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Runtime Complexity: TRS pair #487111360
details
property
value
status
complete
benchmark
#3.22.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n137.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
6.14308 seconds
cpu usage
18.3046
user time
17.1455
system time
1.15908
max virtual memory
1.934246E7
max residence set size
3580080.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^2))
output
WORST_CASE(Omega(n^2), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTypedWeightedCompleteTrs (13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (14) CpxRNTS (15) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CpxRNTS (19) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 247 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 95 ms] (24) CpxRNTS (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 421 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 154 ms] (30) CpxRNTS (31) FinalProof [FINISHED, 0 ms] (32) BOUNDS(1, n^2) (33) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (34) CpxTRS (35) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (36) typed CpxTrs (37) OrderProof [LOWER BOUND(ID), 0 ms] (38) typed CpxTrs (39) RewriteLemmaProof [LOWER BOUND(ID), 257 ms] (40) BEST (41) proven lower bound (42) LowerBoundPropagationProof [FINISHED, 0 ms] (43) BOUNDS(n^1, INF) (44) typed CpxTrs (45) RewriteLemmaProof [LOWER BOUND(ID), 63 ms] (46) proven lower bound (47) LowerBoundPropagationProof [FINISHED, 0 ms] (48) BOUNDS(n^2, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^2, n^2). The TRS R consists of the following rules: times(x, plus(y, s(z))) -> plus(times(x, plus(y, times(s(z), 0))), times(x, s(z))) times(x, 0) -> 0 times(x, s(y)) -> plus(times(x, y), x) plus(x, 0) -> x plus(x, s(y)) -> s(plus(x, y)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The following defined symbols can occur below the 0th argument of plus: plus, times Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: times(x, plus(y, s(z))) -> plus(times(x, plus(y, times(s(z), 0))), times(x, s(z))) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: times(x, 0) -> 0 times(x, s(y)) -> plus(times(x, y), x) plus(x, 0) -> x plus(x, s(y)) -> s(plus(x, y)) S is empty. Rewrite Strategy: FULL ----------------------------------------
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