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Runti Compl Inner Rewri 22807 pair #381904573
details
property
value
status
complete
benchmark
mappplus.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n026.star.cs.uiowa.edu
space
hoca
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.440716982 seconds
cpu usage
321.714856331
max memory
6.407487488E9
stage attributes
key
value
output-size
19299
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
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^2)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (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), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxRNTS (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRNTS (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (16) CpxRNTS (17) IntTrsBoundProof [UPPER BOUND(ID), 318 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 85 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 294 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 106 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 779 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 0 ms] (32) CpxRNTS (33) FinalProof [FINISHED, 0 ms] (34) BOUNDS(1, n^2) (35) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (36) TRS for Loop Detection (37) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (38) BEST (39) proven lower bound (40) LowerBoundPropagationProof [FINISHED, 0 ms] (41) BOUNDS(n^1, INF) (42) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: plus_x#1(0, x8) -> x8 plus_x#1(S(x12), x14) -> S(plus_x#1(x12, x14)) map#2(plus_x(x2), Nil) -> Nil map#2(plus_x(x6), Cons(x4, x2)) -> Cons(plus_x#1(x6, x4), map#2(plus_x(x6), x2)) main(x5, x12) -> map#2(plus_x(x12), x5) 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^2). The TRS R consists of the following rules: plus_x#1(0, x8) -> x8 [1] plus_x#1(S(x12), x14) -> S(plus_x#1(x12, x14)) [1] map#2(plus_x(x2), Nil) -> Nil [1] map#2(plus_x(x6), Cons(x4, x2)) -> Cons(plus_x#1(x6, x4), map#2(plus_x(x6), x2)) [1] main(x5, x12) -> map#2(plus_x(x12), x5) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ----------------------------------------
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