details

property	value
status	complete
benchmark	ExIntrod_GM99_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.617 seconds
cpu usage	468.261
user time	465.09
system time	3.17086
max virtual memory	1.956798E7
max residence set size	5679504.0

stage attributes

key	value
starexec-result	WORST_CASE(?, O(n^1))

output

WORST_CASE(?, O(n^1)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^1). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 437 ms] (4) CpxRelTRS (5) CpxTrsToCdtProof [UPPER BOUND(ID), 0 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)), 243 ms] (18) CdtProblem (19) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 160 ms] (20) CdtProblem (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 159 ms] (22) CdtProblem (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 138 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^1). The TRS R consists of the following rules: primes -> sieve(from(s(s(0)))) from(X) -> cons(X, n__from(s(X))) head(cons(X, Y)) -> X tail(cons(X, Y)) -> activate(Y) if(true, X, Y) -> activate(X) if(false, X, Y) -> activate(Y) filter(s(s(X)), cons(Y, Z)) -> if(divides(s(s(X)), Y), n__filter(s(s(X)), activate(Z)), n__cons(Y, n__filter(X, sieve(Y)))) sieve(cons(X, Y)) -> cons(X, n__filter(X, sieve(activate(Y)))) from(X) -> n__from(X) filter(X1, X2) -> n__filter(X1, X2) cons(X1, X2) -> n__cons(X1, X2) activate(n__from(X)) -> from(X) activate(n__filter(X1, X2)) -> filter(X1, X2) activate(n__cons(X1, X2)) -> cons(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(s(x_1)) -> s(encArg(x_1)) encArg(0) -> 0 encArg(n__from(x_1)) -> n__from(encArg(x_1)) encArg(true) -> true encArg(false) -> false encArg(divides(x_1, x_2)) -> divides(encArg(x_1), encArg(x_2)) encArg(n__filter(x_1, x_2)) -> n__filter(encArg(x_1), encArg(x_2)) encArg(n__cons(x_1, x_2)) -> n__cons(encArg(x_1), encArg(x_2)) encArg(cons_primes) -> primes encArg(cons_from(x_1)) -> from(encArg(x_1)) encArg(cons_head(x_1)) -> head(encArg(x_1)) encArg(cons_tail(x_1)) -> tail(encArg(x_1)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_filter(x_1, x_2)) -> filter(encArg(x_1), encArg(x_2)) encArg(cons_sieve(x_1)) -> sieve(encArg(x_1)) encArg(cons_cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(cons_activate(x_1)) -> activate(encArg(x_1)) encode_primes -> primes encode_sieve(x_1) -> sieve(encArg(x_1)) encode_from(x_1) -> from(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_0 -> 0 encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_n__from(x_1) -> n__from(encArg(x_1)) encode_head(x_1) -> head(encArg(x_1)) encode_tail(x_1) -> tail(encArg(x_1)) encode_activate(x_1) -> activate(encArg(x_1)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_false -> false encode_filter(x_1, x_2) -> filter(encArg(x_1), encArg(x_2)) encode_divides(x_1, x_2) -> divides(encArg(x_1), encArg(x_2)) 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