(or,ffalse),ttrue) -> ttrue
 app(app(or,ttrue),ffalse) -> ttrue
 app(app(or,ttrue),ttrue) -> ttrue
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APP(app(forall,p:S),app(app(cons,x:S),xs:S)) -> APP(app(forall,p:S),xs:S)
 APP(app(forall,p:S),app(app(cons,x:S),xs:S)) -> APP(p:S,x:S)
 APP(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> APP(app(forsome,p:S),xs:S)
 APP(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> APP(p:S,x:S)
->->-> Rules:
 app(app(and,ffalse),ffalse) -> ffalse
 app(app(and,ffalse),ttrue) -> ffalse
 app(app(and,ttrue),ffalse) -> ffalse
 app(app(and,ttrue),ttrue) -> ttrue
 app(app(forall,p:S),app(app(cons,x:S),xs:S)) -> app(app(and,app(p:S,x:S)),app(app(forall,p:S),xs:S))
 app(app(forall,p:S),nil) -> ttrue
 app(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> app(app(or,app(p:S,x:S)),app(app(forsome,p:S),xs:S))
 app(app(forsome,p:S),nil) -> ffalse
 app(app(or,ffalse),ffalse) -> ffalse
 app(app(or,ffalse),ttrue) -> ttrue
 app(app(or,ttrue),ffalse) -> ttrue
 app(app(or,ttrue),ttrue) -> ttrue

Problem 1: 

Subterm Processor:
-> Pairs:
 APP(app(forall,p:S),app(app(cons,x:S),xs:S)) -> APP(app(forall,p:S),xs:S)
 APP(app(forall,p:S),app(app(cons,x:S),xs:S)) -> APP(p:S,x:S)
 APP(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> APP(app(forsome,p:S),xs:S)
 APP(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> APP(p:S,x:S)
-> Rules:
 app(app(and,ffalse),ffalse) -> ffalse
 app(app(and,ffalse),ttrue) -> ffalse
 app(app(and,ttrue),ffalse) -> ffalse
 app(app(and,ttrue),ttrue) -> ttrue
 app(app(forall,p:S),app(app(cons,x:S),xs:S)) -> app(app(and,app(p:S,x:S)),app(app(forall,p:S),xs:S))
 app(app(forall,p:S),nil) -> ttrue
 app(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> app(app(or,app(p:S,x:S)),app(app(forsome,p:S),xs:S))
 app(app(forsome,p:S),nil) -> ffalse
 app(app(or,ffalse),ffalse) -> ffalse
 app(app(or,ffalse),ttrue) -> ttrue
 app(app(or,ttrue),ffalse) -> ttrue
 app(app(or,ttrue),ttrue) -> ttrue
->Projection:
 pi(APP) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 APP(app(forall,p:S),app(app(cons,x:S),xs:S)) -> APP(app(forall,p:S),xs:S)
 APP(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> APP(app(forsome,p:S),xs:S)
-> Rules:
 app(app(and,ffalse),ffalse) -> ffalse
 app(app(and,ffalse),ttrue) -> ffalse
 app(app(and,ttrue),ffalse) -> ffalse
 app(app(and,ttrue),ttrue) -> ttrue
 app(app(forall,p:S),app(app(cons,x:S),xs:S)) -> app(app(and,app(p:S,x:S)),app(app(forall,p:S),xs:S))
 app(app(forall,p:S),nil) -> ttrue
 app(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> app(app(or,app(p:S,x:S)),app(app(forsome,p:S),xs:S))
 app(app(forsome,p:S),nil) -> ffalse
 app(app(or,ffalse),ffalse) -> ffalse
 app(app(or,ffalse),ttrue) -> ttrue
 app(app(or,ttrue),ffalse) -> ttrue
 app(app(or,ttrue),ttrue) -> ttrue
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APP(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> APP(app(forsome,p:S),xs:S)
->->-> Rules:
 app(app(and,ffalse),ffalse) -> ffalse
 app(app(and,ffalse),ttrue) -> ffalse
 app(app(and,ttrue),ffalse) -> ffalse
 app(app(and,ttrue),ttrue) -> ttrue
 app(app(forall,p:S),app(app(cons,x:S),xs:S)) -> app(app(and,app(p:S,x:S)),app(app(forall,p:S),xs:S))
 app(app(forall,p:S),nil) -> ttrue
 app(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> app(app(or,app(p:S,x:S)),app(app(forsome,p:S),xs:S))
 app(app(forsome,p:S),nil) -> ffalse
 app(app(or,ffalse),ffalse) -> ffalse
 app(app(or,ffalse),ttrue) -> ttrue
 app(app(or,ttrue),ffalse) -> ttrue
 app(app(or,ttrue),ttrue) -> ttrue
->->Cycle:
->->-> Pairs:
 APP(app(forall,p:S),app(app(cons,x:S),xs:S)) -> APP(app(forall,p:S),xs:S)
->->-> Rules:
 app(app(and,ffalse),ffalse) -> ffalse
 app(app(and,ffalse),ttrue) -> ffalse
 app(app(and,ttrue),ffalse) -> ffalse
 app(app(and,ttrue),ttrue) -> ttrue
 app(app(forall,p:S),app(app(cons,x:S),xs:S)) -> app(app(and,app(p:S,x:S)),app(app(forall,p:S),xs:S))
 app(app(forall,p:S),nil) -> ttrue
 app(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> app(app(or,app(p:S,x:S)),app(app(forsome,p:S),xs:S))
 app(app(forsome,p:S),nil) -> ffalse
 app(app(or,ffalse),ffalse) -> ffalse
 app(app(or,ffalse),ttrue) -> ttrue
 app(app(or,ttrue),ffalse) -> ttrue
 app(app(or,ttrue),ttrue) -> ttrue


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 APP(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> APP(app(forsome,p:S),xs:S)
-> Rules:
 app(app(and,ffalse),ffalse) -> ffalse
 app(app(and,ffalse),ttrue) -> ffalse
 app(app(and,ttrue),ffalse) -> ffalse
 app(app(and,ttrue),ttrue) -> ttrue
 app(app(forall,p:S),app(app(cons,x:S),xs:S)) -> app(app(and,app(p:S,x:S)),app(app(forall,p:S),xs:S))
 app(app(forall,p:S),nil) -> ttrue
 app(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> app(app(or,app(p:S,x:S)),app(app(forsome,p:S),xs:S))
 app(app(forsome,p:S),nil) -> ffalse
 app(app(or,ffalse),ffalse) -> ffalse
 app(app(or,ffalse),ttrue) -> ttrue
 app(app(or,ttrue),ffalse) -> ttrue
 app(app(or,ttrue),ttrue) -> ttrue
->Projection:
 pi(APP) = 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 app(app(and,ffalse),ffalse) -> ffalse
 app(app(and,ffalse),ttrue) -> ffalse
 app(app(and,ttrue),ffalse) -> ffalse
 app(app(and,ttrue),ttrue) -> ttrue
 app(app(forall,p:S),app(app(cons,x:S),xs:S)) -> app(app(and,app(p:S,x:S)),app(app(forall,p:S),xs:S))
 app(app(forall,p:S),nil) -> ttrue
 app(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> app(app(or,app(p:S,x:S)),app(app(forsome,p:S),xs:S))
 app(app(forsome,p:S),nil) -> ffalse
 app(app(or,ffalse),ffalse) -> ffalse
 app(app(or,ffalse),ttrue) -> ttrue
 app(app(or,ttrue),ffalse) -> ttrue
 app(app(or,ttrue),ttrue) -> ttrue
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 APP(app(forall,p:S),app(app(cons,x:S),xs:S)) -> APP(app(forall,p:S),xs:S)
-> Rules:
 app(app(and,ffalse),ffalse) -> ffalse
 app(app(and,ffalse),ttrue) -> ffalse
 app(app(and,ttrue),ffalse) -> ffalse
 app(app(and,ttrue),ttrue) -> ttrue
 app(app(forall,p:S),app(app(cons,x:S),xs:S)) -> app(app(and,app(p:S,x:S)),app(app(forall,p:S),xs:S))
 app(app(forall,p:S),nil) -> ttrue
 app(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> app(app(or,app(p:S,x:S)),app(app(forsome,p:S),xs:S))
 app(app(forsome,p:S),nil) -> ffalse
 app(app(or,ffalse),ffalse) -> ffalse
 app(app(or,ffalse),ttrue) -> ttrue
 app(app(or,ttrue),ffalse) -> ttrue
 app(app(or,ttrue),ttrue) -> ttrue
->Projection:
 pi(APP) = 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 app(app(and,ffalse),ffalse) -> ffalse
 app(app(and,ffalse),ttrue) -> ffalse
 app(app(and,ttrue),ffalse) -> ffalse
 app(app(and,ttrue),ttrue) -> ttrue
 app(app(forall,p:S),app(app(cons,x:S),xs:S)) -> app(app(and,app(p:S,x:S)),app(app(forall,p:S),xs:S))
 app(app(forall,p:S),nil) -> ttrue
 app(app(forsome,p:S),app(app(cons,x:S),xs:S)) -> app(app(or,app(p:S,x:S)),app(app(forsome,p:S),xs:S))
 app(app(forsome,p:S),nil) -> ffalse
 app(app(or,ffalse),ffalse) -> ffalse
 app(app(or,ffalse),ttrue) -> ttrue
 app(app(or,ttrue),ffalse) -> ttrue
 app(app(or,ttrue),ttrue) -> ttrue
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.