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Derivational Complexity: TRS Innermost pair #487109420
details
property
value
status
complete
benchmark
cade17.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
GTSSK07
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
292.284 seconds
cpu usage
1128.38
user time
1115.7
system time
12.6822
max virtual memory
3.7716252E7
max residence set size
1.5033812E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 303 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 1 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 520 ms] (12) BEST (13) proven lower bound (14) LowerBoundPropagationProof [FINISHED, 0 ms] (15) BOUNDS(n^1, INF) (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 58 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 105 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 764 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 346 ms] (24) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: log(x, s(s(y))) -> cond(le(x, s(s(y))), x, y) cond(true, x, y) -> s(0) cond(false, x, y) -> double(log(x, square(s(s(y))))) le(0, v) -> true le(s(u), 0) -> false le(s(u), s(v)) -> le(u, v) double(0) -> 0 double(s(x)) -> s(s(double(x))) square(0) -> 0 square(s(x)) -> s(plus(square(x), double(x))) plus(n, 0) -> n plus(n, s(m)) -> s(plus(n, m)) 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(s(x_1)) -> s(encArg(x_1)) encArg(true) -> true encArg(0) -> 0 encArg(false) -> false encArg(cons_log(x_1, x_2)) -> log(encArg(x_1), encArg(x_2)) encArg(cons_cond(x_1, x_2, x_3)) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encArg(cons_le(x_1, x_2)) -> le(encArg(x_1), encArg(x_2)) encArg(cons_double(x_1)) -> double(encArg(x_1)) encArg(cons_square(x_1)) -> square(encArg(x_1)) encArg(cons_plus(x_1, x_2)) -> plus(encArg(x_1), encArg(x_2)) encode_log(x_1, x_2) -> log(encArg(x_1), encArg(x_2)) encode_s(x_1) -> s(encArg(x_1)) encode_cond(x_1, x_2, x_3) -> cond(encArg(x_1), encArg(x_2), encArg(x_3)) encode_le(x_1, x_2) -> le(encArg(x_1), encArg(x_2)) encode_true -> true encode_0 -> 0 encode_false -> false encode_double(x_1) -> double(encArg(x_1)) encode_square(x_1) -> square(encArg(x_1)) encode_plus(x_1, x_2) -> plus(encArg(x_1), encArg(x_2)) ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: log(x, s(s(y))) -> cond(le(x, s(s(y))), x, y) cond(true, x, y) -> s(0) cond(false, x, y) -> double(log(x, square(s(s(y))))) le(0, v) -> true le(s(u), 0) -> false le(s(u), s(v)) -> le(u, v)
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return to Derivational Complexity: TRS Innermost