40.04/40.19	NO
40.04/40.19	
40.04/40.19	Problem 1: 
40.04/40.19	
40.04/40.19	(VAR v_NonEmpty:S x:S z:S)
40.04/40.19	(RULES
40.04/40.19	a -> f(a)
40.04/40.19	f(x:S) -> b | f(x:S) ->* z:S, x:S ->* z:S
40.04/40.19	)
40.04/40.19	
40.04/40.19	Problem 1: 
40.04/40.19	Valid CTRS Processor:
40.04/40.19	-> Rules:
40.04/40.19	 a -> f(a)
40.04/40.19	 f(x:S) -> b | f(x:S) ->* z:S, x:S ->* z:S
40.04/40.19	-> The system is a deterministic 3-CTRS.
40.04/40.19	
40.04/40.19	Problem 1: 
40.04/40.19	
40.04/40.19	Dependency Pairs Processor:
40.04/40.19	
40.04/40.19	Conditional Termination Problem 1:
40.04/40.19	-> Pairs:
40.04/40.19	 A -> A
40.04/40.19	 A -> F(a)
40.04/40.19	-> QPairs:
40.04/40.19	 Empty
40.04/40.19	-> Rules:
40.04/40.19	 a -> f(a)
40.04/40.19	 f(x:S) -> b | f(x:S) ->* z:S, x:S ->* z:S
40.04/40.19	
40.04/40.19	Conditional Termination Problem 2:
40.04/40.19	-> Pairs:
40.04/40.19	 F(x:S) -> F(x:S)
40.04/40.19	-> QPairs:
40.04/40.19	 Empty
40.04/40.19	-> Rules:
40.04/40.19	 a -> f(a)
40.04/40.19	 f(x:S) -> b | f(x:S) ->* z:S, x:S ->* z:S
40.04/40.19	
40.04/40.19	Problem 1: 
40.04/40.19	
40.04/40.19	SCC Processor:
40.04/40.19	-> Pairs:
40.04/40.19	 A -> A
40.04/40.19	 A -> F(a)
40.04/40.19	-> QPairs:
40.04/40.19	 Empty
40.04/40.19	-> Rules:
40.04/40.19	 a -> f(a)
40.04/40.19	 f(x:S) -> b | f(x:S) ->* z:S, x:S ->* z:S
40.04/40.19	->Strongly Connected Components:
40.04/40.19	->->Cycle:
40.04/40.19	->->-> Pairs:
40.04/40.19	 A -> A
40.04/40.19	-> QPairs:
40.04/40.19	 Empty
40.04/40.19	->->-> Rules:
40.04/40.19	 a -> f(a)
40.04/40.19	 f(x:S) -> b | f(x:S) ->* z:S, x:S ->* z:S
40.04/40.19	
40.04/40.19	Problem 1: 
40.04/40.19	
40.04/40.19	Infinite Processor:
40.04/40.19	-> Pairs:
40.04/40.19	 A -> A
40.04/40.19	-> QPairs:
40.04/40.19	 Empty
40.04/40.19	-> Rules:
40.04/40.19	 a -> f(a)
40.04/40.19	 f(x:S) -> b | f(x:S) ->* z:S, x:S ->* z:S
40.04/40.19	-> Pairs in cycle:
40.04/40.19	 A -> A
40.04/40.19	
40.04/40.19	The problem is infinite.
40.04/40.19	EOF