details

property	value
status	complete
benchmark	secret1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n045.star.cs.uiowa.edu
space	Secret_07_TRS

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	5.01724505424 seconds
cpu usage	15.384472365
max memory	3.131383808E9

stage attributes

key	value
output-size	20270
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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), 13 ms] (2) CpxTRS (3) NonCtorToCtorProof [UPPER BOUND(ID), 1 ms] (4) CpxRelTRS (5) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (8) CdtProblem (9) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CdtProblem (13) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CdtProblem (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 90 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 19 ms] (18) CdtProblem (19) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (20) BOUNDS(1, 1) (21) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (22) TRS for Loop Detection (23) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (24) BEST (25) proven lower bound (26) LowerBoundPropagationProof [FINISHED, 0 ms] (27) BOUNDS(n^1, INF) (28) TRS for Loop Detection ---------------------------------------- (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: D(t) -> s(h) D(constant) -> h D(b(x, y)) -> b(D(x), D(y)) D(c(x, y)) -> b(c(y, D(x)), c(x, D(y))) D(m(x, y)) -> m(D(x), D(y)) D(opp(x)) -> opp(D(x)) D(div(x, y)) -> m(div(D(x), y), div(c(x, D(y)), pow(y, 2))) D(ln(x)) -> div(D(x), x) D(pow(x, y)) -> b(c(c(y, pow(x, m(y, 1))), D(x)), c(c(pow(x, y), ln(x)), D(y))) b(h, x) -> x b(x, h) -> x b(s(x), s(y)) -> s(s(b(x, y))) b(b(x, y), z) -> b(x, b(y, z)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The following defined symbols can occur below the 0th argument of b: b, D The following defined symbols can occur below the 1th argument of b: b, D Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: D(b(x, y)) -> b(D(x), D(y)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: D(t) -> s(h) D(constant) -> h D(c(x, y)) -> b(c(y, D(x)), c(x, D(y))) D(m(x, y)) -> m(D(x), D(y)) D(opp(x)) -> opp(D(x)) D(div(x, y)) -> m(div(D(x), y), div(c(x, D(y)), pow(y, 2))) D(ln(x)) -> div(D(x), x) D(pow(x, y)) -> b(c(c(y, pow(x, m(y, 1))), D(x)), c(c(pow(x, y), ln(x)), D(y))) b(h, x) -> x b(x, h) -> x b(s(x), s(y)) -> s(s(b(x, y))) b(b(x, y), z) -> b(x, b(y, z)) popout

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

job log

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actions

all output return to Runti Compl Full Rewri 10127