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Runti Compl Full Rewri 10127 pair #381903321
details
property
value
status
complete
benchmark
ExIntrod_GM99_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n075.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.63391208649 seconds
cpu usage
3.681629344
max memory
2.18128384E8
stage attributes
key
value
output-size
6823
starexec-result
WORST_CASE(NON_POLY, ?)
output
/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). (0) CpxTRS (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (2) TRS for Loop Detection (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (4) BEST (5) proven lower bound (6) LowerBoundPropagationProof [FINISHED, 0 ms] (7) BOUNDS(n^1, INF) (8) TRS for Loop Detection (9) DecreasingLoopProof [FINISHED, 62 ms] (10) BOUNDS(EXP, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). The TRS R consists of the following rules: primes -> sieve(from(s(s(0)))) from(X) -> cons(X, n__from(n__s(X))) head(cons(X, Y)) -> X tail(cons(X, Y)) -> activate(Y) if(true, X, Y) -> activate(X) if(false, X, Y) -> activate(Y) filter(s(s(X)), cons(Y, Z)) -> if(divides(s(s(X)), Y), n__filter(n__s(n__s(X)), activate(Z)), n__cons(Y, n__filter(X, n__sieve(Y)))) sieve(cons(X, Y)) -> cons(X, n__filter(X, n__sieve(activate(Y)))) from(X) -> n__from(X) s(X) -> n__s(X) filter(X1, X2) -> n__filter(X1, X2) cons(X1, X2) -> n__cons(X1, X2) sieve(X) -> n__sieve(X) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__filter(X1, X2)) -> filter(activate(X1), activate(X2)) activate(n__cons(X1, X2)) -> cons(activate(X1), X2) activate(n__sieve(X)) -> sieve(activate(X)) activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (2) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). The TRS R consists of the following rules: primes -> sieve(from(s(s(0)))) from(X) -> cons(X, n__from(n__s(X))) head(cons(X, Y)) -> X tail(cons(X, Y)) -> activate(Y) if(true, X, Y) -> activate(X) if(false, X, Y) -> activate(Y) filter(s(s(X)), cons(Y, Z)) -> if(divides(s(s(X)), Y), n__filter(n__s(n__s(X)), activate(Z)), n__cons(Y, n__filter(X, n__sieve(Y)))) sieve(cons(X, Y)) -> cons(X, n__filter(X, n__sieve(activate(Y)))) from(X) -> n__from(X) s(X) -> n__s(X) filter(X1, X2) -> n__filter(X1, X2) cons(X1, X2) -> n__cons(X1, X2) sieve(X) -> n__sieve(X) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(n__filter(X1, X2)) -> filter(activate(X1), activate(X2)) activate(n__cons(X1, X2)) -> cons(activate(X1), X2) activate(n__sieve(X)) -> sieve(activate(X)) activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence
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