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Runti Compl Inner Rewri 22807 pair #381904530
details
property
value
status
complete
benchmark
member.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n049.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.09190201759 seconds
cpu usage
17.156409979
max memory
4.059058176E9
stage attributes
key
value
output-size
23292
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxRelTRS (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 170 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) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) CompleteCoflocoProof [FINISHED, 323 ms] (12) BOUNDS(1, n^1) (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRelTRS (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (16) typed CpxTrs (17) OrderProof [LOWER BOUND(ID), 0 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 290 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 12 ms] (22) proven lower bound (23) LowerBoundPropagationProof [FINISHED, 0 ms] (24) BOUNDS(n^1, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: member(x', Cons(x, xs)) -> member[Ite][True][Ite](!EQ(x', x), x', Cons(x, xs)) member(x, Nil) -> False notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False goal(x, xs) -> member(x, xs) The (relative) TRS S consists of the following rules: !EQ(S(x), S(y)) -> !EQ(x, y) !EQ(0, S(y)) -> False !EQ(S(x), 0) -> False !EQ(0, 0) -> True member[Ite][True][Ite](False, x', Cons(x, xs)) -> member(x', xs) member[Ite][True][Ite](True, x, xs) -> True Rewrite Strategy: INNERMOST ---------------------------------------- (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved termination of relative rules ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: member(x', Cons(x, xs)) -> member[Ite][True][Ite](!EQ(x', x), x', Cons(x, xs)) member(x, Nil) -> False notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False goal(x, xs) -> member(x, xs) The (relative) TRS S consists of the following rules: !EQ(S(x), S(y)) -> !EQ(x, y) !EQ(0, S(y)) -> False !EQ(S(x), 0) -> False !EQ(0, 0) -> True member[Ite][True][Ite](False, x', Cons(x, xs)) -> member(x', xs) member[Ite][True][Ite](True, x, xs) -> True Rewrite Strategy: INNERMOST ---------------------------------------- (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ----------------------------------------
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