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Derivational Complexity: TRS Innermost pair #487108168
details
property
value
status
complete
benchmark
Ex49_GM04_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n149.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.587 seconds
cpu usage
772.982
user time
767.352
system time
5.62923
max virtual memory
5.6011072E7
max residence set size
5873240.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).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), 250 ms] (4) CpxRelTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 6 ms] (6) CdtProblem (7) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (8) CdtProblem (9) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CdtProblem (13) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (14) CdtProblem (15) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 248 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 129 ms] (20) CdtProblem (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 111 ms] (22) CdtProblem (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 431 ms] (24) CdtProblem (25) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 393 ms] (26) CdtProblem (27) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 379 ms] (28) CdtProblem (29) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 317 ms] (30) CdtProblem (31) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 239 ms] (32) CdtProblem (33) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (34) BOUNDS(1, 1) (35) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (36) CpxRelTRS (37) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (38) typed CpxTrs (39) OrderProof [LOWER BOUND(ID), 0 ms] (40) typed CpxTrs (41) RewriteLemmaProof [LOWER BOUND(ID), 775 ms] (42) BEST (43) proven lower bound (44) LowerBoundPropagationProof [FINISHED, 0 ms] (45) BOUNDS(n^1, INF) (46) typed CpxTrs (47) RewriteLemmaProof [LOWER BOUND(ID), 80 ms] (48) typed CpxTrs (49) RewriteLemmaProof [LOWER BOUND(ID), 513 ms] (50) BOUNDS(1, INF) ---------------------------------------- (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: minus(n__0, Y) -> 0 minus(n__s(X), n__s(Y)) -> minus(activate(X), activate(Y)) geq(X, n__0) -> true geq(n__0, n__s(Y)) -> false geq(n__s(X), n__s(Y)) -> geq(activate(X), activate(Y)) div(0, n__s(Y)) -> 0 div(s(X), n__s(Y)) -> if(geq(X, activate(Y)), n__s(div(minus(X, activate(Y)), n__s(activate(Y)))), n__0) if(true, X, Y) -> activate(X) if(false, X, Y) -> activate(Y) 0 -> n__0 s(X) -> n__s(X) activate(n__0) -> 0 activate(n__s(X)) -> s(X) activate(X) -> 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(n__0) -> n__0 encArg(n__s(x_1)) -> n__s(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(cons_minus(x_1, x_2)) -> minus(encArg(x_1), encArg(x_2)) encArg(cons_geq(x_1, x_2)) -> geq(encArg(x_1), encArg(x_2)) encArg(cons_div(x_1, x_2)) -> div(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_0) -> 0
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