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Runti Compl Inner Rewri 22807 pair #381904373
details
property
value
status
complete
benchmark
gcd2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n054.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
293.194766045 seconds
cpu usage
1160.42289033
max memory
1.560082432E10
stage attributes
key
value
output-size
31493
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
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^3)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). (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), 4 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 1511 ms] (10) BOUNDS(1, n^3) (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^3). The TRS R consists of the following rules: minus(s(x), y) -> if(gt(s(x), y), x, y) if(true, x, y) -> s(minus(x, y)) if(false, x, y) -> 0 gcd(x, y) -> if1(ge(x, y), x, y) if1(true, x, y) -> if2(gt(y, 0), x, y) if1(false, x, y) -> if3(gt(x, 0), x, y) if2(true, x, y) -> gcd(minus(x, y), y) if2(false, x, y) -> x if3(true, x, y) -> gcd(x, minus(y, x)) if3(false, x, y) -> y gt(0, y) -> false gt(s(x), 0) -> true gt(s(x), s(y)) -> gt(x, y) ge(x, 0) -> true ge(0, s(x)) -> false ge(s(x), s(y)) -> ge(x, y) 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^3). The TRS R consists of the following rules: minus(s(x), y) -> if(gt(s(x), y), x, y) [1] if(true, x, y) -> s(minus(x, y)) [1] if(false, x, y) -> 0 [1] gcd(x, y) -> if1(ge(x, y), x, y) [1] if1(true, x, y) -> if2(gt(y, 0), x, y) [1] if1(false, x, y) -> if3(gt(x, 0), x, y) [1] if2(true, x, y) -> gcd(minus(x, y), y) [1] if2(false, x, y) -> x [1] if3(true, x, y) -> gcd(x, minus(y, x)) [1] if3(false, x, y) -> y [1] gt(0, y) -> false [1] gt(s(x), 0) -> true [1] gt(s(x), s(y)) -> gt(x, y) [1] ge(x, 0) -> true [1] ge(0, s(x)) -> false [1] ge(s(x), s(y)) -> ge(x, y) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4)
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