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Runti Compl Full Rewri 10127 pair #381902221
details
property
value
status
complete
benchmark
selsort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n054.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.472489119 seconds
cpu usage
308.038793719
max memory
5.281468416E9
stage attributes
key
value
output-size
19954
starexec-result
WORST_CASE(Omega(n^2), ?)
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^2), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF).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), 325 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), 50 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 25 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 29 ms] (18) proven lower bound (19) LowerBoundPropagationProof [FINISHED, 0 ms] (20) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: eq(0, 0) -> true eq(0, s(Y)) -> 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) min(cons(0, nil)) -> 0 min(cons(s(N), nil)) -> s(N) min(cons(N, cons(M, L))) -> ifmin(le(N, M), cons(N, cons(M, L))) ifmin(true, cons(N, cons(M, L))) -> min(cons(N, L)) ifmin(false, cons(N, cons(M, L))) -> min(cons(M, L)) replace(N, M, nil) -> nil replace(N, M, cons(K, L)) -> ifrepl(eq(N, K), N, M, cons(K, L)) ifrepl(true, N, M, cons(K, L)) -> cons(M, L) ifrepl(false, N, M, cons(K, L)) -> cons(K, replace(N, M, L)) selsort(nil) -> nil selsort(cons(N, L)) -> ifselsort(eq(N, min(cons(N, L))), cons(N, L)) ifselsort(true, cons(N, L)) -> cons(N, selsort(L)) ifselsort(false, cons(N, L)) -> cons(min(cons(N, L)), selsort(replace(min(cons(N, L)), N, L))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). The TRS R consists of the following rules: eq(0', 0') -> true eq(0', s(Y)) -> 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) min(cons(0', nil)) -> 0' min(cons(s(N), nil)) -> s(N) min(cons(N, cons(M, L))) -> ifmin(le(N, M), cons(N, cons(M, L))) ifmin(true, cons(N, cons(M, L))) -> min(cons(N, L)) ifmin(false, cons(N, cons(M, L))) -> min(cons(M, L)) replace(N, M, nil) -> nil replace(N, M, cons(K, L)) -> ifrepl(eq(N, K), N, M, cons(K, L)) ifrepl(true, N, M, cons(K, L)) -> cons(M, L) ifrepl(false, N, M, cons(K, L)) -> cons(K, replace(N, M, L)) selsort(nil) -> nil selsort(cons(N, L)) -> ifselsort(eq(N, min(cons(N, L))), cons(N, L)) ifselsort(true, cons(N, L)) -> cons(N, selsort(L))
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