2.95/1.66	WORST_CASE(NON_POLY, ?)
2.95/1.67	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
2.95/1.67	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
2.95/1.67	
2.95/1.67	
2.95/1.67	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
2.95/1.67	
2.95/1.67	(0) CpxTRS
2.95/1.67	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
2.95/1.67	(2) TRS for Loop Detection
2.95/1.67	(3) DecreasingLoopProof [FINISHED, 0 ms]
2.95/1.67	(4) BOUNDS(EXP, INF)
2.95/1.67	
2.95/1.67	
2.95/1.67	----------------------------------------
2.95/1.67	
2.95/1.67	(0)
2.95/1.67	Obligation:
2.95/1.67	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
2.95/1.67	
2.95/1.67	
2.95/1.67	The TRS R consists of the following rules:
2.95/1.67	
2.95/1.67	   merge(nil, y) -> y
2.95/1.67	   merge(x, nil) -> x
2.95/1.67	   merge(.(x, y), .(u, v)) -> if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
2.95/1.67	   ++(nil, y) -> y
2.95/1.67	   ++(.(x, y), z) -> .(x, ++(y, z))
2.95/1.67	   if(true, x, y) -> x
2.95/1.67	   if(false, x, y) -> x
2.95/1.67	
2.95/1.67	S is empty.
2.95/1.67	Rewrite Strategy: FULL
2.95/1.67	----------------------------------------
2.95/1.67	
2.95/1.67	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
2.95/1.67	Transformed a relative TRS into a decreasing-loop problem.
2.95/1.67	----------------------------------------
2.95/1.67	
2.95/1.67	(2)
2.95/1.67	Obligation:
2.95/1.67	Analyzing the following TRS for decreasing loops:
2.95/1.67	
2.95/1.67	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF).
2.95/1.67	
2.95/1.67	
2.95/1.67	The TRS R consists of the following rules:
2.95/1.67	
2.95/1.67	   merge(nil, y) -> y
2.95/1.67	   merge(x, nil) -> x
2.95/1.67	   merge(.(x, y), .(u, v)) -> if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
2.95/1.67	   ++(nil, y) -> y
2.95/1.67	   ++(.(x, y), z) -> .(x, ++(y, z))
2.95/1.67	   if(true, x, y) -> x
2.95/1.67	   if(false, x, y) -> x
2.95/1.67	
2.95/1.67	S is empty.
2.95/1.67	Rewrite Strategy: FULL
2.95/1.67	----------------------------------------
2.95/1.67	
2.95/1.67	(3) DecreasingLoopProof (FINISHED)
2.95/1.67	The following loop(s) give(s) rise to the lower bound EXP:
2.95/1.67	
2.95/1.67	The rewrite sequence
2.95/1.67	
2.95/1.67	merge(.(x, y), .(u, v)) ->^+ if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
2.95/1.67	
2.95/1.67	gives rise to a decreasing loop by considering the right hand sides subterm at position [1,1].
2.95/1.67	
2.95/1.67	The pumping substitution is [y / .(x, y)].
2.95/1.67	
2.95/1.67	The result substitution is [ ].
2.95/1.67	
2.95/1.67	
2.95/1.67	
2.95/1.67	The rewrite sequence
2.95/1.67	
2.95/1.67	merge(.(x, y), .(u, v)) ->^+ if(<(x, u), .(x, merge(y, .(u, v))), .(u, merge(.(x, y), v)))
2.95/1.67	
2.95/1.67	gives rise to a decreasing loop by considering the right hand sides subterm at position [2,1].
2.95/1.67	
2.95/1.67	The pumping substitution is [v / .(u, v)].
2.95/1.67	
2.95/1.67	The result substitution is [ ].
2.95/1.67	
2.95/1.67	
2.95/1.67	
2.95/1.67	
2.95/1.67	----------------------------------------
2.95/1.67	
2.95/1.67	(4)
2.95/1.67	BOUNDS(EXP, INF)
3.19/1.71	EOF