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Runti Compl Inner Rewri 22807 pair #381904982
details
property
value
status
complete
benchmark
thiemann11.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n070.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.541990042 seconds
cpu usage
1131.98473627
max memory
1.570527232E10
stage attributes
key
value
output-size
51271
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
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^2)) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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), 259 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 67 ms] (20) CpxRNTS (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (22) CpxRNTS (23) IntTrsBoundProof [UPPER BOUND(ID), 384 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 105 ms] (26) CpxRNTS (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (28) CpxRNTS (29) IntTrsBoundProof [UPPER BOUND(ID), 331 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 116 ms] (32) CpxRNTS (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (34) CpxRNTS (35) IntTrsBoundProof [UPPER BOUND(ID), 107 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 53 ms] (38) CpxRNTS (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (40) CpxRNTS (41) IntTrsBoundProof [UPPER BOUND(ID), 3962 ms] (42) CpxRNTS (43) IntTrsBoundProof [UPPER BOUND(ID), 1264 ms] (44) CpxRNTS (45) FinalProof [FINISHED, 0 ms] (46) BOUNDS(1, n^2) (47) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (48) TRS for Loop Detection (49) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (50) BEST (51) proven lower bound (52) LowerBoundPropagationProof [FINISHED, 0 ms] (53) BOUNDS(n^1, INF) (54) 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: le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) zero(0) -> true zero(s(x)) -> false id(0) -> 0 id(s(x)) -> s(id(x)) minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) mod(x, y) -> if_mod(zero(x), zero(y), le(y, x), id(x), id(y)) if_mod(true, b1, b2, x, y) -> 0 if_mod(false, b1, b2, x, y) -> if2(b1, b2, x, y) if2(true, b2, x, y) -> 0 if2(false, b2, x, y) -> if3(b2, x, y) if3(true, x, y) -> mod(minus(x, y), s(y)) if3(false, x, y) -> x S is empty. Rewrite Strategy: INNERMOST ----------------------------------------
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