YES

Problem 1: 

(VAR v_NonEmpty:S f:S x:S)
(RULES
app(app(F,app(app(F,f:S),x:S)),x:S) -> app(app(F,app(G,app(app(F,f:S),x:S))),app(f:S,x:S))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 APP(app(F,app(app(F,f:S),x:S)),x:S) -> APP(app(F,app(G,app(app(F,f:S),x:S))),app(f:S,x:S))
 APP(app(F,app(app(F,f:S),x:S)),x:S) -> APP(F,app(G,app(app(F,f:S),x:S)))
 APP(app(F,app(app(F,f:S),x:S)),x:S) -> APP(G,app(app(F,f:S),x:S))
 APP(app(F,app(app(F,f:S),x:S)),x:S) -> APP(f:S,x:S)
-> Rules:
 app(app(F,app(app(F,f:S),x:S)),x:S) -> app(app(F,app(G,app(app(F,f:S),x:S))),app(f:S,x:S))

Problem 1: 

SCC Processor:
-> Pairs:
 APP(app(F,app(app(F,f:S),x:S)),x:S) -> APP(app(F,app(G,app(app(F,f:S),x:S))),app(f:S,x:S))
 APP(app(F,app(app(F,f:S),x:S)),x:S) -> APP(F,app(G,app(app(F,f:S),x:S)))
 APP(app(F,app(app(F,f:S),x:S)),x:S) -> APP(G,app(app(F,f:S),x:S))
 APP(app(F,app(app(F,f:S),x:S)),x:S) -> APP(f:S,x:S)
-> Rules:
 app(app(F,app(app(F,f:S),x:S)),x:S) -> app(app(F,app(G,app(app(F,f:S),x:S))),app(f:S,x:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APP(app(F,app(app(F,f:S),x:S)),x:S) -> APP(f:S,x:S)
->->-> Rules:
 app(app(F,app(app(F,f:S),x:S)),x:S) -> app(app(F,app(G,app(app(F,f:S),x:S))),app(f:S,x:S))

Problem 1: 

Subterm Processor:
-> Pairs:
 APP(app(F,app(app(F,f:S),x:S)),x:S) -> APP(f:S,x:S)
-> Rules:
 app(app(F,app(app(F,f:S),x:S)),x:S) -> app(app(F,app(G,app(app(F,f:S),x:S))),app(f:S,x:S))
->Projection:
 pi(APP) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 app(app(F,app(app(F,f:S),x:S)),x:S) -> app(app(F,app(G,app(app(F,f:S),x:S))),app(f:S,x:S))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.