0.00/0.02	YES
0.00/0.02	
0.00/0.02	Problem 1: 
0.00/0.02	
0.00/0.02	(VAR v_NonEmpty:S x:S)
0.00/0.02	(RULES
0.00/0.02	even(0) -> ttrue
0.00/0.02	even(s(x:S)) -> ffalse | odd(x:S) ->* ffalse
0.00/0.02	even(s(x:S)) -> ttrue | odd(x:S) ->* ttrue
0.00/0.02	odd(0) -> ffalse
0.00/0.02	odd(s(x:S)) -> ffalse | even(x:S) ->* ffalse
0.00/0.02	odd(s(x:S)) -> ttrue | even(x:S) ->* ttrue
0.00/0.02	)
0.00/0.02	
0.00/0.02	Problem 1: 
0.00/0.02	Valid CTRS Processor:
0.00/0.02	-> Rules:
0.00/0.02	 even(0) -> ttrue
0.00/0.02	 even(s(x:S)) -> ffalse | odd(x:S) ->* ffalse
0.00/0.02	 even(s(x:S)) -> ttrue | odd(x:S) ->* ttrue
0.00/0.02	 odd(0) -> ffalse
0.00/0.02	 odd(s(x:S)) -> ffalse | even(x:S) ->* ffalse
0.00/0.02	 odd(s(x:S)) -> ttrue | even(x:S) ->* ttrue
0.00/0.02	-> The system is a deterministic 3-CTRS.
0.00/0.02	
0.00/0.02	Problem 1: 
0.00/0.02	
0.00/0.02	Dependency Pairs Processor:
0.00/0.02	
0.00/0.02	Conditional Termination Problem 1:
0.00/0.02	-> Pairs:
0.00/0.02	 Empty
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 even(0) -> ttrue
0.00/0.02	 even(s(x:S)) -> ffalse | odd(x:S) ->* ffalse
0.00/0.02	 even(s(x:S)) -> ttrue | odd(x:S) ->* ttrue
0.00/0.02	 odd(0) -> ffalse
0.00/0.02	 odd(s(x:S)) -> ffalse | even(x:S) ->* ffalse
0.00/0.02	 odd(s(x:S)) -> ttrue | even(x:S) ->* ttrue
0.00/0.02	
0.00/0.02	Conditional Termination Problem 2:
0.00/0.02	-> Pairs:
0.00/0.02	 EVEN(s(x:S)) -> ODD(x:S)
0.00/0.02	 ODD(s(x:S)) -> EVEN(x:S)
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 even(0) -> ttrue
0.00/0.02	 even(s(x:S)) -> ffalse | odd(x:S) ->* ffalse
0.00/0.02	 even(s(x:S)) -> ttrue | odd(x:S) ->* ttrue
0.00/0.02	 odd(0) -> ffalse
0.00/0.02	 odd(s(x:S)) -> ffalse | even(x:S) ->* ffalse
0.00/0.02	 odd(s(x:S)) -> ttrue | even(x:S) ->* ttrue
0.00/0.02	
0.00/0.02	
0.00/0.02	The problem is decomposed in 2 subproblems.
0.00/0.02	
0.00/0.02	Problem 1.1: 
0.00/0.02	
0.00/0.02	SCC Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 Empty
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 even(0) -> ttrue
0.00/0.02	 even(s(x:S)) -> ffalse | odd(x:S) ->* ffalse
0.00/0.02	 even(s(x:S)) -> ttrue | odd(x:S) ->* ttrue
0.00/0.02	 odd(0) -> ffalse
0.00/0.02	 odd(s(x:S)) -> ffalse | even(x:S) ->* ffalse
0.00/0.02	 odd(s(x:S)) -> ttrue | even(x:S) ->* ttrue
0.00/0.02	->Strongly Connected Components:
0.00/0.02	 There is no strongly connected component
0.00/0.02	
0.00/0.02	The problem is finite.
0.00/0.02	
0.00/0.02	Problem 1.2: 
0.00/0.02	
0.00/0.02	SCC Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 EVEN(s(x:S)) -> ODD(x:S)
0.00/0.02	 ODD(s(x:S)) -> EVEN(x:S)
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 even(0) -> ttrue
0.00/0.02	 even(s(x:S)) -> ffalse | odd(x:S) ->* ffalse
0.00/0.02	 even(s(x:S)) -> ttrue | odd(x:S) ->* ttrue
0.00/0.02	 odd(0) -> ffalse
0.00/0.02	 odd(s(x:S)) -> ffalse | even(x:S) ->* ffalse
0.00/0.02	 odd(s(x:S)) -> ttrue | even(x:S) ->* ttrue
0.00/0.02	->Strongly Connected Components:
0.00/0.02	->->Cycle:
0.00/0.02	->->-> Pairs:
0.00/0.02	 EVEN(s(x:S)) -> ODD(x:S)
0.00/0.02	 ODD(s(x:S)) -> EVEN(x:S)
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	->->-> Rules:
0.00/0.02	 even(0) -> ttrue
0.00/0.02	 even(s(x:S)) -> ffalse | odd(x:S) ->* ffalse
0.00/0.02	 even(s(x:S)) -> ttrue | odd(x:S) ->* ttrue
0.00/0.02	 odd(0) -> ffalse
0.00/0.02	 odd(s(x:S)) -> ffalse | even(x:S) ->* ffalse
0.00/0.02	 odd(s(x:S)) -> ttrue | even(x:S) ->* ttrue
0.00/0.02	
0.00/0.02	Problem 1.2: 
0.00/0.02	
0.00/0.02	Conditional Subterm Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 EVEN(s(x:S)) -> ODD(x:S)
0.00/0.02	 ODD(s(x:S)) -> EVEN(x:S)
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 even(0) -> ttrue
0.00/0.02	 even(s(x:S)) -> ffalse | odd(x:S) ->* ffalse
0.00/0.02	 even(s(x:S)) -> ttrue | odd(x:S) ->* ttrue
0.00/0.02	 odd(0) -> ffalse
0.00/0.02	 odd(s(x:S)) -> ffalse | even(x:S) ->* ffalse
0.00/0.02	 odd(s(x:S)) -> ttrue | even(x:S) ->* ttrue
0.00/0.02	->Projection:
0.00/0.02	 pi(EVEN) = 1
0.00/0.02	 pi(ODD) = 1
0.00/0.02	
0.00/0.02	Problem 1.2: 
0.00/0.02	
0.00/0.02	SCC Processor:
0.00/0.02	-> Pairs:
0.00/0.02	 Empty
0.00/0.02	-> QPairs:
0.00/0.02	 Empty
0.00/0.02	-> Rules:
0.00/0.02	 even(0) -> ttrue
0.00/0.02	 even(s(x:S)) -> ffalse | odd(x:S) ->* ffalse
0.00/0.02	 even(s(x:S)) -> ttrue | odd(x:S) ->* ttrue
0.00/0.02	 odd(0) -> ffalse
0.00/0.02	 odd(s(x:S)) -> ffalse | even(x:S) ->* ffalse
0.00/0.02	 odd(s(x:S)) -> ttrue | even(x:S) ->* ttrue
0.00/0.02	->Strongly Connected Components:
0.00/0.02	 There is no strongly connected component
0.00/0.02	
0.00/0.02	The problem is finite.
0.00/0.02	EOF