87.50/88.12	YES
87.50/88.12	
87.50/88.12	Problem 1: 
87.50/88.12	
87.50/88.12	(VAR v_NonEmpty:S x:S)
87.50/88.12	(RULES
87.50/88.12	a(c(x:S)) -> x:S
87.50/88.12	a(d(x:S)) -> d(c(b(a(x:S))))
87.50/88.12	b(c(x:S)) -> c(d(a(b(x:S))))
87.50/88.12	b(d(x:S)) -> x:S
87.50/88.12	) 
87.50/88.12	(STRATEGY INNERMOST)
87.50/88.12	
87.50/88.12	Problem 1: 
87.50/88.12	
87.50/88.12	Dependency Pairs Processor:
87.50/88.12	-> Pairs:
87.50/88.12	 A(d(x:S)) -> A(x:S)
87.50/88.12	 A(d(x:S)) -> B(a(x:S))
87.50/88.12	 B(c(x:S)) -> A(b(x:S))
87.50/88.12	 B(c(x:S)) -> B(x:S)
87.50/88.12	-> Rules:
87.50/88.12	 a(c(x:S)) -> x:S
87.50/88.12	 a(d(x:S)) -> d(c(b(a(x:S))))
87.50/88.12	 b(c(x:S)) -> c(d(a(b(x:S))))
87.50/88.12	 b(d(x:S)) -> x:S
87.50/88.12	
87.50/88.12	Problem 1: 
87.50/88.12	
87.50/88.12	SCC Processor:
87.50/88.12	-> Pairs:
87.50/88.12	 A(d(x:S)) -> A(x:S)
87.50/88.12	 A(d(x:S)) -> B(a(x:S))
87.50/88.12	 B(c(x:S)) -> A(b(x:S))
87.50/88.12	 B(c(x:S)) -> B(x:S)
87.50/88.12	-> Rules:
87.50/88.12	 a(c(x:S)) -> x:S
87.50/88.12	 a(d(x:S)) -> d(c(b(a(x:S))))
87.50/88.12	 b(c(x:S)) -> c(d(a(b(x:S))))
87.50/88.12	 b(d(x:S)) -> x:S
87.50/88.12	->Strongly Connected Components:
87.50/88.12	->->Cycle:
87.50/88.12	->->-> Pairs:
87.50/88.12	 A(d(x:S)) -> A(x:S)
87.50/88.12	 A(d(x:S)) -> B(a(x:S))
87.50/88.12	 B(c(x:S)) -> A(b(x:S))
87.50/88.12	 B(c(x:S)) -> B(x:S)
87.50/88.12	->->-> Rules:
87.50/88.12	 a(c(x:S)) -> x:S
87.50/88.12	 a(d(x:S)) -> d(c(b(a(x:S))))
87.50/88.12	 b(c(x:S)) -> c(d(a(b(x:S))))
87.50/88.12	 b(d(x:S)) -> x:S
87.50/88.12	
87.50/88.12	Problem 1: 
87.50/88.12	
87.50/88.12	Narrowing Processor:
87.50/88.12	-> Pairs:
87.50/88.12	 A(d(x:S)) -> A(x:S)
87.50/88.12	 A(d(x:S)) -> B(a(x:S))
87.50/88.12	 B(c(x:S)) -> A(b(x:S))
87.50/88.12	 B(c(x:S)) -> B(x:S)
87.50/88.12	-> Rules:
87.50/88.12	 a(c(x:S)) -> x:S
87.50/88.12	 a(d(x:S)) -> d(c(b(a(x:S))))
87.50/88.12	 b(c(x:S)) -> c(d(a(b(x:S))))
87.50/88.12	 b(d(x:S)) -> x:S
87.50/88.12	->Narrowed Pairs:
87.50/88.12	->->Original Pair:
87.50/88.12	 A(d(x:S)) -> B(a(x:S))
87.50/88.12	->-> Narrowed pairs:
87.50/88.12	 A(d(c(x:S))) -> B(x:S)
87.50/88.12	 A(d(d(x:S))) -> B(d(c(b(a(x:S)))))
87.50/88.12	->->Original Pair:
87.50/88.12	 B(c(x:S)) -> A(b(x:S))
87.50/88.12	->-> Narrowed pairs:
87.50/88.12	 B(c(c(x:S))) -> A(c(d(a(b(x:S)))))
87.50/88.12	 B(c(d(x:S))) -> A(x:S)
87.50/88.12	
87.50/88.12	Problem 1: 
87.50/88.12	
87.50/88.12	SCC Processor:
87.50/88.12	-> Pairs:
87.50/88.12	 A(d(c(x:S))) -> B(x:S)
87.50/88.12	 A(d(d(x:S))) -> B(d(c(b(a(x:S)))))
87.50/88.12	 A(d(x:S)) -> A(x:S)
87.50/88.12	 B(c(c(x:S))) -> A(c(d(a(b(x:S)))))
87.50/88.12	 B(c(d(x:S))) -> A(x:S)
87.50/88.12	 B(c(x:S)) -> B(x:S)
87.50/88.12	-> Rules:
87.50/88.12	 a(c(x:S)) -> x:S
87.50/88.12	 a(d(x:S)) -> d(c(b(a(x:S))))
87.50/88.12	 b(c(x:S)) -> c(d(a(b(x:S))))
87.50/88.12	 b(d(x:S)) -> x:S
87.50/88.12	->Strongly Connected Components:
87.50/88.12	->->Cycle:
87.50/88.12	->->-> Pairs:
87.50/88.12	 A(d(c(x:S))) -> B(x:S)
87.50/88.12	 A(d(x:S)) -> A(x:S)
87.50/88.12	 B(c(d(x:S))) -> A(x:S)
87.50/88.12	 B(c(x:S)) -> B(x:S)
87.50/88.12	->->-> Rules:
87.50/88.12	 a(c(x:S)) -> x:S
87.50/88.12	 a(d(x:S)) -> d(c(b(a(x:S))))
87.50/88.12	 b(c(x:S)) -> c(d(a(b(x:S))))
87.50/88.12	 b(d(x:S)) -> x:S
87.50/88.12	
87.50/88.12	Problem 1: 
87.50/88.12	
87.50/88.12	Subterm Processor:
87.50/88.12	-> Pairs:
87.50/88.12	 A(d(c(x:S))) -> B(x:S)
87.50/88.12	 A(d(x:S)) -> A(x:S)
87.50/88.12	 B(c(d(x:S))) -> A(x:S)
87.50/88.12	 B(c(x:S)) -> B(x:S)
87.50/88.12	-> Rules:
87.50/88.12	 a(c(x:S)) -> x:S
87.50/88.12	 a(d(x:S)) -> d(c(b(a(x:S))))
87.50/88.12	 b(c(x:S)) -> c(d(a(b(x:S))))
87.50/88.12	 b(d(x:S)) -> x:S
87.50/88.12	->Projection:
87.50/88.12	 pi(A) = 1
87.50/88.12	 pi(B) = 1
87.50/88.12	
87.50/88.12	Problem 1: 
87.50/88.12	
87.50/88.12	SCC Processor:
87.50/88.12	-> Pairs:
87.50/88.12	 Empty
87.50/88.12	-> Rules:
87.50/88.12	 a(c(x:S)) -> x:S
87.50/88.12	 a(d(x:S)) -> d(c(b(a(x:S))))
87.50/88.12	 b(c(x:S)) -> c(d(a(b(x:S))))
87.50/88.12	 b(d(x:S)) -> x:S
87.50/88.12	->Strongly Connected Components:
87.50/88.12	 There is no strongly connected component
87.50/88.12	
87.50/88.12	The problem is finite.
87.50/88.13	EOF