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Derivational Complexity: TRS Innermost pair #487108418
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
n138.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.687 seconds
cpu usage
1141.71
user time
1130.97
system time
10.7327
max virtual memory
2.0247184E7
max residence set size
1.4653192E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 495 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 401 ms] (12) BEST (13) proven lower bound (14) LowerBoundPropagationProof [FINISHED, 0 ms] (15) BOUNDS(n^1, INF) (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 136 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 114 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 153 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 168 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 118 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 153 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 100 ms] (30) typed CpxTrs (31) RewriteLemmaProof [LOWER BOUND(ID), 91 ms] (32) typed CpxTrs ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs 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))
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