details

property	value
status	complete
benchmark	PEANO_nokinds_FR.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	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	rcdcRelativeAlsoLower
runtime (wallclock)	296.113 seconds
cpu usage	1154.78
user time	1144.54
system time	10.2358
max virtual memory	3.8333096E7
max residence set size	1.4948416E7

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF).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), 419 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 3 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), 489 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), 5475 ms] (18) 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: U11(tt, N) -> activate(N) U21(tt, M, N) -> s(plus(activate(N), activate(M))) and(tt, X) -> activate(X) isNat(n__0) -> tt isNat(n__plus(V1, V2)) -> and(isNat(activate(V1)), n__isNat(activate(V2))) isNat(n__s(V1)) -> isNat(activate(V1)) plus(N, 0) -> U11(isNat(N), N) plus(N, s(M)) -> U21(and(isNat(M), n__isNat(N)), M, N) 0 -> n__0 plus(X1, X2) -> n__plus(X1, X2) isNat(X) -> n__isNat(X) s(X) -> n__s(X) activate(n__0) -> 0 activate(n__plus(X1, X2)) -> plus(activate(X1), activate(X2)) activate(n__isNat(X)) -> isNat(X) activate(n__s(X)) -> s(activate(X)) 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(tt) -> tt encArg(n__0) -> n__0 encArg(n__plus(x_1, x_2)) -> n__plus(encArg(x_1), encArg(x_2)) encArg(n__isNat(x_1)) -> n__isNat(encArg(x_1)) encArg(n__s(x_1)) -> n__s(encArg(x_1)) encArg(cons_U11(x_1, x_2)) -> U11(encArg(x_1), encArg(x_2)) encArg(cons_U21(x_1, x_2, x_3)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_and(x_1, x_2)) -> and(encArg(x_1), encArg(x_2)) encArg(cons_isNat(x_1)) -> isNat(encArg(x_1)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encArg(cons_0) -> 0 encArg(cons_s(x_1)) -> s(encArg(x_1)) encArg(cons_activate(x_1)) -> activate(encArg(x_1)) encode_U11(x_1, x_2) -> U11(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_activate(x_1) -> activate(encArg(x_1)) encode_U21(x_1, x_2, x_3) -> U21(encArg(x_1), encArg(x_2), encArg(x_3)) encode_s(x_1) -> s(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) encode_and(x_1, x_2) -> and(encArg(x_1), encArg(x_2)) encode_isNat(x_1) -> isNat(encArg(x_1)) encode_n__0 -> n__0 encode_n__plus(x_1, x_2) -> n__plus(encArg(x_1), encArg(x_2)) encode_n__isNat(x_1) -> n__isNat(encArg(x_1)) encode_n__s(x_1) -> n__s(encArg(x_1)) encode_0 -> 0 ---------------------------------------- (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: U11(tt, N) -> activate(N) popout

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

job log

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actions

all output return to Derivational Complexity: TRS Innermost