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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313552
details
property
value
status
complete
benchmark
#4.36.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n139.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.871 seconds
cpu usage
1111.45
user time
1104.09
system time
7.35134
max virtual memory
3.7656672E7
max residence set size
7578636.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^3))
output
1110.10/291.55 WORST_CASE(Omega(n^2), O(n^3)) 1111.03/291.75 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1111.03/291.75 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1111.03/291.75 1111.03/291.75 1111.03/291.75 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^3). 1111.03/291.75 1111.03/291.75 (0) CpxTRS 1111.03/291.75 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1111.03/291.75 (2) CpxWeightedTrs 1111.03/291.75 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1111.03/291.75 (4) CpxTypedWeightedTrs 1111.03/291.75 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1111.03/291.75 (6) CpxTypedWeightedCompleteTrs 1111.03/291.75 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 1111.03/291.75 (8) CpxTypedWeightedCompleteTrs 1111.03/291.75 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 3 ms] 1111.03/291.75 (10) CpxRNTS 1111.03/291.75 (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 1111.03/291.75 (12) CpxRNTS 1111.03/291.75 (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 1111.03/291.75 (14) CpxRNTS 1111.03/291.75 (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1111.03/291.75 (16) CpxRNTS 1111.03/291.75 (17) IntTrsBoundProof [UPPER BOUND(ID), 342 ms] 1111.03/291.75 (18) CpxRNTS 1111.03/291.75 (19) IntTrsBoundProof [UPPER BOUND(ID), 168 ms] 1111.03/291.75 (20) CpxRNTS 1111.03/291.75 (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1111.03/291.75 (22) CpxRNTS 1111.03/291.75 (23) IntTrsBoundProof [UPPER BOUND(ID), 383 ms] 1111.03/291.75 (24) CpxRNTS 1111.03/291.75 (25) IntTrsBoundProof [UPPER BOUND(ID), 137 ms] 1111.03/291.75 (26) CpxRNTS 1111.03/291.75 (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1111.03/291.75 (28) CpxRNTS 1111.03/291.75 (29) IntTrsBoundProof [UPPER BOUND(ID), 1155 ms] 1111.03/291.75 (30) CpxRNTS 1111.03/291.75 (31) IntTrsBoundProof [UPPER BOUND(ID), 374 ms] 1111.03/291.75 (32) CpxRNTS 1111.03/291.75 (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1111.03/291.75 (34) CpxRNTS 1111.03/291.75 (35) IntTrsBoundProof [UPPER BOUND(ID), 1888 ms] 1111.03/291.75 (36) CpxRNTS 1111.03/291.75 (37) IntTrsBoundProof [UPPER BOUND(ID), 622 ms] 1111.03/291.75 (38) CpxRNTS 1111.03/291.75 (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1111.03/291.75 (40) CpxRNTS 1111.03/291.75 (41) IntTrsBoundProof [UPPER BOUND(ID), 784 ms] 1111.03/291.75 (42) CpxRNTS 1111.03/291.75 (43) IntTrsBoundProof [UPPER BOUND(ID), 165 ms] 1111.03/291.75 (44) CpxRNTS 1111.03/291.75 (45) FinalProof [FINISHED, 0 ms] 1111.03/291.75 (46) BOUNDS(1, n^3) 1111.03/291.75 (47) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1111.03/291.75 (48) CpxTRS 1111.03/291.75 (49) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1111.03/291.75 (50) typed CpxTrs 1111.03/291.75 (51) OrderProof [LOWER BOUND(ID), 4 ms] 1111.03/291.75 (52) typed CpxTrs 1111.03/291.75 (53) RewriteLemmaProof [LOWER BOUND(ID), 272 ms] 1111.03/291.75 (54) BEST 1111.03/291.75 (55) proven lower bound 1111.03/291.75 (56) LowerBoundPropagationProof [FINISHED, 0 ms] 1111.03/291.75 (57) BOUNDS(n^1, INF) 1111.03/291.75 (58) typed CpxTrs 1111.03/291.75 (59) RewriteLemmaProof [LOWER BOUND(ID), 52 ms] 1111.03/291.75 (60) typed CpxTrs 1111.03/291.75 (61) RewriteLemmaProof [LOWER BOUND(ID), 39 ms] 1111.03/291.75 (62) typed CpxTrs 1111.03/291.75 (63) RewriteLemmaProof [LOWER BOUND(ID), 976 ms] 1111.03/291.75 (64) proven lower bound 1111.03/291.75 (65) LowerBoundPropagationProof [FINISHED, 0 ms] 1111.03/291.75 (66) BOUNDS(n^2, INF) 1111.03/291.75 1111.03/291.75 1111.03/291.75 ---------------------------------------- 1111.03/291.75 1111.03/291.75 (0) 1111.03/291.75 Obligation: 1111.03/291.75 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, n^3). 1111.03/291.75 1111.03/291.75 1111.03/291.75 The TRS R consists of the following rules: 1111.03/291.75 1111.03/291.75 eq(0, 0) -> true 1111.03/291.75 eq(0, s(m)) -> false 1111.03/291.75 eq(s(n), 0) -> false 1111.03/291.75 eq(s(n), s(m)) -> eq(n, m) 1111.03/291.75 le(0, m) -> true 1111.03/291.75 le(s(n), 0) -> false 1111.03/291.75 le(s(n), s(m)) -> le(n, m) 1111.03/291.75 min(cons(0, nil)) -> 0 1111.03/291.75 min(cons(s(n), nil)) -> s(n) 1111.03/291.75 min(cons(n, cons(m, x))) -> if_min(le(n, m), cons(n, cons(m, x))) 1111.03/291.75 if_min(true, cons(n, cons(m, x))) -> min(cons(n, x)) 1111.03/291.75 if_min(false, cons(n, cons(m, x))) -> min(cons(m, x)) 1111.03/291.75 replace(n, m, nil) -> nil 1111.03/291.75 replace(n, m, cons(k, x)) -> if_replace(eq(n, k), n, m, cons(k, x)) 1111.03/291.75 if_replace(true, n, m, cons(k, x)) -> cons(m, x)
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