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Derivational Complexity: TRS Innermost pair #487109466
details
property
value
status
complete
benchmark
thiemann40_modified.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n146.star.cs.uiowa.edu
space
AProVE_08
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
292.975 seconds
cpu usage
1152.16
user time
1140.36
system time
11.8
max virtual memory
3.8365524E7
max residence set size
1.5237976E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), O(n^3))
output
WORST_CASE(Omega(n^2), O(n^3)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^2, n^3). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 251 ms] (4) CpxRelTRS (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) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 193.4 s] (14) BOUNDS(1, n^3) (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRelTRS (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (18) typed CpxTrs (19) OrderProof [LOWER BOUND(ID), 5 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 261 ms] (22) BEST (23) proven lower bound (24) LowerBoundPropagationProof [FINISHED, 0 ms] (25) BOUNDS(n^1, INF) (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 104 ms] (28) BEST (29) proven lower bound (30) LowerBoundPropagationProof [FINISHED, 0 ms] (31) BOUNDS(n^2, INF) (32) typed CpxTrs (33) RewriteLemmaProof [LOWER BOUND(ID), 479 ms] (34) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^2, n^3). The TRS R consists of the following rules: nonZero(0) -> false nonZero(s(x)) -> true p(s(0)) -> 0 p(s(s(x))) -> s(p(s(x))) id_inc(x) -> x id_inc(x) -> s(x) random(x) -> rand(x, 0) rand(x, y) -> if(nonZero(x), x, y) if(false, x, y) -> y if(true, x, y) -> rand(p(x), id_inc(y)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(0) -> 0 encArg(false) -> false encArg(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(cons_nonZero(x_1)) -> nonZero(encArg(x_1)) encArg(cons_p(x_1)) -> p(encArg(x_1)) encArg(cons_id_inc(x_1)) -> id_inc(encArg(x_1)) encArg(cons_random(x_1)) -> random(encArg(x_1)) encArg(cons_rand(x_1, x_2)) -> rand(encArg(x_1), encArg(x_2)) encArg(cons_if(x_1, x_2, x_3)) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) encode_nonZero(x_1) -> nonZero(encArg(x_1)) encode_0 -> 0 encode_false -> false encode_s(x_1) -> s(encArg(x_1)) encode_true -> true encode_p(x_1) -> p(encArg(x_1)) encode_id_inc(x_1) -> id_inc(encArg(x_1)) encode_random(x_1) -> random(encArg(x_1)) encode_rand(x_1, x_2) -> rand(encArg(x_1), encArg(x_2)) encode_if(x_1, x_2, x_3) -> if(encArg(x_1), encArg(x_2), encArg(x_3)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^2, n^3).
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