Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runti Compl Inner Rewri 22807 pair #381904825
details
property
value
status
complete
benchmark
thiemann38.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n052.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.484648943 seconds
cpu usage
1141.26384647
max memory
1.5404539904E10
stage attributes
key
value
output-size
21177
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 6 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 592 ms] (10) BOUNDS(1, n^2) (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (12) TRS for Loop Detection (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: length(nil) -> 0 length(cons(x, l)) -> s(length(l)) lt(x, 0) -> false lt(0, s(y)) -> true lt(s(x), s(y)) -> lt(x, y) head(cons(x, l)) -> x head(nil) -> undefined tail(nil) -> nil tail(cons(x, l)) -> l reverse(l) -> rev(0, l, nil, l) rev(x, l, accu, orig) -> if(lt(x, length(orig)), x, l, accu, orig) if(true, x, l, accu, orig) -> rev(s(x), tail(l), cons(head(l), accu), orig) if(false, x, l, accu, orig) -> accu S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: length(nil) -> 0 [1] length(cons(x, l)) -> s(length(l)) [1] lt(x, 0) -> false [1] lt(0, s(y)) -> true [1] lt(s(x), s(y)) -> lt(x, y) [1] head(cons(x, l)) -> x [1] head(nil) -> undefined [1] tail(nil) -> nil [1] tail(cons(x, l)) -> l [1] reverse(l) -> rev(0, l, nil, l) [1] rev(x, l, accu, orig) -> if(lt(x, length(orig)), x, l, accu, orig) [1] if(true, x, l, accu, orig) -> rev(s(x), tail(l), cons(head(l), accu), orig) [1] if(false, x, l, accu, orig) -> accu [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: length(nil) -> 0 [1] length(cons(x, l)) -> s(length(l)) [1]
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runti Compl Inner Rewri 22807