YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S)
(RULES
divp(x:S,y:S) -> =(rem(x:S,y:S),0)
prime(0) -> ffalse
prime(s(0)) -> ffalse
prime(s(s(x:S))) -> prime1(s(s(x:S)),s(x:S))
prime1(x:S,0) -> ffalse
prime1(x:S,s(0)) -> ttrue
prime1(x:S,s(s(y:S))) -> and(not(divp(s(s(y:S)),x:S)),prime1(x:S,s(y:S)))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 divp(x:S,y:S) -> =(rem(x:S,y:S),0)
 prime(0) -> ffalse
 prime(s(0)) -> ffalse
 prime(s(s(x:S))) -> prime1(s(s(x:S)),s(x:S))
 prime1(x:S,0) -> ffalse
 prime1(x:S,s(0)) -> ttrue
 prime1(x:S,s(s(y:S))) -> and(not(divp(s(s(y:S)),x:S)),prime1(x:S,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:
 PRIME(s(s(x:S))) -> PRIME1(s(s(x:S)),s(x:S))
 PRIME1(x:S,s(s(y:S))) -> DIVP(s(s(y:S)),x:S)
 PRIME1(x:S,s(s(y:S))) -> PRIME1(x:S,s(y:S))
-> Rules:
 divp(x:S,y:S) -> =(rem(x:S,y:S),0)
 prime(0) -> ffalse
 prime(s(0)) -> ffalse
 prime(s(s(x:S))) -> prime1(s(s(x:S)),s(x:S))
 prime1(x:S,0) -> ffalse
 prime1(x:S,s(0)) -> ttrue
 prime1(x:S,s(s(y:S))) -> and(not(divp(s(s(y:S)),x:S)),prime1(x:S,s(y:S)))

Problem 1: 

SCC Processor:
-> Pairs:
 PRIME(s(s(x:S))) -> PRIME1(s(s(x:S)),s(x:S))
 PRIME1(x:S,s(s(y:S))) -> DIVP(s(s(y:S)),x:S)
 PRIME1(x:S,s(s(y:S))) -> PRIME1(x:S,s(y:S))
-> Rules:
 divp(x:S,y:S) -> =(rem(x:S,y:S),0)
 prime(0) -> ffalse
 prime(s(0)) -> ffalse
 prime(s(s(x:S))) -> prime1(s(s(x:S)),s(x:S))
 prime1(x:S,0) -> ffalse
 prime1(x:S,s(0)) -> ttrue
 prime1(x:S,s(s(y:S))) -> and(not(divp(s(s(y:S)),x:S)),prime1(x:S,s(y:S)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 PRIME1(x:S,s(s(y:S))) -> PRIME1(x:S,s(y:S))
->->-> Rules:
 divp(x:S,y:S) -> =(rem(x:S,y:S),0)
 prime(0) -> ffalse
 prime(s(0)) -> ffalse
 prime(s(s(x:S))) -> prime1(s(s(x:S)),s(x:S))
 prime1(x:S,0) -> ffalse
 prime1(x:S,s(0)) -> ttrue
 prime1(x:S,s(s(y:S))) -> and(not(divp(s(s(y:S)),x:S)),prime1(x:S,s(y:S)))

Problem 1: 

Subterm Processor:
-> Pairs:
 PRIME1(x:S,s(s(y:S))) -> PRIME1(x:S,s(y:S))
-> Rules:
 divp(x:S,y:S) -> =(rem(x:S,y:S),0)
 prime(0) -> ffalse
 prime(s(0)) -> ffalse
 prime(s(s(x:S))) -> prime1(s(s(x:S)),s(x:S))
 prime1(x:S,0) -> ffalse
 prime1(x:S,s(0)) -> ttrue
 prime1(x:S,s(s(y:S))) -> and(not(divp(s(s(y:S)),x:S)),prime1(x:S,s(y:S)))
->Projection:
 pi(PRIME1) = 2

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 divp(x:S,y:S) -> =(rem(x:S,y:S),0)
 prime(0) -> ffalse
 prime(s(0)) -> ffalse
 prime(s(s(x:S))) -> prime1(s(s(x:S)),s(x:S))
 prime1(x:S,0) -> ffalse
 prime1(x:S,s(0)) -> ttrue
 prime1(x:S,s(s(y:S))) -> and(not(divp(s(s(y:S)),x:S)),prime1(x:S,s(y:S)))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.