Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runti Compl Inner Rewri 22807 pair #381904412
details
property
value
status
complete
benchmark
#3.10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n027.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
294.063980818 seconds
cpu usage
1142.26524995
max memory
1.3005160448E10
stage attributes
key
value
output-size
66538
starexec-result
WORST_CASE(Omega(n^1), O(n^4))
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^4)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^4). (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), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 8139 ms] (10) BOUNDS(1, n^4) (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^4). The TRS R consists of the following rules: eq(0, 0) -> true eq(0, s(x)) -> false eq(s(x), 0) -> false eq(s(x), s(y)) -> eq(x, y) le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) app(nil, y) -> y app(add(n, x), y) -> add(n, app(x, y)) min(add(n, nil)) -> n min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) if_min(true, add(n, add(m, x))) -> min(add(n, x)) if_min(false, add(n, add(m, x))) -> min(add(m, x)) rm(n, nil) -> nil rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) if_rm(true, n, add(m, x)) -> rm(n, x) if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) minsort(nil, nil) -> nil minsort(add(n, x), y) -> if_minsort(eq(n, min(add(n, x))), add(n, x), y) if_minsort(true, add(n, x), y) -> add(n, minsort(app(rm(n, x), y), nil)) if_minsort(false, add(n, x), y) -> minsort(x, add(n, y)) 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^4). The TRS R consists of the following rules: eq(0, 0) -> true [1] eq(0, s(x)) -> false [1] eq(s(x), 0) -> false [1] eq(s(x), s(y)) -> eq(x, y) [1] le(0, y) -> true [1] le(s(x), 0) -> false [1] le(s(x), s(y)) -> le(x, y) [1] app(nil, y) -> y [1] app(add(n, x), y) -> add(n, app(x, y)) [1] min(add(n, nil)) -> n [1] min(add(n, add(m, x))) -> if_min(le(n, m), add(n, add(m, x))) [1] if_min(true, add(n, add(m, x))) -> min(add(n, x)) [1] if_min(false, add(n, add(m, x))) -> min(add(m, x)) [1] rm(n, nil) -> nil [1] rm(n, add(m, x)) -> if_rm(eq(n, m), n, add(m, x)) [1] if_rm(true, n, add(m, x)) -> rm(n, x) [1] if_rm(false, n, add(m, x)) -> add(m, rm(n, x)) [1] minsort(nil, nil) -> nil [1] minsort(add(n, x), y) -> if_minsort(eq(n, min(add(n, x))), add(n, x), y) [1] if_minsort(true, add(n, x), y) -> add(n, minsort(app(rm(n, x), y), nil)) [1]
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runti Compl Inner Rewri 22807