87.38/87.63	YES
87.38/87.63	
87.38/87.63	Problem 1: 
87.38/87.63	
87.38/87.63	(VAR v_NonEmpty:S x1:S)
87.38/87.63	(RULES
87.38/87.63	A(a(x1:S)) -> x1:S
87.38/87.63	A(b(x1:S)) -> b(a(B(A(x1:S))))
87.38/87.63	B(a(x1:S)) -> a(b(A(B(x1:S))))
87.38/87.63	B(b(x1:S)) -> x1:S
87.38/87.63	)
87.38/87.63	
87.38/87.63	Problem 1: 
87.38/87.63	
87.38/87.63	Innermost Equivalent Processor:
87.38/87.63	-> Rules:
87.38/87.63	 A(a(x1:S)) -> x1:S
87.38/87.63	 A(b(x1:S)) -> b(a(B(A(x1:S))))
87.38/87.63	 B(a(x1:S)) -> a(b(A(B(x1:S))))
87.38/87.63	 B(b(x1:S)) -> x1:S
87.38/87.63	-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
87.38/87.63	 
87.38/87.63	
87.38/87.63	Problem 1: 
87.38/87.63	
87.38/87.63	Dependency Pairs Processor:
87.38/87.63	-> Pairs:
87.38/87.63	 A#(b(x1:S)) -> A#(x1:S)
87.38/87.63	 A#(b(x1:S)) -> B#(A(x1:S))
87.38/87.63	 B#(a(x1:S)) -> A#(B(x1:S))
87.38/87.63	 B#(a(x1:S)) -> B#(x1:S)
87.38/87.63	-> Rules:
87.38/87.63	 A(a(x1:S)) -> x1:S
87.38/87.63	 A(b(x1:S)) -> b(a(B(A(x1:S))))
87.38/87.63	 B(a(x1:S)) -> a(b(A(B(x1:S))))
87.38/87.63	 B(b(x1:S)) -> x1:S
87.38/87.63	
87.38/87.63	Problem 1: 
87.38/87.63	
87.38/87.63	SCC Processor:
87.38/87.63	-> Pairs:
87.38/87.63	 A#(b(x1:S)) -> A#(x1:S)
87.38/87.63	 A#(b(x1:S)) -> B#(A(x1:S))
87.38/87.63	 B#(a(x1:S)) -> A#(B(x1:S))
87.38/87.63	 B#(a(x1:S)) -> B#(x1:S)
87.38/87.63	-> Rules:
87.38/87.63	 A(a(x1:S)) -> x1:S
87.38/87.63	 A(b(x1:S)) -> b(a(B(A(x1:S))))
87.38/87.63	 B(a(x1:S)) -> a(b(A(B(x1:S))))
87.38/87.63	 B(b(x1:S)) -> x1:S
87.38/87.63	->Strongly Connected Components:
87.38/87.63	->->Cycle:
87.38/87.63	->->-> Pairs:
87.38/87.63	 A#(b(x1:S)) -> A#(x1:S)
87.38/87.63	 A#(b(x1:S)) -> B#(A(x1:S))
87.38/87.63	 B#(a(x1:S)) -> A#(B(x1:S))
87.38/87.63	 B#(a(x1:S)) -> B#(x1:S)
87.38/87.63	->->-> Rules:
87.38/87.63	 A(a(x1:S)) -> x1:S
87.38/87.63	 A(b(x1:S)) -> b(a(B(A(x1:S))))
87.38/87.63	 B(a(x1:S)) -> a(b(A(B(x1:S))))
87.38/87.63	 B(b(x1:S)) -> x1:S
87.38/87.63	
87.38/87.63	Problem 1: 
87.38/87.63	
87.38/87.63	Narrowing Processor:
87.38/87.63	-> Pairs:
87.38/87.63	 A#(b(x1:S)) -> A#(x1:S)
87.38/87.63	 A#(b(x1:S)) -> B#(A(x1:S))
87.38/87.63	 B#(a(x1:S)) -> A#(B(x1:S))
87.38/87.63	 B#(a(x1:S)) -> B#(x1:S)
87.38/87.63	-> Rules:
87.38/87.63	 A(a(x1:S)) -> x1:S
87.38/87.63	 A(b(x1:S)) -> b(a(B(A(x1:S))))
87.38/87.63	 B(a(x1:S)) -> a(b(A(B(x1:S))))
87.38/87.63	 B(b(x1:S)) -> x1:S
87.38/87.63	->Narrowed Pairs:
87.38/87.63	->->Original Pair:
87.38/87.63	 A#(b(x1:S)) -> B#(A(x1:S))
87.38/87.63	->-> Narrowed pairs:
87.38/87.63	 A#(b(a(x1:S))) -> B#(x1:S)
87.38/87.63	 A#(b(b(x1:S))) -> B#(b(a(B(A(x1:S)))))
87.38/87.63	->->Original Pair:
87.38/87.63	 B#(a(x1:S)) -> A#(B(x1:S))
87.38/87.63	->-> Narrowed pairs:
87.38/87.63	 B#(a(a(x1:S))) -> A#(a(b(A(B(x1:S)))))
87.38/87.63	 B#(a(b(x1:S))) -> A#(x1:S)
87.38/87.63	
87.38/87.63	Problem 1: 
87.38/87.63	
87.38/87.63	SCC Processor:
87.38/87.63	-> Pairs:
87.38/87.63	 A#(b(a(x1:S))) -> B#(x1:S)
87.38/87.63	 A#(b(b(x1:S))) -> B#(b(a(B(A(x1:S)))))
87.38/87.63	 A#(b(x1:S)) -> A#(x1:S)
87.38/87.63	 B#(a(a(x1:S))) -> A#(a(b(A(B(x1:S)))))
87.38/87.63	 B#(a(b(x1:S))) -> A#(x1:S)
87.38/87.63	 B#(a(x1:S)) -> B#(x1:S)
87.38/87.63	-> Rules:
87.38/87.63	 A(a(x1:S)) -> x1:S
87.38/87.63	 A(b(x1:S)) -> b(a(B(A(x1:S))))
87.38/87.63	 B(a(x1:S)) -> a(b(A(B(x1:S))))
87.38/87.63	 B(b(x1:S)) -> x1:S
87.38/87.63	->Strongly Connected Components:
87.38/87.63	->->Cycle:
87.38/87.63	->->-> Pairs:
87.38/87.63	 A#(b(a(x1:S))) -> B#(x1:S)
87.38/87.63	 A#(b(x1:S)) -> A#(x1:S)
87.38/87.63	 B#(a(b(x1:S))) -> A#(x1:S)
87.38/87.63	 B#(a(x1:S)) -> B#(x1:S)
87.38/87.63	->->-> Rules:
87.38/87.63	 A(a(x1:S)) -> x1:S
87.38/87.63	 A(b(x1:S)) -> b(a(B(A(x1:S))))
87.38/87.63	 B(a(x1:S)) -> a(b(A(B(x1:S))))
87.38/87.63	 B(b(x1:S)) -> x1:S
87.38/87.63	
87.38/87.63	Problem 1: 
87.38/87.63	
87.38/87.63	Subterm Processor:
87.38/87.63	-> Pairs:
87.38/87.63	 A#(b(a(x1:S))) -> B#(x1:S)
87.38/87.63	 A#(b(x1:S)) -> A#(x1:S)
87.38/87.63	 B#(a(b(x1:S))) -> A#(x1:S)
87.38/87.63	 B#(a(x1:S)) -> B#(x1:S)
87.38/87.63	-> Rules:
87.38/87.63	 A(a(x1:S)) -> x1:S
87.38/87.63	 A(b(x1:S)) -> b(a(B(A(x1:S))))
87.38/87.63	 B(a(x1:S)) -> a(b(A(B(x1:S))))
87.38/87.63	 B(b(x1:S)) -> x1:S
87.38/87.63	->Projection:
87.38/87.63	 pi(A#) = 1
87.38/87.63	 pi(B#) = 1
87.38/87.63	
87.38/87.63	Problem 1: 
87.38/87.63	
87.38/87.63	SCC Processor:
87.38/87.63	-> Pairs:
87.38/87.63	 Empty
87.38/87.63	-> Rules:
87.38/87.63	 A(a(x1:S)) -> x1:S
87.38/87.63	 A(b(x1:S)) -> b(a(B(A(x1:S))))
87.38/87.63	 B(a(x1:S)) -> a(b(A(B(x1:S))))
87.38/87.63	 B(b(x1:S)) -> x1:S
87.38/87.63	->Strongly Connected Components:
87.38/87.63	 There is no strongly connected component
87.38/87.63	
87.38/87.63	The problem is finite.
87.38/87.63	EOF