3.28/1.61	WORST_CASE(NON_POLY, ?)
3.28/1.62	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.28/1.62	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.28/1.62	
3.28/1.62	
3.28/1.62	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.28/1.62	
3.28/1.62	(0) CpxTRS
3.28/1.62	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.28/1.62	(2) TRS for Loop Detection
3.28/1.62	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
3.28/1.62	(4) BEST
3.28/1.62	    (5) proven lower bound
3.28/1.62	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
3.28/1.62	        (7) BOUNDS(n^1, INF)
3.28/1.62	    (8) TRS for Loop Detection
3.28/1.62	        (9) DecreasingLoopProof [FINISHED, 0 ms]
3.28/1.62	        (10) BOUNDS(EXP, INF)
3.28/1.62	
3.28/1.62	
3.28/1.62	----------------------------------------
3.28/1.62	
3.28/1.62	(0)
3.28/1.62	Obligation:
3.28/1.62	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.28/1.62	
3.28/1.62	
3.28/1.62	The TRS R consists of the following rules:
3.28/1.62	
3.28/1.62	   a__f(g(X), Y) -> a__f(mark(X), f(g(X), Y))
3.28/1.62	   mark(f(X1, X2)) -> a__f(mark(X1), X2)
3.28/1.62	   mark(g(X)) -> g(mark(X))
3.28/1.62	   a__f(X1, X2) -> f(X1, X2)
3.28/1.62	
3.28/1.62	S is empty.
3.28/1.62	Rewrite Strategy: FULL
3.28/1.62	----------------------------------------
3.28/1.62	
3.28/1.62	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.28/1.62	Transformed a relative TRS into a decreasing-loop problem.
3.28/1.62	----------------------------------------
3.28/1.62	
3.28/1.62	(2)
3.28/1.62	Obligation:
3.28/1.62	Analyzing the following TRS for decreasing loops:
3.28/1.62	
3.28/1.62	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.28/1.62	
3.28/1.62	
3.28/1.62	The TRS R consists of the following rules:
3.28/1.62	
3.28/1.62	   a__f(g(X), Y) -> a__f(mark(X), f(g(X), Y))
3.28/1.62	   mark(f(X1, X2)) -> a__f(mark(X1), X2)
3.28/1.62	   mark(g(X)) -> g(mark(X))
3.28/1.62	   a__f(X1, X2) -> f(X1, X2)
3.28/1.62	
3.28/1.62	S is empty.
3.28/1.62	Rewrite Strategy: FULL
3.28/1.62	----------------------------------------
3.28/1.62	
3.28/1.62	(3) DecreasingLoopProof (LOWER BOUND(ID))
3.28/1.62	The following loop(s) give(s) rise to the lower bound Omega(n^1):
3.28/1.62	
3.28/1.62	The rewrite sequence
3.28/1.62	
3.28/1.62	mark(f(X1, X2)) ->^+ a__f(mark(X1), X2)
3.28/1.62	
3.28/1.62	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
3.28/1.62	
3.28/1.62	The pumping substitution is [X1 / f(X1, X2)].
3.28/1.62	
3.28/1.62	The result substitution is [ ].
3.28/1.62	
3.28/1.62	
3.28/1.62	
3.28/1.62	
3.28/1.62	----------------------------------------
3.28/1.62	
3.28/1.62	(4)
3.28/1.62	Complex Obligation (BEST)
3.28/1.62	
3.28/1.62	----------------------------------------
3.28/1.62	
3.28/1.62	(5)
3.28/1.62	Obligation:
3.28/1.62	Proved the lower bound n^1 for the following obligation:
3.28/1.62	
3.28/1.62	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.28/1.62	
3.28/1.62	
3.28/1.62	The TRS R consists of the following rules:
3.28/1.62	
3.28/1.62	   a__f(g(X), Y) -> a__f(mark(X), f(g(X), Y))
3.28/1.62	   mark(f(X1, X2)) -> a__f(mark(X1), X2)
3.28/1.62	   mark(g(X)) -> g(mark(X))
3.28/1.62	   a__f(X1, X2) -> f(X1, X2)
3.28/1.62	
3.28/1.62	S is empty.
3.28/1.62	Rewrite Strategy: FULL
3.28/1.62	----------------------------------------
3.28/1.62	
3.28/1.62	(6) LowerBoundPropagationProof (FINISHED)
3.28/1.62	Propagated lower bound.
3.28/1.62	----------------------------------------
3.28/1.62	
3.28/1.62	(7)
3.28/1.62	BOUNDS(n^1, INF)
3.28/1.62	
3.28/1.62	----------------------------------------
3.28/1.62	
3.28/1.62	(8)
3.28/1.62	Obligation:
3.28/1.62	Analyzing the following TRS for decreasing loops:
3.28/1.62	
3.28/1.62	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.28/1.62	
3.28/1.62	
3.28/1.62	The TRS R consists of the following rules:
3.28/1.62	
3.28/1.62	   a__f(g(X), Y) -> a__f(mark(X), f(g(X), Y))
3.28/1.62	   mark(f(X1, X2)) -> a__f(mark(X1), X2)
3.28/1.62	   mark(g(X)) -> g(mark(X))
3.28/1.62	   a__f(X1, X2) -> f(X1, X2)
3.28/1.62	
3.28/1.62	S is empty.
3.28/1.62	Rewrite Strategy: FULL
3.28/1.62	----------------------------------------
3.28/1.62	
3.28/1.62	(9) DecreasingLoopProof (FINISHED)
3.28/1.62	The following loop(s) give(s) rise to the lower bound EXP:
3.28/1.62	
3.28/1.62	The rewrite sequence
3.28/1.62	
3.28/1.62	mark(f(g(X1_0), X2)) ->^+ a__f(mark(mark(X1_0)), f(g(mark(X1_0)), X2))
3.28/1.62	
3.28/1.62	gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0].
3.28/1.62	
3.28/1.62	The pumping substitution is [X1_0 / f(g(X1_0), X2)].
3.28/1.62	
3.28/1.62	The result substitution is [ ].
3.28/1.62	
3.28/1.62	
3.28/1.62	
3.28/1.62	The rewrite sequence
3.28/1.62	
3.28/1.62	mark(f(g(X1_0), X2)) ->^+ a__f(mark(mark(X1_0)), f(g(mark(X1_0)), X2))
3.28/1.62	
3.28/1.62	gives rise to a decreasing loop by considering the right hand sides subterm at position [1,0,0].
3.28/1.62	
3.28/1.62	The pumping substitution is [X1_0 / f(g(X1_0), X2)].
3.28/1.62	
3.28/1.62	The result substitution is [ ].
3.28/1.62	
3.28/1.62	
3.28/1.62	
3.28/1.62	
3.28/1.62	----------------------------------------
3.28/1.62	
3.28/1.62	(10)
3.28/1.62	BOUNDS(EXP, INF)
3.54/1.65	EOF