2.96/1.48	WORST_CASE(NON_POLY, ?)
2.96/1.49	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.96/1.49	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.96/1.49	
2.96/1.49	
2.96/1.49	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.96/1.49	
2.96/1.49	(0) CpxTRS
2.96/1.49	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
2.96/1.49	(2) TRS for Loop Detection
2.96/1.49	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
2.96/1.49	(4) BOUNDS(INF, INF)
2.96/1.49	
2.96/1.49	
2.96/1.49	----------------------------------------
2.96/1.49	
2.96/1.49	(0)
2.96/1.49	Obligation:
2.96/1.49	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.96/1.49	
2.96/1.49	
2.96/1.49	The TRS R consists of the following rules:
2.96/1.49	
2.96/1.49	   cons(x, cons(y, z)) -> big
2.96/1.49	   inf(x) -> cons(x, inf(s(x)))
2.96/1.49	
2.96/1.49	S is empty.
2.96/1.49	Rewrite Strategy: FULL
2.96/1.49	----------------------------------------
2.96/1.49	
2.96/1.49	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
2.96/1.49	Transformed a relative TRS into a decreasing-loop problem.
2.96/1.49	----------------------------------------
2.96/1.49	
2.96/1.49	(2)
2.96/1.49	Obligation:
2.96/1.49	Analyzing the following TRS for decreasing loops:
2.96/1.49	
2.96/1.49	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.96/1.49	
2.96/1.49	
2.96/1.49	The TRS R consists of the following rules:
2.96/1.49	
2.96/1.49	   cons(x, cons(y, z)) -> big
2.96/1.49	   inf(x) -> cons(x, inf(s(x)))
2.96/1.49	
2.96/1.49	S is empty.
2.96/1.49	Rewrite Strategy: FULL
2.96/1.49	----------------------------------------
2.96/1.49	
2.96/1.49	(3) InfiniteLowerBoundProof (FINISHED)
2.96/1.49	The following loop proves infinite runtime complexity:
2.96/1.49	
2.96/1.49	The rewrite sequence
2.96/1.49	
2.96/1.49	inf(x) ->^+ cons(x, inf(s(x)))
2.96/1.49	
2.96/1.49	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
2.96/1.49	
2.96/1.49	The pumping substitution is [ ].
2.96/1.49	
2.96/1.49	The result substitution is [x / s(x)].
2.96/1.49	
2.96/1.49	
2.96/1.49	
2.96/1.49	
2.96/1.49	----------------------------------------
2.96/1.49	
2.96/1.49	(4)
2.96/1.49	BOUNDS(INF, INF)
3.03/1.53	EOF