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Runtime Complexity: TRS Innermost pair #487112908
details
property
value
status
complete
benchmark
polo2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n151.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.68764 seconds
cpu usage
15.3399
user time
14.2962
system time
1.04365
max virtual memory
1.913904E7
max residence set size
3059608.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 10 ms] (2) CdtProblem (3) CdtLeafRemovalProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CdtProblem (5) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 65 ms] (8) CdtProblem (9) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (10) BOUNDS(1, 1) (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (12) CpxTRS (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (14) typed CpxTrs (15) OrderProof [LOWER BOUND(ID), 0 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 1095 ms] (18) proven lower bound (19) LowerBoundPropagationProof [FINISHED, 0 ms] (20) BOUNDS(n^1, INF) ---------------------------------------- (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: dx(X) -> one dx(a) -> zero dx(plus(ALPHA, BETA)) -> plus(dx(ALPHA), dx(BETA)) dx(times(ALPHA, BETA)) -> plus(times(BETA, dx(ALPHA)), times(ALPHA, dx(BETA))) dx(minus(ALPHA, BETA)) -> minus(dx(ALPHA), dx(BETA)) dx(neg(ALPHA)) -> neg(dx(ALPHA)) dx(div(ALPHA, BETA)) -> minus(div(dx(ALPHA), BETA), times(ALPHA, div(dx(BETA), exp(BETA, two)))) dx(ln(ALPHA)) -> div(dx(ALPHA), ALPHA) dx(exp(ALPHA, BETA)) -> plus(times(BETA, times(exp(ALPHA, minus(BETA, one)), dx(ALPHA))), times(exp(ALPHA, BETA), times(ln(ALPHA), dx(BETA)))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: dx(z0) -> one dx(a) -> zero dx(plus(z0, z1)) -> plus(dx(z0), dx(z1)) dx(times(z0, z1)) -> plus(times(z1, dx(z0)), times(z0, dx(z1))) dx(minus(z0, z1)) -> minus(dx(z0), dx(z1)) dx(neg(z0)) -> neg(dx(z0)) dx(div(z0, z1)) -> minus(div(dx(z0), z1), times(z0, div(dx(z1), exp(z1, two)))) dx(ln(z0)) -> div(dx(z0), z0) dx(exp(z0, z1)) -> plus(times(z1, times(exp(z0, minus(z1, one)), dx(z0))), times(exp(z0, z1), times(ln(z0), dx(z1)))) Tuples: DX(z0) -> c DX(a) -> c1 DX(plus(z0, z1)) -> c2(DX(z0), DX(z1)) DX(times(z0, z1)) -> c3(DX(z0), DX(z1)) DX(minus(z0, z1)) -> c4(DX(z0), DX(z1)) DX(neg(z0)) -> c5(DX(z0)) DX(div(z0, z1)) -> c6(DX(z0), DX(z1)) DX(ln(z0)) -> c7(DX(z0)) DX(exp(z0, z1)) -> c8(DX(z0), DX(z1)) S tuples: DX(z0) -> c DX(a) -> c1 DX(plus(z0, z1)) -> c2(DX(z0), DX(z1)) DX(times(z0, z1)) -> c3(DX(z0), DX(z1)) DX(minus(z0, z1)) -> c4(DX(z0), DX(z1)) DX(neg(z0)) -> c5(DX(z0)) DX(div(z0, z1)) -> c6(DX(z0), DX(z1)) DX(ln(z0)) -> c7(DX(z0)) DX(exp(z0, z1)) -> c8(DX(z0), DX(z1)) K tuples:none Defined Rule Symbols: dx_1 Defined Pair Symbols: DX_1 Compound Symbols: c, c1, c2_2, c3_2, c4_2, c5_1, c6_2, c7_1, c8_2 ----------------------------------------
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