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Runti Compl Full Rewri 10127 pair #381902184
details
property
value
status
complete
benchmark
14.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n073.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.257467985 seconds
cpu usage
623.165022528
max memory
6.916673536E9
stage attributes
key
value
output-size
74253
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 25 ms] (2) CpxTRS (3) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms] (4) CpxRelTRS (5) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) CpxTrsToCdtProof [UPPER BOUND(ID), 5 ms] (8) CdtProblem (9) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (10) CdtProblem (11) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CdtProblem (13) CdtGraphSplitRhsProof [BOTH BOUNDS(ID, ID), 1 ms] (14) CdtProblem (15) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (16) CdtProblem (17) CdtKnowledgeProof [BOTH BOUNDS(ID, ID), 0 ms] (18) CdtProblem (19) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (20) CdtProblem (21) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 136 ms] (22) CdtProblem (23) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 71 ms] (24) CdtProblem (25) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 65 ms] (26) CdtProblem (27) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 50 ms] (28) CdtProblem (29) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 384 ms] (30) CdtProblem (31) CdtRuleRemovalProof [UPPER BOUND(ADD(n^2)), 338 ms] (32) CdtProblem (33) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (34) BOUNDS(1, 1) (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 (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: O(0) -> 0 +(0, x) -> x +(x, 0) -> x +(O(x), O(y)) -> O(+(x, y)) +(O(x), I(y)) -> I(+(x, y)) +(I(x), O(y)) -> I(+(x, y)) +(I(x), I(y)) -> O(+(+(x, y), I(0))) +(x, +(y, z)) -> +(+(x, y), z) -(x, 0) -> x -(0, x) -> 0 -(O(x), O(y)) -> O(-(x, y)) -(O(x), I(y)) -> I(-(-(x, y), I(1))) -(I(x), O(y)) -> I(-(x, y)) -(I(x), I(y)) -> O(-(x, y)) not(true) -> false not(false) -> true and(x, true) -> x and(x, false) -> false if(true, x, y) -> x if(false, x, y) -> y ge(O(x), O(y)) -> ge(x, y) ge(O(x), I(y)) -> not(ge(y, x)) ge(I(x), O(y)) -> ge(x, y) ge(I(x), I(y)) -> ge(x, y) ge(x, 0) -> true ge(0, O(x)) -> ge(0, x) ge(0, I(x)) -> false Log'(0) -> 0 Log'(I(x)) -> +(Log'(x), I(0)) Log'(O(x)) -> if(ge(x, I(0)), +(Log'(x), I(0)), 0) Log(x) -> -(Log'(x), I(0)) Val(L(x)) -> x Val(N(x, l, r)) -> x
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