3.16/1.53	WORST_CASE(NON_POLY, ?)
3.16/1.54	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.16/1.54	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.16/1.54	
3.16/1.54	
3.16/1.54	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.16/1.54	
3.16/1.54	(0) CpxTRS
3.16/1.54	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.16/1.54	(2) TRS for Loop Detection
3.16/1.54	(3) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.16/1.54	(4) BOUNDS(INF, INF)
3.16/1.54	
3.16/1.54	
3.16/1.54	----------------------------------------
3.16/1.54	
3.16/1.54	(0)
3.16/1.54	Obligation:
3.16/1.54	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.16/1.54	
3.16/1.54	
3.16/1.54	The TRS R consists of the following rules:
3.16/1.54	
3.16/1.54	   __(__(X, Y), Z) -> __(X, __(Y, Z))
3.16/1.54	   __(X, nil) -> X
3.16/1.54	   __(nil, X) -> X
3.16/1.54	   U11(tt) -> tt
3.16/1.54	   U21(tt) -> U22(isList)
3.16/1.54	   U22(tt) -> tt
3.16/1.54	   U31(tt) -> tt
3.16/1.54	   U41(tt) -> U42(isNeList)
3.16/1.54	   U42(tt) -> tt
3.16/1.54	   U51(tt) -> U52(isList)
3.16/1.54	   U52(tt) -> tt
3.16/1.54	   U61(tt) -> tt
3.16/1.54	   U71(tt) -> U72(isPal)
3.16/1.54	   U72(tt) -> tt
3.16/1.54	   U81(tt) -> tt
3.16/1.54	   isList -> U11(isNeList)
3.16/1.54	   isList -> tt
3.16/1.54	   isList -> U21(isList)
3.16/1.54	   isNeList -> U31(isQid)
3.16/1.54	   isNeList -> U41(isList)
3.16/1.54	   isNeList -> U51(isNeList)
3.16/1.54	   isNePal -> U61(isQid)
3.16/1.54	   isNePal -> U71(isQid)
3.16/1.54	   isPal -> U81(isNePal)
3.16/1.54	   isPal -> tt
3.16/1.54	   isQid -> tt
3.16/1.54	
3.16/1.54	S is empty.
3.16/1.54	Rewrite Strategy: FULL
3.16/1.54	----------------------------------------
3.16/1.54	
3.16/1.54	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.16/1.54	Transformed a relative TRS into a decreasing-loop problem.
3.16/1.54	----------------------------------------
3.16/1.54	
3.16/1.54	(2)
3.16/1.54	Obligation:
3.16/1.54	Analyzing the following TRS for decreasing loops:
3.16/1.54	
3.16/1.54	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.16/1.54	
3.16/1.54	
3.16/1.54	The TRS R consists of the following rules:
3.16/1.54	
3.16/1.54	   __(__(X, Y), Z) -> __(X, __(Y, Z))
3.16/1.54	   __(X, nil) -> X
3.16/1.54	   __(nil, X) -> X
3.16/1.54	   U11(tt) -> tt
3.16/1.54	   U21(tt) -> U22(isList)
3.16/1.54	   U22(tt) -> tt
3.16/1.54	   U31(tt) -> tt
3.16/1.54	   U41(tt) -> U42(isNeList)
3.16/1.54	   U42(tt) -> tt
3.16/1.54	   U51(tt) -> U52(isList)
3.16/1.54	   U52(tt) -> tt
3.16/1.54	   U61(tt) -> tt
3.16/1.54	   U71(tt) -> U72(isPal)
3.16/1.54	   U72(tt) -> tt
3.16/1.54	   U81(tt) -> tt
3.16/1.54	   isList -> U11(isNeList)
3.16/1.54	   isList -> tt
3.16/1.54	   isList -> U21(isList)
3.16/1.54	   isNeList -> U31(isQid)
3.16/1.54	   isNeList -> U41(isList)
3.16/1.54	   isNeList -> U51(isNeList)
3.16/1.54	   isNePal -> U61(isQid)
3.16/1.54	   isNePal -> U71(isQid)
3.16/1.54	   isPal -> U81(isNePal)
3.16/1.54	   isPal -> tt
3.16/1.54	   isQid -> tt
3.16/1.54	
3.16/1.54	S is empty.
3.16/1.54	Rewrite Strategy: FULL
3.16/1.54	----------------------------------------
3.16/1.54	
3.16/1.54	(3) InfiniteLowerBoundProof (FINISHED)
3.16/1.54	The following loop proves infinite runtime complexity:
3.16/1.54	
3.16/1.54	The rewrite sequence
3.16/1.54	
3.16/1.54	isList ->^+ U21(isList)
3.16/1.54	
3.16/1.54	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
3.16/1.54	
3.16/1.54	The pumping substitution is [ ].
3.16/1.54	
3.16/1.54	The result substitution is [ ].
3.16/1.54	
3.16/1.54	
3.16/1.54	
3.16/1.54	
3.16/1.54	----------------------------------------
3.16/1.54	
3.16/1.54	(4)
3.16/1.54	BOUNDS(INF, INF)
3.27/1.57	EOF