details

property	value
status	complete
benchmark	ExAppendixB_AEL03_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n047.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	6.31520915031 seconds
cpu usage	19.803885086
max memory	3.316965376E9

stage attributes

key	value
output-size	40510
starexec-result	WORST_CASE(Omega(n^2), O(n^2))

output

/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 8 ms] (2) CdtProblem (3) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (4) CdtProblem (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 122 ms] (12) CdtProblem (13) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 20 ms] (14) CdtProblem (15) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CdtProblem (17) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 86 ms] (18) CdtProblem (19) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (20) BOUNDS(1, 1) (21) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (22) CpxTRS (23) SlicingProof [LOWER BOUND(ID), 0 ms] (24) CpxTRS (25) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (26) typed CpxTrs (27) OrderProof [LOWER BOUND(ID), 0 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 271 ms] (30) BEST (31) proven lower bound (32) LowerBoundPropagationProof [FINISHED, 0 ms] (33) BOUNDS(n^1, INF) (34) typed CpxTrs (35) RewriteLemmaProof [LOWER BOUND(ID), 106 ms] (36) BEST (37) proven lower bound (38) LowerBoundPropagationProof [FINISHED, 0 ms] (39) BOUNDS(n^2, INF) (40) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). The TRS R consists of the following rules: from(X) -> cons(X, n__from(s(X))) 2ndspos(0, Z) -> rnil 2ndspos(s(N), cons(X, Z)) -> 2ndspos(s(N), cons2(X, activate(Z))) 2ndspos(s(N), cons2(X, cons(Y, Z))) -> rcons(posrecip(Y), 2ndsneg(N, activate(Z))) 2ndsneg(0, Z) -> rnil 2ndsneg(s(N), cons(X, Z)) -> 2ndsneg(s(N), cons2(X, activate(Z))) 2ndsneg(s(N), cons2(X, cons(Y, Z))) -> rcons(negrecip(Y), 2ndspos(N, activate(Z))) pi(X) -> 2ndspos(X, from(0)) plus(0, Y) -> Y plus(s(X), Y) -> s(plus(X, Y)) times(0, Y) -> 0 times(s(X), Y) -> plus(Y, times(X, Y)) square(X) -> times(X, X) from(X) -> n__from(X) activate(n__from(X)) -> from(X) activate(X) -> X S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: from(z0) -> cons(z0, n__from(s(z0))) from(z0) -> n__from(z0) 2ndspos(0, z0) -> rnil 2ndspos(s(z0), cons(z1, z2)) -> 2ndspos(s(z0), cons2(z1, activate(z2))) 2ndspos(s(z0), cons2(z1, cons(z2, z3))) -> rcons(posrecip(z2), 2ndsneg(z0, activate(z3))) popout

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

job log

popout

actions

all output return to Runti Compl Inner Rewri 22807