Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308103

details

property	value
status	complete
benchmark	Ex2_Luc02a_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n050.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.91374 seconds
cpu usage	26.0195
user time	24.2707
system time	1.74885
max virtual memory	5.6998888E7
max residence set size	4179972.0

stage attributes

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

output

25.68/7.83	WORST_CASE(Omega(n^1), O(n^1))
25.68/7.85	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
25.68/7.85	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
25.68/7.85	
25.68/7.85	
25.68/7.85	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
25.68/7.85	
25.68/7.85	(0) CpxTRS
25.68/7.85	(1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms]
25.68/7.85	(2) CpxTRS
25.68/7.85	    (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms]
25.68/7.85	    (4) CpxTRS
25.68/7.85	    (5) CpxTrsMatchBoundsTAProof [FINISHED, 75 ms]
25.68/7.85	    (6) BOUNDS(1, n^1)
25.68/7.85	(7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms]
25.68/7.85	(8) CpxTRS
25.68/7.85	    (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
25.68/7.85	    (10) typed CpxTrs
25.68/7.85	    (11) OrderProof [LOWER BOUND(ID), 0 ms]
25.68/7.85	    (12) typed CpxTrs
25.68/7.85	    (13) RewriteLemmaProof [LOWER BOUND(ID), 467 ms]
25.68/7.85	    (14) BEST
25.68/7.85	        (15) proven lower bound
25.68/7.85	            (16) LowerBoundPropagationProof [FINISHED, 0 ms]
25.68/7.85	            (17) BOUNDS(n^1, INF)
25.68/7.85	        (18) typed CpxTrs
25.68/7.85	            (19) RewriteLemmaProof [LOWER BOUND(ID), 125 ms]
25.68/7.85	            (20) typed CpxTrs
25.68/7.85	            (21) RewriteLemmaProof [LOWER BOUND(ID), 126 ms]
25.68/7.85	            (22) typed CpxTrs
25.68/7.85	            (23) RewriteLemmaProof [LOWER BOUND(ID), 135 ms]
25.68/7.85	            (24) typed CpxTrs
25.68/7.85	            (25) RewriteLemmaProof [LOWER BOUND(ID), 54 ms]
25.68/7.85	            (26) typed CpxTrs
25.68/7.85	            (27) RewriteLemmaProof [LOWER BOUND(ID), 125 ms]
25.68/7.85	            (28) typed CpxTrs
25.68/7.85	            (29) RewriteLemmaProof [LOWER BOUND(ID), 63 ms]
25.68/7.85	            (30) typed CpxTrs
25.68/7.85	            (31) RewriteLemmaProof [LOWER BOUND(ID), 134 ms]
25.68/7.85	            (32) typed CpxTrs
25.68/7.85	
25.68/7.85	
25.68/7.85	----------------------------------------
25.68/7.85	
25.68/7.85	(0)
25.68/7.85	Obligation:
25.68/7.85	The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).
25.68/7.85	
25.68/7.85	
25.68/7.85	The TRS R consists of the following rules:
25.68/7.85	
25.68/7.85	   active(terms(N)) -> mark(cons(recip(sqr(N)), terms(s(N))))
25.68/7.85	   active(sqr(0)) -> mark(0)
25.68/7.85	   active(sqr(s(X))) -> mark(s(add(sqr(X), dbl(X))))
25.68/7.85	   active(dbl(0)) -> mark(0)
25.68/7.85	   active(dbl(s(X))) -> mark(s(s(dbl(X))))
25.68/7.85	   active(add(0, X)) -> mark(X)
25.68/7.85	   active(add(s(X), Y)) -> mark(s(add(X, Y)))
25.68/7.85	   active(first(0, X)) -> mark(nil)
25.68/7.85	   active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z)))
25.68/7.85	   active(terms(X)) -> terms(active(X))
25.68/7.85	   active(cons(X1, X2)) -> cons(active(X1), X2)
25.68/7.85	   active(recip(X)) -> recip(active(X))
25.68/7.85	   active(sqr(X)) -> sqr(active(X))
25.68/7.85	   active(s(X)) -> s(active(X))
25.68/7.85	   active(add(X1, X2)) -> add(active(X1), X2)
25.68/7.85	   active(add(X1, X2)) -> add(X1, active(X2))
25.68/7.85	   active(dbl(X)) -> dbl(active(X))
25.68/7.85	   active(first(X1, X2)) -> first(active(X1), X2)
25.68/7.85	   active(first(X1, X2)) -> first(X1, active(X2))
25.68/7.85	   terms(mark(X)) -> mark(terms(X))
25.68/7.85	   cons(mark(X1), X2) -> mark(cons(X1, X2))
25.68/7.85	   recip(mark(X)) -> mark(recip(X))
25.68/7.85	   sqr(mark(X)) -> mark(sqr(X))
25.68/7.85	   s(mark(X)) -> mark(s(X))
25.68/7.85	   add(mark(X1), X2) -> mark(add(X1, X2))
25.68/7.85	   add(X1, mark(X2)) -> mark(add(X1, X2))
25.68/7.85	   dbl(mark(X)) -> mark(dbl(X))
25.68/7.85	   first(mark(X1), X2) -> mark(first(X1, X2))
25.68/7.85	   first(X1, mark(X2)) -> mark(first(X1, X2))
25.68/7.85	   proper(terms(X)) -> terms(proper(X))
25.68/7.85	   proper(cons(X1, X2)) -> cons(proper(X1), proper(X2))
25.68/7.85	   proper(recip(X)) -> recip(proper(X))
25.68/7.85	   proper(sqr(X)) -> sqr(proper(X))
25.68/7.85	   proper(s(X)) -> s(proper(X))
25.68/7.85	   proper(0) -> ok(0)
25.68/7.85	   proper(add(X1, X2)) -> add(proper(X1), proper(X2))
25.68/7.85	   proper(dbl(X)) -> dbl(proper(X))
25.68/7.85	   proper(first(X1, X2)) -> first(proper(X1), proper(X2))
25.68/7.85	   proper(nil) -> ok(nil)
25.68/7.85	   terms(ok(X)) -> ok(terms(X))
25.68/7.85	   cons(ok(X1), ok(X2)) -> ok(cons(X1, X2))
25.68/7.85	   recip(ok(X)) -> ok(recip(X))
25.68/7.85	   sqr(ok(X)) -> ok(sqr(X))
25.68/7.85	   s(ok(X)) -> ok(s(X))
25.68/7.85	   add(ok(X1), ok(X2)) -> ok(add(X1, X2))
25.68/7.85	   dbl(ok(X)) -> ok(dbl(X))
25.68/7.85	   first(ok(X1), ok(X2)) -> ok(first(X1, X2))
25.68/7.85	   top(mark(X)) -> top(proper(X))
25.68/7.85	   top(ok(X)) -> top(active(X))

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