YES

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(b(c(x1:S))) -> A(x1:S)
 A(b(c(x1:S))) -> B(a(x1:S))
 A(b(c(x1:S))) -> C(b(a(x1:S)))
 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
 B(a(a(a(x1:S)))) -> A(a(b(x1:S)))
 B(a(a(a(x1:S)))) -> A(b(x1:S))
 B(a(a(a(x1:S)))) -> B(x1:S)
 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
 C(b(a(a(x1:S)))) -> B(c(x1:S))
 C(b(a(a(x1:S)))) -> C(x1:S)
 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
 C(c(b(b(x1:S)))) -> C(c(x1:S))
 C(c(b(b(x1:S)))) -> C(x1:S)
-> Rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
-> Usable rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = X
[b](X) = 2.X + 2
[c](X) = 2.X + 2
[A](X) = X
[B](X) = 2.X + 2
[C](X) = 2.X + 2

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(b(c(x1:S))) -> B(a(x1:S))
 A(b(c(x1:S))) -> C(b(a(x1:S)))
 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
 B(a(a(a(x1:S)))) -> A(a(b(x1:S)))
 B(a(a(a(x1:S)))) -> A(b(x1:S))
 B(a(a(a(x1:S)))) -> B(x1:S)
 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
 C(b(a(a(x1:S)))) -> B(c(x1:S))
 C(b(a(a(x1:S)))) -> C(x1:S)
 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
 C(c(b(b(x1:S)))) -> C(c(x1:S))
 C(c(b(b(x1:S)))) -> C(x1:S)
-> Rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
-> Usable rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 2.X + 2
[b](X) = 2.X + 2
[c](X) = 2.X + 2
[A](X) = 2.X
[B](X) = 2.X
[C](X) = 2.X

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(b(c(x1:S))) -> C(b(a(x1:S)))
 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
 B(a(a(a(x1:S)))) -> A(a(b(x1:S)))
 B(a(a(a(x1:S)))) -> A(b(x1:S))
 B(a(a(a(x1:S)))) -> B(x1:S)
 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
 C(b(a(a(x1:S)))) -> B(c(x1:S))
 C(b(a(a(x1:S)))) -> C(x1:S)
 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
 C(c(b(b(x1:S)))) -> C(c(x1:S))
 C(c(b(b(x1:S)))) -> C(x1:S)
-> Rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
-> Usable rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 2.X + 2
[b](X) = 2.X + 2
[c](X) = 2.X + 2
[A](X) = X
[B](X) = X
[C](X) = X

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(b(c(x1:S))) -> C(b(a(x1:S)))
 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
 B(a(a(a(x1:S)))) -> A(b(x1:S))
 B(a(a(a(x1:S)))) -> B(x1:S)
 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
 C(b(a(a(x1:S)))) -> B(c(x1:S))
 C(b(a(a(x1:S)))) -> C(x1:S)
 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
 C(c(b(b(x1:S)))) -> C(c(x1:S))
 C(c(b(b(x1:S)))) -> C(x1:S)
-> Rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
-> Usable rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 2.X + 2
[b](X) = 2.X + 2
[c](X) = X
[A](X) = 2.X + 2
[B](X) = 2.X + 2
[C](X) = X

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(b(c(x1:S))) -> C(b(a(x1:S)))
 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
 B(a(a(a(x1:S)))) -> B(x1:S)
 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
 C(b(a(a(x1:S)))) -> B(c(x1:S))
 C(b(a(a(x1:S)))) -> C(x1:S)
 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
 C(c(b(b(x1:S)))) -> C(c(x1:S))
 C(c(b(b(x1:S)))) -> C(x1:S)
-> Rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
-> Usable rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = X + 1
[b](X) = X + 2
[c](X) = X + 2
[A](X) = 2.X
[B](X) = 2.X + 2
[C](X) = 2.X + 2

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(b(c(x1:S))) -> C(b(a(x1:S)))
 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
 C(b(a(a(x1:S)))) -> A(b(c(x1:S)))
 C(b(a(a(x1:S)))) -> B(c(x1:S))
 C(b(a(a(x1:S)))) -> C(x1:S)
 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
 C(c(b(b(x1:S)))) -> C(c(x1:S))
 C(c(b(b(x1:S)))) -> C(x1:S)
-> Rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
-> Usable rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = X + 2
[b](X) = X + 2
[c](X) = X + 2
[A](X) = 2.X + 2
[B](X) = 2.X + 2
[C](X) = 2.X + 2

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(b(c(x1:S))) -> C(b(a(x1:S)))
 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
 C(b(a(a(x1:S)))) -> B(c(x1:S))
 C(b(a(a(x1:S)))) -> C(x1:S)
 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
 C(c(b(b(x1:S)))) -> C(c(x1:S))
 C(c(b(b(x1:S)))) -> C(x1:S)
-> Rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
-> Usable rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 2.X + 2
[b](X) = 2.X + 2
[c](X) = 2.X + 2
[A](X) = 2.X + 2
[B](X) = 2.X + 2
[C](X) = 2.X + 2

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(b(c(x1:S))) -> C(b(a(x1:S)))
 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
 C(b(a(a(x1:S)))) -> C(x1:S)
 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
 C(c(b(b(x1:S)))) -> C(c(x1:S))
 C(c(b(b(x1:S)))) -> C(x1:S)
-> Rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
-> Usable rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 2.X + 2
[b](X) = 2.X + 2
[c](X) = 2.X + 2
[A](X) = 2.X + 2
[B](X) = 2.X + 2
[C](X) = 2.X + 2

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(b(c(x1:S))) -> C(b(a(x1:S)))
 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
 C(c(b(b(x1:S)))) -> B(c(c(x1:S)))
 C(c(b(b(x1:S)))) -> C(c(x1:S))
 C(c(b(b(x1:S)))) -> C(x1:S)
-> Rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
-> Usable rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = X + 2
[b](X) = X + 2
[c](X) = X + 2
[A](X) = 2.X + 2
[B](X) = 2.X + 2
[C](X) = 2.X + 2

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(b(c(x1:S))) -> C(b(a(x1:S)))
 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
 C(c(b(b(x1:S)))) -> C(c(x1:S))
 C(c(b(b(x1:S)))) -> C(x1:S)
-> Rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
-> Usable rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 2.X + 2
[b](X) = 2.X + 2
[c](X) = 2.X + 2
[A](X) = 2.X + 2
[B](X) = 2.X + 2
[C](X) = 2.X + 2

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(b(c(x1:S))) -> C(b(a(x1:S)))
 B(a(a(a(x1:S)))) -> A(a(a(b(x1:S))))
 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
 C(c(b(b(x1:S)))) -> B(b(c(c(x1:S))))
 C(c(b(b(x1:S)))) -> C(x1:S)
-> Rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
-> Usable rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a](X) = 2.X + 2
[b](X) = 2.X + 2
[c](X) = 2.X + 2
[A](X) = 2.X + 2
[B](X) = 2.X + 2
[C](X) = 2.X + 2

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A(b(c(x1:S))) -> C(b(a(x1:S)))
 C(b(a(a(x1:S)))) -> A(a(b(c(x1:S))))
-> Rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
-> Usable rules:
 a(b(c(x1:S))) -> c(b(a(x1:S)))
 b(a(a(a(x1:S)))) -> a(a(a(b(x1:S))))
 c(b(a(a(x1:S)))) -> a(a(b(c(x1:S))))
 c(c(b(b(x1:S)))) -> b(b(c(c(x1:S))))
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 2
->Bound:
 1
->Interpretation:
 
[a](X) = [0 1;0 0].X + [0;1]
[b](X) = [0 0;1 0].X + [1;0]
[c](X) = [0 1;1 0].X + [1;0]
[A](X) = [0 1;0 1].X + [1;1]
[C](X) = [0 1;1 0].X + [1;1]

Problem 1: 

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

The problem is finite.