details

property	value
status	complete
benchmark	17.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n151.star.cs.uiowa.edu
space	Beerendonk_07

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	294.803 seconds
cpu usage	1144.22
user time	1133.05
system time	11.1658
max virtual memory	3.8118844E7
max residence set size	1.5065172E7

stage attributes

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

output

WORST_CASE(Omega(n^1), ?) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 281 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), 520 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), 100 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 188 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 731 ms] (22) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond1(gr(add(x, y), 0), p(x), y) cond2(false, x, y) -> cond3(eq(x, y), x, y) cond3(true, x, y) -> cond1(gr(add(x, y), 0), p(x), y) cond3(false, x, y) -> cond1(gr(add(x, y), 0), x, p(y)) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) add(0, x) -> x add(s(x), y) -> s(add(x, y)) eq(0, 0) -> true eq(0, s(x)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) p(0) -> 0 p(s(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(true) -> true encArg(0) -> 0 encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(cons_cond1(x_1, x_2, x_3)) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_cond2(x_1, x_2, x_3)) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_cond3(x_1, x_2, x_3)) -> cond3(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_gr(x_1, x_2)) -> gr(encArg(x_1), encArg(x_2)) encArg(cons_add(x_1, x_2)) -> add(encArg(x_1), encArg(x_2)) encArg(cons_eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encode_cond1(x_1, x_2, x_3) -> cond1(encArg(x_1), encArg(x_2), encArg(x_3)) encode_true -> true encode_cond2(x_1, x_2, x_3) -> cond2(encArg(x_1), encArg(x_2), encArg(x_3)) encode_gr(x_1, x_2) -> gr(encArg(x_1), encArg(x_2)) encode_add(x_1, x_2) -> add(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_p(x_1) -> p(encArg(x_1)) encode_false -> false encode_cond3(x_1, x_2, x_3) -> cond3(encArg(x_1), encArg(x_2), encArg(x_3)) encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: cond1(true, x, y) -> cond2(gr(x, y), x, y) cond2(true, x, y) -> cond1(gr(add(x, y), 0), p(x), y) popout

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

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actions

all output return to Derivational Complexity: TRS Innermost