YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 B(b(x1:S)) -> C(d(x1:S))
 B(b(x1:S)) -> D(x1:S)
 C(c(x1:S)) -> D(d(d(x1:S)))
 C(c(x1:S)) -> D(d(x1:S))
 C(c(x1:S)) -> D(x1:S)
 C(x1:S) -> G(x1:S)
 D(d(d(x1:S))) -> C(x1:S)
 D(d(d(x1:S))) -> G(c(x1:S))
 D(d(x1:S)) -> C(f(x1:S))
 D(d(x1:S)) -> F(x1:S)
 F(x1:S) -> G(x1:S)
 G(g(x1:S)) -> B(c(x1:S))
 G(g(x1:S)) -> C(x1:S)
 G(x1:S) -> B(x1:S)
-> Rules:
 b(b(x1:S)) -> c(d(x1:S))
 c(c(x1:S)) -> d(d(d(x1:S)))
 c(x1:S) -> g(x1:S)
 d(d(d(x1:S))) -> g(c(x1:S))
 d(d(x1:S)) -> c(f(x1:S))
 f(x1:S) -> a(g(x1:S))
 g(g(x1:S)) -> b(c(x1:S))
 g(x1:S) -> d(a(b(x1:S)))
-> Usable rules:
 b(b(x1:S)) -> c(d(x1:S))
 c(c(x1:S)) -> d(d(d(x1:S)))
 c(x1:S) -> g(x1:S)
 d(d(d(x1:S))) -> g(c(x1:S))
 d(d(x1:S)) -> c(f(x1:S))
 f(x1:S) -> a(g(x1:S))
 g(g(x1:S)) -> b(c(x1:S))
 g(x1:S) -> d(a(b(x1:S)))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[b](X) = X + 1
[c](X) = X + 1
[d](X) = X + 2/3
[f](X) = X
[g](X) = X + 1
[a](X) = 0
[B](X) = 1/2.X + 2/3
[C](X) = 1/2.X + 3/4
[D](X) = 1/2.X + 1/2
[F](X) = 1/2.X + 3/4
[G](X) = 1/2.X + 2/3

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 B(b(x1:S)) -> D(x1:S)
 C(c(x1:S)) -> D(d(d(x1:S)))
 C(c(x1:S)) -> D(d(x1:S))
 C(c(x1:S)) -> D(x1:S)
 C(x1:S) -> G(x1:S)
 D(d(d(x1:S))) -> C(x1:S)
 D(d(d(x1:S))) -> G(c(x1:S))
 D(d(x1:S)) -> C(f(x1:S))
 D(d(x1:S)) -> F(x1:S)
 F(x1:S) -> G(x1:S)
 G(g(x1:S)) -> B(c(x1:S))
 G(g(x1:S)) -> C(x1:S)
 G(x1:S) -> B(x1:S)
-> Rules:
 b(b(x1:S)) -> c(d(x1:S))
 c(c(x1:S)) -> d(d(d(x1:S)))
 c(x1:S) -> g(x1:S)
 d(d(d(x1:S))) -> g(c(x1:S))
 d(d(x1:S)) -> c(f(x1:S))
 f(x1:S) -> a(g(x1:S))
 g(g(x1:S)) -> b(c(x1:S))
 g(x1:S) -> d(a(b(x1:S)))
-> Usable rules:
 b(b(x1:S)) -> c(d(x1:S))
 c(c(x1:S)) -> d(d(d(x1:S)))
 c(x1:S) -> g(x1:S)
 d(d(d(x1:S))) -> g(c(x1:S))
 d(d(x1:S)) -> c(f(x1:S))
 f(x1:S) -> a(g(x1:S))
 g(g(x1:S)) -> b(c(x1:S))
 g(x1:S) -> d(a(b(x1:S)))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[b](X) = X + 1
[c](X) = X + 1
[d](X) = X + 2/3
[f](X) = 3/4.X
[g](X) = X + 1
[a](X) = 0
[B](X) = 4.X + 4/3
[C](X) = 4.X + 3
[D](X) = 4.X + 1/3
[F](X) = 4.X + 3/2
[G](X) = 4.X + 4/3

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 C(c(x1:S)) -> D(d(x1:S))
 C(c(x1:S)) -> D(x1:S)
 C(x1:S) -> G(x1:S)
 D(d(d(x1:S))) -> C(x1:S)
 D(d(d(x1:S))) -> G(c(x1:S))
 D(d(x1:S)) -> C(f(x1:S))
 D(d(x1:S)) -> F(x1:S)
 F(x1:S) -> G(x1:S)
 G(g(x1:S)) -> C(x1:S)
-> Rules:
 b(b(x1:S)) -> c(d(x1:S))
 c(c(x1:S)) -> d(d(d(x1:S)))
 c(x1:S) -> g(x1:S)
 d(d(d(x1:S))) -> g(c(x1:S))
 d(d(x1:S)) -> c(f(x1:S))
 f(x1:S) -> a(g(x1:S))
 g(g(x1:S)) -> b(c(x1:S))
 g(x1:S) -> d(a(b(x1:S)))
-> Usable rules:
 b(b(x1:S)) -> c(d(x1:S))
 c(c(x1:S)) -> d(d(d(x1:S)))
 c(x1:S) -> g(x1:S)
 d(d(d(x1:S))) -> g(c(x1:S))
 d(d(x1:S)) -> c(f(x1:S))
 f(x1:S) -> a(g(x1:S))
 g(g(x1:S)) -> b(c(x1:S))
 g(x1:S) -> d(a(b(x1:S)))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[b](X) = X + 3/4
[c](X) = X + 3/4
[d](X) = X + 1/2
[f](X) = 0
[g](X) = X + 3/4
[a](X) = 0
[C](X) = 1/4.X + 1/3
[D](X) = 1/4.X + 1/3
[F](X) = 1/4.X + 1/4
[G](X) = 1/4.X + 1/4

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 C(c(x1:S)) -> D(x1:S)
 C(x1:S) -> G(x1:S)
 D(d(d(x1:S))) -> C(x1:S)
 D(d(d(x1:S))) -> G(c(x1:S))
 D(d(x1:S)) -> C(f(x1:S))
 D(d(x1:S)) -> F(x1:S)
 F(x1:S) -> G(x1:S)
 G(g(x1:S)) -> C(x1:S)
-> Rules:
 b(b(x1:S)) -> c(d(x1:S))
 c(c(x1:S)) -> d(d(d(x1:S)))
 c(x1:S) -> g(x1:S)
 d(d(d(x1:S))) -> g(c(x1:S))
 d(d(x1:S)) -> c(f(x1:S))
 f(x1:S) -> a(g(x1:S))
 g(g(x1:S)) -> b(c(x1:S))
 g(x1:S) -> d(a(b(x1:S)))
-> Usable rules:
 b(b(x1:S)) -> c(d(x1:S))
 c(c(x1:S)) -> d(d(d(x1:S)))
 c(x1:S) -> g(x1:S)
 d(d(d(x1:S))) -> g(c(x1:S))
 d(d(x1:S)) -> c(f(x1:S))
 f(x1:S) -> a(g(x1:S))
 g(g(x1:S)) -> b(c(x1:S))
 g(x1:S) -> d(a(b(x1:S)))
->Interpretation type:
 Linear
->Coefficients:
 All rationals
->Dimension:
 1
->Bound:
 4
->Interpretation:
 
[b](X) = X + 2
[c](X) = X + 2
[d](X) = X + 4/3
[f](X) = X
[g](X) = X + 2
[a](X) = 0
[C](X) = 1/3.X
[D](X) = 1/3.X + 1/3
[F](X) = 1/3.X + 1/4
[G](X) = 1/3.X

Problem 1: 

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

Problem 1: 

Subterm Processor:
-> Pairs:
 C(x1:S) -> G(x1:S)
 G(g(x1:S)) -> C(x1:S)
-> Rules:
 b(b(x1:S)) -> c(d(x1:S))
 c(c(x1:S)) -> d(d(d(x1:S)))
 c(x1:S) -> g(x1:S)
 d(d(d(x1:S))) -> g(c(x1:S))
 d(d(x1:S)) -> c(f(x1:S))
 f(x1:S) -> a(g(x1:S))
 g(g(x1:S)) -> b(c(x1:S))
 g(x1:S) -> d(a(b(x1:S)))
->Projection:
 pi(C) = 1
 pi(G) = 1

Problem 1: 

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

The problem is finite.