43.65/43.75	NO
43.65/43.75	
43.65/43.75	Problem 1: 
43.65/43.75	
43.65/43.75	(VAR v_NonEmpty:S x:S y:S)
43.65/43.75	(RULES
43.65/43.75	b -> b
43.65/43.75	f(x:S,y:S) -> g(s(x:S)) | c(g(x:S)) ->* c(a)
43.65/43.75	f(x:S,y:S) -> h(s(x:S)) | c(h(x:S)) ->* c(a)
43.65/43.75	g(s(x:S)) -> x:S
43.65/43.75	h(s(x:S)) -> x:S
43.65/43.75	)
43.65/43.75	
43.65/43.75	Problem 1: 
43.65/43.75	Valid CTRS Processor:
43.65/43.75	-> Rules:
43.65/43.75	 b -> b
43.65/43.75	 f(x:S,y:S) -> g(s(x:S)) | c(g(x:S)) ->* c(a)
43.65/43.75	 f(x:S,y:S) -> h(s(x:S)) | c(h(x:S)) ->* c(a)
43.65/43.75	 g(s(x:S)) -> x:S
43.65/43.75	 h(s(x:S)) -> x:S
43.65/43.75	-> The system is a deterministic 3-CTRS.
43.65/43.75	
43.65/43.75	Problem 1: 
43.65/43.75	
43.65/43.75	Dependency Pairs Processor:
43.65/43.75	
43.65/43.75	Conditional Termination Problem 1:
43.65/43.75	-> Pairs:
43.65/43.75	 B -> B
43.65/43.75	 F(x:S,y:S) -> G(s(x:S)) | c(g(x:S)) ->* c(a)
43.65/43.75	 F(x:S,y:S) -> H(s(x:S)) | c(h(x:S)) ->* c(a)
43.65/43.75	-> QPairs:
43.65/43.75	 Empty
43.65/43.75	-> Rules:
43.65/43.75	 b -> b
43.65/43.75	 f(x:S,y:S) -> g(s(x:S)) | c(g(x:S)) ->* c(a)
43.65/43.75	 f(x:S,y:S) -> h(s(x:S)) | c(h(x:S)) ->* c(a)
43.65/43.75	 g(s(x:S)) -> x:S
43.65/43.75	 h(s(x:S)) -> x:S
43.65/43.75	
43.65/43.75	Conditional Termination Problem 2:
43.65/43.75	-> Pairs:
43.65/43.75	 F(x:S,y:S) -> G(x:S)
43.65/43.75	 F(x:S,y:S) -> H(x:S)
43.65/43.75	-> QPairs:
43.65/43.75	 Empty
43.65/43.75	-> Rules:
43.65/43.75	 b -> b
43.65/43.75	 f(x:S,y:S) -> g(s(x:S)) | c(g(x:S)) ->* c(a)
43.65/43.75	 f(x:S,y:S) -> h(s(x:S)) | c(h(x:S)) ->* c(a)
43.65/43.75	 g(s(x:S)) -> x:S
43.65/43.75	 h(s(x:S)) -> x:S
43.65/43.75	
43.65/43.75	Problem 1: 
43.65/43.75	
43.65/43.75	SCC Processor:
43.65/43.75	-> Pairs:
43.65/43.75	 B -> B
43.65/43.75	 F(x:S,y:S) -> G(s(x:S)) | c(g(x:S)) ->* c(a)
43.65/43.75	 F(x:S,y:S) -> H(s(x:S)) | c(h(x:S)) ->* c(a)
43.65/43.75	-> QPairs:
43.65/43.75	 Empty
43.65/43.75	-> Rules:
43.65/43.75	 b -> b
43.65/43.75	 f(x:S,y:S) -> g(s(x:S)) | c(g(x:S)) ->* c(a)
43.65/43.75	 f(x:S,y:S) -> h(s(x:S)) | c(h(x:S)) ->* c(a)
43.65/43.75	 g(s(x:S)) -> x:S
43.65/43.75	 h(s(x:S)) -> x:S
43.65/43.75	->Strongly Connected Components:
43.65/43.75	->->Cycle:
43.65/43.75	->->-> Pairs:
43.65/43.75	 B -> B
43.65/43.75	-> QPairs:
43.65/43.75	 Empty
43.65/43.75	->->-> Rules:
43.65/43.75	 b -> b
43.65/43.75	 f(x:S,y:S) -> g(s(x:S)) | c(g(x:S)) ->* c(a)
43.65/43.75	 f(x:S,y:S) -> h(s(x:S)) | c(h(x:S)) ->* c(a)
43.65/43.75	 g(s(x:S)) -> x:S
43.65/43.75	 h(s(x:S)) -> x:S
43.65/43.75	
43.65/43.75	Problem 1: 
43.65/43.75	
43.65/43.75	Infinite Processor:
43.65/43.75	-> Pairs:
43.65/43.75	 B -> B
43.65/43.75	-> QPairs:
43.65/43.75	 Empty
43.65/43.75	-> Rules:
43.65/43.75	 b -> b
43.65/43.75	 f(x:S,y:S) -> g(s(x:S)) | c(g(x:S)) ->* c(a)
43.65/43.75	 f(x:S,y:S) -> h(s(x:S)) | c(h(x:S)) ->* c(a)
43.65/43.75	 g(s(x:S)) -> x:S
43.65/43.75	 h(s(x:S)) -> x:S
43.65/43.75	-> Pairs in cycle:
43.65/43.75	 B -> B
43.65/43.75	
43.65/43.75	The problem is infinite.
43.65/43.76	EOF