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Derivational Complexity: TRS Innermost pair #487108714
details
property
value
status
complete
benchmark
Ex9_Luc06_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.531 seconds
cpu usage
330.987
user time
327.55
system time
3.43716
max virtual memory
1.9115268E7
max residence set size
5624092.0
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/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2).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), 167 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), 0 ms] (10) CdtProblem (11) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (12) CdtProblem (13) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CdtProblem (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 113 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 132 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 133 ms] (20) CdtProblem (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 94 ms] (22) CdtProblem (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 110 ms] (24) CdtProblem (25) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (26) BOUNDS(1, 1) (27) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (28) CpxRelTRS (29) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (30) typed CpxTrs (31) OrderProof [LOWER BOUND(ID), 0 ms] (32) typed CpxTrs (33) RewriteLemmaProof [LOWER BOUND(ID), 6913 ms] (34) BEST (35) proven lower bound (36) LowerBoundPropagationProof [FINISHED, 0 ms] (37) BOUNDS(n^1, INF) (38) typed CpxTrs (39) RewriteLemmaProof [LOWER BOUND(ID), 55 ms] (40) 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: a__f(a, X, X) -> a__f(X, a__b, b) a__b -> a mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3) mark(b) -> a__b mark(a) -> a a__f(X1, X2, X3) -> f(X1, X2, X3) a__b -> b 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(a) -> a encArg(b) -> b encArg(f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_a__f(x_1, x_2, x_3)) -> a__f(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_a__b) -> a__b encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encode_a__f(x_1, x_2, x_3) -> a__f(encArg(x_1), encArg(x_2), encArg(x_3)) encode_a -> a encode_a__b -> a__b encode_b -> b encode_mark(x_1) -> mark(encArg(x_1)) encode_f(x_1, x_2, x_3) -> f(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). The TRS R consists of the following rules: a__f(a, X, X) -> a__f(X, a__b, b) a__b -> a mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3)
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