3.23/1.56	WORST_CASE(NON_POLY, ?)
3.23/1.57	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.23/1.57	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.23/1.57	
3.23/1.57	
3.23/1.57	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.23/1.57	
3.23/1.57	(0) CpxTRS
3.23/1.57	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.23/1.57	(2) TRS for Loop Detection
3.23/1.57	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
3.23/1.57	(4) BEST
3.23/1.57	    (5) proven lower bound
3.23/1.57	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
3.23/1.57	        (7) BOUNDS(n^1, INF)
3.23/1.57	    (8) TRS for Loop Detection
3.23/1.57	        (9) DecreasingLoopProof [FINISHED, 0 ms]
3.23/1.57	        (10) BOUNDS(EXP, INF)
3.23/1.57	
3.23/1.57	
3.23/1.57	----------------------------------------
3.23/1.57	
3.23/1.57	(0)
3.23/1.57	Obligation:
3.23/1.57	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.23/1.57	
3.23/1.57	
3.23/1.57	The TRS R consists of the following rules:
3.23/1.57	
3.23/1.57	   a__f(a, b, X) -> a__f(X, X, mark(X))
3.23/1.57	   a__c -> a
3.23/1.57	   a__c -> b
3.23/1.57	   mark(f(X1, X2, X3)) -> a__f(X1, X2, mark(X3))
3.23/1.57	   mark(c) -> a__c
3.23/1.57	   mark(a) -> a
3.23/1.57	   mark(b) -> b
3.23/1.57	   a__f(X1, X2, X3) -> f(X1, X2, X3)
3.23/1.57	   a__c -> c
3.23/1.57	
3.23/1.57	S is empty.
3.23/1.57	Rewrite Strategy: FULL
3.23/1.57	----------------------------------------
3.23/1.57	
3.23/1.57	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.23/1.57	Transformed a relative TRS into a decreasing-loop problem.
3.23/1.57	----------------------------------------
3.23/1.57	
3.23/1.57	(2)
3.23/1.57	Obligation:
3.23/1.57	Analyzing the following TRS for decreasing loops:
3.23/1.57	
3.23/1.57	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.23/1.57	
3.23/1.57	
3.23/1.57	The TRS R consists of the following rules:
3.23/1.57	
3.23/1.57	   a__f(a, b, X) -> a__f(X, X, mark(X))
3.23/1.57	   a__c -> a
3.23/1.57	   a__c -> b
3.23/1.57	   mark(f(X1, X2, X3)) -> a__f(X1, X2, mark(X3))
3.23/1.57	   mark(c) -> a__c
3.23/1.57	   mark(a) -> a
3.23/1.57	   mark(b) -> b
3.23/1.57	   a__f(X1, X2, X3) -> f(X1, X2, X3)
3.23/1.57	   a__c -> c
3.23/1.57	
3.23/1.57	S is empty.
3.23/1.57	Rewrite Strategy: FULL
3.23/1.57	----------------------------------------
3.23/1.57	
3.23/1.57	(3) DecreasingLoopProof (LOWER BOUND(ID))
3.23/1.57	The following loop(s) give(s) rise to the lower bound Omega(n^1):
3.23/1.57	
3.23/1.57	The rewrite sequence
3.23/1.57	
3.23/1.57	mark(f(X1, X2, X3)) ->^+ a__f(X1, X2, mark(X3))
3.23/1.57	
3.23/1.57	gives rise to a decreasing loop by considering the right hand sides subterm at position [2].
3.23/1.57	
3.23/1.57	The pumping substitution is [X3 / f(X1, X2, X3)].
3.23/1.57	
3.23/1.57	The result substitution is [ ].
3.23/1.57	
3.23/1.57	
3.23/1.57	
3.23/1.57	
3.23/1.57	----------------------------------------
3.23/1.57	
3.23/1.57	(4)
3.23/1.57	Complex Obligation (BEST)
3.23/1.57	
3.23/1.57	----------------------------------------
3.23/1.57	
3.23/1.57	(5)
3.23/1.57	Obligation:
3.23/1.57	Proved the lower bound n^1 for the following obligation:
3.23/1.57	
3.23/1.57	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.23/1.57	
3.23/1.57	
3.23/1.57	The TRS R consists of the following rules:
3.23/1.57	
3.23/1.57	   a__f(a, b, X) -> a__f(X, X, mark(X))
3.23/1.57	   a__c -> a
3.23/1.57	   a__c -> b
3.23/1.57	   mark(f(X1, X2, X3)) -> a__f(X1, X2, mark(X3))
3.23/1.57	   mark(c) -> a__c
3.23/1.57	   mark(a) -> a
3.23/1.57	   mark(b) -> b
3.23/1.57	   a__f(X1, X2, X3) -> f(X1, X2, X3)
3.23/1.57	   a__c -> c
3.23/1.57	
3.23/1.57	S is empty.
3.23/1.57	Rewrite Strategy: FULL
3.23/1.57	----------------------------------------
3.23/1.57	
3.23/1.57	(6) LowerBoundPropagationProof (FINISHED)
3.23/1.57	Propagated lower bound.
3.23/1.57	----------------------------------------
3.23/1.57	
3.23/1.57	(7)
3.23/1.57	BOUNDS(n^1, INF)
3.23/1.57	
3.23/1.57	----------------------------------------
3.23/1.57	
3.23/1.57	(8)
3.23/1.57	Obligation:
3.23/1.57	Analyzing the following TRS for decreasing loops:
3.23/1.57	
3.23/1.57	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.23/1.57	
3.23/1.57	
3.23/1.57	The TRS R consists of the following rules:
3.23/1.57	
3.23/1.57	   a__f(a, b, X) -> a__f(X, X, mark(X))
3.23/1.57	   a__c -> a
3.23/1.57	   a__c -> b
3.23/1.57	   mark(f(X1, X2, X3)) -> a__f(X1, X2, mark(X3))
3.23/1.57	   mark(c) -> a__c
3.23/1.57	   mark(a) -> a
3.23/1.57	   mark(b) -> b
3.23/1.57	   a__f(X1, X2, X3) -> f(X1, X2, X3)
3.23/1.57	   a__c -> c
3.23/1.57	
3.23/1.57	S is empty.
3.23/1.57	Rewrite Strategy: FULL
3.23/1.57	----------------------------------------
3.23/1.57	
3.23/1.57	(9) DecreasingLoopProof (FINISHED)
3.23/1.57	The following loop(s) give(s) rise to the lower bound EXP:
3.23/1.57	
3.23/1.57	The rewrite sequence
3.23/1.57	
3.23/1.57	mark(f(a, b, X3)) ->^+ a__f(mark(X3), mark(X3), mark(mark(X3)))
3.23/1.57	
3.23/1.57	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
3.23/1.57	
3.23/1.57	The pumping substitution is [X3 / f(a, b, X3)].
3.23/1.57	
3.23/1.57	The result substitution is [ ].
3.23/1.57	
3.23/1.57	
3.23/1.57	
3.23/1.57	The rewrite sequence
3.23/1.57	
3.23/1.57	mark(f(a, b, X3)) ->^+ a__f(mark(X3), mark(X3), mark(mark(X3)))
3.23/1.57	
3.23/1.57	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
3.23/1.57	
3.23/1.57	The pumping substitution is [X3 / f(a, b, X3)].
3.23/1.57	
3.23/1.57	The result substitution is [ ].
3.23/1.57	
3.23/1.57	
3.23/1.57	
3.23/1.57	
3.23/1.57	----------------------------------------
3.23/1.57	
3.23/1.57	(10)
3.23/1.57	BOUNDS(EXP, INF)
3.23/1.61	EOF