YES

Problem 1: 

(VAR v_NonEmpty:S x:S y:S z:S)
(RULES
+(x:S,+(y:S,z:S)) -> +(+(x:S,y:S),z:S)
f(+(x:S,0)) -> f(x:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 +#(x:S,+(y:S,z:S)) -> +#(+(x:S,y:S),z:S)
 +#(x:S,+(y:S,z:S)) -> +#(x:S,y:S)
 F(+(x:S,0)) -> F(x:S)
-> Rules:
 +(x:S,+(y:S,z:S)) -> +(+(x:S,y:S),z:S)
 f(+(x:S,0)) -> f(x:S)

Problem 1: 

SCC Processor:
-> Pairs:
 +#(x:S,+(y:S,z:S)) -> +#(+(x:S,y:S),z:S)
 +#(x:S,+(y:S,z:S)) -> +#(x:S,y:S)
 F(+(x:S,0)) -> F(x:S)
-> Rules:
 +(x:S,+(y:S,z:S)) -> +(+(x:S,y:S),z:S)
 f(+(x:S,0)) -> f(x:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(+(x:S,0)) -> F(x:S)
->->-> Rules:
 +(x:S,+(y:S,z:S)) -> +(+(x:S,y:S),z:S)
 f(+(x:S,0)) -> f(x:S)
->->Cycle:
->->-> Pairs:
 +#(x:S,+(y:S,z:S)) -> +#(+(x:S,y:S),z:S)
 +#(x:S,+(y:S,z:S)) -> +#(x:S,y:S)
->->-> Rules:
 +(x:S,+(y:S,z:S)) -> +(+(x:S,y:S),z:S)
 f(+(x:S,0)) -> f(x:S)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 F(+(x:S,0)) -> F(x:S)
-> Rules:
 +(x:S,+(y:S,z:S)) -> +(+(x:S,y:S),z:S)
 f(+(x:S,0)) -> f(x:S)
->Projection:
 pi(F) = 1

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 +#(x:S,+(y:S,z:S)) -> +#(+(x:S,y:S),z:S)
 +#(x:S,+(y:S,z:S)) -> +#(x:S,y:S)
-> Rules:
 +(x:S,+(y:S,z:S)) -> +(+(x:S,y:S),z:S)
 f(+(x:S,0)) -> f(x:S)
->Projection:
 pi(+#) = 2

Problem 1.2: 

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

The problem is finite.