Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime Complexity: TRS Innermost pair #487112754
details
property
value
status
complete
benchmark
factorial1.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
AProVE_06
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.62 seconds
cpu usage
1121.38
user time
1113.04
system time
8.34
max virtual memory
3.8170836E7
max residence set size
8145476.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^4), ?)
output
WORST_CASE(Omega(n^4), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^4, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 247 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 26 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^2, INF) (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 19 ms] (20) BEST (21) proven lower bound (22) LowerBoundPropagationProof [FINISHED, 0 ms] (23) BOUNDS(n^3, INF) (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 1100 ms] (26) proven lower bound (27) LowerBoundPropagationProof [FINISHED, 0 ms] (28) BOUNDS(n^4, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^4, INF). The TRS R consists of the following rules: plus(0, x) -> x plus(s(x), y) -> s(plus(p(s(x)), y)) times(0, y) -> 0 times(s(x), y) -> plus(y, times(p(s(x)), y)) p(s(0)) -> 0 p(s(s(x))) -> s(p(s(x))) fac(0, x) -> x fac(s(x), y) -> fac(p(s(x)), times(s(x), y)) factorial(x) -> fac(x, s(0)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^4, INF). The TRS R consists of the following rules: plus(0', x) -> x plus(s(x), y) -> s(plus(p(s(x)), y)) times(0', y) -> 0' times(s(x), y) -> plus(y, times(p(s(x)), y)) p(s(0')) -> 0' p(s(s(x))) -> s(p(s(x))) fac(0', x) -> x fac(s(x), y) -> fac(p(s(x)), times(s(x), y)) factorial(x) -> fac(x, s(0')) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Innermost TRS: Rules: plus(0', x) -> x plus(s(x), y) -> s(plus(p(s(x)), y)) times(0', y) -> 0' times(s(x), y) -> plus(y, times(p(s(x)), y)) p(s(0')) -> 0' p(s(s(x))) -> s(p(s(x)))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime Complexity: TRS Innermost