details

property	value
status	complete
benchmark	ExIntrod_GM01_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n147.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.532 seconds
cpu usage	1132.83
user time	1119.29
system time	13.5444
max virtual memory	3.7661868E7
max residence set size	1.493238E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 350 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), 8 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 713 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), 108.9 s] (18) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: a__incr(nil) -> nil a__incr(cons(X, L)) -> cons(s(mark(X)), incr(L)) a__adx(nil) -> nil a__adx(cons(X, L)) -> a__incr(cons(mark(X), adx(L))) a__nats -> a__adx(a__zeros) a__zeros -> cons(0, zeros) a__head(cons(X, L)) -> mark(X) a__tail(cons(X, L)) -> mark(L) mark(incr(X)) -> a__incr(mark(X)) mark(adx(X)) -> a__adx(mark(X)) mark(nats) -> a__nats mark(zeros) -> a__zeros mark(head(X)) -> a__head(mark(X)) mark(tail(X)) -> a__tail(mark(X)) mark(nil) -> nil mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(s(X)) -> s(mark(X)) mark(0) -> 0 a__incr(X) -> incr(X) a__adx(X) -> adx(X) a__nats -> nats a__zeros -> zeros a__head(X) -> head(X) a__tail(X) -> tail(X) 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(nil) -> nil encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(s(x_1)) -> s(encArg(x_1)) encArg(incr(x_1)) -> incr(encArg(x_1)) encArg(adx(x_1)) -> adx(encArg(x_1)) encArg(0) -> 0 encArg(zeros) -> zeros encArg(nats) -> nats encArg(head(x_1)) -> head(encArg(x_1)) encArg(tail(x_1)) -> tail(encArg(x_1)) encArg(cons_a__incr(x_1)) -> a__incr(encArg(x_1)) encArg(cons_a__adx(x_1)) -> a__adx(encArg(x_1)) encArg(cons_a__nats) -> a__nats encArg(cons_a__zeros) -> a__zeros encArg(cons_a__head(x_1)) -> a__head(encArg(x_1)) encArg(cons_a__tail(x_1)) -> a__tail(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encode_a__incr(x_1) -> a__incr(encArg(x_1)) encode_nil -> nil encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_incr(x_1) -> incr(encArg(x_1)) encode_a__adx(x_1) -> a__adx(encArg(x_1)) encode_adx(x_1) -> adx(encArg(x_1)) encode_a__nats -> a__nats encode_a__zeros -> a__zeros encode_0 -> 0 encode_zeros -> zeros encode_a__head(x_1) -> a__head(encArg(x_1)) encode_a__tail(x_1) -> a__tail(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