3.48/1.58	WORST_CASE(NON_POLY, ?)
3.48/1.59	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.48/1.59	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.48/1.59	
3.48/1.59	
3.48/1.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.48/1.59	
3.48/1.59	(0) CpxTRS
3.48/1.59	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.48/1.59	(2) TRS for Loop Detection
3.48/1.59	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
3.48/1.59	(4) BEST
3.48/1.59	    (5) proven lower bound
3.48/1.59	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
3.48/1.59	        (7) BOUNDS(n^1, INF)
3.48/1.59	    (8) TRS for Loop Detection
3.48/1.59	        (9) DecreasingLoopProof [FINISHED, 0 ms]
3.48/1.59	        (10) BOUNDS(EXP, INF)
3.48/1.59	
3.48/1.59	
3.48/1.59	----------------------------------------
3.48/1.59	
3.48/1.59	(0)
3.48/1.59	Obligation:
3.48/1.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.48/1.59	
3.48/1.59	
3.48/1.59	The TRS R consists of the following rules:
3.48/1.59	
3.48/1.59	   2nd(cons1(X, cons(Y, Z))) -> Y
3.48/1.59	   2nd(cons(X, X1)) -> 2nd(cons1(X, activate(X1)))
3.48/1.59	   from(X) -> cons(X, n__from(n__s(X)))
3.48/1.59	   from(X) -> n__from(X)
3.48/1.59	   s(X) -> n__s(X)
3.48/1.59	   activate(n__from(X)) -> from(activate(X))
3.48/1.59	   activate(n__s(X)) -> s(activate(X))
3.48/1.59	   activate(X) -> X
3.48/1.59	
3.48/1.59	S is empty.
3.48/1.59	Rewrite Strategy: FULL
3.48/1.59	----------------------------------------
3.48/1.59	
3.48/1.59	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.48/1.59	Transformed a relative TRS into a decreasing-loop problem.
3.48/1.59	----------------------------------------
3.48/1.59	
3.48/1.59	(2)
3.48/1.59	Obligation:
3.48/1.59	Analyzing the following TRS for decreasing loops:
3.48/1.59	
3.48/1.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.48/1.59	
3.48/1.59	
3.48/1.59	The TRS R consists of the following rules:
3.48/1.59	
3.48/1.59	   2nd(cons1(X, cons(Y, Z))) -> Y
3.48/1.59	   2nd(cons(X, X1)) -> 2nd(cons1(X, activate(X1)))
3.48/1.59	   from(X) -> cons(X, n__from(n__s(X)))
3.48/1.59	   from(X) -> n__from(X)
3.48/1.59	   s(X) -> n__s(X)
3.48/1.59	   activate(n__from(X)) -> from(activate(X))
3.48/1.59	   activate(n__s(X)) -> s(activate(X))
3.48/1.59	   activate(X) -> X
3.48/1.59	
3.48/1.59	S is empty.
3.48/1.59	Rewrite Strategy: FULL
3.48/1.59	----------------------------------------
3.48/1.59	
3.48/1.59	(3) DecreasingLoopProof (LOWER BOUND(ID))
3.48/1.59	The following loop(s) give(s) rise to the lower bound Omega(n^1):
3.48/1.59	
3.48/1.59	The rewrite sequence
3.48/1.59	
3.48/1.59	activate(n__s(X)) ->^+ s(activate(X))
3.48/1.59	
3.48/1.59	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
3.48/1.59	
3.48/1.59	The pumping substitution is [X / n__s(X)].
3.48/1.59	
3.48/1.59	The result substitution is [ ].
3.48/1.59	
3.48/1.59	
3.48/1.59	
3.48/1.59	
3.48/1.59	----------------------------------------
3.48/1.59	
3.48/1.59	(4)
3.48/1.59	Complex Obligation (BEST)
3.48/1.59	
3.48/1.59	----------------------------------------
3.48/1.59	
3.48/1.59	(5)
3.48/1.59	Obligation:
3.48/1.59	Proved the lower bound n^1 for the following obligation:
3.48/1.59	
3.48/1.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.48/1.59	
3.48/1.59	
3.48/1.59	The TRS R consists of the following rules:
3.48/1.59	
3.48/1.59	   2nd(cons1(X, cons(Y, Z))) -> Y
3.48/1.59	   2nd(cons(X, X1)) -> 2nd(cons1(X, activate(X1)))
3.48/1.59	   from(X) -> cons(X, n__from(n__s(X)))
3.48/1.59	   from(X) -> n__from(X)
3.48/1.59	   s(X) -> n__s(X)
3.48/1.59	   activate(n__from(X)) -> from(activate(X))
3.48/1.59	   activate(n__s(X)) -> s(activate(X))
3.48/1.59	   activate(X) -> X
3.48/1.59	
3.48/1.59	S is empty.
3.48/1.59	Rewrite Strategy: FULL
3.48/1.59	----------------------------------------
3.48/1.59	
3.48/1.59	(6) LowerBoundPropagationProof (FINISHED)
3.48/1.59	Propagated lower bound.
3.48/1.59	----------------------------------------
3.48/1.59	
3.48/1.59	(7)
3.48/1.59	BOUNDS(n^1, INF)
3.48/1.59	
3.48/1.59	----------------------------------------
3.48/1.59	
3.48/1.59	(8)
3.48/1.59	Obligation:
3.48/1.59	Analyzing the following TRS for decreasing loops:
3.48/1.59	
3.48/1.59	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
3.48/1.59	
3.48/1.59	
3.48/1.59	The TRS R consists of the following rules:
3.48/1.59	
3.48/1.59	   2nd(cons1(X, cons(Y, Z))) -> Y
3.48/1.59	   2nd(cons(X, X1)) -> 2nd(cons1(X, activate(X1)))
3.48/1.59	   from(X) -> cons(X, n__from(n__s(X)))
3.48/1.59	   from(X) -> n__from(X)
3.48/1.59	   s(X) -> n__s(X)
3.48/1.59	   activate(n__from(X)) -> from(activate(X))
3.48/1.59	   activate(n__s(X)) -> s(activate(X))
3.48/1.59	   activate(X) -> X
3.48/1.59	
3.48/1.59	S is empty.
3.48/1.59	Rewrite Strategy: FULL
3.48/1.59	----------------------------------------
3.48/1.59	
3.48/1.59	(9) DecreasingLoopProof (FINISHED)
3.48/1.59	The following loop(s) give(s) rise to the lower bound EXP:
3.48/1.59	
3.48/1.59	The rewrite sequence
3.48/1.59	
3.48/1.59	activate(n__from(X)) ->^+ cons(activate(X), n__from(n__s(activate(X))))
3.48/1.59	
3.48/1.59	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
3.48/1.59	
3.48/1.59	The pumping substitution is [X / n__from(X)].
3.48/1.59	
3.48/1.59	The result substitution is [ ].
3.48/1.59	
3.48/1.59	
3.48/1.59	
3.48/1.59	The rewrite sequence
3.48/1.59	
3.48/1.59	activate(n__from(X)) ->^+ cons(activate(X), n__from(n__s(activate(X))))
3.48/1.59	
3.48/1.59	gives rise to a decreasing loop by considering the right hand sides subterm at position [1,0,0].
3.48/1.59	
3.48/1.59	The pumping substitution is [X / n__from(X)].
3.48/1.59	
3.48/1.59	The result substitution is [ ].
3.48/1.59	
3.48/1.59	
3.48/1.59	
3.48/1.59	
3.48/1.59	----------------------------------------
3.48/1.59	
3.48/1.59	(10)
3.48/1.59	BOUNDS(EXP, INF)
3.48/1.61	EOF