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Runtime Complexity: TRS pair #487109700
details
property
value
status
complete
benchmark
ExIntrod_GM99_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.84 seconds
cpu usage
356.974
user time
351.489
system time
5.48473
max virtual memory
1.8279408E7
max residence set size
8998172.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). (0) CpxTRS (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) typed CpxTrs (5) OrderProof [LOWER BOUND(ID), 0 ms] (6) typed CpxTrs (7) RewriteLemmaProof [LOWER BOUND(ID), 448 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 94 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 104 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 89 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 102 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 54 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 94 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 35 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 60 ms] (28) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: active(primes) -> mark(sieve(from(s(s(0))))) active(from(X)) -> mark(cons(X, from(s(X)))) active(head(cons(X, Y))) -> mark(X) active(tail(cons(X, Y))) -> mark(Y) active(if(true, X, Y)) -> mark(X) active(if(false, X, Y)) -> mark(Y) active(filter(s(s(X)), cons(Y, Z))) -> mark(if(divides(s(s(X)), Y), filter(s(s(X)), Z), cons(Y, filter(X, sieve(Y))))) active(sieve(cons(X, Y))) -> mark(cons(X, filter(X, sieve(Y)))) active(sieve(X)) -> sieve(active(X)) active(from(X)) -> from(active(X)) active(s(X)) -> s(active(X)) active(cons(X1, X2)) -> cons(active(X1), X2) active(head(X)) -> head(active(X)) active(tail(X)) -> tail(active(X)) active(if(X1, X2, X3)) -> if(active(X1), X2, X3) active(filter(X1, X2)) -> filter(active(X1), X2) active(filter(X1, X2)) -> filter(X1, active(X2)) active(divides(X1, X2)) -> divides(active(X1), X2) active(divides(X1, X2)) -> divides(X1, active(X2)) sieve(mark(X)) -> mark(sieve(X)) from(mark(X)) -> mark(from(X)) s(mark(X)) -> mark(s(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) head(mark(X)) -> mark(head(X)) tail(mark(X)) -> mark(tail(X)) if(mark(X1), X2, X3) -> mark(if(X1, X2, X3)) filter(mark(X1), X2) -> mark(filter(X1, X2)) filter(X1, mark(X2)) -> mark(filter(X1, X2)) divides(mark(X1), X2) -> mark(divides(X1, X2)) divides(X1, mark(X2)) -> mark(divides(X1, X2)) proper(primes) -> ok(primes) proper(sieve(X)) -> sieve(proper(X)) proper(from(X)) -> from(proper(X)) proper(s(X)) -> s(proper(X)) proper(0) -> ok(0) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(head(X)) -> head(proper(X)) proper(tail(X)) -> tail(proper(X)) proper(if(X1, X2, X3)) -> if(proper(X1), proper(X2), proper(X3)) proper(true) -> ok(true) proper(false) -> ok(false) proper(filter(X1, X2)) -> filter(proper(X1), proper(X2)) proper(divides(X1, X2)) -> divides(proper(X1), proper(X2)) sieve(ok(X)) -> ok(sieve(X)) from(ok(X)) -> ok(from(X)) s(ok(X)) -> ok(s(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) head(ok(X)) -> ok(head(X)) tail(ok(X)) -> ok(tail(X)) if(ok(X1), ok(X2), ok(X3)) -> ok(if(X1, X2, X3)) filter(ok(X1), ok(X2)) -> ok(filter(X1, X2)) divides(ok(X1), ok(X2)) -> ok(divides(X1, X2)) top(mark(X)) -> top(proper(X))
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