3.35/1.58	WORST_CASE(NON_POLY, ?)
3.35/1.58	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.35/1.58	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.35/1.58	
3.35/1.58	
3.35/1.58	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.35/1.58	
3.35/1.58	(0) CpxTRS
3.35/1.58	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.35/1.58	(2) TRS for Loop Detection
3.35/1.58	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
3.35/1.58	(4) BEST
3.35/1.58	    (5) proven lower bound
3.35/1.58	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
3.35/1.58	        (7) BOUNDS(n^1, INF)
3.35/1.58	    (8) TRS for Loop Detection
3.35/1.58	        (9) DecreasingLoopProof [FINISHED, 0 ms]
3.35/1.58	        (10) BOUNDS(EXP, INF)
3.35/1.58	
3.35/1.58	
3.35/1.58	----------------------------------------
3.35/1.58	
3.35/1.58	(0)
3.35/1.58	Obligation:
3.35/1.58	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.35/1.58	
3.35/1.58	
3.35/1.58	The TRS R consists of the following rules:
3.35/1.58	
3.35/1.58	   a__f(b, X, c) -> a__f(X, a__c, X)
3.35/1.58	   a__c -> b
3.35/1.58	   mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3)
3.35/1.58	   mark(c) -> a__c
3.35/1.58	   mark(b) -> b
3.35/1.58	   a__f(X1, X2, X3) -> f(X1, X2, X3)
3.35/1.58	   a__c -> c
3.35/1.58	
3.35/1.58	S is empty.
3.35/1.58	Rewrite Strategy: FULL
3.35/1.58	----------------------------------------
3.35/1.58	
3.35/1.58	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.35/1.58	Transformed a relative TRS into a decreasing-loop problem.
3.35/1.58	----------------------------------------
3.35/1.58	
3.35/1.58	(2)
3.35/1.58	Obligation:
3.35/1.58	Analyzing the following TRS for decreasing loops:
3.35/1.58	
3.35/1.58	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.35/1.58	
3.35/1.58	
3.35/1.58	The TRS R consists of the following rules:
3.35/1.58	
3.35/1.58	   a__f(b, X, c) -> a__f(X, a__c, X)
3.35/1.58	   a__c -> b
3.35/1.58	   mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3)
3.35/1.58	   mark(c) -> a__c
3.35/1.58	   mark(b) -> b
3.35/1.58	   a__f(X1, X2, X3) -> f(X1, X2, X3)
3.35/1.58	   a__c -> c
3.35/1.58	
3.35/1.58	S is empty.
3.35/1.58	Rewrite Strategy: FULL
3.35/1.58	----------------------------------------
3.35/1.58	
3.35/1.58	(3) DecreasingLoopProof (LOWER BOUND(ID))
3.35/1.58	The following loop(s) give(s) rise to the lower bound Omega(n^1):
3.35/1.58	
3.35/1.58	The rewrite sequence
3.35/1.58	
3.35/1.58	mark(f(X1, X2, X3)) ->^+ a__f(X1, mark(X2), X3)
3.35/1.58	
3.35/1.58	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
3.35/1.58	
3.35/1.58	The pumping substitution is [X2 / f(X1, X2, X3)].
3.35/1.58	
3.35/1.58	The result substitution is [ ].
3.35/1.58	
3.35/1.58	
3.35/1.58	
3.35/1.58	
3.35/1.58	----------------------------------------
3.35/1.58	
3.35/1.58	(4)
3.35/1.58	Complex Obligation (BEST)
3.35/1.58	
3.35/1.58	----------------------------------------
3.35/1.58	
3.35/1.58	(5)
3.35/1.58	Obligation:
3.35/1.58	Proved the lower bound n^1 for the following obligation:
3.35/1.58	
3.35/1.58	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.35/1.58	
3.35/1.58	
3.35/1.58	The TRS R consists of the following rules:
3.35/1.58	
3.35/1.58	   a__f(b, X, c) -> a__f(X, a__c, X)
3.35/1.58	   a__c -> b
3.35/1.58	   mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3)
3.35/1.58	   mark(c) -> a__c
3.35/1.58	   mark(b) -> b
3.35/1.58	   a__f(X1, X2, X3) -> f(X1, X2, X3)
3.35/1.58	   a__c -> c
3.35/1.58	
3.35/1.58	S is empty.
3.35/1.58	Rewrite Strategy: FULL
3.35/1.58	----------------------------------------
3.35/1.58	
3.35/1.58	(6) LowerBoundPropagationProof (FINISHED)
3.35/1.58	Propagated lower bound.
3.35/1.58	----------------------------------------
3.35/1.58	
3.35/1.58	(7)
3.35/1.58	BOUNDS(n^1, INF)
3.35/1.58	
3.35/1.58	----------------------------------------
3.35/1.58	
3.35/1.58	(8)
3.35/1.58	Obligation:
3.35/1.58	Analyzing the following TRS for decreasing loops:
3.35/1.58	
3.35/1.58	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.35/1.58	
3.35/1.58	
3.35/1.58	The TRS R consists of the following rules:
3.35/1.58	
3.35/1.58	   a__f(b, X, c) -> a__f(X, a__c, X)
3.35/1.58	   a__c -> b
3.35/1.58	   mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3)
3.35/1.58	   mark(c) -> a__c
3.35/1.58	   mark(b) -> b
3.35/1.58	   a__f(X1, X2, X3) -> f(X1, X2, X3)
3.35/1.58	   a__c -> c
3.35/1.58	
3.35/1.58	S is empty.
3.35/1.58	Rewrite Strategy: FULL
3.35/1.58	----------------------------------------
3.35/1.58	
3.35/1.58	(9) DecreasingLoopProof (FINISHED)
3.35/1.58	The following loop(s) give(s) rise to the lower bound EXP:
3.35/1.58	
3.35/1.58	The rewrite sequence
3.35/1.58	
3.35/1.58	mark(f(b, X2, c)) ->^+ a__f(mark(X2), a__c, mark(X2))
3.35/1.58	
3.35/1.58	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
3.35/1.58	
3.35/1.58	The pumping substitution is [X2 / f(b, X2, c)].
3.35/1.58	
3.35/1.58	The result substitution is [ ].
3.35/1.58	
3.35/1.58	
3.35/1.58	
3.35/1.58	The rewrite sequence
3.35/1.58	
3.35/1.58	mark(f(b, X2, c)) ->^+ a__f(mark(X2), a__c, mark(X2))
3.35/1.58	
3.35/1.58	gives rise to a decreasing loop by considering the right hand sides subterm at position [2].
3.35/1.58	
3.35/1.58	The pumping substitution is [X2 / f(b, X2, c)].
3.35/1.58	
3.35/1.58	The result substitution is [ ].
3.35/1.58	
3.35/1.58	
3.35/1.58	
3.35/1.58	
3.35/1.58	----------------------------------------
3.35/1.58	
3.35/1.58	(10)
3.35/1.58	BOUNDS(EXP, INF)
3.45/1.62	EOF