32.39/32.47	NO
32.39/32.47	
32.39/32.47	Problem 1: 
32.39/32.47	
32.39/32.47	(VAR v_NonEmpty:S x:S y:S z:S)
32.39/32.47	(RULES
32.39/32.47	between(x:S,y:S,z:S) -> ttrue | up(x:S) ->* y:S, down(z:S) ->* y:S
32.39/32.47	down(s(x:S)) -> down(x:S)
32.39/32.47	down(x:S) -> x:S
32.39/32.47	up(x:S) -> up(s(x:S))
32.39/32.47	up(x:S) -> x:S
32.39/32.47	)
32.39/32.47	
32.39/32.47	Problem 1: 
32.39/32.47	Valid CTRS Processor:
32.39/32.47	-> Rules:
32.39/32.47	 between(x:S,y:S,z:S) -> ttrue | up(x:S) ->* y:S, down(z:S) ->* y:S
32.39/32.47	 down(s(x:S)) -> down(x:S)
32.39/32.47	 down(x:S) -> x:S
32.39/32.47	 up(x:S) -> up(s(x:S))
32.39/32.47	 up(x:S) -> x:S
32.39/32.47	-> The system is a deterministic 3-CTRS.
32.39/32.47	
32.39/32.47	Problem 1: 
32.39/32.47	
32.39/32.47	Dependency Pairs Processor:
32.39/32.47	
32.39/32.47	Conditional Termination Problem 1:
32.39/32.47	-> Pairs:
32.39/32.47	 DOWN(s(x:S)) -> DOWN(x:S)
32.39/32.47	 UP(x:S) -> UP(s(x:S))
32.39/32.47	-> QPairs:
32.39/32.47	 Empty
32.39/32.47	-> Rules:
32.39/32.47	 between(x:S,y:S,z:S) -> ttrue | up(x:S) ->* y:S, down(z:S) ->* y:S
32.39/32.47	 down(s(x:S)) -> down(x:S)
32.39/32.47	 down(x:S) -> x:S
32.39/32.47	 up(x:S) -> up(s(x:S))
32.39/32.47	 up(x:S) -> x:S
32.39/32.47	
32.39/32.47	Conditional Termination Problem 2:
32.39/32.47	-> Pairs:
32.39/32.47	 BETWEEN(x:S,y:S,z:S) -> DOWN(z:S) | up(x:S) ->* y:S
32.39/32.47	 BETWEEN(x:S,y:S,z:S) -> UP(x:S)
32.39/32.47	-> QPairs:
32.39/32.47	 DOWN(s(x:S)) -> DOWN(x:S)
32.39/32.47	 UP(x:S) -> UP(s(x:S))
32.39/32.47	-> Rules:
32.39/32.47	 between(x:S,y:S,z:S) -> ttrue | up(x:S) ->* y:S, down(z:S) ->* y:S
32.39/32.47	 down(s(x:S)) -> down(x:S)
32.39/32.47	 down(x:S) -> x:S
32.39/32.47	 up(x:S) -> up(s(x:S))
32.39/32.47	 up(x:S) -> x:S
32.39/32.47	
32.39/32.47	Problem 1: 
32.39/32.47	
32.39/32.47	SCC Processor:
32.39/32.47	-> Pairs:
32.39/32.47	 DOWN(s(x:S)) -> DOWN(x:S)
32.39/32.47	 UP(x:S) -> UP(s(x:S))
32.39/32.47	-> QPairs:
32.39/32.47	 Empty
32.39/32.47	-> Rules:
32.39/32.47	 between(x:S,y:S,z:S) -> ttrue | up(x:S) ->* y:S, down(z:S) ->* y:S
32.39/32.47	 down(s(x:S)) -> down(x:S)
32.39/32.47	 down(x:S) -> x:S
32.39/32.47	 up(x:S) -> up(s(x:S))
32.39/32.47	 up(x:S) -> x:S
32.39/32.47	->Strongly Connected Components:
32.39/32.47	->->Cycle:
32.39/32.47	->->-> Pairs:
32.39/32.47	 UP(x:S) -> UP(s(x:S))
32.39/32.47	-> QPairs:
32.39/32.47	 Empty
32.39/32.47	->->-> Rules:
32.39/32.47	 between(x:S,y:S,z:S) -> ttrue | up(x:S) ->* y:S, down(z:S) ->* y:S
32.39/32.47	 down(s(x:S)) -> down(x:S)
32.39/32.47	 down(x:S) -> x:S
32.39/32.47	 up(x:S) -> up(s(x:S))
32.39/32.47	 up(x:S) -> x:S
32.39/32.47	->->Cycle:
32.39/32.47	->->-> Pairs:
32.39/32.47	 DOWN(s(x:S)) -> DOWN(x:S)
32.39/32.47	-> QPairs:
32.39/32.47	 Empty
32.39/32.47	->->-> Rules:
32.39/32.47	 between(x:S,y:S,z:S) -> ttrue | up(x:S) ->* y:S, down(z:S) ->* y:S
32.39/32.47	 down(s(x:S)) -> down(x:S)
32.39/32.47	 down(x:S) -> x:S
32.39/32.47	 up(x:S) -> up(s(x:S))
32.39/32.47	 up(x:S) -> x:S
32.39/32.47	
32.39/32.47	Problem 1: 
32.39/32.47	
32.39/32.47	Infinite Processor:
32.39/32.47	-> Pairs:
32.39/32.47	 UP(x:S) -> UP(s(x:S))
32.39/32.47	-> QPairs:
32.39/32.47	 Empty
32.39/32.47	-> Rules:
32.39/32.47	 between(x:S,y:S,z:S) -> ttrue | up(x:S) ->* y:S, down(z:S) ->* y:S
32.39/32.47	 down(s(x:S)) -> down(x:S)
32.39/32.47	 down(x:S) -> x:S
32.39/32.47	 up(x:S) -> up(s(x:S))
32.39/32.47	 up(x:S) -> x:S
32.39/32.47	-> Pairs in cycle:
32.39/32.47	 UP(x:S) -> UP(s(x:S))
32.39/32.47	
32.39/32.47	The problem is infinite.
32.39/32.47	EOF