3.14/1.70	WORST_CASE(NON_POLY, ?)
3.41/1.71	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.41/1.71	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.41/1.71	
3.41/1.71	
3.41/1.71	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.41/1.71	
3.41/1.71	(0) CpxTRS
3.41/1.71	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.41/1.71	(2) TRS for Loop Detection
3.41/1.71	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
3.41/1.71	(4) BEST
3.41/1.71	    (5) proven lower bound
3.41/1.71	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
3.41/1.71	        (7) BOUNDS(n^1, INF)
3.41/1.71	    (8) TRS for Loop Detection
3.41/1.71	        (9) DecreasingLoopProof [FINISHED, 0 ms]
3.41/1.71	        (10) BOUNDS(EXP, INF)
3.41/1.71	
3.41/1.71	
3.41/1.71	----------------------------------------
3.41/1.71	
3.41/1.71	(0)
3.41/1.71	Obligation:
3.41/1.71	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.41/1.71	
3.41/1.71	
3.41/1.71	The TRS R consists of the following rules:
3.41/1.71	
3.41/1.71	   f(g(X), Y) -> f(X, n__f(n__g(X), activate(Y)))
3.41/1.71	   f(X1, X2) -> n__f(X1, X2)
3.41/1.71	   g(X) -> n__g(X)
3.41/1.71	   activate(n__f(X1, X2)) -> f(activate(X1), X2)
3.41/1.71	   activate(n__g(X)) -> g(activate(X))
3.41/1.71	   activate(X) -> X
3.41/1.71	
3.41/1.71	S is empty.
3.41/1.71	Rewrite Strategy: FULL
3.41/1.71	----------------------------------------
3.41/1.71	
3.41/1.71	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.41/1.71	Transformed a relative TRS into a decreasing-loop problem.
3.41/1.71	----------------------------------------
3.41/1.71	
3.41/1.71	(2)
3.41/1.71	Obligation:
3.41/1.71	Analyzing the following TRS for decreasing loops:
3.41/1.71	
3.41/1.71	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.41/1.71	
3.41/1.71	
3.41/1.71	The TRS R consists of the following rules:
3.41/1.71	
3.41/1.71	   f(g(X), Y) -> f(X, n__f(n__g(X), activate(Y)))
3.41/1.71	   f(X1, X2) -> n__f(X1, X2)
3.41/1.71	   g(X) -> n__g(X)
3.41/1.71	   activate(n__f(X1, X2)) -> f(activate(X1), X2)
3.41/1.71	   activate(n__g(X)) -> g(activate(X))
3.41/1.71	   activate(X) -> X
3.41/1.71	
3.41/1.71	S is empty.
3.41/1.71	Rewrite Strategy: FULL
3.41/1.71	----------------------------------------
3.41/1.71	
3.41/1.71	(3) DecreasingLoopProof (LOWER BOUND(ID))
3.41/1.71	The following loop(s) give(s) rise to the lower bound Omega(n^1):
3.41/1.71	
3.41/1.71	The rewrite sequence
3.41/1.71	
3.41/1.71	activate(n__f(X1, X2)) ->^+ f(activate(X1), X2)
3.41/1.71	
3.41/1.71	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
3.41/1.71	
3.41/1.71	The pumping substitution is [X1 / n__f(X1, X2)].
3.41/1.71	
3.41/1.71	The result substitution is [ ].
3.41/1.71	
3.41/1.71	
3.41/1.71	
3.41/1.71	
3.41/1.71	----------------------------------------
3.41/1.71	
3.41/1.71	(4)
3.41/1.71	Complex Obligation (BEST)
3.41/1.71	
3.41/1.71	----------------------------------------
3.41/1.71	
3.41/1.71	(5)
3.41/1.71	Obligation:
3.41/1.71	Proved the lower bound n^1 for the following obligation:
3.41/1.71	
3.41/1.71	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.41/1.71	
3.41/1.71	
3.41/1.71	The TRS R consists of the following rules:
3.41/1.71	
3.41/1.71	   f(g(X), Y) -> f(X, n__f(n__g(X), activate(Y)))
3.41/1.71	   f(X1, X2) -> n__f(X1, X2)
3.41/1.71	   g(X) -> n__g(X)
3.41/1.71	   activate(n__f(X1, X2)) -> f(activate(X1), X2)
3.41/1.71	   activate(n__g(X)) -> g(activate(X))
3.41/1.71	   activate(X) -> X
3.41/1.71	
3.41/1.71	S is empty.
3.41/1.71	Rewrite Strategy: FULL
3.41/1.71	----------------------------------------
3.41/1.71	
3.41/1.71	(6) LowerBoundPropagationProof (FINISHED)
3.41/1.71	Propagated lower bound.
3.41/1.71	----------------------------------------
3.41/1.71	
3.41/1.71	(7)
3.41/1.71	BOUNDS(n^1, INF)
3.41/1.71	
3.41/1.71	----------------------------------------
3.41/1.71	
3.41/1.71	(8)
3.41/1.71	Obligation:
3.41/1.71	Analyzing the following TRS for decreasing loops:
3.41/1.71	
3.41/1.71	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.41/1.71	
3.41/1.71	
3.41/1.71	The TRS R consists of the following rules:
3.41/1.71	
3.41/1.71	   f(g(X), Y) -> f(X, n__f(n__g(X), activate(Y)))
3.41/1.71	   f(X1, X2) -> n__f(X1, X2)
3.41/1.71	   g(X) -> n__g(X)
3.41/1.71	   activate(n__f(X1, X2)) -> f(activate(X1), X2)
3.41/1.71	   activate(n__g(X)) -> g(activate(X))
3.41/1.71	   activate(X) -> X
3.41/1.71	
3.41/1.71	S is empty.
3.41/1.71	Rewrite Strategy: FULL
3.41/1.71	----------------------------------------
3.41/1.71	
3.41/1.71	(9) DecreasingLoopProof (FINISHED)
3.41/1.71	The following loop(s) give(s) rise to the lower bound EXP:
3.41/1.71	
3.41/1.71	The rewrite sequence
3.41/1.71	
3.41/1.71	activate(n__f(n__g(X1_0), X2)) ->^+ f(activate(X1_0), n__f(n__g(activate(X1_0)), activate(X2)))
3.41/1.71	
3.41/1.71	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
3.41/1.71	
3.41/1.71	The pumping substitution is [X1_0 / n__f(n__g(X1_0), X2)].
3.41/1.71	
3.41/1.71	The result substitution is [ ].
3.41/1.71	
3.41/1.71	
3.41/1.71	
3.41/1.71	The rewrite sequence
3.41/1.71	
3.41/1.71	activate(n__f(n__g(X1_0), X2)) ->^+ f(activate(X1_0), n__f(n__g(activate(X1_0)), activate(X2)))
3.41/1.71	
3.41/1.71	gives rise to a decreasing loop by considering the right hand sides subterm at position [1,0,0].
3.41/1.71	
3.41/1.71	The pumping substitution is [X1_0 / n__f(n__g(X1_0), X2)].
3.41/1.71	
3.41/1.71	The result substitution is [ ].
3.41/1.71	
3.41/1.71	
3.41/1.71	
3.41/1.71	
3.41/1.71	----------------------------------------
3.41/1.71	
3.41/1.71	(10)
3.41/1.71	BOUNDS(EXP, INF)
3.41/1.73	EOF