YES

Problem 1: 

(VAR v_NonEmpty:S X:S Y:S)
(RULES
ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S)
u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S)
 u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACKIN(s(X:S),s(Y:S)) -> ACKIN(s(X:S),Y:S)
 ACKIN(s(X:S),s(Y:S)) -> U21(ackin(s(X:S),Y:S),X:S)
 U21(ackout(X:S),Y:S) -> ACKIN(Y:S,X:S)
-> Rules:
 ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S)
 u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S))

Problem 1: 

SCC Processor:
-> Pairs:
 ACKIN(s(X:S),s(Y:S)) -> ACKIN(s(X:S),Y:S)
 ACKIN(s(X:S),s(Y:S)) -> U21(ackin(s(X:S),Y:S),X:S)
 U21(ackout(X:S),Y:S) -> ACKIN(Y:S,X:S)
-> Rules:
 ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S)
 u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACKIN(s(X:S),s(Y:S)) -> ACKIN(s(X:S),Y:S)
 ACKIN(s(X:S),s(Y:S)) -> U21(ackin(s(X:S),Y:S),X:S)
 U21(ackout(X:S),Y:S) -> ACKIN(Y:S,X:S)
->->-> Rules:
 ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S)
 u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S))

Problem 1: 

Subterm Processor:
-> Pairs:
 ACKIN(s(X:S),s(Y:S)) -> ACKIN(s(X:S),Y:S)
 ACKIN(s(X:S),s(Y:S)) -> U21(ackin(s(X:S),Y:S),X:S)
 U21(ackout(X:S),Y:S) -> ACKIN(Y:S,X:S)
-> Rules:
 ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S)
 u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S))
->Projection:
 pi(ACKIN) = 1
 pi(U21) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 ACKIN(s(X:S),s(Y:S)) -> ACKIN(s(X:S),Y:S)
 U21(ackout(X:S),Y:S) -> ACKIN(Y:S,X:S)
-> Rules:
 ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S)
 u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACKIN(s(X:S),s(Y:S)) -> ACKIN(s(X:S),Y:S)
->->-> Rules:
 ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S)
 u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S))

Problem 1: 

Subterm Processor:
-> Pairs:
 ACKIN(s(X:S),s(Y:S)) -> ACKIN(s(X:S),Y:S)
-> Rules:
 ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S)
 u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S))
->Projection:
 pi(ACKIN) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 ackin(s(X:S),s(Y:S)) -> u21(ackin(s(X:S),Y:S),X:S)
 u21(ackout(X:S),Y:S) -> u22(ackin(Y:S,X:S))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.