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Runti Compl Inner Rewri 22807 pair #381904798
details
property
value
status
complete
benchmark
2.29.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n045.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
4.8120470047 seconds
cpu usage
16.088446063
max memory
3.849678848E9
stage attributes
key
value
output-size
8767
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
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^1)) 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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) CpxTrsToCdtProof [UPPER BOUND(ID), 0 ms] (2) CdtProblem (3) CdtLeafRemovalProof [ComplexityIfPolyImplication, 0 ms] (4) CdtProblem (5) CdtRhsSimplificationProcessorProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CdtProblem (7) CdtUsableRulesProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CdtProblem (9) CdtRuleRemovalProof [UPPER BOUND(ADD(n^1)), 18 ms] (10) CdtProblem (11) SIsEmptyProof [BOTH BOUNDS(ID, ID), 0 ms] (12) BOUNDS(1, 1) (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (16) BEST (17) proven lower bound (18) LowerBoundPropagationProof [FINISHED, 0 ms] (19) BOUNDS(n^1, INF) (20) 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: prime(0) -> false prime(s(0)) -> false prime(s(s(x))) -> prime1(s(s(x)), s(x)) prime1(x, 0) -> false prime1(x, s(0)) -> true prime1(x, s(s(y))) -> and(not(divp(s(s(y)), x)), prime1(x, s(y))) divp(x, y) -> =(rem(x, y), 0) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) CpxTrsToCdtProof (UPPER BOUND(ID)) Converted Cpx (relative) TRS to CDT ---------------------------------------- (2) Obligation: Complexity Dependency Tuples Problem Rules: prime(0) -> false prime(s(0)) -> false prime(s(s(z0))) -> prime1(s(s(z0)), s(z0)) prime1(z0, 0) -> false prime1(z0, s(0)) -> true prime1(z0, s(s(z1))) -> and(not(divp(s(s(z1)), z0)), prime1(z0, s(z1))) divp(z0, z1) -> =(rem(z0, z1), 0) Tuples: PRIME(0) -> c PRIME(s(0)) -> c1 PRIME(s(s(z0))) -> c2(PRIME1(s(s(z0)), s(z0))) PRIME1(z0, 0) -> c3 PRIME1(z0, s(0)) -> c4 PRIME1(z0, s(s(z1))) -> c5(DIVP(s(s(z1)), z0), PRIME1(z0, s(z1))) DIVP(z0, z1) -> c6 S tuples: PRIME(0) -> c PRIME(s(0)) -> c1 PRIME(s(s(z0))) -> c2(PRIME1(s(s(z0)), s(z0))) PRIME1(z0, 0) -> c3 PRIME1(z0, s(0)) -> c4 PRIME1(z0, s(s(z1))) -> c5(DIVP(s(s(z1)), z0), PRIME1(z0, s(z1))) DIVP(z0, z1) -> c6 K tuples:none Defined Rule Symbols: prime_1, prime1_2, divp_2 Defined Pair Symbols: PRIME_1, PRIME1_2, DIVP_2 Compound Symbols: c, c1, c2_1, c3, c4, c5_2, c6 ---------------------------------------- (3) CdtLeafRemovalProof (ComplexityIfPolyImplication)
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