3.04/1.50	WORST_CASE(NON_POLY, ?)
3.04/1.51	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.04/1.51	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.04/1.51	
3.04/1.51	
3.04/1.51	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.04/1.51	
3.04/1.51	(0) CpxTRS
3.04/1.51	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.04/1.51	(2) TRS for Loop Detection
3.04/1.51	(3) DecreasingLoopProof [FINISHED, 0 ms]
3.04/1.51	(4) BOUNDS(EXP, INF)
3.04/1.51	
3.04/1.51	
3.04/1.51	----------------------------------------
3.04/1.51	
3.04/1.51	(0)
3.04/1.51	Obligation:
3.04/1.51	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.04/1.51	
3.04/1.51	
3.04/1.51	The TRS R consists of the following rules:
3.04/1.51	
3.04/1.51	   f(g(x)) -> f(a(g(g(f(x))), g(f(x))))
3.04/1.51	
3.04/1.51	S is empty.
3.04/1.51	Rewrite Strategy: FULL
3.04/1.51	----------------------------------------
3.04/1.51	
3.04/1.51	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.04/1.51	Transformed a relative TRS into a decreasing-loop problem.
3.04/1.51	----------------------------------------
3.04/1.51	
3.04/1.51	(2)
3.04/1.51	Obligation:
3.04/1.51	Analyzing the following TRS for decreasing loops:
3.04/1.51	
3.04/1.51	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.04/1.51	
3.04/1.51	
3.04/1.51	The TRS R consists of the following rules:
3.04/1.51	
3.04/1.51	   f(g(x)) -> f(a(g(g(f(x))), g(f(x))))
3.04/1.51	
3.04/1.51	S is empty.
3.04/1.51	Rewrite Strategy: FULL
3.04/1.51	----------------------------------------
3.04/1.51	
3.04/1.51	(3) DecreasingLoopProof (FINISHED)
3.04/1.51	The following loop(s) give(s) rise to the lower bound EXP:
3.04/1.51	
3.04/1.51	The rewrite sequence
3.04/1.51	
3.04/1.51	f(g(x)) ->^+ f(a(g(g(f(x))), g(f(x))))
3.04/1.51	
3.04/1.51	gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0,0,0].
3.04/1.51	
3.04/1.51	The pumping substitution is [x / g(x)].
3.04/1.51	
3.04/1.51	The result substitution is [ ].
3.04/1.51	
3.04/1.51	
3.04/1.51	
3.04/1.51	The rewrite sequence
3.04/1.51	
3.04/1.51	f(g(x)) ->^+ f(a(g(g(f(x))), g(f(x))))
3.04/1.51	
3.04/1.51	gives rise to a decreasing loop by considering the right hand sides subterm at position [0,1,0].
3.04/1.51	
3.04/1.51	The pumping substitution is [x / g(x)].
3.04/1.51	
3.04/1.51	The result substitution is [ ].
3.04/1.51	
3.04/1.51	
3.04/1.51	
3.04/1.51	
3.04/1.51	----------------------------------------
3.04/1.51	
3.04/1.51	(4)
3.04/1.51	BOUNDS(EXP, INF)
3.21/1.55	EOF