details

property	value
status	complete
benchmark	aprove08.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n137.star.cs.uiowa.edu
space	Secret_07_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.748 seconds
cpu usage	1146.34
user time	1132.67
system time	13.6688
max virtual memory	3.8046528E7
max residence set size	1.5100748E7

stage attributes

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

output

WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 3406 ms] (10) BOUNDS(1, n^2) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) SlicingProof [LOWER BOUND(ID), 0 ms] (14) CpxTRS (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (16) typed CpxTrs (17) OrderProof [LOWER BOUND(ID), 0 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 306 ms] (20) BEST (21) proven lower bound (22) LowerBoundPropagationProof [FINISHED, 0 ms] (23) BOUNDS(n^1, INF) (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 42 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 24 ms] (28) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: gcd(x, y) -> gcd2(x, y, 0) gcd2(x, y, i) -> if1(le(x, 0), le(y, 0), le(x, y), le(y, x), x, y, inc(i)) if1(true, b1, b2, b3, x, y, i) -> pair(result(y), neededIterations(i)) if1(false, b1, b2, b3, x, y, i) -> if2(b1, b2, b3, x, y, i) if2(true, b2, b3, x, y, i) -> pair(result(x), neededIterations(i)) if2(false, b2, b3, x, y, i) -> if3(b2, b3, x, y, i) if3(false, b3, x, y, i) -> gcd2(minus(x, y), y, i) if3(true, b3, x, y, i) -> if4(b3, x, y, i) if4(false, x, y, i) -> gcd2(x, minus(y, x), i) if4(true, x, y, i) -> pair(result(x), neededIterations(i)) inc(0) -> 0 inc(s(i)) -> s(inc(i)) le(s(x), 0) -> false le(0, y) -> true le(s(x), s(y)) -> le(x, y) minus(x, 0) -> x minus(0, y) -> 0 minus(s(x), s(y)) -> minus(x, y) a -> b a -> c S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: gcd(x, y) -> gcd2(x, y, 0) [1] gcd2(x, y, i) -> if1(le(x, 0), le(y, 0), le(x, y), le(y, x), x, y, inc(i)) [1] if1(true, b1, b2, b3, x, y, i) -> pair(result(y), neededIterations(i)) [1] if1(false, b1, b2, b3, x, y, i) -> if2(b1, b2, b3, x, y, i) [1] if2(true, b2, b3, x, y, i) -> pair(result(x), neededIterations(i)) [1] if2(false, b2, b3, x, y, i) -> if3(b2, b3, x, y, i) [1] if3(false, b3, x, y, i) -> gcd2(minus(x, y), y, i) [1] if3(true, b3, x, y, i) -> if4(b3, x, y, i) [1] if4(false, x, y, i) -> gcd2(x, minus(y, x), i) [1] if4(true, x, y, i) -> pair(result(x), neededIterations(i)) [1] inc(0) -> 0 [1] inc(s(i)) -> s(inc(i)) [1] le(s(x), 0) -> false [1] le(0, y) -> true [1] le(s(x), s(y)) -> le(x, y) [1] minus(x, 0) -> x [1] minus(0, y) -> 0 [1] popout

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

job log

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actions

all output return to Runtime Complexity: TRS Innermost