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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433307821
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
n039.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.628 seconds
cpu usage
305.889
user time
304.149
system time
1.74071
max virtual memory
1.828154E7
max residence set size
5140660.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
305.75/291.59 WORST_CASE(Omega(n^2), ?) 305.75/291.60 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 305.75/291.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 305.75/291.60 305.75/291.60 305.75/291.60 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 305.75/291.60 305.75/291.60 (0) CpxTRS 305.75/291.60 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 305.75/291.60 (2) CpxTRS 305.75/291.60 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 305.75/291.60 (4) typed CpxTrs 305.75/291.60 (5) OrderProof [LOWER BOUND(ID), 0 ms] 305.75/291.60 (6) typed CpxTrs 305.75/291.60 (7) RewriteLemmaProof [LOWER BOUND(ID), 307 ms] 305.75/291.60 (8) BEST 305.75/291.60 (9) proven lower bound 305.75/291.60 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 305.75/291.60 (11) BOUNDS(n^1, INF) 305.75/291.60 (12) typed CpxTrs 305.75/291.60 (13) RewriteLemmaProof [LOWER BOUND(ID), 42 ms] 305.75/291.60 (14) typed CpxTrs 305.75/291.60 (15) RewriteLemmaProof [LOWER BOUND(ID), 19 ms] 305.75/291.60 (16) typed CpxTrs 305.75/291.60 (17) RewriteLemmaProof [LOWER BOUND(ID), 50 ms] 305.75/291.60 (18) proven lower bound 305.75/291.60 (19) LowerBoundPropagationProof [FINISHED, 0 ms] 305.75/291.60 (20) BOUNDS(n^2, INF) 305.75/291.60 305.75/291.60 305.75/291.60 ---------------------------------------- 305.75/291.60 305.75/291.60 (0) 305.75/291.60 Obligation: 305.75/291.60 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 305.75/291.60 305.75/291.60 305.75/291.60 The TRS R consists of the following rules: 305.75/291.60 305.75/291.60 eq(0, 0) -> true 305.75/291.60 eq(0, s(Y)) -> false 305.75/291.60 eq(s(X), 0) -> false 305.75/291.60 eq(s(X), s(Y)) -> eq(X, Y) 305.75/291.60 le(0, Y) -> true 305.75/291.60 le(s(X), 0) -> false 305.75/291.60 le(s(X), s(Y)) -> le(X, Y) 305.75/291.60 min(cons(0, nil)) -> 0 305.75/291.60 min(cons(s(N), nil)) -> s(N) 305.75/291.60 min(cons(N, cons(M, L))) -> ifmin(le(N, M), cons(N, cons(M, L))) 305.75/291.60 ifmin(true, cons(N, cons(M, L))) -> min(cons(N, L)) 305.75/291.60 ifmin(false, cons(N, cons(M, L))) -> min(cons(M, L)) 305.75/291.60 replace(N, M, nil) -> nil 305.75/291.60 replace(N, M, cons(K, L)) -> ifrepl(eq(N, K), N, M, cons(K, L)) 305.75/291.60 ifrepl(true, N, M, cons(K, L)) -> cons(M, L) 305.75/291.60 ifrepl(false, N, M, cons(K, L)) -> cons(K, replace(N, M, L)) 305.75/291.60 selsort(nil) -> nil 305.75/291.60 selsort(cons(N, L)) -> ifselsort(eq(N, min(cons(N, L))), cons(N, L)) 305.75/291.60 ifselsort(true, cons(N, L)) -> cons(N, selsort(L)) 305.75/291.60 ifselsort(false, cons(N, L)) -> cons(min(cons(N, L)), selsort(replace(min(cons(N, L)), N, L))) 305.75/291.60 305.75/291.60 S is empty. 305.75/291.60 Rewrite Strategy: FULL 305.75/291.60 ---------------------------------------- 305.75/291.60 305.75/291.60 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 305.75/291.60 Renamed function symbols to avoid clashes with predefined symbol. 305.75/291.60 ---------------------------------------- 305.75/291.60 305.75/291.60 (2) 305.75/291.60 Obligation: 305.75/291.60 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 305.75/291.60 305.75/291.60 305.75/291.60 The TRS R consists of the following rules: 305.75/291.60 305.75/291.60 eq(0', 0') -> true 305.75/291.60 eq(0', s(Y)) -> false 305.75/291.60 eq(s(X), 0') -> false 305.75/291.60 eq(s(X), s(Y)) -> eq(X, Y) 305.75/291.60 le(0', Y) -> true 305.75/291.60 le(s(X), 0') -> false 305.75/291.60 le(s(X), s(Y)) -> le(X, Y) 305.75/291.60 min(cons(0', nil)) -> 0' 305.75/291.60 min(cons(s(N), nil)) -> s(N) 305.75/291.60 min(cons(N, cons(M, L))) -> ifmin(le(N, M), cons(N, cons(M, L))) 305.75/291.60 ifmin(true, cons(N, cons(M, L))) -> min(cons(N, L)) 305.75/291.60 ifmin(false, cons(N, cons(M, L))) -> min(cons(M, L)) 305.75/291.60 replace(N, M, nil) -> nil 305.75/291.60 replace(N, M, cons(K, L)) -> ifrepl(eq(N, K), N, M, cons(K, L)) 305.75/291.60 ifrepl(true, N, M, cons(K, L)) -> cons(M, L) 305.75/291.60 ifrepl(false, N, M, cons(K, L)) -> cons(K, replace(N, M, L)) 305.75/291.60 selsort(nil) -> nil 305.75/291.60 selsort(cons(N, L)) -> ifselsort(eq(N, min(cons(N, L))), cons(N, L)) 305.75/291.60 ifselsort(true, cons(N, L)) -> cons(N, selsort(L)) 305.75/291.60 ifselsort(false, cons(N, L)) -> cons(min(cons(N, L)), selsort(replace(min(cons(N, L)), N, L))) 305.75/291.60 305.75/291.60 S is empty. 305.75/291.60 Rewrite Strategy: FULL 305.75/291.60 ---------------------------------------- 305.75/291.60
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