3.21/1.53	WORST_CASE(NON_POLY, ?)
3.21/1.54	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.21/1.54	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.21/1.54	
3.21/1.54	
3.21/1.54	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.21/1.54	
3.21/1.54	(0) CpxTRS
3.21/1.54	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.21/1.54	(2) TRS for Loop Detection
3.21/1.54	(3) DecreasingLoopProof [FINISHED, 0 ms]
3.21/1.54	(4) BOUNDS(EXP, INF)
3.21/1.54	
3.21/1.54	
3.21/1.54	----------------------------------------
3.21/1.54	
3.21/1.54	(0)
3.21/1.54	Obligation:
3.21/1.54	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.21/1.54	
3.21/1.54	
3.21/1.54	The TRS R consists of the following rules:
3.21/1.54	
3.21/1.54	   g(f(x, y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))
3.21/1.54	
3.21/1.54	S is empty.
3.21/1.54	Rewrite Strategy: INNERMOST
3.21/1.54	----------------------------------------
3.21/1.54	
3.21/1.54	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.21/1.54	Transformed a relative TRS into a decreasing-loop problem.
3.21/1.54	----------------------------------------
3.21/1.54	
3.21/1.54	(2)
3.21/1.54	Obligation:
3.21/1.54	Analyzing the following TRS for decreasing loops:
3.21/1.54	
3.21/1.54	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.21/1.54	
3.21/1.54	
3.21/1.54	The TRS R consists of the following rules:
3.21/1.54	
3.21/1.54	   g(f(x, y)) -> f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))
3.21/1.54	
3.21/1.54	S is empty.
3.21/1.54	Rewrite Strategy: INNERMOST
3.21/1.54	----------------------------------------
3.21/1.54	
3.21/1.54	(3) DecreasingLoopProof (FINISHED)
3.21/1.54	The following loop(s) give(s) rise to the lower bound EXP:
3.21/1.54	
3.21/1.54	The rewrite sequence
3.21/1.54	
3.21/1.54	g(f(x, y)) ->^+ f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))
3.21/1.54	
3.21/1.54	gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0,0].
3.21/1.54	
3.21/1.54	The pumping substitution is [x / f(x, y)].
3.21/1.54	
3.21/1.54	The result substitution is [ ].
3.21/1.54	
3.21/1.54	
3.21/1.54	
3.21/1.54	The rewrite sequence
3.21/1.54	
3.21/1.54	g(f(x, y)) ->^+ f(f(g(g(x)), g(g(y))), f(g(g(x)), g(g(y))))
3.21/1.54	
3.21/1.54	gives rise to a decreasing loop by considering the right hand sides subterm at position [1,0,0].
3.21/1.54	
3.21/1.54	The pumping substitution is [x / f(x, y)].
3.21/1.54	
3.21/1.54	The result substitution is [ ].
3.21/1.54	
3.21/1.54	
3.21/1.54	
3.21/1.54	
3.21/1.54	----------------------------------------
3.21/1.54	
3.21/1.54	(4)
3.21/1.54	BOUNDS(EXP, INF)
3.21/1.56	EOF