details

property	value
status	complete
benchmark	Ex6_15_AEL02.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	Strategy_removed_CSR_05

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	2.10943 seconds
cpu usage	5.13994
user time	4.9143
system time	0.22564
max virtual memory	1.8478552E7
max residence set size	298396.0

stage attributes

key	value
starexec-result	WORST_CASE(NON_POLY, ?)

output

WORST_CASE(NON_POLY, ?) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(INF, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 527 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 4 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection (13) InfiniteLowerBoundProof [FINISHED, 0 ms] (14) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: sel(s(X), cons(Y, Z)) -> sel(X, Z) sel(0, cons(X, Z)) -> X first(0, Z) -> nil first(s(X), cons(Y, Z)) -> cons(Y, first(X, Z)) from(X) -> cons(X, from(s(X))) sel1(s(X), cons(Y, Z)) -> sel1(X, Z) sel1(0, cons(X, Z)) -> quote(X) first1(0, Z) -> nil1 first1(s(X), cons(Y, Z)) -> cons1(quote(Y), first1(X, Z)) quote(0) -> 01 quote1(cons(X, Z)) -> cons1(quote(X), quote1(Z)) quote1(nil) -> nil1 quote(s(X)) -> s1(quote(X)) quote(sel(X, Z)) -> sel1(X, Z) quote1(first(X, Z)) -> first1(X, Z) unquote(01) -> 0 unquote(s1(X)) -> s(unquote(X)) unquote1(nil1) -> nil unquote1(cons1(X, Z)) -> fcons(unquote(X), unquote1(Z)) fcons(X, Z) -> cons(X, Z) 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(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(0) -> 0 encArg(nil) -> nil encArg(nil1) -> nil1 encArg(cons1(x_1, x_2)) -> cons1(encArg(x_1), encArg(x_2)) encArg(01) -> 01 encArg(s1(x_1)) -> s1(encArg(x_1)) encArg(cons_sel(x_1, x_2)) -> sel(encArg(x_1), encArg(x_2)) encArg(cons_first(x_1, x_2)) -> first(encArg(x_1), encArg(x_2)) encArg(cons_from(x_1)) -> from(encArg(x_1)) encArg(cons_sel1(x_1, x_2)) -> sel1(encArg(x_1), encArg(x_2)) encArg(cons_first1(x_1, x_2)) -> first1(encArg(x_1), encArg(x_2)) encArg(cons_quote(x_1)) -> quote(encArg(x_1)) encArg(cons_quote1(x_1)) -> quote1(encArg(x_1)) encArg(cons_unquote(x_1)) -> unquote(encArg(x_1)) encArg(cons_unquote1(x_1)) -> unquote1(encArg(x_1)) encArg(cons_fcons(x_1, x_2)) -> fcons(encArg(x_1), encArg(x_2)) encode_sel(x_1, x_2) -> sel(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_first(x_1, x_2) -> first(encArg(x_1), encArg(x_2)) encode_nil -> nil encode_from(x_1) -> from(encArg(x_1)) encode_sel1(x_1, x_2) -> sel1(encArg(x_1), encArg(x_2)) encode_quote(x_1) -> quote(encArg(x_1)) encode_first1(x_1, x_2) -> first1(encArg(x_1), encArg(x_2)) encode_nil1 -> nil1 encode_cons1(x_1, x_2) -> cons1(encArg(x_1), encArg(x_2)) encode_01 -> 01 encode_quote1(x_1) -> quote1(encArg(x_1)) encode_s1(x_1) -> s1(encArg(x_1)) encode_unquote(x_1) -> unquote(encArg(x_1)) encode_unquote1(x_1) -> unquote1(encArg(x_1)) encode_fcons(x_1, x_2) -> fcons(encArg(x_1), encArg(x_2)) ---------------------------------------- popout

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

job log

popout

actions

all output return to Derivational Complexity: TRS Innermost