YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S z:S)
(RULES
f(f(y:S,z:S),f(x:S,f(a,x:S))) -> f(f(f(a,z:S),f(x:S,a)),f(a,y:S))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(f(y:S,z:S),f(x:S,f(a,x:S))) -> F(f(f(a,z:S),f(x:S,a)),f(a,y:S))
-> Rules:
 f(f(y:S,z:S),f(x:S,f(a,x:S))) -> f(f(f(a,z:S),f(x:S,a)),f(a,y:S))

Problem 1: 

SCC Processor:
-> Pairs:
 F(f(y:S,z:S),f(x:S,f(a,x:S))) -> F(f(f(a,z:S),f(x:S,a)),f(a,y:S))
-> Rules:
 f(f(y:S,z:S),f(x:S,f(a,x:S))) -> f(f(f(a,z:S),f(x:S,a)),f(a,y:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(f(y:S,z:S),f(x:S,f(a,x:S))) -> F(f(f(a,z:S),f(x:S,a)),f(a,y:S))
->->-> Rules:
 f(f(y:S,z:S),f(x:S,f(a,x:S))) -> f(f(f(a,z:S),f(x:S,a)),f(a,y:S))

Problem 1: 

Instantiation Processor:
-> Pairs:
 F(f(y:S,z:S),f(x:S,f(a,x:S))) -> F(f(f(a,z:S),f(x:S,a)),f(a,y:S))
-> Rules:
 f(f(y:S,z:S),f(x:S,f(a,x:S))) -> f(f(f(a,z:S),f(x:S,a)),f(a,y:S))
->Instantiated Pairs:
->->Original Pair:
 F(f(y:S,z:S),f(x:S,f(a,x:S))) -> F(f(f(a,z:S),f(x:S,a)),f(a,y:S))
->-> Instantiated pairs:
 F(f(f(a,x4:S),f(x5:S,a)),f(a,f(a,a))) -> F(f(f(a,f(x5:S,a)),f(a,a)),f(a,f(a,x4:S)))

Problem 1: 

SCC Processor:
-> Pairs:
 F(f(f(a,x4:S),f(x5:S,a)),f(a,f(a,a))) -> F(f(f(a,f(x5:S,a)),f(a,a)),f(a,f(a,x4:S)))
-> Rules:
 f(f(y:S,z:S),f(x:S,f(a,x:S))) -> f(f(f(a,z:S),f(x:S,a)),f(a,y:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(f(f(a,x4:S),f(x5:S,a)),f(a,f(a,a))) -> F(f(f(a,f(x5:S,a)),f(a,a)),f(a,f(a,x4:S)))
->->-> Rules:
 f(f(y:S,z:S),f(x:S,f(a,x:S))) -> f(f(f(a,z:S),f(x:S,a)),f(a,y:S))

Problem 1: 

Instantiation Processor:
-> Pairs:
 F(f(f(a,x4:S),f(x5:S,a)),f(a,f(a,a))) -> F(f(f(a,f(x5:S,a)),f(a,a)),f(a,f(a,x4:S)))
-> Rules:
 f(f(y:S,z:S),f(x:S,f(a,x:S))) -> f(f(f(a,z:S),f(x:S,a)),f(a,y:S))
->Instantiated Pairs:
->->Original Pair:
 F(f(f(a,x4:S),f(x5:S,a)),f(a,f(a,a))) -> F(f(f(a,f(x5:S,a)),f(a,a)),f(a,f(a,x4:S)))
->-> Instantiated pairs:
 F(f(f(a,f(x6:S,a)),f(a,a)),f(a,f(a,a))) -> F(f(f(a,f(a,a)),f(a,a)),f(a,f(a,f(x6:S,a))))

Problem 1: 

SCC Processor:
-> Pairs:
 F(f(f(a,f(x6:S,a)),f(a,a)),f(a,f(a,a))) -> F(f(f(a,f(a,a)),f(a,a)),f(a,f(a,f(x6:S,a))))
-> Rules:
 f(f(y:S,z:S),f(x:S,f(a,x:S))) -> f(f(f(a,z:S),f(x:S,a)),f(a,y:S))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.