1.47/1.69	WORST_CASE(NON_POLY, ?)
3.16/1.70	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
3.16/1.70	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.16/1.70	
3.16/1.70	
3.16/1.70	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.16/1.70	
3.16/1.70	(0) CpxTRS
3.16/1.70	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.16/1.70	(2) TRS for Loop Detection
3.16/1.70	(3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
3.16/1.70	(4) BEST
3.16/1.70	    (5) proven lower bound
3.16/1.70	        (6) LowerBoundPropagationProof [FINISHED, 0 ms]
3.16/1.70	        (7) BOUNDS(n^1, INF)
3.16/1.70	    (8) TRS for Loop Detection
3.16/1.70	        (9) InfiniteLowerBoundProof [FINISHED, 0 ms]
3.16/1.70	        (10) BOUNDS(INF, INF)
3.16/1.70	
3.16/1.70	
3.16/1.70	----------------------------------------
3.16/1.70	
3.16/1.70	(0)
3.16/1.70	Obligation:
3.16/1.70	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.16/1.70	
3.16/1.70	
3.16/1.70	The TRS R consists of the following rules:
3.16/1.70	
3.16/1.70	   *(*(x, y), z) -> *(x, *(y, z))
3.16/1.70	   *(+(x, y), z) -> +(*(x, z), *(y, z))
3.16/1.70	   *(x, +(y, f(z))) -> *(g(x, z), +(y, y))
3.16/1.70	
3.16/1.70	S is empty.
3.16/1.70	Rewrite Strategy: FULL
3.16/1.70	----------------------------------------
3.16/1.70	
3.16/1.70	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.16/1.70	Transformed a relative TRS into a decreasing-loop problem.
3.16/1.70	----------------------------------------
3.16/1.70	
3.16/1.70	(2)
3.16/1.70	Obligation:
3.16/1.70	Analyzing the following TRS for decreasing loops:
3.16/1.70	
3.16/1.70	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.16/1.70	
3.16/1.70	
3.16/1.70	The TRS R consists of the following rules:
3.16/1.70	
3.16/1.70	   *(*(x, y), z) -> *(x, *(y, z))
3.16/1.70	   *(+(x, y), z) -> +(*(x, z), *(y, z))
3.16/1.70	   *(x, +(y, f(z))) -> *(g(x, z), +(y, y))
3.16/1.70	
3.16/1.70	S is empty.
3.16/1.70	Rewrite Strategy: FULL
3.16/1.70	----------------------------------------
3.16/1.70	
3.16/1.70	(3) DecreasingLoopProof (LOWER BOUND(ID))
3.16/1.70	The following loop(s) give(s) rise to the lower bound Omega(n^1):
3.16/1.70	
3.16/1.70	The rewrite sequence
3.16/1.70	
3.16/1.70	*(+(x, y), z) ->^+ +(*(x, z), *(y, z))
3.16/1.70	
3.16/1.70	gives rise to a decreasing loop by considering the right hand sides subterm at position [0].
3.16/1.70	
3.16/1.70	The pumping substitution is [x / +(x, y)].
3.16/1.70	
3.16/1.70	The result substitution is [ ].
3.16/1.70	
3.16/1.70	
3.16/1.70	
3.16/1.70	
3.16/1.70	----------------------------------------
3.16/1.70	
3.16/1.70	(4)
3.16/1.70	Complex Obligation (BEST)
3.16/1.70	
3.16/1.70	----------------------------------------
3.16/1.70	
3.16/1.70	(5)
3.16/1.70	Obligation:
3.16/1.70	Proved the lower bound n^1 for the following obligation:
3.16/1.70	
3.16/1.70	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.16/1.70	
3.16/1.70	
3.16/1.70	The TRS R consists of the following rules:
3.16/1.70	
3.16/1.70	   *(*(x, y), z) -> *(x, *(y, z))
3.16/1.70	   *(+(x, y), z) -> +(*(x, z), *(y, z))
3.16/1.70	   *(x, +(y, f(z))) -> *(g(x, z), +(y, y))
3.16/1.70	
3.16/1.70	S is empty.
3.16/1.70	Rewrite Strategy: FULL
3.16/1.70	----------------------------------------
3.16/1.70	
3.16/1.70	(6) LowerBoundPropagationProof (FINISHED)
3.16/1.70	Propagated lower bound.
3.16/1.70	----------------------------------------
3.16/1.70	
3.16/1.70	(7)
3.16/1.70	BOUNDS(n^1, INF)
3.16/1.70	
3.16/1.70	----------------------------------------
3.16/1.70	
3.16/1.70	(8)
3.16/1.70	Obligation:
3.16/1.70	Analyzing the following TRS for decreasing loops:
3.16/1.70	
3.16/1.70	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.16/1.70	
3.16/1.70	
3.16/1.70	The TRS R consists of the following rules:
3.16/1.70	
3.16/1.70	   *(*(x, y), z) -> *(x, *(y, z))
3.16/1.70	   *(+(x, y), z) -> +(*(x, z), *(y, z))
3.16/1.70	   *(x, +(y, f(z))) -> *(g(x, z), +(y, y))
3.16/1.70	
3.16/1.70	S is empty.
3.16/1.70	Rewrite Strategy: FULL
3.16/1.70	----------------------------------------
3.16/1.70	
3.16/1.70	(9) InfiniteLowerBoundProof (FINISHED)
3.16/1.70	The following loop proves infinite runtime complexity:
3.16/1.70	
3.16/1.70	The rewrite sequence
3.16/1.70	
3.16/1.70	*(x, +(f(z3_0), f(z))) ->^+ *(g(g(x, z), z3_0), +(f(z3_0), f(z3_0)))
3.16/1.70	
3.16/1.70	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
3.16/1.70	
3.16/1.70	The pumping substitution is [ ].
3.16/1.70	
3.16/1.70	The result substitution is [x / g(g(x, z), z3_0), z / z3_0].
3.16/1.70	
3.16/1.70	
3.16/1.70	
3.16/1.70	
3.16/1.70	----------------------------------------
3.16/1.70	
3.16/1.70	(10)
3.16/1.70	BOUNDS(INF, INF)
3.16/1.71	EOF