details

property	value
status	complete
benchmark	ExProp7_Luc06_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n142.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	291.52 seconds
cpu usage	365.387
user time	357.572
system time	7.81536
max virtual memory	3.7439572E7
max residence set size	1.0756164E7

stage attributes

key	value
starexec-result	WORST_CASE(Omega(n^1), O(n^2))

output

WORST_CASE(Omega(n^1), O(n^2)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 216 ms] (4) CpxRelTRS (5) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (6) CpxRelTRS (7) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxWeightedTrs (9) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxWeightedTrs (11) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedTrs (13) CompletionProof [UPPER BOUND(ID), 0 ms] (14) CpxTypedWeightedCompleteTrs (15) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (16) CpxRNTS (17) CompleteCoflocoProof [FINISHED, 794 ms] (18) BOUNDS(1, n^2) (19) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (20) TRS for Loop Detection (21) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (22) BEST (23) proven lower bound (24) LowerBoundPropagationProof [FINISHED, 0 ms] (25) BOUNDS(n^1, INF) (26) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: f(0) -> cons(0, n__f(n__s(n__0))) f(s(0)) -> f(p(s(0))) p(s(X)) -> X f(X) -> n__f(X) s(X) -> n__s(X) 0 -> n__0 activate(n__f(X)) -> f(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__0) -> 0 activate(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(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(n__f(x_1)) -> n__f(encArg(x_1)) encArg(n__s(x_1)) -> n__s(encArg(x_1)) encArg(n__0) -> n__0 encArg(cons_f(x_1)) -> f(encArg(x_1)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_0) -> 0 encArg(cons_activate(x_1)) -> activate(encArg(x_1)) encode_f(x_1) -> f(encArg(x_1)) encode_0 -> 0 encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_n__f(x_1) -> n__f(encArg(x_1)) encode_n__s(x_1) -> n__s(encArg(x_1)) encode_n__0 -> n__0 encode_s(x_1) -> s(encArg(x_1)) encode_p(x_1) -> p(encArg(x_1)) encode_activate(x_1) -> activate(encArg(x_1)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: f(0) -> cons(0, n__f(n__s(n__0))) f(s(0)) -> f(p(s(0))) p(s(X)) -> X f(X) -> n__f(X) s(X) -> n__s(X) 0 -> n__0 activate(n__f(X)) -> f(activate(X)) activate(n__s(X)) -> s(activate(X)) popout

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

job log

popout

actions

all output return to Derivational Complexity: TRS Innermost