details

property	value
status	complete
benchmark	PEANO_nosorts_noand_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n139.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.666 seconds
cpu usage	1140.87
user time	1128.86
system time	12.005
max virtual memory	3.7376868E7
max residence set size	1.4965432E7

stage attributes

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

output

WORST_CASE(Omega(n^2), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^2, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 230 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 675 ms] (12) BEST (13) proven lower bound (14) LowerBoundPropagationProof [FINISHED, 0 ms] (15) BOUNDS(n^1, INF) (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 163 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^2, INF) (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 151 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 143 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 31 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 165 ms] (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 93 ms] (32) typed CpxTrs (33) RewriteLemmaProof [LOWER BOUND(ID), 263 ms] (34) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: a__U11(tt, M, N) -> a__U12(tt, M, N) a__U12(tt, M, N) -> s(a__plus(mark(N), mark(M))) a__plus(N, 0) -> mark(N) a__plus(N, s(M)) -> a__U11(tt, M, N) mark(U11(X1, X2, X3)) -> a__U11(mark(X1), X2, X3) mark(U12(X1, X2, X3)) -> a__U12(mark(X1), X2, X3) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__U11(X1, X2, X3) -> U11(X1, X2, X3) a__U12(X1, X2, X3) -> U12(X1, X2, X3) a__plus(X1, X2) -> plus(X1, X2) S is empty. Rewrite Strategy: FULL ---------------------------------------- (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(tt) -> tt encArg(s(x_1)) -> s(encArg(x_1)) encArg(0) -> 0 encArg(U11(x_1, x_2, x_3)) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(U12(x_1, x_2, x_3)) -> U12(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_a__U11(x_1, x_2, x_3)) -> a__U11(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_a__U12(x_1, x_2, x_3)) -> a__U12(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_a__plus(x_1, x_2)) -> a__plus(encArg(x_1), encArg(x_2)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encode_a__U11(x_1, x_2, x_3) -> a__U11(encArg(x_1), encArg(x_2), encArg(x_3)) encode_tt -> tt encode_a__U12(x_1, x_2, x_3) -> a__U12(encArg(x_1), encArg(x_2), encArg(x_3)) encode_s(x_1) -> s(encArg(x_1)) encode_a__plus(x_1, x_2) -> a__plus(encArg(x_1), encArg(x_2)) encode_mark(x_1) -> mark(encArg(x_1)) encode_0 -> 0 encode_U11(x_1, x_2, x_3) -> U11(encArg(x_1), encArg(x_2), encArg(x_3)) encode_U12(x_1, x_2, x_3) -> U12(encArg(x_1), encArg(x_2), encArg(x_3)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) ---------------------------------------- (2) Obligation: popout

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

job log

popout

actions

all output return to Derivational Complexity: TRS