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Runtime Complexity: TRS pair #487110306
details
property
value
status
complete
benchmark
OvConsOS_nokinds_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)
294.337 seconds
cpu usage
1152.18
user time
1138.4
system time
13.7775
max virtual memory
5.7131084E7
max residence set size
1.5122804E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF).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), 449 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), 109 ms] (14) typed CpxTrs (15) RewriteLemmaProof [LOWER BOUND(ID), 82 ms] (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 94 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 133 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 78 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 127 ms] (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 237 ms] (26) 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(zeros) -> mark(cons(0, zeros)) active(U11(tt, L)) -> mark(s(length(L))) active(U21(tt)) -> mark(nil) active(U31(tt, IL, M, N)) -> mark(cons(N, take(M, IL))) active(and(tt, X)) -> mark(X) active(isNat(0)) -> mark(tt) active(isNat(length(V1))) -> mark(isNatList(V1)) active(isNat(s(V1))) -> mark(isNat(V1)) active(isNatIList(V)) -> mark(isNatList(V)) active(isNatIList(zeros)) -> mark(tt) active(isNatIList(cons(V1, V2))) -> mark(and(isNat(V1), isNatIList(V2))) active(isNatList(nil)) -> mark(tt) active(isNatList(cons(V1, V2))) -> mark(and(isNat(V1), isNatList(V2))) active(isNatList(take(V1, V2))) -> mark(and(isNat(V1), isNatIList(V2))) active(length(nil)) -> mark(0) active(length(cons(N, L))) -> mark(U11(and(isNatList(L), isNat(N)), L)) active(take(0, IL)) -> mark(U21(isNatIList(IL))) active(take(s(M), cons(N, IL))) -> mark(U31(and(isNatIList(IL), and(isNat(M), isNat(N))), IL, M, N)) active(cons(X1, X2)) -> cons(active(X1), X2) active(U11(X1, X2)) -> U11(active(X1), X2) active(s(X)) -> s(active(X)) active(length(X)) -> length(active(X)) active(U21(X)) -> U21(active(X)) active(U31(X1, X2, X3, X4)) -> U31(active(X1), X2, X3, X4) active(take(X1, X2)) -> take(active(X1), X2) active(take(X1, X2)) -> take(X1, active(X2)) active(and(X1, X2)) -> and(active(X1), X2) cons(mark(X1), X2) -> mark(cons(X1, X2)) U11(mark(X1), X2) -> mark(U11(X1, X2)) s(mark(X)) -> mark(s(X)) length(mark(X)) -> mark(length(X)) U21(mark(X)) -> mark(U21(X)) U31(mark(X1), X2, X3, X4) -> mark(U31(X1, X2, X3, X4)) take(mark(X1), X2) -> mark(take(X1, X2)) take(X1, mark(X2)) -> mark(take(X1, X2)) and(mark(X1), X2) -> mark(and(X1, X2)) proper(zeros) -> ok(zeros) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(0) -> ok(0) proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) proper(tt) -> ok(tt) proper(s(X)) -> s(proper(X)) proper(length(X)) -> length(proper(X)) proper(U21(X)) -> U21(proper(X)) proper(nil) -> ok(nil) proper(U31(X1, X2, X3, X4)) -> U31(proper(X1), proper(X2), proper(X3), proper(X4)) proper(take(X1, X2)) -> take(proper(X1), proper(X2)) proper(and(X1, X2)) -> and(proper(X1), proper(X2)) proper(isNat(X)) -> isNat(proper(X)) proper(isNatList(X)) -> isNatList(proper(X)) proper(isNatIList(X)) -> isNatIList(proper(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) s(ok(X)) -> ok(s(X)) length(ok(X)) -> ok(length(X))
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