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Runti Compl Inner Rewri 22807 pair #381904286
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
n070.star.cs.uiowa.edu
space
Secret_07_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
297.463236809 seconds
cpu usage
1176.17334105
max memory
1.5333064704E10
stage attributes
key
value
output-size
32823
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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, 3390 ms] (10) BOUNDS(1, n^2) (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (12) TRS for Loop Detection (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) TRS for Loop Detection ---------------------------------------- (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] minus(s(x), s(y)) -> minus(x, y) [1] a -> b [1] a -> c [1]
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