3.13/1.54	WORST_CASE(NON_POLY, ?)
3.13/1.55	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.13/1.55	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.13/1.55	
3.13/1.55	
3.13/1.55	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.13/1.55	
3.13/1.55	(0) CpxTRS
3.13/1.55	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.13/1.55	(2) TRS for Loop Detection
3.13/1.55	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.13/1.55	(4) BOUNDS(INF, INF)
3.13/1.55	
3.13/1.55	
3.13/1.55	----------------------------------------
3.13/1.55	
3.13/1.55	(0)
3.13/1.55	Obligation:
3.13/1.55	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.13/1.55	
3.13/1.55	
3.13/1.55	The TRS R consists of the following rules:
3.13/1.55	
3.13/1.55	   g(Cons(x, xs), y) -> Cons(x, xs)
3.13/1.55	   h(Nil, y) -> h(Nil, y)
3.13/1.55	   h(Cons(x, xs), y) -> f(Cons(x, xs), y)
3.13/1.55	   g(Nil, y) -> h(Nil, y)
3.13/1.55	   f(Nil, y) -> g(Nil, y)
3.13/1.55	   f(Cons(x, xs), y) -> h(Cons(x, xs), y)
3.13/1.55	   sp1(x, y) -> f(x, y)
3.13/1.55	   r(x, y) -> x
3.13/1.55	
3.13/1.55	S is empty.
3.13/1.55	Rewrite Strategy: INNERMOST
3.13/1.55	----------------------------------------
3.13/1.55	
3.13/1.55	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.13/1.55	Transformed a relative TRS into a decreasing-loop problem.
3.13/1.55	----------------------------------------
3.13/1.55	
3.13/1.55	(2)
3.13/1.55	Obligation:
3.13/1.55	Analyzing the following TRS for decreasing loops:
3.13/1.55	
3.13/1.55	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.13/1.55	
3.13/1.55	
3.13/1.55	The TRS R consists of the following rules:
3.13/1.55	
3.13/1.55	   g(Cons(x, xs), y) -> Cons(x, xs)
3.13/1.55	   h(Nil, y) -> h(Nil, y)
3.13/1.55	   h(Cons(x, xs), y) -> f(Cons(x, xs), y)
3.13/1.55	   g(Nil, y) -> h(Nil, y)
3.13/1.55	   f(Nil, y) -> g(Nil, y)
3.13/1.55	   f(Cons(x, xs), y) -> h(Cons(x, xs), y)
3.13/1.55	   sp1(x, y) -> f(x, y)
3.13/1.55	   r(x, y) -> x
3.13/1.55	
3.13/1.55	S is empty.
3.13/1.55	Rewrite Strategy: INNERMOST
3.13/1.55	----------------------------------------
3.13/1.55	
3.13/1.55	(3) InfiniteLowerBoundProof (FINISHED)
3.13/1.55	The following loop proves infinite runtime complexity:
3.13/1.55	
3.13/1.55	The rewrite sequence
3.13/1.55	
3.13/1.55	h(Nil, y) ->^+ h(Nil, y)
3.13/1.55	
3.13/1.55	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
3.13/1.55	
3.13/1.55	The pumping substitution is [ ].
3.13/1.55	
3.13/1.55	The result substitution is [ ].
3.13/1.55	
3.13/1.55	
3.13/1.55	
3.13/1.55	
3.13/1.55	----------------------------------------
3.13/1.55	
3.13/1.55	(4)
3.13/1.55	BOUNDS(INF, INF)
3.13/1.60	EOF