3.10/1.62	WORST_CASE(NON_POLY, ?)
3.10/1.62	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.10/1.62	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.10/1.62	
3.10/1.62	
3.10/1.62	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.10/1.62	
3.10/1.62	(0) CpxTRS
3.10/1.62	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.10/1.62	(2) TRS for Loop Detection
3.10/1.62	(3) DecreasingLoopProof [FINISHED, 0 ms]
3.10/1.62	(4) BOUNDS(EXP, INF)
3.10/1.62	
3.10/1.62	
3.10/1.62	----------------------------------------
3.10/1.62	
3.10/1.62	(0)
3.10/1.62	Obligation:
3.10/1.62	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.10/1.62	
3.10/1.62	
3.10/1.62	The TRS R consists of the following rules:
3.10/1.62	
3.10/1.62	   bin(x, 0) -> s(0)
3.10/1.62	   bin(0, s(y)) -> 0
3.10/1.62	   bin(s(x), s(y)) -> +(bin(x, s(y)), bin(x, y))
3.10/1.62	
3.10/1.62	S is empty.
3.10/1.62	Rewrite Strategy: INNERMOST
3.10/1.62	----------------------------------------
3.10/1.62	
3.10/1.62	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.10/1.62	Transformed a relative TRS into a decreasing-loop problem.
3.10/1.62	----------------------------------------
3.10/1.62	
3.10/1.62	(2)
3.10/1.62	Obligation:
3.10/1.62	Analyzing the following TRS for decreasing loops:
3.10/1.62	
3.10/1.62	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.10/1.62	
3.10/1.62	
3.10/1.62	The TRS R consists of the following rules:
3.10/1.62	
3.10/1.62	   bin(x, 0) -> s(0)
3.10/1.62	   bin(0, s(y)) -> 0
3.10/1.62	   bin(s(x), s(y)) -> +(bin(x, s(y)), bin(x, y))
3.10/1.62	
3.10/1.62	S is empty.
3.10/1.62	Rewrite Strategy: INNERMOST
3.10/1.62	----------------------------------------
3.10/1.62	
3.10/1.62	(3) DecreasingLoopProof (FINISHED)
3.10/1.62	The following loop(s) give(s) rise to the lower bound EXP:
3.10/1.62	
3.10/1.62	The rewrite sequence
3.10/1.62	
3.10/1.62	bin(s(x), s(y)) ->^+ +(bin(x, s(y)), bin(x, y))
3.10/1.62	
3.10/1.62	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
3.10/1.62	
3.10/1.62	The pumping substitution is [x / s(x)].
3.10/1.62	
3.10/1.62	The result substitution is [ ].
3.10/1.62	
3.10/1.62	
3.10/1.62	
3.10/1.62	The rewrite sequence
3.10/1.62	
3.10/1.62	bin(s(x), s(y)) ->^+ +(bin(x, s(y)), bin(x, y))
3.10/1.62	
3.10/1.62	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
3.10/1.62	
3.10/1.62	The pumping substitution is [x / s(x), y / s(y)].
3.10/1.62	
3.10/1.62	The result substitution is [ ].
3.10/1.62	
3.10/1.62	
3.10/1.62	
3.10/1.62	
3.10/1.62	----------------------------------------
3.10/1.62	
3.10/1.62	(4)
3.10/1.62	BOUNDS(EXP, INF)
3.10/1.64	EOF