YES

Problem 1: 

(VAR v_NonEmpty:S x1:S)
(RULES
a(x1:S) -> g(d(x1:S))
b(b(b(x1:S))) -> c(d(c(x1:S)))
b(b(x1:S)) -> a(g(g(x1:S)))
c(d(x1:S)) -> g(g(x1:S))
g(g(g(x1:S))) -> b(b(x1:S))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 B(b(b(x1:S))) -> C(d(c(x1:S)))
 B(b(b(x1:S))) -> C(x1:S)
 B(b(x1:S)) -> A(g(g(x1:S)))
 B(b(x1:S)) -> G(g(x1:S))
 B(b(x1:S)) -> G(x1:S)
 C(d(x1:S)) -> G(g(x1:S))
 C(d(x1:S)) -> G(x1:S)
 G(g(g(x1:S))) -> B(b(x1:S))
 G(g(g(x1:S))) -> B(x1:S)
-> Rules:
 a(x1:S) -> g(d(x1:S))
 b(b(b(x1:S))) -> c(d(c(x1:S)))
 b(b(x1:S)) -> a(g(g(x1:S)))
 c(d(x1:S)) -> g(g(x1:S))
 g(g(g(x1:S))) -> b(b(x1:S))

Problem 1: 

SCC Processor:
-> Pairs:
 B(b(b(x1:S))) -> C(d(c(x1:S)))
 B(b(b(x1:S))) -> C(x1:S)
 B(b(x1:S)) -> A(g(g(x1:S)))
 B(b(x1:S)) -> G(g(x1:S))
 B(b(x1:S)) -> G(x1:S)
 C(d(x1:S)) -> G(g(x1:S))
 C(d(x1:S)) -> G(x1:S)
 G(g(g(x1:S))) -> B(b(x1:S))
 G(g(g(x1:S))) -> B(x1:S)
-> Rules:
 a(x1:S) -> g(d(x1:S))
 b(b(b(x1:S))) -> c(d(c(x1:S)))
 b(b(x1:S)) -> a(g(g(x1:S)))
 c(d(x1:S)) -> g(g(x1:S))
 g(g(g(x1:S))) -> b(b(x1:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 B(b(b(x1:S))) -> C(d(c(x1:S)))
 B(b(b(x1:S))) -> C(x1:S)
 B(b(x1:S)) -> G(g(x1:S))
 B(b(x1:S)) -> G(x1:S)
 C(d(x1:S)) -> G(g(x1:S))
 C(d(x1:S)) -> G(x1:S)
 G(g(g(x1:S))) -> B(b(x1:S))
 G(g(g(x1:S))) -> B(x1:S)
->->-> Rules:
 a(x1:S) -> g(d(x1:S))
 b(b(b(x1:S))) -> c(d(c(x1:S)))
 b(b(x1:S)) -> a(g(g(x1:S)))
 c(d(x1:S)) -> g(g(x1:S))
 g(g(g(x1:S))) -> b(b(x1:S))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 B(b(b(x1:S))) -> C(d(c(x1:S)))
 B(b(b(x1:S))) -> C(x1:S)
 B(b(x1:S)) -> G(g(x1:S))
 B(b(x1:S)) -> G(x1:S)
 C(d(x1:S)) -> G(g(x1:S))
 C(d(x1:S)) -> G(x1:S)
 G(g(g(x1:S))) -> B(b(x1:S))
 G(g(g(x1:S))) -> B(x1:S)
-> Rules:
 a(x1:S) -> g(d(x1:S))
 b(b(b(x1:S))) -> c(d(c(x1:S)))
 b(b(x1:S)) -> a(g(g(x1:S)))
 c(d(x1:S)) -> g(g(x1:S))
 g(g(g(x1:S))) -> b(b(x1:S))
-> Usable rules:
 a(x1:S) -> g(d(x1:S))
 b(b(b(x1:S))) -> c(d(c(x1:S)))
 b(b(x1:S)) -> a(g(g(x1:S)))
 c(d(x1:S)) -> g(g(x1:S))
 g(g(g(x1:S))) -> b(b(x1:S))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[a](X) = X + 2/3
[b](X) = X + 1
[c](X) = X + 4/3
[g](X) = X + 2/3
[d](X) = X
[B](X) = 1/2.X + 3/4
[C](X) = 1/2.X + 1
[G](X) = 1/2.X + 2/3

Problem 1: 

SCC Processor:
-> Pairs:
 B(b(b(x1:S))) -> C(x1:S)
 B(b(x1:S)) -> G(g(x1:S))
 B(b(x1:S)) -> G(x1:S)
 C(d(x1:S)) -> G(g(x1:S))
 C(d(x1:S)) -> G(x1:S)
 G(g(g(x1:S))) -> B(b(x1:S))
 G(g(g(x1:S))) -> B(x1:S)
-> Rules:
 a(x1:S) -> g(d(x1:S))
 b(b(b(x1:S))) -> c(d(c(x1:S)))
 b(b(x1:S)) -> a(g(g(x1:S)))
 c(d(x1:S)) -> g(g(x1:S))
 g(g(g(x1:S))) -> b(b(x1:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 B(b(b(x1:S))) -> C(x1:S)
 B(b(x1:S)) -> G(g(x1:S))
 B(b(x1:S)) -> G(x1:S)
 C(d(x1:S)) -> G(g(x1:S))
 C(d(x1:S)) -> G(x1:S)
 G(g(g(x1:S))) -> B(b(x1:S))
 G(g(g(x1:S))) -> B(x1:S)
->->-> Rules:
 a(x1:S) -> g(d(x1:S))
 b(b(b(x1:S))) -> c(d(c(x1:S)))
 b(b(x1:S)) -> a(g(g(x1:S)))
 c(d(x1:S)) -> g(g(x1:S))
 g(g(g(x1:S))) -> b(b(x1:S))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 B(b(b(x1:S))) -> C(x1:S)
 B(b(x1:S)) -> G(g(x1:S))
 B(b(x1:S)) -> G(x1:S)
 C(d(x1:S)) -> G(g(x1:S))
 C(d(x1:S)) -> G(x1:S)
 G(g(g(x1:S))) -> B(b(x1:S))
 G(g(g(x1:S))) -> B(x1:S)
-> Rules:
 a(x1:S) -> g(d(x1:S))
 b(b(b(x1:S))) -> c(d(c(x1:S)))
 b(b(x1:S)) -> a(g(g(x1:S)))
 c(d(x1:S)) -> g(g(x1:S))
 g(g(g(x1:S))) -> b(b(x1:S))
-> Usable rules:
 a(x1:S) -> g(d(x1:S))
 b(b(b(x1:S))) -> c(d(c(x1:S)))
 b(b(x1:S)) -> a(g(g(x1:S)))
 c(d(x1:S)) -> g(g(x1:S))
 g(g(g(x1:S))) -> b(b(x1:S))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[a](X) = X + 1/2
[b](X) = X + 3/4
[c](X) = X + 1
[g](X) = X + 1/2
[d](X) = X
[B](X) = 2.X + 4/3
[C](X) = 2.X + 4
[G](X) = 2.X + 4/3

Problem 1: 

SCC Processor:
-> Pairs:
 B(b(x1:S)) -> G(g(x1:S))
 B(b(x1:S)) -> G(x1:S)
 C(d(x1:S)) -> G(g(x1:S))
 C(d(x1:S)) -> G(x1:S)
 G(g(g(x1:S))) -> B(b(x1:S))
 G(g(g(x1:S))) -> B(x1:S)
-> Rules:
 a(x1:S) -> g(d(x1:S))
 b(b(b(x1:S))) -> c(d(c(x1:S)))
 b(b(x1:S)) -> a(g(g(x1:S)))
 c(d(x1:S)) -> g(g(x1:S))
 g(g(g(x1:S))) -> b(b(x1:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 B(b(x1:S)) -> G(g(x1:S))
 B(b(x1:S)) -> G(x1:S)
 G(g(g(x1:S))) -> B(b(x1:S))
 G(g(g(x1:S))) -> B(x1:S)
->->-> Rules:
 a(x1:S) -> g(d(x1:S))
 b(b(b(x1:S))) -> c(d(c(x1:S)))
 b(b(x1:S)) -> a(g(g(x1:S)))
 c(d(x1:S)) -> g(g(x1:S))
 g(g(g(x1:S))) -> b(b(x1:S))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 B(b(x1:S)) -> G(g(x1:S))
 B(b(x1:S)) -> G(x1:S)
 G(g(g(x1:S))) -> B(b(x1:S))
 G(g(g(x1:S))) -> B(x1:S)
-> Rules:
 a(x1:S) -> g(d(x1:S))
 b(b(b(x1:S))) -> c(d(c(x1:S)))
 b(b(x1:S)) -> a(g(g(x1:S)))
 c(d(x1:S)) -> g(g(x1:S))
 g(g(g(x1:S))) -> b(b(x1:S))
-> Usable rules:
 a(x1:S) -> g(d(x1:S))
 b(b(b(x1:S))) -> c(d(c(x1:S)))
 b(b(x1:S)) -> a(g(g(x1:S)))
 c(d(x1:S)) -> g(g(x1:S))
 g(g(g(x1:S))) -> b(b(x1:S))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[a](X) = X + 1/2
[b](X) = X + 3/4
[c](X) = X + 1
[g](X) = X + 1/2
[d](X) = X
[B](X) = 2/3.X + 1/2
[G](X) = 2/3.X + 1/3

Problem 1: 

SCC Processor:
-> Pairs:
 B(b(x1:S)) -> G(x1:S)
 G(g(g(x1:S))) -> B(b(x1:S))
 G(g(g(x1:S))) -> B(x1:S)
-> Rules:
 a(x1:S) -> g(d(x1:S))
 b(b(b(x1:S))) -> c(d(c(x1:S)))
 b(b(x1:S)) -> a(g(g(x1:S)))
 c(d(x1:S)) -> g(g(x1:S))
 g(g(g(x1:S))) -> b(b(x1:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 B(b(x1:S)) -> G(x1:S)
 G(g(g(x1:S))) -> B(b(x1:S))
 G(g(g(x1:S))) -> B(x1:S)
->->-> Rules:
 a(x1:S) -> g(d(x1:S))
 b(b(b(x1:S))) -> c(d(c(x1:S)))
 b(b(x1:S)) -> a(g(g(x1:S)))
 c(d(x1:S)) -> g(g(x1:S))
 g(g(g(x1:S))) -> b(b(x1:S))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 B(b(x1:S)) -> G(x1:S)
 G(g(g(x1:S))) -> B(b(x1:S))
 G(g(g(x1:S))) -> B(x1:S)
-> Rules:
 a(x1:S) -> g(d(x1:S))
 b(b(b(x1:S))) -> c(d(c(x1:S)))
 b(b(x1:S)) -> a(g(g(x1:S)))
 c(d(x1:S)) -> g(g(x1:S))
 g(g(g(x1:S))) -> b(b(x1:S))
-> Usable rules:
 a(x1:S) -> g(d(x1:S))
 b(b(b(x1:S))) -> c(d(c(x1:S)))
 b(b(x1:S)) -> a(g(g(x1:S)))
 c(d(x1:S)) -> g(g(x1:S))
 g(g(g(x1:S))) -> b(b(x1:S))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[a](X) = X + 1
[b](X) = X + 3/2
[c](X) = X + 2
[g](X) = X + 1
[d](X) = X
[B](X) = 3.X + 3/4
[G](X) = 3.X + 4

Problem 1: 

SCC Processor:
-> Pairs:
 G(g(g(x1:S))) -> B(b(x1:S))
 G(g(g(x1:S))) -> B(x1:S)
-> Rules:
 a(x1:S) -> g(d(x1:S))
 b(b(b(x1:S))) -> c(d(c(x1:S)))
 b(b(x1:S)) -> a(g(g(x1:S)))
 c(d(x1:S)) -> g(g(x1:S))
 g(g(g(x1:S))) -> b(b(x1:S))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.