43.23/43.33	NO
43.23/43.33	
43.23/43.33	Problem 1: 
43.23/43.33	
43.23/43.33	(VAR v_NonEmpty:S x:S y:S)
43.23/43.33	(RULES
43.23/43.33	b -> b
43.23/43.33	f(x:S,y:S) -> g(x:S) | c(g(x:S)) ->* c(a)
43.23/43.33	f(x:S,y:S) -> h(x:S) | c(h(x:S)) ->* c(a)
43.23/43.33	g(s(x:S)) -> x:S
43.23/43.33	h(s(x:S)) -> x:S
43.23/43.33	)
43.23/43.33	
43.23/43.33	Problem 1: 
43.23/43.33	Valid CTRS Processor:
43.23/43.33	-> Rules:
43.23/43.33	 b -> b
43.23/43.33	 f(x:S,y:S) -> g(x:S) | c(g(x:S)) ->* c(a)
43.23/43.33	 f(x:S,y:S) -> h(x:S) | c(h(x:S)) ->* c(a)
43.23/43.33	 g(s(x:S)) -> x:S
43.23/43.33	 h(s(x:S)) -> x:S
43.23/43.33	-> The system is a deterministic 3-CTRS.
43.23/43.33	
43.23/43.33	Problem 1: 
43.23/43.33	
43.23/43.33	Dependency Pairs Processor:
43.23/43.33	
43.23/43.33	Conditional Termination Problem 1:
43.23/43.33	-> Pairs:
43.23/43.33	 B -> B
43.23/43.33	 F(x:S,y:S) -> G(x:S) | c(g(x:S)) ->* c(a)
43.23/43.33	 F(x:S,y:S) -> H(x:S) | c(h(x:S)) ->* c(a)
43.23/43.33	-> QPairs:
43.23/43.33	 Empty
43.23/43.33	-> Rules:
43.23/43.33	 b -> b
43.23/43.33	 f(x:S,y:S) -> g(x:S) | c(g(x:S)) ->* c(a)
43.23/43.33	 f(x:S,y:S) -> h(x:S) | c(h(x:S)) ->* c(a)
43.23/43.33	 g(s(x:S)) -> x:S
43.23/43.33	 h(s(x:S)) -> x:S
43.23/43.33	
43.23/43.33	Conditional Termination Problem 2:
43.23/43.33	-> Pairs:
43.23/43.33	 F(x:S,y:S) -> G(x:S)
43.23/43.33	 F(x:S,y:S) -> H(x:S)
43.23/43.33	-> QPairs:
43.23/43.33	 Empty
43.23/43.33	-> Rules:
43.23/43.33	 b -> b
43.23/43.33	 f(x:S,y:S) -> g(x:S) | c(g(x:S)) ->* c(a)
43.23/43.33	 f(x:S,y:S) -> h(x:S) | c(h(x:S)) ->* c(a)
43.23/43.33	 g(s(x:S)) -> x:S
43.23/43.33	 h(s(x:S)) -> x:S
43.23/43.33	
43.23/43.33	Problem 1: 
43.23/43.33	
43.23/43.33	SCC Processor:
43.23/43.33	-> Pairs:
43.23/43.33	 B -> B
43.23/43.33	 F(x:S,y:S) -> G(x:S) | c(g(x:S)) ->* c(a)
43.23/43.33	 F(x:S,y:S) -> H(x:S) | c(h(x:S)) ->* c(a)
43.23/43.33	-> QPairs:
43.23/43.33	 Empty
43.23/43.33	-> Rules:
43.23/43.33	 b -> b
43.23/43.33	 f(x:S,y:S) -> g(x:S) | c(g(x:S)) ->* c(a)
43.23/43.33	 f(x:S,y:S) -> h(x:S) | c(h(x:S)) ->* c(a)
43.23/43.33	 g(s(x:S)) -> x:S
43.23/43.33	 h(s(x:S)) -> x:S
43.23/43.33	->Strongly Connected Components:
43.23/43.33	->->Cycle:
43.23/43.33	->->-> Pairs:
43.23/43.33	 B -> B
43.23/43.33	-> QPairs:
43.23/43.33	 Empty
43.23/43.33	->->-> Rules:
43.23/43.33	 b -> b
43.23/43.33	 f(x:S,y:S) -> g(x:S) | c(g(x:S)) ->* c(a)
43.23/43.33	 f(x:S,y:S) -> h(x:S) | c(h(x:S)) ->* c(a)
43.23/43.33	 g(s(x:S)) -> x:S
43.23/43.33	 h(s(x:S)) -> x:S
43.23/43.33	
43.23/43.33	Problem 1: 
43.23/43.33	
43.23/43.33	Infinite Processor:
43.23/43.33	-> Pairs:
43.23/43.33	 B -> B
43.23/43.33	-> QPairs:
43.23/43.33	 Empty
43.23/43.33	-> Rules:
43.23/43.33	 b -> b
43.23/43.33	 f(x:S,y:S) -> g(x:S) | c(g(x:S)) ->* c(a)
43.23/43.33	 f(x:S,y:S) -> h(x:S) | c(h(x:S)) ->* c(a)
43.23/43.33	 g(s(x:S)) -> x:S
43.23/43.33	 h(s(x:S)) -> x:S
43.23/43.33	-> Pairs in cycle:
43.23/43.33	 B -> B
43.23/43.33	
43.23/43.33	The problem is infinite.
43.23/43.33	EOF