YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S)
(RULES
ack(0,y:S) -> s(y:S)
ack(s(x:S),0) -> ack(x:S,s(0))
ack(s(x:S),s(y:S)) -> ack(x:S,ack(s(x:S),y:S))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 ack(0,y:S) -> s(y:S)
 ack(s(x:S),0) -> ack(x:S,s(0))
 ack(s(x:S),s(y:S)) -> ack(x:S,ack(s(x:S),y:S))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACK(s(x:S),0) -> ACK(x:S,s(0))
 ACK(s(x:S),s(y:S)) -> ACK(s(x:S),y:S)
 ACK(s(x:S),s(y:S)) -> ACK(x:S,ack(s(x:S),y:S))
-> Rules:
 ack(0,y:S) -> s(y:S)
 ack(s(x:S),0) -> ack(x:S,s(0))
 ack(s(x:S),s(y:S)) -> ack(x:S,ack(s(x:S),y:S))

Problem 1: 

SCC Processor:
-> Pairs:
 ACK(s(x:S),0) -> ACK(x:S,s(0))
 ACK(s(x:S),s(y:S)) -> ACK(s(x:S),y:S)
 ACK(s(x:S),s(y:S)) -> ACK(x:S,ack(s(x:S),y:S))
-> Rules:
 ack(0,y:S) -> s(y:S)
 ack(s(x:S),0) -> ack(x:S,s(0))
 ack(s(x:S),s(y:S)) -> ack(x:S,ack(s(x:S),y:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACK(s(x:S),0) -> ACK(x:S,s(0))
 ACK(s(x:S),s(y:S)) -> ACK(s(x:S),y:S)
 ACK(s(x:S),s(y:S)) -> ACK(x:S,ack(s(x:S),y:S))
->->-> Rules:
 ack(0,y:S) -> s(y:S)
 ack(s(x:S),0) -> ack(x:S,s(0))
 ack(s(x:S),s(y:S)) -> ack(x:S,ack(s(x:S),y:S))

Problem 1: 

Subterm Processor:
-> Pairs:
 ACK(s(x:S),0) -> ACK(x:S,s(0))
 ACK(s(x:S),s(y:S)) -> ACK(s(x:S),y:S)
 ACK(s(x:S),s(y:S)) -> ACK(x:S,ack(s(x:S),y:S))
-> Rules:
 ack(0,y:S) -> s(y:S)
 ack(s(x:S),0) -> ack(x:S,s(0))
 ack(s(x:S),s(y:S)) -> ack(x:S,ack(s(x:S),y:S))
->Projection:
 pi(ACK) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 ACK(s(x:S),s(y:S)) -> ACK(s(x:S),y:S)
-> Rules:
 ack(0,y:S) -> s(y:S)
 ack(s(x:S),0) -> ack(x:S,s(0))
 ack(s(x:S),s(y:S)) -> ack(x:S,ack(s(x:S),y:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACK(s(x:S),s(y:S)) -> ACK(s(x:S),y:S)
->->-> Rules:
 ack(0,y:S) -> s(y:S)
 ack(s(x:S),0) -> ack(x:S,s(0))
 ack(s(x:S),s(y:S)) -> ack(x:S,ack(s(x:S),y:S))

Problem 1: 

Subterm Processor:
-> Pairs:
 ACK(s(x:S),s(y:S)) -> ACK(s(x:S),y:S)
-> Rules:
 ack(0,y:S) -> s(y:S)
 ack(s(x:S),0) -> ack(x:S,s(0))
 ack(s(x:S),s(y:S)) -> ack(x:S,ack(s(x:S),y:S))
->Projection:
 pi(ACK) = 2

Problem 1: 

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

The problem is finite.