/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem 1: 

(VAR x1)
(RULES
A(a(x1)) -> x1
A(c(b(x1))) -> b(c(A(x1)))
B(C(a(x1))) -> a(C(B(x1)))
B(b(x1)) -> x1
C(B(A(x1))) -> A(B(C(x1)))
C(c(x1)) -> x1
a(A(x1)) -> x1
a(b(c(x1))) -> c(b(a(x1)))
b(B(x1)) -> x1
b(a(C(x1))) -> C(a(b(x1)))
c(A(B(x1))) -> B(A(c(x1)))
c(C(x1)) -> x1
)

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A#(c(b(x1))) -> A#(x1)
 A#(c(b(x1))) -> B(c(A(x1)))
 A#(c(b(x1))) -> C(A(x1))
 B#(C(a(x1))) -> B#(x1)
 B#(C(a(x1))) -> C#(B(x1))
 B#(C(a(x1))) -> A(C(B(x1)))
 C#(B(A(x1))) -> A#(B(C(x1)))
 C#(B(A(x1))) -> B#(C(x1))
 C#(B(A(x1))) -> C#(x1)
 A(b(c(x1))) -> A(x1)
 A(b(c(x1))) -> B(a(x1))
 A(b(c(x1))) -> C(b(a(x1)))
 B(a(C(x1))) -> C#(a(b(x1)))
 B(a(C(x1))) -> A(b(x1))
 B(a(C(x1))) -> B(x1)
 C(A(B(x1))) -> A#(c(x1))
 C(A(B(x1))) -> B#(A(c(x1)))
 C(A(B(x1))) -> C(x1)
-> Rules:
 A(a(x1)) -> x1
 A(c(b(x1))) -> b(c(A(x1)))
 B(C(a(x1))) -> a(C(B(x1)))
 B(b(x1)) -> x1
 C(B(A(x1))) -> A(B(C(x1)))
 C(c(x1)) -> x1
 a(A(x1)) -> x1
 a(b(c(x1))) -> c(b(a(x1)))
 b(B(x1)) -> x1
 b(a(C(x1))) -> C(a(b(x1)))
 c(A(B(x1))) -> B(A(c(x1)))
 c(C(x1)) -> x1
-> Usable rules:
 A(a(x1)) -> x1
 A(c(b(x1))) -> b(c(A(x1)))
 B(C(a(x1))) -> a(C(B(x1)))
 B(b(x1)) -> x1
 C(B(A(x1))) -> A(B(C(x1)))
 C(c(x1)) -> x1
 a(A(x1)) -> x1
 a(b(c(x1))) -> c(b(a(x1)))
 b(B(x1)) -> x1
 b(a(C(x1))) -> C(a(b(x1)))
 c(A(B(x1))) -> B(A(c(x1)))
 c(C(x1)) -> x1
->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) = X
[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) = X

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 A#(c(b(x1))) -> C(A(x1))
 B#(C(a(x1))) -> B#(x1)
 B#(C(a(x1))) -> C#(B(x1))
 B#(C(a(x1))) -> A(C(B(x1)))
 C#(B(A(x1))) -> A#(B(C(x1)))
 C#(B(A(x1))) -> B#(C(x1))
 C#(B(A(x1))) -> C#(x1)
 A(b(c(x1))) -> A(x1)
 A(b(c(x1))) -> B(a(x1))
 A(b(c(x1))) -> C(b(a(x1)))
 B(a(C(x1))) -> C#(a(b(x1)))
 B(a(C(x1))) -> A(b(x1))
 B(a(C(x1))) -> B(x1)
 C(A(B(x1))) -> A#(c(x1))
 C(A(B(x1))) -> B#(A(c(x1)))
 C(A(B(x1))) -> C(x1)
-> Rules:
 A(a(x1)) -> x1
 A(c(b(x1))) -> b(c(A(x1)))
 B(C(a(x1))) -> a(C(B(x1)))
 B(b(x1)) -> x1
 C(B(A(x1))) -> A(B(C(x1)))
 C(c(x1)) -> x1
 a(A(x1)) -> x1
 a(b(c(x1))) -> c(b(a(x1)))
 b(B(x1)) -> x1
 b(a(C(x1))) -> C(a(b(x1)))
 c(A(B(x1))) -> B(A(c(x1)))
 c(C(x1)) -> x1
-> Usable rules:
 A(a(x1)) -> x1
 A(c(b(x1))) -> b(c(A(x1)))
 B(C(a(x1))) -> a(C(B(x1)))
 B(b(x1)) -> x1
 C(B(A(x1))) -> A(B(C(x1)))
 C(c(x1)) -> x1
 a(A(x1)) -> x1
 a(b(c(x1))) -> c(b(a(x1)))
 b(B(x1)) -> x1
 b(a(C(x1))) -> C(a(b(x1)))
 c(A(B(x1))) -> B(A(c(x1)))
 c(C(x1)) -> x1
->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) = X
[A#](X) = X + 1
[B#](X) = 2.X + 2
[C#](X) = 2.X
[A](X) = 2.X + 2
[B](X) = 2.X
[C](X) = X

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 B#(C(a(x1))) -> B#(x1)
 B#(C(a(x1))) -> C#(B(x1))
 B#(C(a(x1))) -> A(C(B(x1)))
 C#(B(A(x1))) -> B#(C(x1))
 C#(B(A(x1))) -> C#(x1)
 A(b(c(x1))) -> A(x1)
 A(b(c(x1))) -> B(a(x1))
 A(b(c(x1))) -> C(b(a(x1)))
 B(a(C(x1))) -> C#(a(b(x1)))
 B(a(C(x1))) -> A(b(x1))
 B(a(C(x1))) -> B(x1)
 C(A(B(x1))) -> B#(A(c(x1)))
 C(A(B(x1))) -> C(x1)
-> Rules:
 A(a(x1)) -> x1
 A(c(b(x1))) -> b(c(A(x1)))
 B(C(a(x1))) -> a(C(B(x1)))
 B(b(x1)) -> x1
 C(B(A(x1))) -> A(B(C(x1)))
 C(c(x1)) -> x1
 a(A(x1)) -> x1
 a(b(c(x1))) -> c(b(a(x1)))
 b(B(x1)) -> x1
 b(a(C(x1))) -> C(a(b(x1)))
 c(A(B(x1))) -> B(A(c(x1)))
 c(C(x1)) -> x1
-> Usable rules:
 A(a(x1)) -> x1
 A(c(b(x1))) -> b(c(A(x1)))
 B(C(a(x1))) -> a(C(B(x1)))
 B(b(x1)) -> x1
 C(B(A(x1))) -> A(B(C(x1)))
 C(c(x1)) -> x1
 a(A(x1)) -> x1
 a(b(c(x1))) -> c(b(a(x1)))
 b(B(x1)) -> x1
 b(a(C(x1))) -> C(a(b(x1)))
 c(A(B(x1))) -> B(A(c(x1)))
 c(C(x1)) -> x1
->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) = 2.X + 2
[B#](X) = 2.X + 1
[C#](X) = X
[A](X) = 2.X + 1
[B](X) = 2.X + 2
[C](X) = 2.X + 1

Problem 1: 

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

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 B#(C(a(x1))) -> C#(B(x1))
 B#(C(a(x1))) -> A(C(B(x1)))
 C#(B(A(x1))) -> B#(C(x1))
 C#(B(A(x1))) -> C#(x1)
 A(b(c(x1))) -> A(x1)
 A(b(c(x1))) -> B(a(x1))
 A(b(c(x1))) -> C(b(a(x1)))
 B(a(C(x1))) -> C#(a(b(x1)))
 B(a(C(x1))) -> A(b(x1))
 B(a(C(x1))) -> B(x1)
 C(A(B(x1))) -> B#(A(c(x1)))
 C(A(B(x1))) -> C(x1)
-> Rules:
 A(a(x1)) -> x1
 A(c(b(x1))) -> b(c(A(x1)))
 B(C(a(x1))) -> a(C(B(x1)))
 B(b(x1)) -> x1
 C(B(A(x1))) -> A(B(C(x1)))
 C(c(x1)) -> x1
 a(A(x1)) -> x1
 a(b(c(x1))) -> c(b(a(x1)))
 b(B(x1)) -> x1
 b(a(C(x1))) -> C(a(b(x1)))
 c(A(B(x1))) -> B(A(c(x1)))
 c(C(x1)) -> x1
-> Usable rules:
 A(a(x1)) -> x1
 A(c(b(x1))) -> b(c(A(x1)))
 B(C(a(x1))) -> a(C(B(x1)))
 B(b(x1)) -> x1
 C(B(A(x1))) -> A(B(C(x1)))
 C(c(x1)) -> x1
 a(A(x1)) -> x1
 a(b(c(x1))) -> c(b(a(x1)))
 b(B(x1)) -> x1
 b(a(C(x1))) -> C(a(b(x1)))
 c(A(B(x1))) -> B(A(c(x1)))
 c(C(x1)) -> x1
->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
[B#](X) = X + 1
[C#](X) = 2.X
[A](X) = X + 1
[B](X) = 2.X + 2
[C](X) = X + 1

Problem 1: 

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

Problem 1: 

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

Problem 1: 

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


The problem is decomposed in 3 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 C(A(B(x1))) -> C(x1)
-> Rules:
 A(a(x1)) -> x1
 A(c(b(x1))) -> b(c(A(x1)))
 B(C(a(x1))) -> a(C(B(x1)))
 B(b(x1)) -> x1
 C(B(A(x1))) -> A(B(C(x1)))
 C(c(x1)) -> x1
 a(A(x1)) -> x1
 a(b(c(x1))) -> c(b(a(x1)))
 b(B(x1)) -> x1
 b(a(C(x1))) -> C(a(b(x1)))
 c(A(B(x1))) -> B(A(c(x1)))
 c(C(x1)) -> x1
->Projection:
 pi(C) = 1

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 C#(B(A(x1))) -> C#(x1)
-> Rules:
 A(a(x1)) -> x1
 A(c(b(x1))) -> b(c(A(x1)))
 B(C(a(x1))) -> a(C(B(x1)))
 B(b(x1)) -> x1
 C(B(A(x1))) -> A(B(C(x1)))
 C(c(x1)) -> x1
 a(A(x1)) -> x1
 a(b(c(x1))) -> c(b(a(x1)))
 b(B(x1)) -> x1
 b(a(C(x1))) -> C(a(b(x1)))
 c(A(B(x1))) -> B(A(c(x1)))
 c(C(x1)) -> x1
->Projection:
 pi(C#) = 1

Problem 1.2: 

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

The problem is finite.

Problem 1.3: 

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

Problem 1.3: 

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

Problem 1.3: 

Reduction Pair Processor:
-> Pairs:
 A(b(c(x1))) -> B(a(x1))
 B(a(C(x1))) -> A(b(x1))
 B(a(C(x1))) -> B(x1)
-> Rules:
 A(a(x1)) -> x1
 A(c(b(x1))) -> b(c(A(x1)))
 B(C(a(x1))) -> a(C(B(x1)))
 B(b(x1)) -> x1
 C(B(A(x1))) -> A(B(C(x1)))
 C(c(x1)) -> x1
 a(A(x1)) -> x1
 a(b(c(x1))) -> c(b(a(x1)))
 b(B(x1)) -> x1
 b(a(C(x1))) -> C(a(b(x1)))
 c(A(B(x1))) -> B(A(c(x1)))
 c(C(x1)) -> x1
-> Usable rules:
 A(a(x1)) -> x1
 A(c(b(x1))) -> b(c(A(x1)))
 B(C(a(x1))) -> a(C(B(x1)))
 B(b(x1)) -> x1
 C(B(A(x1))) -> A(B(C(x1)))
 C(c(x1)) -> x1
 a(A(x1)) -> x1
 a(b(c(x1))) -> c(b(a(x1)))
 b(B(x1)) -> x1
 b(a(C(x1))) -> C(a(b(x1)))
 c(A(B(x1))) -> B(A(c(x1)))
 c(C(x1)) -> x1
->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
[A](X) = 2.X + 2
[B](X) = X + 1

Problem 1.3: 

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

Problem 1.3: 

Subterm Processor:
-> Pairs:
 B(a(C(x1))) -> B(x1)
-> Rules:
 A(a(x1)) -> x1
 A(c(b(x1))) -> b(c(A(x1)))
 B(C(a(x1))) -> a(C(B(x1)))
 B(b(x1)) -> x1
 C(B(A(x1))) -> A(B(C(x1)))
 C(c(x1)) -> x1
 a(A(x1)) -> x1
 a(b(c(x1))) -> c(b(a(x1)))
 b(B(x1)) -> x1
 b(a(C(x1))) -> C(a(b(x1)))
 c(A(B(x1))) -> B(A(c(x1)))
 c(C(x1)) -> x1
->Projection:
 pi(B) = 1

Problem 1.3: 

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

The problem is finite.