3.46/1.60	WORST_CASE(NON_POLY, ?)
3.46/1.61	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.46/1.61	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.46/1.61	
3.46/1.61	
3.46/1.61	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.46/1.61	
3.46/1.61	(0) CpxTRS
3.46/1.61	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.46/1.61	(2) TRS for Loop Detection
3.46/1.61	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
3.46/1.61	(4) BEST
3.46/1.61	    (5) proven lower bound
3.46/1.61	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
3.46/1.61	        (7) BOUNDS(n^1, INF)
3.46/1.61	    (8) TRS for Loop Detection
3.46/1.61	        (9) DecreasingLoopProof [FINISHED, 0 ms]
3.46/1.61	        (10) BOUNDS(EXP, INF)
3.46/1.61	
3.46/1.61	
3.46/1.61	----------------------------------------
3.46/1.61	
3.46/1.61	(0)
3.46/1.61	Obligation:
3.46/1.61	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.46/1.61	
3.46/1.61	
3.46/1.61	The TRS R consists of the following rules:
3.46/1.61	
3.46/1.61	   a__from(X) -> cons(mark(X), from(s(X)))
3.46/1.61	   a__length(nil) -> 0
3.46/1.61	   a__length(cons(X, Y)) -> s(a__length1(Y))
3.46/1.61	   a__length1(X) -> a__length(X)
3.46/1.61	   mark(from(X)) -> a__from(mark(X))
3.46/1.61	   mark(length(X)) -> a__length(X)
3.46/1.61	   mark(length1(X)) -> a__length1(X)
3.46/1.61	   mark(cons(X1, X2)) -> cons(mark(X1), X2)
3.46/1.61	   mark(s(X)) -> s(mark(X))
3.46/1.61	   mark(nil) -> nil
3.46/1.61	   mark(0) -> 0
3.46/1.61	   a__from(X) -> from(X)
3.46/1.61	   a__length(X) -> length(X)
3.46/1.61	   a__length1(X) -> length1(X)
3.46/1.61	
3.46/1.61	S is empty.
3.46/1.61	Rewrite Strategy: FULL
3.46/1.61	----------------------------------------
3.46/1.61	
3.46/1.61	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.46/1.61	Transformed a relative TRS into a decreasing-loop problem.
3.46/1.61	----------------------------------------
3.46/1.61	
3.46/1.61	(2)
3.46/1.61	Obligation:
3.46/1.61	Analyzing the following TRS for decreasing loops:
3.46/1.61	
3.46/1.61	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.46/1.61	
3.46/1.61	
3.46/1.61	The TRS R consists of the following rules:
3.46/1.61	
3.46/1.61	   a__from(X) -> cons(mark(X), from(s(X)))
3.46/1.61	   a__length(nil) -> 0
3.46/1.61	   a__length(cons(X, Y)) -> s(a__length1(Y))
3.46/1.61	   a__length1(X) -> a__length(X)
3.46/1.61	   mark(from(X)) -> a__from(mark(X))
3.46/1.61	   mark(length(X)) -> a__length(X)
3.46/1.61	   mark(length1(X)) -> a__length1(X)
3.46/1.61	   mark(cons(X1, X2)) -> cons(mark(X1), X2)
3.46/1.61	   mark(s(X)) -> s(mark(X))
3.46/1.61	   mark(nil) -> nil
3.46/1.61	   mark(0) -> 0
3.46/1.61	   a__from(X) -> from(X)
3.46/1.61	   a__length(X) -> length(X)
3.46/1.61	   a__length1(X) -> length1(X)
3.46/1.61	
3.46/1.61	S is empty.
3.46/1.61	Rewrite Strategy: FULL
3.46/1.61	----------------------------------------
3.46/1.61	
3.46/1.61	(3) DecreasingLoopProof (LOWER BOUND(ID))
3.46/1.61	The following loop(s) give(s) rise to the lower bound Omega(n^1):
3.46/1.61	
3.46/1.61	The rewrite sequence
3.46/1.61	
3.46/1.61	mark(from(X)) ->^+ a__from(mark(X))
3.46/1.61	
3.46/1.61	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
3.46/1.61	
3.46/1.61	The pumping substitution is [X / from(X)].
3.46/1.61	
3.46/1.61	The result substitution is [ ].
3.46/1.61	
3.46/1.61	
3.46/1.61	
3.46/1.61	
3.46/1.61	----------------------------------------
3.46/1.61	
3.46/1.61	(4)
3.46/1.61	Complex Obligation (BEST)
3.46/1.61	
3.46/1.61	----------------------------------------
3.46/1.61	
3.46/1.61	(5)
3.46/1.61	Obligation:
3.46/1.61	Proved the lower bound n^1 for the following obligation:
3.46/1.61	
3.46/1.61	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.46/1.61	
3.46/1.61	
3.46/1.61	The TRS R consists of the following rules:
3.46/1.61	
3.46/1.61	   a__from(X) -> cons(mark(X), from(s(X)))
3.46/1.61	   a__length(nil) -> 0
3.46/1.61	   a__length(cons(X, Y)) -> s(a__length1(Y))
3.46/1.61	   a__length1(X) -> a__length(X)
3.46/1.61	   mark(from(X)) -> a__from(mark(X))
3.46/1.61	   mark(length(X)) -> a__length(X)
3.46/1.61	   mark(length1(X)) -> a__length1(X)
3.46/1.61	   mark(cons(X1, X2)) -> cons(mark(X1), X2)
3.46/1.61	   mark(s(X)) -> s(mark(X))
3.46/1.61	   mark(nil) -> nil
3.46/1.61	   mark(0) -> 0
3.46/1.61	   a__from(X) -> from(X)
3.46/1.61	   a__length(X) -> length(X)
3.46/1.61	   a__length1(X) -> length1(X)
3.46/1.61	
3.46/1.61	S is empty.
3.46/1.61	Rewrite Strategy: FULL
3.46/1.61	----------------------------------------
3.46/1.61	
3.46/1.61	(6) LowerBoundPropagationProof (FINISHED)
3.46/1.61	Propagated lower bound.
3.46/1.61	----------------------------------------
3.46/1.61	
3.46/1.61	(7)
3.46/1.61	BOUNDS(n^1, INF)
3.46/1.61	
3.46/1.61	----------------------------------------
3.46/1.61	
3.46/1.61	(8)
3.46/1.61	Obligation:
3.46/1.61	Analyzing the following TRS for decreasing loops:
3.46/1.61	
3.46/1.61	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.46/1.61	
3.46/1.61	
3.46/1.61	The TRS R consists of the following rules:
3.46/1.61	
3.46/1.61	   a__from(X) -> cons(mark(X), from(s(X)))
3.46/1.61	   a__length(nil) -> 0
3.46/1.61	   a__length(cons(X, Y)) -> s(a__length1(Y))
3.46/1.61	   a__length1(X) -> a__length(X)
3.46/1.61	   mark(from(X)) -> a__from(mark(X))
3.46/1.61	   mark(length(X)) -> a__length(X)
3.46/1.61	   mark(length1(X)) -> a__length1(X)
3.46/1.61	   mark(cons(X1, X2)) -> cons(mark(X1), X2)
3.46/1.61	   mark(s(X)) -> s(mark(X))
3.46/1.61	   mark(nil) -> nil
3.46/1.61	   mark(0) -> 0
3.46/1.61	   a__from(X) -> from(X)
3.46/1.61	   a__length(X) -> length(X)
3.46/1.61	   a__length1(X) -> length1(X)
3.46/1.61	
3.46/1.61	S is empty.
3.46/1.61	Rewrite Strategy: FULL
3.46/1.61	----------------------------------------
3.46/1.61	
3.46/1.61	(9) DecreasingLoopProof (FINISHED)
3.46/1.61	The following loop(s) give(s) rise to the lower bound EXP:
3.46/1.61	
3.46/1.61	The rewrite sequence
3.46/1.61	
3.46/1.61	mark(from(X)) ->^+ cons(mark(mark(X)), from(s(mark(X))))
3.46/1.61	
3.46/1.61	gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0].
3.46/1.61	
3.46/1.61	The pumping substitution is [X / from(X)].
3.46/1.61	
3.46/1.61	The result substitution is [ ].
3.46/1.61	
3.46/1.61	
3.46/1.61	
3.46/1.61	The rewrite sequence
3.46/1.61	
3.46/1.61	mark(from(X)) ->^+ cons(mark(mark(X)), from(s(mark(X))))
3.46/1.61	
3.46/1.61	gives rise to a decreasing loop by considering the right hand sides subterm at position [1,0,0].
3.46/1.61	
3.46/1.61	The pumping substitution is [X / from(X)].
3.46/1.61	
3.46/1.61	The result substitution is [ ].
3.46/1.61	
3.46/1.61	
3.46/1.61	
3.46/1.61	
3.46/1.61	----------------------------------------
3.46/1.61	
3.46/1.61	(10)
3.46/1.61	BOUNDS(EXP, INF)
3.53/1.64	EOF