details

property	value
status	complete
benchmark	Ex26_Luc03b_Z.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)	291.592 seconds
cpu usage	362.742
user time	359.068
system time	3.67455
max virtual memory	1.9191924E7
max residence set size	6600988.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(n^2))

output

WORST_CASE(?, 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^2). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 489 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), 2 ms] (10) CdtProblem (11) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (12) CdtProblem (13) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 12 ms] (14) CdtProblem (15) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 604 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 188 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 368 ms] (20) CdtProblem (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 149 ms] (22) CdtProblem (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 108 ms] (24) CdtProblem (25) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (26) BOUNDS(1, 1) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: terms(N) -> cons(recip(sqr(N)), n__terms(s(N))) sqr(0) -> 0 sqr(s(X)) -> s(n__add(sqr(activate(X)), dbl(activate(X)))) dbl(0) -> 0 dbl(s(X)) -> s(n__s(n__dbl(activate(X)))) add(0, X) -> X add(s(X), Y) -> s(n__add(activate(X), Y)) first(0, X) -> nil first(s(X), cons(Y, Z)) -> cons(Y, n__first(activate(X), activate(Z))) terms(X) -> n__terms(X) add(X1, X2) -> n__add(X1, X2) s(X) -> n__s(X) dbl(X) -> n__dbl(X) first(X1, X2) -> n__first(X1, X2) activate(n__terms(X)) -> terms(X) activate(n__add(X1, X2)) -> add(X1, X2) activate(n__s(X)) -> s(X) activate(n__dbl(X)) -> dbl(X) activate(n__first(X1, X2)) -> first(X1, X2) 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(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(recip(x_1)) -> recip(encArg(x_1)) encArg(n__terms(x_1)) -> n__terms(encArg(x_1)) encArg(0) -> 0 encArg(n__add(x_1, x_2)) -> n__add(encArg(x_1), encArg(x_2)) encArg(n__s(x_1)) -> n__s(encArg(x_1)) encArg(n__dbl(x_1)) -> n__dbl(encArg(x_1)) encArg(nil) -> nil encArg(n__first(x_1, x_2)) -> n__first(encArg(x_1), encArg(x_2)) encArg(cons_terms(x_1)) -> terms(encArg(x_1)) encArg(cons_sqr(x_1)) -> sqr(encArg(x_1)) encArg(cons_dbl(x_1)) -> dbl(encArg(x_1)) encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) encArg(cons_first(x_1, x_2)) -> first(encArg(x_1), encArg(x_2)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_activate(x_1)) -> activate(encArg(x_1)) encode_terms(x_1) -> terms(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_recip(x_1) -> recip(encArg(x_1)) encode_sqr(x_1) -> sqr(encArg(x_1)) encode_n__terms(x_1) -> n__terms(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0 encode_n__add(x_1, x_2) -> n__add(encArg(x_1), encArg(x_2)) encode_activate(x_1) -> activate(encArg(x_1)) encode_dbl(x_1) -> dbl(encArg(x_1)) encode_n__s(x_1) -> n__s(encArg(x_1)) popout

output may be truncated. 'popout' for the full output.

job log

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actions

all output return to Derivational Complexity: TRS Innermost