0.00/0.26	YES
0.00/0.26	
0.00/0.26	Problem 1: 
0.00/0.26	
0.00/0.26	(VAR v_NonEmpty:S x1:S)
0.00/0.26	(RULES
0.00/0.26	a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.26	a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.26	a(d(x1:S)) -> d(a(x1:S))
0.00/0.26	b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.26	b(d(x1:S)) -> a(b(x1:S))
0.00/0.26	c(a(x1:S)) -> a(c(x1:S))
0.00/0.26	c(b(x1:S)) -> b(a(x1:S))
0.00/0.26	)
0.00/0.26	
0.00/0.26	Problem 1: 
0.00/0.26	
0.00/0.26	Dependency Pairs Processor:
0.00/0.26	-> Pairs:
0.00/0.26	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.26	 A(a(b(x1:S))) -> B(a(x1:S))
0.00/0.26	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.26	 A(a(x1:S)) -> B(a(x1:S))
0.00/0.26	 A(d(x1:S)) -> A(x1:S)
0.00/0.26	 B(a(a(x1:S))) -> A(b(c(x1:S)))
0.00/0.26	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.26	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.26	 B(d(x1:S)) -> A(b(x1:S))
0.00/0.26	 B(d(x1:S)) -> B(x1:S)
0.00/0.26	 C(a(x1:S)) -> A(c(x1:S))
0.00/0.26	 C(a(x1:S)) -> C(x1:S)
0.00/0.26	 C(b(x1:S)) -> A(x1:S)
0.00/0.26	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.26	-> Rules:
0.00/0.26	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.26	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.26	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.26	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.26	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.26	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.26	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.26	
0.00/0.26	Problem 1: 
0.00/0.26	
0.00/0.26	SCC Processor:
0.00/0.26	-> Pairs:
0.00/0.26	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.26	 A(a(b(x1:S))) -> B(a(x1:S))
0.00/0.26	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.26	 A(a(x1:S)) -> B(a(x1:S))
0.00/0.26	 A(d(x1:S)) -> A(x1:S)
0.00/0.26	 B(a(a(x1:S))) -> A(b(c(x1:S)))
0.00/0.26	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.26	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.26	 B(d(x1:S)) -> A(b(x1:S))
0.00/0.26	 B(d(x1:S)) -> B(x1:S)
0.00/0.26	 C(a(x1:S)) -> A(c(x1:S))
0.00/0.26	 C(a(x1:S)) -> C(x1:S)
0.00/0.26	 C(b(x1:S)) -> A(x1:S)
0.00/0.26	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.26	-> Rules:
0.00/0.26	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.26	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.26	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.26	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.26	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.26	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.26	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.26	->Strongly Connected Components:
0.00/0.26	->->Cycle:
0.00/0.26	->->-> Pairs:
0.00/0.26	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.26	 A(a(b(x1:S))) -> B(a(x1:S))
0.00/0.26	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.26	 A(a(x1:S)) -> B(a(x1:S))
0.00/0.26	 A(d(x1:S)) -> A(x1:S)
0.00/0.26	 B(a(a(x1:S))) -> A(b(c(x1:S)))
0.00/0.26	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.26	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.26	 B(d(x1:S)) -> A(b(x1:S))
0.00/0.26	 B(d(x1:S)) -> B(x1:S)
0.00/0.26	 C(a(x1:S)) -> A(c(x1:S))
0.00/0.26	 C(a(x1:S)) -> C(x1:S)
0.00/0.26	 C(b(x1:S)) -> A(x1:S)
0.00/0.26	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.26	->->-> Rules:
0.00/0.26	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.26	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.26	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.26	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.26	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.26	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.26	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.26	
0.00/0.26	Problem 1: 
0.00/0.26	
0.00/0.26	Reduction Pair Processor:
0.00/0.26	-> Pairs:
0.00/0.26	 A(a(b(x1:S))) -> A(x1:S)
0.00/0.26	 A(a(b(x1:S))) -> B(a(x1:S))
0.00/0.26	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.26	 A(a(x1:S)) -> B(a(x1:S))
0.00/0.26	 A(d(x1:S)) -> A(x1:S)
0.00/0.26	 B(a(a(x1:S))) -> A(b(c(x1:S)))
0.00/0.26	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.26	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.26	 B(d(x1:S)) -> A(b(x1:S))
0.00/0.26	 B(d(x1:S)) -> B(x1:S)
0.00/0.26	 C(a(x1:S)) -> A(c(x1:S))
0.00/0.26	 C(a(x1:S)) -> C(x1:S)
0.00/0.26	 C(b(x1:S)) -> A(x1:S)
0.00/0.26	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.26	-> Rules:
0.00/0.26	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.26	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.26	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.26	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.26	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.26	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.26	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.26	-> Usable rules:
0.00/0.26	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.26	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.26	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.26	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.26	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.26	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.26	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.26	->Interpretation type:
0.00/0.26	 Linear
0.00/0.26	->Coefficients:
0.00/0.26	 Natural Numbers
0.00/0.26	->Dimension:
0.00/0.26	 1
0.00/0.26	->Bound:
0.00/0.26	 2
0.00/0.26	->Interpretation:
0.00/0.26	 
0.00/0.26	[a](X) = 2.X + 2
0.00/0.27	[b](X) = X
0.00/0.27	[c](X) = 2.X + 2
0.00/0.27	[d](X) = 2.X + 2
0.00/0.27	[A](X) = 2.X + 2
0.00/0.27	[B](X) = X
0.00/0.27	[C](X) = 2.X + 2
0.00/0.27	
0.00/0.27	Problem 1: 
0.00/0.27	
0.00/0.27	SCC Processor:
0.00/0.27	-> Pairs:
0.00/0.27	 A(a(b(x1:S))) -> B(a(x1:S))
0.00/0.27	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.27	 A(a(x1:S)) -> B(a(x1:S))
0.00/0.27	 A(d(x1:S)) -> A(x1:S)
0.00/0.27	 B(a(a(x1:S))) -> A(b(c(x1:S)))
0.00/0.27	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.27	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.27	 B(d(x1:S)) -> A(b(x1:S))
0.00/0.27	 B(d(x1:S)) -> B(x1:S)
0.00/0.27	 C(a(x1:S)) -> A(c(x1:S))
0.00/0.27	 C(a(x1:S)) -> C(x1:S)
0.00/0.27	 C(b(x1:S)) -> A(x1:S)
0.00/0.27	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.27	-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->Strongly Connected Components:
0.00/0.27	->->Cycle:
0.00/0.27	->->-> Pairs:
0.00/0.27	 A(a(b(x1:S))) -> B(a(x1:S))
0.00/0.27	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.27	 A(a(x1:S)) -> B(a(x1:S))
0.00/0.27	 A(d(x1:S)) -> A(x1:S)
0.00/0.27	 B(a(a(x1:S))) -> A(b(c(x1:S)))
0.00/0.27	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.27	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.27	 B(d(x1:S)) -> A(b(x1:S))
0.00/0.27	 B(d(x1:S)) -> B(x1:S)
0.00/0.27	 C(a(x1:S)) -> A(c(x1:S))
0.00/0.27	 C(a(x1:S)) -> C(x1:S)
0.00/0.27	 C(b(x1:S)) -> A(x1:S)
0.00/0.27	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.27	->->-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	
0.00/0.27	Problem 1: 
0.00/0.27	
0.00/0.27	Reduction Pair Processor:
0.00/0.27	-> Pairs:
0.00/0.27	 A(a(b(x1:S))) -> B(a(x1:S))
0.00/0.27	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.27	 A(a(x1:S)) -> B(a(x1:S))
0.00/0.27	 A(d(x1:S)) -> A(x1:S)
0.00/0.27	 B(a(a(x1:S))) -> A(b(c(x1:S)))
0.00/0.27	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.27	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.27	 B(d(x1:S)) -> A(b(x1:S))
0.00/0.27	 B(d(x1:S)) -> B(x1:S)
0.00/0.27	 C(a(x1:S)) -> A(c(x1:S))
0.00/0.27	 C(a(x1:S)) -> C(x1:S)
0.00/0.27	 C(b(x1:S)) -> A(x1:S)
0.00/0.27	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.27	-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	-> Usable rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->Interpretation type:
0.00/0.27	 Linear
0.00/0.27	->Coefficients:
0.00/0.27	 Natural Numbers
0.00/0.27	->Dimension:
0.00/0.27	 1
0.00/0.27	->Bound:
0.00/0.27	 2
0.00/0.27	->Interpretation:
0.00/0.27	 
0.00/0.27	[a](X) = 2.X + 2
0.00/0.27	[b](X) = X
0.00/0.27	[c](X) = 2.X + 2
0.00/0.27	[d](X) = 2.X + 2
0.00/0.27	[A](X) = X + 1
0.00/0.27	[B](X) = X
0.00/0.27	[C](X) = 2.X + 2
0.00/0.27	
0.00/0.27	Problem 1: 
0.00/0.27	
0.00/0.27	SCC Processor:
0.00/0.27	-> Pairs:
0.00/0.27	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.27	 A(a(x1:S)) -> B(a(x1:S))
0.00/0.27	 A(d(x1:S)) -> A(x1:S)
0.00/0.27	 B(a(a(x1:S))) -> A(b(c(x1:S)))
0.00/0.27	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.27	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.27	 B(d(x1:S)) -> A(b(x1:S))
0.00/0.27	 B(d(x1:S)) -> B(x1:S)
0.00/0.27	 C(a(x1:S)) -> A(c(x1:S))
0.00/0.27	 C(a(x1:S)) -> C(x1:S)
0.00/0.27	 C(b(x1:S)) -> A(x1:S)
0.00/0.27	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.27	-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->Strongly Connected Components:
0.00/0.27	->->Cycle:
0.00/0.27	->->-> Pairs:
0.00/0.27	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.27	 A(a(x1:S)) -> B(a(x1:S))
0.00/0.27	 A(d(x1:S)) -> A(x1:S)
0.00/0.27	 B(a(a(x1:S))) -> A(b(c(x1:S)))
0.00/0.27	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.27	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.27	 B(d(x1:S)) -> A(b(x1:S))
0.00/0.27	 B(d(x1:S)) -> B(x1:S)
0.00/0.27	 C(a(x1:S)) -> A(c(x1:S))
0.00/0.27	 C(a(x1:S)) -> C(x1:S)
0.00/0.27	 C(b(x1:S)) -> A(x1:S)
0.00/0.27	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.27	->->-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	
0.00/0.27	Problem 1: 
0.00/0.27	
0.00/0.27	Reduction Pair Processor:
0.00/0.27	-> Pairs:
0.00/0.27	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.27	 A(a(x1:S)) -> B(a(x1:S))
0.00/0.27	 A(d(x1:S)) -> A(x1:S)
0.00/0.27	 B(a(a(x1:S))) -> A(b(c(x1:S)))
0.00/0.27	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.27	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.27	 B(d(x1:S)) -> A(b(x1:S))
0.00/0.27	 B(d(x1:S)) -> B(x1:S)
0.00/0.27	 C(a(x1:S)) -> A(c(x1:S))
0.00/0.27	 C(a(x1:S)) -> C(x1:S)
0.00/0.27	 C(b(x1:S)) -> A(x1:S)
0.00/0.27	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.27	-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	-> Usable rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->Interpretation type:
0.00/0.27	 Linear
0.00/0.27	->Coefficients:
0.00/0.27	 Natural Numbers
0.00/0.27	->Dimension:
0.00/0.27	 1
0.00/0.27	->Bound:
0.00/0.27	 2
0.00/0.27	->Interpretation:
0.00/0.27	 
0.00/0.27	[a](X) = X + 1
0.00/0.27	[b](X) = X
0.00/0.27	[c](X) = X + 1
0.00/0.27	[d](X) = X + 1
0.00/0.27	[A](X) = 2.X + 2
0.00/0.27	[B](X) = 2.X
0.00/0.27	[C](X) = 2.X + 2
0.00/0.27	
0.00/0.27	Problem 1: 
0.00/0.27	
0.00/0.27	SCC Processor:
0.00/0.27	-> Pairs:
0.00/0.27	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.27	 A(d(x1:S)) -> A(x1:S)
0.00/0.27	 B(a(a(x1:S))) -> A(b(c(x1:S)))
0.00/0.27	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.27	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.27	 B(d(x1:S)) -> A(b(x1:S))
0.00/0.27	 B(d(x1:S)) -> B(x1:S)
0.00/0.27	 C(a(x1:S)) -> A(c(x1:S))
0.00/0.27	 C(a(x1:S)) -> C(x1:S)
0.00/0.27	 C(b(x1:S)) -> A(x1:S)
0.00/0.27	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.27	-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->Strongly Connected Components:
0.00/0.27	->->Cycle:
0.00/0.27	->->-> Pairs:
0.00/0.27	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.27	 A(d(x1:S)) -> A(x1:S)
0.00/0.27	->->-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->->Cycle:
0.00/0.27	->->-> Pairs:
0.00/0.27	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.27	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.27	 B(d(x1:S)) -> B(x1:S)
0.00/0.27	 C(a(x1:S)) -> C(x1:S)
0.00/0.27	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.27	->->-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	
0.00/0.27	
0.00/0.27	The problem is decomposed in 2 subproblems.
0.00/0.27	
0.00/0.27	Problem 1.1: 
0.00/0.27	
0.00/0.27	Reduction Pair Processor:
0.00/0.27	-> Pairs:
0.00/0.27	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.27	 A(d(x1:S)) -> A(x1:S)
0.00/0.27	-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	-> Usable rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->Interpretation type:
0.00/0.27	 Linear
0.00/0.27	->Coefficients:
0.00/0.27	 Natural Numbers
0.00/0.27	->Dimension:
0.00/0.27	 1
0.00/0.27	->Bound:
0.00/0.27	 2
0.00/0.27	->Interpretation:
0.00/0.27	 
0.00/0.27	[a](X) = 2.X + 2
0.00/0.27	[b](X) = X
0.00/0.27	[c](X) = 2.X + 2
0.00/0.27	[d](X) = 2.X + 2
0.00/0.27	[A](X) = X
0.00/0.27	
0.00/0.27	Problem 1.1: 
0.00/0.27	
0.00/0.27	SCC Processor:
0.00/0.27	-> Pairs:
0.00/0.27	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.27	-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->Strongly Connected Components:
0.00/0.27	->->Cycle:
0.00/0.27	->->-> Pairs:
0.00/0.27	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.27	->->-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	
0.00/0.27	Problem 1.1: 
0.00/0.27	
0.00/0.27	Reduction Pair Processor:
0.00/0.27	-> Pairs:
0.00/0.27	 A(a(x1:S)) -> A(b(a(x1:S)))
0.00/0.27	-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	-> Usable rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->Interpretation type:
0.00/0.27	 Linear
0.00/0.27	->Coefficients:
0.00/0.27	 All rationals
0.00/0.27	->Dimension:
0.00/0.27	 1
0.00/0.27	->Bound:
0.00/0.27	 2
0.00/0.27	->Interpretation:
0.00/0.27	 
0.00/0.27	[a](X) = 2.X + 1
0.00/0.27	[b](X) = 1/2.X
0.00/0.27	[c](X) = 2.X + 1/2
0.00/0.27	[d](X) = 2.X + 2
0.00/0.27	[A](X) = 2.X
0.00/0.27	
0.00/0.27	Problem 1.1: 
0.00/0.27	
0.00/0.27	SCC Processor:
0.00/0.27	-> Pairs:
0.00/0.27	 Empty
0.00/0.27	-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->Strongly Connected Components:
0.00/0.27	 There is no strongly connected component
0.00/0.27	
0.00/0.27	The problem is finite.
0.00/0.27	
0.00/0.27	Problem 1.2: 
0.00/0.27	
0.00/0.27	Reduction Pair Processor:
0.00/0.27	-> Pairs:
0.00/0.27	 B(a(a(x1:S))) -> B(c(x1:S))
0.00/0.27	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.27	 B(d(x1:S)) -> B(x1:S)
0.00/0.27	 C(a(x1:S)) -> C(x1:S)
0.00/0.27	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.27	-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	-> Usable rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->Interpretation type:
0.00/0.27	 Linear
0.00/0.27	->Coefficients:
0.00/0.27	 Natural Numbers
0.00/0.27	->Dimension:
0.00/0.27	 1
0.00/0.27	->Bound:
0.00/0.27	 2
0.00/0.27	->Interpretation:
0.00/0.27	 
0.00/0.27	[a](X) = 2.X + 2
0.00/0.27	[b](X) = X
0.00/0.27	[c](X) = 2.X + 2
0.00/0.27	[d](X) = 2.X + 2
0.00/0.27	[B](X) = X
0.00/0.27	[C](X) = 2.X + 2
0.00/0.27	
0.00/0.27	Problem 1.2: 
0.00/0.27	
0.00/0.27	SCC Processor:
0.00/0.27	-> Pairs:
0.00/0.27	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.27	 B(d(x1:S)) -> B(x1:S)
0.00/0.27	 C(a(x1:S)) -> C(x1:S)
0.00/0.27	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.27	-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->Strongly Connected Components:
0.00/0.27	->->Cycle:
0.00/0.27	->->-> Pairs:
0.00/0.27	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.27	 B(d(x1:S)) -> B(x1:S)
0.00/0.27	 C(a(x1:S)) -> C(x1:S)
0.00/0.27	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.27	->->-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	
0.00/0.27	Problem 1.2: 
0.00/0.27	
0.00/0.27	Reduction Pair Processor:
0.00/0.27	-> Pairs:
0.00/0.27	 B(a(a(x1:S))) -> C(x1:S)
0.00/0.27	 B(d(x1:S)) -> B(x1:S)
0.00/0.27	 C(a(x1:S)) -> C(x1:S)
0.00/0.27	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.27	-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	-> Usable rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->Interpretation type:
0.00/0.27	 Linear
0.00/0.27	->Coefficients:
0.00/0.27	 Natural Numbers
0.00/0.27	->Dimension:
0.00/0.27	 1
0.00/0.27	->Bound:
0.00/0.27	 2
0.00/0.27	->Interpretation:
0.00/0.27	 
0.00/0.27	[a](X) = 2.X + 2
0.00/0.27	[b](X) = X
0.00/0.27	[c](X) = 2.X + 2
0.00/0.27	[d](X) = 2.X + 2
0.00/0.27	[B](X) = X
0.00/0.27	[C](X) = 2.X + 2
0.00/0.27	
0.00/0.27	Problem 1.2: 
0.00/0.27	
0.00/0.27	SCC Processor:
0.00/0.27	-> Pairs:
0.00/0.27	 B(d(x1:S)) -> B(x1:S)
0.00/0.27	 C(a(x1:S)) -> C(x1:S)
0.00/0.27	 C(b(x1:S)) -> B(a(x1:S))
0.00/0.27	-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->Strongly Connected Components:
0.00/0.27	->->Cycle:
0.00/0.27	->->-> Pairs:
0.00/0.27	 B(d(x1:S)) -> B(x1:S)
0.00/0.27	->->-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->->Cycle:
0.00/0.27	->->-> Pairs:
0.00/0.27	 C(a(x1:S)) -> C(x1:S)
0.00/0.27	->->-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	
0.00/0.27	
0.00/0.27	The problem is decomposed in 2 subproblems.
0.00/0.27	
0.00/0.27	Problem 1.2.1: 
0.00/0.27	
0.00/0.27	Subterm Processor:
0.00/0.27	-> Pairs:
0.00/0.27	 B(d(x1:S)) -> B(x1:S)
0.00/0.27	-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->Projection:
0.00/0.27	 pi(B) = 1
0.00/0.27	
0.00/0.27	Problem 1.2.1: 
0.00/0.27	
0.00/0.27	SCC Processor:
0.00/0.27	-> Pairs:
0.00/0.27	 Empty
0.00/0.27	-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->Strongly Connected Components:
0.00/0.27	 There is no strongly connected component
0.00/0.27	
0.00/0.27	The problem is finite.
0.00/0.27	
0.00/0.27	Problem 1.2.2: 
0.00/0.27	
0.00/0.27	Subterm Processor:
0.00/0.27	-> Pairs:
0.00/0.27	 C(a(x1:S)) -> C(x1:S)
0.00/0.27	-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->Projection:
0.00/0.27	 pi(C) = 1
0.00/0.27	
0.00/0.27	Problem 1.2.2: 
0.00/0.27	
0.00/0.27	SCC Processor:
0.00/0.27	-> Pairs:
0.00/0.27	 Empty
0.00/0.27	-> Rules:
0.00/0.27	 a(a(b(x1:S))) -> d(b(a(x1:S)))
0.00/0.27	 a(a(x1:S)) -> a(b(a(x1:S)))
0.00/0.27	 a(d(x1:S)) -> d(a(x1:S))
0.00/0.27	 b(a(a(x1:S))) -> a(b(c(x1:S)))
0.00/0.27	 b(d(x1:S)) -> a(b(x1:S))
0.00/0.27	 c(a(x1:S)) -> a(c(x1:S))
0.00/0.27	 c(b(x1:S)) -> b(a(x1:S))
0.00/0.27	->Strongly Connected Components:
0.00/0.27	 There is no strongly connected component
0.00/0.27	
0.00/0.27	The problem is finite.
0.00/0.27	EOF