3.05/1.56	WORST_CASE(NON_POLY, ?)
3.22/1.56	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.22/1.56	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.22/1.56	
3.22/1.56	
3.22/1.56	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.22/1.56	
3.22/1.56	(0) CpxTRS
3.22/1.56	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.22/1.56	(2) TRS for Loop Detection
3.22/1.56	(3) DecreasingLoopProof [FINISHED, 0 ms]
3.22/1.56	(4) BOUNDS(EXP, INF)
3.22/1.56	
3.22/1.56	
3.22/1.56	----------------------------------------
3.22/1.56	
3.22/1.56	(0)
3.22/1.56	Obligation:
3.22/1.56	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.22/1.56	
3.22/1.56	
3.22/1.56	The TRS R consists of the following rules:
3.22/1.56	
3.22/1.56	   f(0) -> 1
3.22/1.56	   f(s(x)) -> g(f(x))
3.22/1.56	   g(x) -> +(x, s(x))
3.22/1.56	   f(s(x)) -> +(f(x), s(f(x)))
3.22/1.56	
3.22/1.56	S is empty.
3.22/1.56	Rewrite Strategy: INNERMOST
3.22/1.56	----------------------------------------
3.22/1.56	
3.22/1.56	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.22/1.56	Transformed a relative TRS into a decreasing-loop problem.
3.22/1.56	----------------------------------------
3.22/1.56	
3.22/1.56	(2)
3.22/1.56	Obligation:
3.22/1.56	Analyzing the following TRS for decreasing loops:
3.22/1.56	
3.22/1.56	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.22/1.56	
3.22/1.56	
3.22/1.56	The TRS R consists of the following rules:
3.22/1.56	
3.22/1.56	   f(0) -> 1
3.22/1.56	   f(s(x)) -> g(f(x))
3.22/1.56	   g(x) -> +(x, s(x))
3.22/1.56	   f(s(x)) -> +(f(x), s(f(x)))
3.22/1.56	
3.22/1.56	S is empty.
3.22/1.56	Rewrite Strategy: INNERMOST
3.22/1.56	----------------------------------------
3.22/1.56	
3.22/1.56	(3) DecreasingLoopProof (FINISHED)
3.22/1.56	The following loop(s) give(s) rise to the lower bound EXP:
3.22/1.56	
3.22/1.56	The rewrite sequence
3.22/1.56	
3.22/1.56	f(s(x)) ->^+ +(f(x), s(f(x)))
3.22/1.56	
3.22/1.56	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
3.22/1.56	
3.22/1.56	The pumping substitution is [x / s(x)].
3.22/1.56	
3.22/1.56	The result substitution is [ ].
3.22/1.56	
3.22/1.56	
3.22/1.56	
3.22/1.56	The rewrite sequence
3.22/1.56	
3.22/1.56	f(s(x)) ->^+ +(f(x), s(f(x)))
3.22/1.56	
3.22/1.56	gives rise to a decreasing loop by considering the right hand sides subterm at position [1,0].
3.22/1.56	
3.22/1.56	The pumping substitution is [x / s(x)].
3.22/1.56	
3.22/1.56	The result substitution is [ ].
3.22/1.56	
3.22/1.56	
3.22/1.56	
3.22/1.56	
3.22/1.56	----------------------------------------
3.22/1.56	
3.22/1.56	(4)
3.22/1.56	BOUNDS(EXP, INF)
3.22/1.60	EOF