details

property	value
status	complete
benchmark	power.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.556 seconds
cpu usage	740.46
user time	734.995
system time	5.46539
max virtual memory	5.6306104E7
max residence set size	7519488.0

stage attributes

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

output

WORST_CASE(Omega(n^2), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^2, INF). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 144 ms] (2) CpxRelTRS (3) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxRelTRS (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) typed CpxTrs (7) OrderProof [LOWER BOUND(ID), 0 ms] (8) typed CpxTrs (9) RewriteLemmaProof [LOWER BOUND(ID), 268 ms] (10) BEST (11) proven lower bound (12) LowerBoundPropagationProof [FINISHED, 0 ms] (13) BOUNDS(n^1, INF) (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 11 ms] (16) BEST (17) proven lower bound (18) LowerBoundPropagationProof [FINISHED, 0 ms] (19) BOUNDS(n^2, INF) (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 54 ms] (22) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: power(x', S(x)) -> mult(x', power(x', x)) mult(x', S(x)) -> add0(x', mult(x', x)) add0(x', S(x)) -> +(S(0), add0(x', x)) power(x, 0) -> S(0) mult(x, 0) -> 0 add0(x, 0) -> x The (relative) TRS S consists of the following rules: +(x, S(0)) -> S(x) +(S(0), y) -> S(y) Rewrite Strategy: INNERMOST ---------------------------------------- (1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: power(x', S(x)) -> mult(x', power(x', x)) mult(x', S(x)) -> add0(x', mult(x', x)) add0(x', S(x)) -> +(S(0), add0(x', x)) power(x, 0) -> S(0) mult(x, 0) -> 0 add0(x, 0) -> x The (relative) TRS S consists of the following rules: +(x, S(0)) -> S(x) +(S(0), y) -> S(y) Rewrite Strategy: INNERMOST ---------------------------------------- (3) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: power(x', S(x)) -> mult(x', power(x', x)) mult(x', S(x)) -> add0(x', mult(x', x)) add0(x', S(x)) -> +'(S(0'), add0(x', x)) power(x, 0') -> S(0') mult(x, 0') -> 0' add0(x, 0') -> x popout

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

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actions

all output return to Runtime Complexity: TRS Innermost