YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S)
(RULES
.(/(y:S,x:S),x:S) -> y:S
.(e,x:S) -> x:S
.(x:S,\(x:S,y:S)) -> y:S
.(x:S,e) -> x:S
/(.(y:S,x:S),x:S) -> y:S
/(x:S,\(y:S,x:S)) -> y:S
/(x:S,e) -> x:S
/(x:S,x:S) -> e
\(/(x:S,y:S),x:S) -> y:S
\(e,x:S) -> x:S
\(x:S,.(x:S,y:S)) -> y:S
\(x:S,x:S) -> e
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 Empty
-> Rules:
 .(/(y:S,x:S),x:S) -> y:S
 .(e,x:S) -> x:S
 .(x:S,\(x:S,y:S)) -> y:S
 .(x:S,e) -> x:S
 /(.(y:S,x:S),x:S) -> y:S
 /(x:S,\(y:S,x:S)) -> y:S
 /(x:S,e) -> x:S
 /(x:S,x:S) -> e
 \(/(x:S,y:S),x:S) -> y:S
 \(e,x:S) -> x:S
 \(x:S,.(x:S,y:S)) -> y:S
 \(x:S,x:S) -> e

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 .(/(y:S,x:S),x:S) -> y:S
 .(e,x:S) -> x:S
 .(x:S,\(x:S,y:S)) -> y:S
 .(x:S,e) -> x:S
 /(.(y:S,x:S),x:S) -> y:S
 /(x:S,\(y:S,x:S)) -> y:S
 /(x:S,e) -> x:S
 /(x:S,x:S) -> e
 \(/(x:S,y:S),x:S) -> y:S
 \(e,x:S) -> x:S
 \(x:S,.(x:S,y:S)) -> y:S
 \(x:S,x:S) -> e
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.