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Runtime Complexity: TRS Innermost pair #487111894
details
property
value
status
complete
benchmark
strmatch.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.638 seconds
cpu usage
565.221
user time
558.947
system time
6.2737
max virtual memory
3.871698E7
max residence set size
8014676.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
WORST_CASE(Omega(n^1), O(n^2)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 311 ms] (2) CpxRelTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTypedWeightedTrs (7) CompletionProof [UPPER BOUND(ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (12) CpxRNTS (13) InliningProof [UPPER BOUND(ID), 1505 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), 52 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (24) CpxRNTS (25) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 350 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 55 ms] (30) CpxRNTS (31) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 171 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 64 ms] (36) CpxRNTS (37) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 2747 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 1097 ms] (42) CpxRNTS (43) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (44) CpxRNTS (45) IntTrsBoundProof [UPPER BOUND(ID), 881 ms] (46) CpxRNTS (47) IntTrsBoundProof [UPPER BOUND(ID), 810 ms] (48) CpxRNTS (49) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (50) CpxRNTS (51) IntTrsBoundProof [UPPER BOUND(ID), 3344 ms] (52) CpxRNTS (53) IntTrsBoundProof [UPPER BOUND(ID), 823 ms] (54) CpxRNTS (55) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (56) CpxRNTS (57) IntTrsBoundProof [UPPER BOUND(ID), 668 ms] (58) CpxRNTS (59) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (60) CpxRNTS (61) FinalProof [FINISHED, 0 ms] (62) BOUNDS(1, n^2) (63) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (64) TRS for Loop Detection (65) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (66) BEST (67) proven lower bound (68) LowerBoundPropagationProof [FINISHED, 0 ms] (69) BOUNDS(n^1, INF) (70) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: prefix(Cons(x', xs'), Cons(x, xs)) -> and(!EQ(x', x), prefix(xs', xs)) domatch(Cons(x, xs), Nil, n) -> Nil domatch(Nil, Nil, n) -> Cons(n, Nil) prefix(Cons(x, xs), Nil) -> False prefix(Nil, cs) -> True domatch(patcs, Cons(x, xs), n) -> domatch[Ite](prefix(patcs, Cons(x, xs)), patcs, Cons(x, xs), n) eqNatList(Cons(x, xs), Cons(y, ys)) -> eqNatList[Ite](!EQ(x, y), y, ys, x, xs) eqNatList(Cons(x, xs), Nil) -> False eqNatList(Nil, Cons(y, ys)) -> False eqNatList(Nil, Nil) -> True notEmpty(Cons(x, xs)) -> True
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