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Runti Compl Inner Rewri 22807 pair #381904778
details
property
value
status
complete
benchmark
24.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n057.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
19.1314558983 seconds
cpu usage
72.680029776
max memory
4.803108864E9
stage attributes
key
value
output-size
56445
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 4 ms] (10) CpxRNTS (11) InliningProof [UPPER BOUND(ID), 373 ms] (12) CpxRNTS (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRNTS (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] (16) CpxRNTS (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (18) CpxRNTS (19) IntTrsBoundProof [UPPER BOUND(ID), 219 ms] (20) CpxRNTS (21) IntTrsBoundProof [UPPER BOUND(ID), 66 ms] (22) CpxRNTS (23) ResultPropagationProof [UPPER BOUND(ID), 1 ms] (24) CpxRNTS (25) IntTrsBoundProof [UPPER BOUND(ID), 140 ms] (26) CpxRNTS (27) IntTrsBoundProof [UPPER BOUND(ID), 34 ms] (28) CpxRNTS (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (30) CpxRNTS (31) IntTrsBoundProof [UPPER BOUND(ID), 293 ms] (32) CpxRNTS (33) IntTrsBoundProof [UPPER BOUND(ID), 145 ms] (34) CpxRNTS (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms] (36) CpxRNTS (37) IntTrsBoundProof [UPPER BOUND(ID), 3513 ms] (38) CpxRNTS (39) IntTrsBoundProof [UPPER BOUND(ID), 1535 ms] (40) CpxRNTS (41) FinalProof [FINISHED, 0 ms] (42) BOUNDS(1, n^1) (43) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (44) TRS for Loop Detection (45) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (46) BEST (47) proven lower bound (48) LowerBoundPropagationProof [FINISHED, 0 ms] (49) BOUNDS(n^1, INF) (50) TRS for Loop Detection ---------------------------------------- (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(x, y), x, y) cond2(true, x, y) -> cond3(gr(x, 0), x, y) cond2(false, x, y) -> cond4(gr(y, 0), x, y) cond3(true, x, y) -> cond3(gr(x, 0), p(x), y) cond3(false, x, y) -> cond1(and(gr(x, 0), gr(y, 0)), x, y) cond4(true, x, y) -> cond4(gr(y, 0), x, p(y)) cond4(false, x, y) -> cond1(and(gr(x, 0), gr(y, 0)), x, y) gr(0, x) -> false gr(s(x), 0) -> true gr(s(x), s(y)) -> gr(x, y) and(true, true) -> true and(false, x) -> false and(x, false) -> false p(0) -> 0 p(s(x)) -> x S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2)
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