0.00/0.01	YES
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	(VAR v_NonEmpty:S x:S)
0.00/0.01	(RULES
0.00/0.01	a -> c
0.00/0.01	a -> d
0.00/0.01	b -> c
0.00/0.01	b -> d
0.00/0.01	c -> e
0.00/0.01	c -> e'
0.00/0.01	c -> l
0.00/0.01	d -> m
0.00/0.01	f(x:S) -> x:S | x:S ->* e, x:S ->* e'
0.00/0.01	g(d,x:S,x:S) -> A
0.00/0.01	h(x:S,x:S) -> g(x:S,x:S,f(k))
0.00/0.01	k -> l
0.00/0.01	k -> m
0.00/0.01	)
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	Valid CTRS Processor:
0.00/0.01	-> Rules:
0.00/0.01	 a -> c
0.00/0.01	 a -> d
0.00/0.01	 b -> c
0.00/0.01	 b -> d
0.00/0.01	 c -> e
0.00/0.01	 c -> e'
0.00/0.01	 c -> l
0.00/0.01	 d -> m
0.00/0.01	 f(x:S) -> x:S | x:S ->* e, x:S ->* e'
0.00/0.01	 g(d,x:S,x:S) -> A
0.00/0.01	 h(x:S,x:S) -> g(x:S,x:S,f(k))
0.00/0.01	 k -> l
0.00/0.01	 k -> m
0.00/0.01	-> The system is a deterministic 3-CTRS.
0.00/0.01	
0.00/0.01	Problem 1: 
0.00/0.01	
0.00/0.01	Dependency Pairs Processor:
0.00/0.01	
0.00/0.01	Conditional Termination Problem 1:
0.00/0.01	-> Pairs:
0.00/0.01	 a# -> C
0.00/0.01	 a# -> D
0.00/0.01	 B -> C
0.00/0.01	 B -> D
0.00/0.01	 H(x:S,x:S) -> F(k)
0.00/0.01	 H(x:S,x:S) -> G(x:S,x:S,f(k))
0.00/0.01	 H(x:S,x:S) -> K
0.00/0.01	-> QPairs:
0.00/0.01	 Empty
0.00/0.01	-> Rules:
0.00/0.01	 a -> c
0.00/0.01	 a -> d
0.00/0.01	 b -> c
0.00/0.01	 b -> d
0.00/0.01	 c -> e
0.00/0.01	 c -> e'
0.00/0.01	 c -> l
0.00/0.01	 d -> m
0.00/0.01	 f(x:S) -> x:S | x:S ->* e, x:S ->* e'
0.00/0.01	 g(d,x:S,x:S) -> A
0.00/0.01	 h(x:S,x:S) -> g(x:S,x:S,f(k))
0.00/0.01	 k -> l
0.00/0.01	 k -> m
0.00/0.01	
0.00/0.01	Conditional Termination Problem 2:
0.00/0.01	-> Pairs:
0.00/0.01	 Empty
0.00/0.01	-> QPairs:
0.00/0.01	 Empty
0.00/0.01	-> Rules:
0.00/0.01	 a -> c
0.00/0.01	 a -> d
0.00/0.01	 b -> c
0.00/0.01	 b -> d
0.00/0.01	 c -> e
0.00/0.01	 c -> e'
0.00/0.01	 c -> l
0.00/0.01	 d -> m
0.00/0.01	 f(x:S) -> x:S | x:S ->* e, x:S ->* e'
0.00/0.01	 g(d,x:S,x:S) -> A
0.00/0.01	 h(x:S,x:S) -> g(x:S,x:S,f(k))
0.00/0.01	 k -> l
0.00/0.01	 k -> m
0.00/0.01	
0.00/0.01	
0.00/0.01	The problem is decomposed in 2 subproblems.
0.00/0.01	
0.00/0.01	Problem 1.1: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 a# -> C
0.00/0.01	 a# -> D
0.00/0.01	 B -> C
0.00/0.01	 B -> D
0.00/0.01	 H(x:S,x:S) -> F(k)
0.00/0.01	 H(x:S,x:S) -> G(x:S,x:S,f(k))
0.00/0.01	 H(x:S,x:S) -> K
0.00/0.01	-> QPairs:
0.00/0.01	 Empty
0.00/0.01	-> Rules:
0.00/0.01	 a -> c
0.00/0.01	 a -> d
0.00/0.01	 b -> c
0.00/0.01	 b -> d
0.00/0.01	 c -> e
0.00/0.01	 c -> e'
0.00/0.01	 c -> l
0.00/0.01	 d -> m
0.00/0.01	 f(x:S) -> x:S | x:S ->* e, x:S ->* e'
0.00/0.01	 g(d,x:S,x:S) -> A
0.00/0.01	 h(x:S,x:S) -> g(x:S,x:S,f(k))
0.00/0.01	 k -> l
0.00/0.01	 k -> m
0.00/0.01	->Strongly Connected Components:
0.00/0.01	 There is no strongly connected component
0.00/0.01	
0.00/0.01	The problem is finite.
0.00/0.01	
0.00/0.01	Problem 1.2: 
0.00/0.01	
0.00/0.01	SCC Processor:
0.00/0.01	-> Pairs:
0.00/0.01	 Empty
0.00/0.01	-> QPairs:
0.00/0.01	 Empty
0.00/0.01	-> Rules:
0.00/0.01	 a -> c
0.00/0.01	 a -> d
0.00/0.01	 b -> c
0.00/0.01	 b -> d
0.00/0.01	 c -> e
0.00/0.01	 c -> e'
0.00/0.01	 c -> l
0.00/0.01	 d -> m
0.00/0.01	 f(x:S) -> x:S | x:S ->* e, x:S ->* e'
0.00/0.01	 g(d,x:S,x:S) -> A
0.00/0.01	 h(x:S,x:S) -> g(x:S,x:S,f(k))
0.00/0.01	 k -> l
0.00/0.01	 k -> m
0.00/0.01	->Strongly Connected Components:
0.00/0.01	 There is no strongly connected component
0.00/0.01	
0.00/0.01	The problem is finite.
0.00/0.01	EOF