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	n149.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.22502 seconds
cpu usage	24.5835
user time	23.097
system time	1.48644
max virtual memory	3.7846984E7
max residence set size	3934548.0

stage attributes

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

output

WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsMatchBoundsTAProof [FINISHED, 95 ms] (6) BOUNDS(1, n^1) (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 399 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 44 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 66 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 71 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 98 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 90 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 91 ms] (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 100 ms] (32) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: active(terms(N)) -> mark(cons(recip(sqr(N)), terms(s(N)))) active(sqr(0)) -> mark(0) active(sqr(s(X))) -> mark(s(add(sqr(X), dbl(X)))) active(dbl(0)) -> mark(0) active(dbl(s(X))) -> mark(s(s(dbl(X)))) active(add(0, X)) -> mark(X) active(add(s(X), Y)) -> mark(s(add(X, Y))) active(first(0, X)) -> mark(nil) active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))) active(terms(X)) -> terms(active(X)) active(cons(X1, X2)) -> cons(active(X1), X2) active(recip(X)) -> recip(active(X)) active(sqr(X)) -> sqr(active(X)) active(s(X)) -> s(active(X)) active(add(X1, X2)) -> add(active(X1), X2) active(add(X1, X2)) -> add(X1, active(X2)) active(dbl(X)) -> dbl(active(X)) active(first(X1, X2)) -> first(active(X1), X2) active(first(X1, X2)) -> first(X1, active(X2)) terms(mark(X)) -> mark(terms(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) recip(mark(X)) -> mark(recip(X)) sqr(mark(X)) -> mark(sqr(X)) s(mark(X)) -> mark(s(X)) add(mark(X1), X2) -> mark(add(X1, X2)) add(X1, mark(X2)) -> mark(add(X1, X2)) dbl(mark(X)) -> mark(dbl(X)) first(mark(X1), X2) -> mark(first(X1, X2)) first(X1, mark(X2)) -> mark(first(X1, X2)) proper(terms(X)) -> terms(proper(X)) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(recip(X)) -> recip(proper(X)) proper(sqr(X)) -> sqr(proper(X)) proper(s(X)) -> s(proper(X)) proper(0) -> ok(0) proper(add(X1, X2)) -> add(proper(X1), proper(X2)) proper(dbl(X)) -> dbl(proper(X)) proper(first(X1, X2)) -> first(proper(X1), proper(X2)) proper(nil) -> ok(nil) terms(ok(X)) -> ok(terms(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) recip(ok(X)) -> ok(recip(X)) sqr(ok(X)) -> ok(sqr(X)) s(ok(X)) -> ok(s(X)) add(ok(X1), ok(X2)) -> ok(add(X1, X2)) dbl(ok(X)) -> ok(dbl(X)) first(ok(X1), ok(X2)) -> ok(first(X1, X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) popout

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

job log

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actions

all output return to Runtime Complexity: TRS