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Runti Compl Inner Rewri 22807 pair #381904171
details
property
value
status
complete
benchmark
thetrickSize.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n054.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
6.2581679821 seconds
cpu usage
21.234464439
max memory
3.820937216E9
stage attributes
key
value
output-size
39819
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxRelTRS (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 161 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, 529 ms] (12) BOUNDS(1, n^1) (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRelTRS (15) SlicingProof [LOWER BOUND(ID), 0 ms] (16) CpxRelTRS (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (18) typed CpxTrs (19) OrderProof [LOWER BOUND(ID), 0 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 278 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), 76 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 57 ms] (30) BOUNDS(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: lt0(Nil, Cons(x', xs)) -> True lt0(Cons(x', xs'), Cons(x, xs)) -> lt0(xs', xs) g(x, Nil) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))) f(x, Nil) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))) notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False lt0(x, Nil) -> False g(x, Cons(x', xs)) -> g[Ite][False][Ite](lt0(x, Cons(Nil, Nil)), x, Cons(x', xs)) f(x, Cons(x', xs)) -> f[Ite][False][Ite](lt0(x, Cons(Nil, Nil)), x, Cons(x', xs)) number4(n) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))) goal(x, y) -> Cons(f(x, y), Cons(g(x, y), Nil)) The (relative) TRS S consists of the following rules: g[Ite][False][Ite](False, Cons(x, xs), y) -> g(xs, Cons(Cons(Nil, Nil), y)) g[Ite][False][Ite](True, x', Cons(x, xs)) -> g(x', xs) f[Ite][False][Ite](False, Cons(x, xs), y) -> f(xs, Cons(Cons(Nil, Nil), y)) f[Ite][False][Ite](True, x', Cons(x, xs)) -> f(x', xs) 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: lt0(Nil, Cons(x', xs)) -> True lt0(Cons(x', xs'), Cons(x, xs)) -> lt0(xs', xs) g(x, Nil) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))) f(x, Nil) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))) notEmpty(Cons(x, xs)) -> True notEmpty(Nil) -> False lt0(x, Nil) -> False g(x, Cons(x', xs)) -> g[Ite][False][Ite](lt0(x, Cons(Nil, Nil)), x, Cons(x', xs)) f(x, Cons(x', xs)) -> f[Ite][False][Ite](lt0(x, Cons(Nil, Nil)), x, Cons(x', xs)) number4(n) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))) goal(x, y) -> Cons(f(x, y), Cons(g(x, y), Nil))
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