Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313557

details

property	value
status	complete
benchmark	#4.23.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n030.star.cs.uiowa.edu
space	Strategy_removed_AG01

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.601 seconds
cpu usage	431.055
user time	426.902
system time	4.1531
max virtual memory	1.9144508E7
max residence set size	6239812.0

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

430.90/291.54	WORST_CASE(Omega(n^1), O(n^2))
430.99/291.55	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
430.99/291.55	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
430.99/291.55	
430.99/291.55	
430.99/291.55	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).
430.99/291.55	
430.99/291.55	(0) CpxTRS
430.99/291.55	(1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
430.99/291.55	(2) CpxWeightedTrs
430.99/291.55	    (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
430.99/291.55	    (4) CpxTypedWeightedTrs
430.99/291.55	    (5) CompletionProof [UPPER BOUND(ID), 0 ms]
430.99/291.55	    (6) CpxTypedWeightedCompleteTrs
430.99/291.55	    (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms]
430.99/291.55	    (8) CpxTypedWeightedCompleteTrs
430.99/291.55	    (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
430.99/291.55	    (10) CpxRNTS
430.99/291.55	    (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms]
430.99/291.55	    (12) CpxRNTS
430.99/291.55	    (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 4 ms]
430.99/291.55	    (14) CpxRNTS
430.99/291.55	    (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
430.99/291.55	    (16) CpxRNTS
430.99/291.55	    (17) IntTrsBoundProof [UPPER BOUND(ID), 361 ms]
430.99/291.55	    (18) CpxRNTS
430.99/291.55	    (19) IntTrsBoundProof [UPPER BOUND(ID), 98 ms]
430.99/291.55	    (20) CpxRNTS
430.99/291.55	    (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms]
430.99/291.55	    (22) CpxRNTS
430.99/291.55	    (23) IntTrsBoundProof [UPPER BOUND(ID), 639 ms]
430.99/291.55	    (24) CpxRNTS
430.99/291.55	    (25) IntTrsBoundProof [UPPER BOUND(ID), 348 ms]
430.99/291.55	    (26) CpxRNTS
430.99/291.55	    (27) FinalProof [FINISHED, 0 ms]
430.99/291.55	    (28) BOUNDS(1, n^2)
430.99/291.55	(29) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
430.99/291.55	(30) TRS for Loop Detection
430.99/291.55	    (31) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
430.99/291.55	    (32) BEST
430.99/291.55	        (33) proven lower bound
430.99/291.55	            (34) LowerBoundPropagationProof [FINISHED, 0 ms]
430.99/291.55	            (35) BOUNDS(n^1, INF)
430.99/291.55	        (36) TRS for Loop Detection
430.99/291.55	
430.99/291.55	
430.99/291.55	----------------------------------------
430.99/291.55	
430.99/291.55	(0)
430.99/291.55	Obligation:
430.99/291.55	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).
430.99/291.55	
430.99/291.55	
430.99/291.55	The TRS R consists of the following rules:
430.99/291.55	
430.99/291.55	   quot(0, s(y), s(z)) -> 0
430.99/291.55	   quot(s(x), s(y), z) -> quot(x, y, z)
430.99/291.55	   plus(0, y) -> y
430.99/291.55	   plus(s(x), y) -> s(plus(x, y))
430.99/291.55	   quot(x, 0, s(z)) -> s(quot(x, plus(z, s(0)), s(z)))
430.99/291.55	
430.99/291.55	S is empty.
430.99/291.55	Rewrite Strategy: INNERMOST
430.99/291.55	----------------------------------------
430.99/291.55	
430.99/291.55	(1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
430.99/291.55	Transformed relative TRS to weighted TRS
430.99/291.55	----------------------------------------
430.99/291.55	
430.99/291.55	(2)
430.99/291.55	Obligation:
430.99/291.55	The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2).
430.99/291.55	
430.99/291.55	
430.99/291.55	The TRS R consists of the following rules:
430.99/291.55	
430.99/291.55	   quot(0, s(y), s(z)) -> 0 [1]
430.99/291.55	   quot(s(x), s(y), z) -> quot(x, y, z) [1]
430.99/291.55	   plus(0, y) -> y [1]
430.99/291.55	   plus(s(x), y) -> s(plus(x, y)) [1]
430.99/291.55	   quot(x, 0, s(z)) -> s(quot(x, plus(z, s(0)), s(z))) [1]
430.99/291.55	
430.99/291.55	Rewrite Strategy: INNERMOST
430.99/291.55	----------------------------------------
430.99/291.55	
430.99/291.55	(3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
430.99/291.55	Infered types.
430.99/291.55	----------------------------------------
430.99/291.55	
430.99/291.55	(4)
430.99/291.55	Obligation:
430.99/291.55	Runtime Complexity Weighted TRS with Types.
430.99/291.55	The TRS R consists of the following rules:
430.99/291.55	
430.99/291.55	   quot(0, s(y), s(z)) -> 0 [1]
430.99/291.55	   quot(s(x), s(y), z) -> quot(x, y, z) [1]
430.99/291.55	   plus(0, y) -> y [1]
430.99/291.55	   plus(s(x), y) -> s(plus(x, y)) [1]
430.99/291.55	   quot(x, 0, s(z)) -> s(quot(x, plus(z, s(0)), s(z))) [1]
430.99/291.55

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40