YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 B(y:S,b(z:S,a)) -> B(c(f(a),y:S,z:S),z:S)
 B(y:S,b(z:S,a)) -> C(f(a),y:S,z:S)
 C(z:S,x:S,a) -> B(b(f(z:S),z:S),x:S)
 C(z:S,x:S,a) -> B(f(z:S),z:S)
-> Rules:
 b(y:S,b(z:S,a)) -> f(b(c(f(a),y:S,z:S),z:S))
 c(z:S,x:S,a) -> f(b(b(f(z:S),z:S),x:S))
 f(c(c(z:S,a,a),x:S,a)) -> z:S
-> Usable rules:
 b(y:S,b(z:S,a)) -> f(b(c(f(a),y:S,z:S),z:S))
 c(z:S,x:S,a) -> f(b(b(f(z:S),z:S),x:S))
 f(c(c(z:S,a,a),x:S,a)) -> z:S
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[b](X1,X2) = X1 + 2.X2 + 2
[c](X1,X2,X3) = 2.X1 + X2 + 2
[f](X) = 1/2.X
[a] = 2
[B](X1,X2) = 1/2.X1 + 1/2.X2 + 1/2
[C](X1,X2,X3) = 2.X1 + 1/2.X2 + 1/2.X3 + 1/2

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 B(y:S,b(z:S,a)) -> C(f(a),y:S,z:S)
 C(z:S,x:S,a) -> B(b(f(z:S),z:S),x:S)
 C(z:S,x:S,a) -> B(f(z:S),z:S)
-> Rules:
 b(y:S,b(z:S,a)) -> f(b(c(f(a),y:S,z:S),z:S))
 c(z:S,x:S,a) -> f(b(b(f(z:S),z:S),x:S))
 f(c(c(z:S,a,a),x:S,a)) -> z:S
-> Usable rules:
 b(y:S,b(z:S,a)) -> f(b(c(f(a),y:S,z:S),z:S))
 c(z:S,x:S,a) -> f(b(b(f(z:S),z:S),x:S))
 f(c(c(z:S,a,a),x:S,a)) -> z:S
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[b](X1,X2) = 1
[c](X1,X2,X3) = 2.X1 + 2.X2 + 1
[f](X) = X
[a] = 0
[B](X1,X2) = X1 + X2 + 1
[C](X1,X2,X3) = 2.X1 + X2 + 2

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 B(y:S,b(z:S,a)) -> C(f(a),y:S,z:S)
 C(z:S,x:S,a) -> B(b(f(z:S),z:S),x:S)
-> Rules:
 b(y:S,b(z:S,a)) -> f(b(c(f(a),y:S,z:S),z:S))
 c(z:S,x:S,a) -> f(b(b(f(z:S),z:S),x:S))
 f(c(c(z:S,a,a),x:S,a)) -> z:S
-> Usable rules:
 b(y:S,b(z:S,a)) -> f(b(c(f(a),y:S,z:S),z:S))
 c(z:S,x:S,a) -> f(b(b(f(z:S),z:S),x:S))
 f(c(c(z:S,a,a),x:S,a)) -> z:S
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[b](X1,X2) = X1 + 1/2.X2 + 2
[c](X1,X2,X3) = 2.X1 + 2.X2 + 1/2.X3 + 1
[f](X) = 1/2.X
[a] = 2
[B](X1,X2) = 1/2.X1 + 1/2.X2 + 1/2
[C](X1,X2,X3) = 1/2.X1 + 1/2.X2 + 1/2.X3 + 1

Problem 1: 

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

The problem is finite.