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Runti Compl Inner Rewri 22807 pair #381904274
details
property
value
status
complete
benchmark
20.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n046.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
19.4622349739 seconds
cpu usage
71.118706516
max memory
5.151686656E9
stage attributes
key
value
output-size
26220
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 4 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 579 ms] (10) BOUNDS(1, n^1) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 0 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 274 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 78 ms] (24) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: cond1(true, x, y) -> cond2(gr(y, 0), x, y) cond2(true, x, y) -> cond2(gr(y, 0), p(x), p(y)) cond2(false, x, y) -> cond1(and(eq(x, y), gr(x, 0)), x, y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) p(0) -> 0 p(s(x)) -> x eq(0, 0) -> true eq(s(x), 0) -> false eq(0, s(x)) -> false eq(s(x), s(y)) -> eq(x, y) and(true, true) -> true and(false, x) -> false and(x, false) -> false 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^1). The TRS R consists of the following rules: cond1(true, x, y) -> cond2(gr(y, 0), x, y) [1] cond2(true, x, y) -> cond2(gr(y, 0), p(x), p(y)) [1] cond2(false, x, y) -> cond1(and(eq(x, y), gr(x, 0)), x, y) [1] gr(0, x) -> false [1] gr(s(x), 0) -> true [1] gr(s(x), s(y)) -> gr(x, y) [1] p(0) -> 0 [1] p(s(x)) -> x [1] eq(0, 0) -> true [1] eq(s(x), 0) -> false [1] eq(0, s(x)) -> false [1] eq(s(x), s(y)) -> eq(x, y) [1] and(true, true) -> true [1] and(false, x) -> false [1] and(x, false) -> false [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID))
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