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Derivational Complexity: TRS Innermost pair #487104286
details
property
value
status
complete
benchmark
#3.6.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n138.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.531 seconds
cpu usage
632.944
user time
628.582
system time
4.36292
max virtual memory
1.9478316E7
max residence set size
5522096.0
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/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 276 ms] (4) CpxRelTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (6) CdtProblem (7) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (8) CdtProblem (9) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 1 ms] (10) CdtProblem (11) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (12) CdtProblem (13) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 13 ms] (14) CdtProblem (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 237 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 762 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 765 ms] (20) CdtProblem (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 592 ms] (22) CdtProblem (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 453 ms] (24) CdtProblem (25) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 455 ms] (26) CdtProblem (27) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (28) BOUNDS(1, 1) (29) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (30) TRS for Loop Detection (31) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (32) BEST (33) proven lower bound (34) LowerBoundPropagationProof [FINISHED, 0 ms] (35) BOUNDS(n^1, INF) (36) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) pred(s(x)) -> x minus(x, 0) -> x minus(x, s(y)) -> pred(minus(x, y)) gcd(0, y) -> y gcd(s(x), 0) -> s(x) gcd(s(x), s(y)) -> if_gcd(le(y, x), s(x), s(y)) if_gcd(true, s(x), s(y)) -> gcd(minus(x, y), s(y)) if_gcd(false, s(x), s(y)) -> gcd(minus(y, x), s(x)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(0) -> 0 encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_pred(x_1)) -> pred(encArg(x_1)) encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_gcd(x_1, x_2)) -> gcd(encArg(x_1), encArg(x_2)) encArg(cons_if_gcd(x_1, x_2, x_3)) -> if_gcd(encArg(x_1), encArg(x_2), encArg(x_3)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_pred(x_1) -> pred(encArg(x_1)) encode_minus(x_1, x_2) -> minus(encArg(x_1), encArg(x_2)) encode_gcd(x_1, x_2) -> gcd(encArg(x_1), encArg(x_2)) encode_if_gcd(x_1, x_2, x_3) -> if_gcd(encArg(x_1), encArg(x_2), encArg(x_3)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2).
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