3.05/1.76	WORST_CASE(NON_POLY, ?)
3.05/1.76	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.05/1.76	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.05/1.76	
3.05/1.76	
3.05/1.76	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.05/1.76	
3.05/1.76	(0) CpxTRS
3.05/1.76	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.05/1.76	(2) TRS for Loop Detection
3.05/1.76	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.05/1.76	(4) BOUNDS(INF, INF)
3.05/1.76	
3.05/1.76	
3.05/1.76	----------------------------------------
3.05/1.76	
3.05/1.76	(0)
3.05/1.76	Obligation:
3.05/1.76	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.05/1.76	
3.05/1.76	
3.05/1.76	The TRS R consists of the following rules:
3.05/1.76	
3.05/1.76	   equal0(Nil) -> number42(Nil)
3.05/1.76	   equal0(Cons(x, xs)) -> equal0(Cons(x, xs))
3.05/1.76	   number42(x) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil))))))))))))))))))))))))))))))))))))))))))
3.05/1.76	   goal(x) -> equal0(x)
3.05/1.76	
3.05/1.76	S is empty.
3.05/1.76	Rewrite Strategy: INNERMOST
3.05/1.76	----------------------------------------
3.05/1.76	
3.05/1.76	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.05/1.76	Transformed a relative TRS into a decreasing-loop problem.
3.05/1.76	----------------------------------------
3.05/1.76	
3.05/1.76	(2)
3.05/1.76	Obligation:
3.05/1.76	Analyzing the following TRS for decreasing loops:
3.05/1.76	
3.05/1.76	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.05/1.76	
3.05/1.76	
3.05/1.76	The TRS R consists of the following rules:
3.05/1.76	
3.05/1.76	   equal0(Nil) -> number42(Nil)
3.05/1.76	   equal0(Cons(x, xs)) -> equal0(Cons(x, xs))
3.05/1.76	   number42(x) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil))))))))))))))))))))))))))))))))))))))))))
3.05/1.76	   goal(x) -> equal0(x)
3.05/1.76	
3.05/1.76	S is empty.
3.05/1.76	Rewrite Strategy: INNERMOST
3.05/1.76	----------------------------------------
3.05/1.76	
3.05/1.76	(3) InfiniteLowerBoundProof (FINISHED)
3.05/1.76	The following loop proves infinite runtime complexity:
3.05/1.76	
3.05/1.76	The rewrite sequence
3.05/1.76	
3.05/1.76	equal0(Cons(x, xs)) ->^+ equal0(Cons(x, xs))
3.05/1.76	
3.05/1.76	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
3.05/1.76	
3.05/1.76	The pumping substitution is [ ].
3.05/1.76	
3.05/1.76	The result substitution is [ ].
3.05/1.76	
3.05/1.76	
3.05/1.76	
3.05/1.76	
3.05/1.76	----------------------------------------
3.05/1.76	
3.05/1.76	(4)
3.05/1.76	BOUNDS(INF, INF)
3.38/1.79	EOF