Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308176

details

property	value
status	complete
benchmark	Ex1_2_AEL03_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n127.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	12.4243 seconds
cpu usage	42.0248
user time	39.6998
system time	2.32493
max virtual memory	1.94117E7
max residence set size	4238588.0

stage attributes

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

output

41.72/12.35	WORST_CASE(Omega(n^1), O(n^1))
41.72/12.37	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
41.72/12.37	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
41.72/12.37	
41.72/12.37	
41.72/12.37	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
41.72/12.37	
41.72/12.37	(0) CpxTRS
41.72/12.37	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
41.72/12.37	(2) CpxTRS
41.72/12.37	    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
41.72/12.37	    (4) CpxTRS
41.72/12.37	    (5) CpxTrsMatchBoundsTAProof [FINISHED, 268 ms]
41.72/12.37	    (6) BOUNDS(1, n^1)
41.72/12.37	(7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
41.72/12.37	(8) TRS for Loop Detection
41.72/12.37	    (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms]
41.72/12.37	    (10) BEST
41.72/12.37	        (11) proven lower bound
41.72/12.37	            (12) LowerBoundPropagationProof [FINISHED, 0 ms]
41.72/12.37	            (13) BOUNDS(n^1, INF)
41.72/12.37	        (14) TRS for Loop Detection
41.72/12.37	
41.72/12.37	
41.72/12.37	----------------------------------------
41.72/12.37	
41.72/12.37	(0)
41.72/12.37	Obligation:
41.72/12.37	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
41.72/12.37	
41.72/12.37	
41.72/12.37	The TRS R consists of the following rules:
41.72/12.37	
41.72/12.37	   active(from(X)) -> mark(cons(X, from(s(X))))
41.72/12.37	   active(2ndspos(0, Z)) -> mark(rnil)
41.72/12.37	   active(2ndspos(s(N), cons(X, cons(Y, Z)))) -> mark(rcons(posrecip(Y), 2ndsneg(N, Z)))
41.72/12.37	   active(2ndsneg(0, Z)) -> mark(rnil)
41.72/12.37	   active(2ndsneg(s(N), cons(X, cons(Y, Z)))) -> mark(rcons(negrecip(Y), 2ndspos(N, Z)))
41.72/12.37	   active(pi(X)) -> mark(2ndspos(X, from(0)))
41.72/12.37	   active(plus(0, Y)) -> mark(Y)
41.72/12.37	   active(plus(s(X), Y)) -> mark(s(plus(X, Y)))
41.72/12.37	   active(times(0, Y)) -> mark(0)
41.72/12.37	   active(times(s(X), Y)) -> mark(plus(Y, times(X, Y)))
41.72/12.37	   active(square(X)) -> mark(times(X, X))
41.72/12.37	   active(s(X)) -> s(active(X))
41.72/12.37	   active(posrecip(X)) -> posrecip(active(X))
41.72/12.37	   active(negrecip(X)) -> negrecip(active(X))
41.72/12.37	   active(cons(X1, X2)) -> cons(active(X1), X2)
41.72/12.37	   active(rcons(X1, X2)) -> rcons(active(X1), X2)
41.72/12.37	   active(rcons(X1, X2)) -> rcons(X1, active(X2))
41.72/12.37	   active(from(X)) -> from(active(X))
41.72/12.37	   active(2ndspos(X1, X2)) -> 2ndspos(active(X1), X2)
41.72/12.37	   active(2ndspos(X1, X2)) -> 2ndspos(X1, active(X2))
41.72/12.37	   active(2ndsneg(X1, X2)) -> 2ndsneg(active(X1), X2)
41.72/12.37	   active(2ndsneg(X1, X2)) -> 2ndsneg(X1, active(X2))
41.72/12.37	   active(pi(X)) -> pi(active(X))
41.72/12.37	   active(plus(X1, X2)) -> plus(active(X1), X2)
41.72/12.37	   active(plus(X1, X2)) -> plus(X1, active(X2))
41.72/12.37	   active(times(X1, X2)) -> times(active(X1), X2)
41.72/12.37	   active(times(X1, X2)) -> times(X1, active(X2))
41.72/12.37	   active(square(X)) -> square(active(X))
41.72/12.37	   s(mark(X)) -> mark(s(X))
41.72/12.37	   posrecip(mark(X)) -> mark(posrecip(X))
41.72/12.37	   negrecip(mark(X)) -> mark(negrecip(X))
41.72/12.37	   cons(mark(X1), X2) -> mark(cons(X1, X2))
41.72/12.37	   rcons(mark(X1), X2) -> mark(rcons(X1, X2))
41.72/12.37	   rcons(X1, mark(X2)) -> mark(rcons(X1, X2))
41.72/12.37	   from(mark(X)) -> mark(from(X))
41.72/12.37	   2ndspos(mark(X1), X2) -> mark(2ndspos(X1, X2))
41.72/12.37	   2ndspos(X1, mark(X2)) -> mark(2ndspos(X1, X2))
41.72/12.37	   2ndsneg(mark(X1), X2) -> mark(2ndsneg(X1, X2))
41.72/12.37	   2ndsneg(X1, mark(X2)) -> mark(2ndsneg(X1, X2))
41.72/12.37	   pi(mark(X)) -> mark(pi(X))
41.72/12.37	   plus(mark(X1), X2) -> mark(plus(X1, X2))
41.72/12.37	   plus(X1, mark(X2)) -> mark(plus(X1, X2))
41.72/12.37	   times(mark(X1), X2) -> mark(times(X1, X2))
41.72/12.37	   times(X1, mark(X2)) -> mark(times(X1, X2))
41.72/12.37	   square(mark(X)) -> mark(square(X))
41.72/12.37	   proper(0) -> ok(0)
41.72/12.37	   proper(s(X)) -> s(proper(X))
41.72/12.37	   proper(posrecip(X)) -> posrecip(proper(X))
41.72/12.37	   proper(negrecip(X)) -> negrecip(proper(X))
41.72/12.37	   proper(nil) -> ok(nil)
41.72/12.37	   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
41.72/12.37	   proper(rnil) -> ok(rnil)
41.72/12.37	   proper(rcons(X1, X2)) -> rcons(proper(X1), proper(X2))
41.72/12.37	   proper(from(X)) -> from(proper(X))
41.72/12.37	   proper(2ndspos(X1, X2)) -> 2ndspos(proper(X1), proper(X2))
41.72/12.37	   proper(2ndsneg(X1, X2)) -> 2ndsneg(proper(X1), proper(X2))
41.72/12.37	   proper(pi(X)) -> pi(proper(X))
41.72/12.37	   proper(plus(X1, X2)) -> plus(proper(X1), proper(X2))
41.72/12.37	   proper(times(X1, X2)) -> times(proper(X1), proper(X2))
41.72/12.37	   proper(square(X)) -> square(proper(X))
41.72/12.37	   s(ok(X)) -> ok(s(X))
41.72/12.37	   posrecip(ok(X)) -> ok(posrecip(X))
41.72/12.37	   negrecip(ok(X)) -> ok(negrecip(X))
41.72/12.37	   cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
41.72/12.37	   rcons(ok(X1), ok(X2)) -> ok(rcons(X1, X2))
41.72/12.37	   from(ok(X)) -> ok(from(X))
41.72/12.37	   2ndspos(ok(X1), ok(X2)) -> ok(2ndspos(X1, X2))

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actions all output return to Runtime_Complexity_Full_Rewriting 2019-04-01 06.11