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Runti Compl Inner Rewri 22807 pair #381904468
details
property
value
status
complete
benchmark
ExIntrod_GM99.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n070.star.cs.uiowa.edu
space
Strategy_removed_CSR_05
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
1.5244269371 seconds
cpu usage
3.327187793
max memory
2.15498752E8
stage attributes
key
value
output-size
4570
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).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) InfiniteLowerBoundProof [FINISHED, 0 ms] (10) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: primes -> sieve(from(s(s(0)))) from(X) -> cons(X, from(s(X))) head(cons(X, Y)) -> X tail(cons(X, Y)) -> Y if(true, X, Y) -> X if(false, X, Y) -> Y filter(s(s(X)), cons(Y, Z)) -> if(divides(s(s(X)), Y), filter(s(s(X)), Z), cons(Y, filter(X, sieve(Y)))) sieve(cons(X, Y)) -> cons(X, filter(X, sieve(Y))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (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 (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: primes -> sieve(from(s(s(0)))) from(X) -> cons(X, from(s(X))) head(cons(X, Y)) -> X tail(cons(X, Y)) -> Y if(true, X, Y) -> X if(false, X, Y) -> Y filter(s(s(X)), cons(Y, Z)) -> if(divides(s(s(X)), Y), filter(s(s(X)), Z), cons(Y, filter(X, sieve(Y)))) sieve(cons(X, Y)) -> cons(X, filter(X, sieve(Y))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (3) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence sieve(cons(X, Y)) ->^+ cons(X, filter(X, sieve(Y))) gives rise to a decreasing loop by considering the right hand sides subterm at position [1,1]. The pumping substitution is [Y / cons(X, Y)]. The result substitution is [ ]. ---------------------------------------- (4) Complex Obligation (BEST) ---------------------------------------- (5) Obligation: Proved the lower bound n^1 for the following obligation:
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