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Runtime Complexity: TRS Innermost pair #487112092
details
property
value
status
complete
benchmark
10.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.518 seconds
cpu usage
471.524
user time
467.783
system time
3.74077
max virtual memory
3.8380004E7
max residence set size
5563516.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 2 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxRNTS (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRNTS (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (16) CpxRNTS (17) IntTrsBoundProof [UPPER BOUND(ID), 335 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 100 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 70 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 52 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 246 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 84 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 279 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 84 ms] (38) CpxRNTS (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 1752 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 2137 ms] (44) CpxRNTS (45) FinalProof [FINISHED, 0 ms] (46) BOUNDS(1, n^2) (47) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (48) TRS for Loop Detection (49) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (50) BEST (51) proven lower bound (52) LowerBoundPropagationProof [FINISHED, 0 ms] (53) BOUNDS(n^1, INF) (54) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: cond1(true, x) -> cond2(even(x), x) cond2(true, x) -> cond1(neq(x, 0), div2(x)) cond2(false, x) -> cond1(neq(x, 0), p(x)) neq(0, 0) -> false neq(0, s(x)) -> true neq(s(x), 0) -> true neq(s(x), s(y)) -> neq(x, y) even(0) -> true even(s(0)) -> false even(s(s(x))) -> even(x) div2(0) -> 0 div2(s(0)) -> 0 div2(s(s(x))) -> s(div2(x)) p(0) -> 0 p(s(x)) -> x S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2).
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