2.90/1.53	WORST_CASE(NON_POLY, ?)
2.90/1.54	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
2.90/1.54	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.90/1.54	
2.90/1.54	
2.90/1.54	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.90/1.54	
2.90/1.54	(0) CpxTRS
2.90/1.54	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
2.90/1.54	(2) TRS for Loop Detection
2.90/1.54	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
2.90/1.54	(4) BOUNDS(INF, INF)
2.90/1.54	
2.90/1.54	
2.90/1.54	----------------------------------------
2.90/1.54	
2.90/1.54	(0)
2.90/1.54	Obligation:
2.90/1.54	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.90/1.54	
2.90/1.54	
2.90/1.54	The TRS R consists of the following rules:
2.90/1.54	
2.90/1.54	   fst(0, Z) -> nil
2.90/1.54	   fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z))
2.90/1.54	   from(X) -> cons(X, from(s(X)))
2.90/1.54	   add(0, X) -> X
2.90/1.54	   add(s(X), Y) -> s(add(X, Y))
2.90/1.54	   len(nil) -> 0
2.90/1.54	   len(cons(X, Z)) -> s(len(Z))
2.90/1.54	
2.90/1.54	S is empty.
2.90/1.54	Rewrite Strategy: FULL
2.90/1.54	----------------------------------------
2.90/1.54	
2.90/1.54	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
2.90/1.54	Transformed a relative TRS into a decreasing-loop problem.
2.90/1.54	----------------------------------------
2.90/1.54	
2.90/1.54	(2)
2.90/1.54	Obligation:
2.90/1.54	Analyzing the following TRS for decreasing loops:
2.90/1.54	
2.90/1.54	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
2.90/1.54	
2.90/1.54	
2.90/1.54	The TRS R consists of the following rules:
2.90/1.54	
2.90/1.54	   fst(0, Z) -> nil
2.90/1.54	   fst(s(X), cons(Y, Z)) -> cons(Y, fst(X, Z))
2.90/1.54	   from(X) -> cons(X, from(s(X)))
2.90/1.54	   add(0, X) -> X
2.90/1.54	   add(s(X), Y) -> s(add(X, Y))
2.90/1.54	   len(nil) -> 0
2.90/1.54	   len(cons(X, Z)) -> s(len(Z))
2.90/1.54	
2.90/1.54	S is empty.
2.90/1.54	Rewrite Strategy: FULL
2.90/1.54	----------------------------------------
2.90/1.54	
2.90/1.54	(3) InfiniteLowerBoundProof (FINISHED)
2.90/1.54	The following loop proves infinite runtime complexity:
2.90/1.54	
2.90/1.54	The rewrite sequence
2.90/1.54	
2.90/1.54	from(X) ->^+ cons(X, from(s(X)))
2.90/1.54	
2.90/1.54	gives rise to a decreasing loop by considering the right hand sides subterm at position [1].
2.90/1.54	
2.90/1.54	The pumping substitution is [ ].
2.90/1.54	
2.90/1.54	The result substitution is [X / s(X)].
2.90/1.54	
2.90/1.54	
2.90/1.54	
2.90/1.54	
2.90/1.54	----------------------------------------
2.90/1.54	
2.90/1.54	(4)
2.90/1.54	BOUNDS(INF, INF)
3.09/1.57	EOF