YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S)
(RULES
app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S))
app(id,x:S) -> x:S
app(plus,0) -> id
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S))
 app(id,x:S) -> x:S
 app(plus,0) -> id
-> 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(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S)
 APP(app(plus,app(s,x:S)),y:S) -> APP(plus,x:S)
 APP(app(plus,app(s,x:S)),y:S) -> APP(s,app(app(plus,x:S),y:S))
-> Rules:
 app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S))
 app(id,x:S) -> x:S
 app(plus,0) -> id

Problem 1: 

SCC Processor:
-> Pairs:
 APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S)
 APP(app(plus,app(s,x:S)),y:S) -> APP(plus,x:S)
 APP(app(plus,app(s,x:S)),y:S) -> APP(s,app(app(plus,x:S),y:S))
-> Rules:
 app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S))
 app(id,x:S) -> x:S
 app(plus,0) -> id
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S)
->->-> Rules:
 app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S))
 app(id,x:S) -> x:S
 app(plus,0) -> id

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 APP(app(plus,app(s,x:S)),y:S) -> APP(app(plus,x:S),y:S)
-> Rules:
 app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S))
 app(id,x:S) -> x:S
 app(plus,0) -> id
-> Usable rules:
 app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S))
 app(id,x:S) -> x:S
 app(plus,0) -> id
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[app](X1,X2) = X1 + X2 + 2
[0] = 0
[fSNonEmpty] = 0
[id] = 0
[plus] = 1
[s] = 2
[APP](X1,X2) = X1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 app(app(plus,app(s,x:S)),y:S) -> app(s,app(app(plus,x:S),y:S))
 app(id,x:S) -> x:S
 app(plus,0) -> id
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.