Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
Runtime Complexity: TRS pair #487111064
details
property
value
status
complete
benchmark
kabasci01.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n148.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.00404 seconds
cpu usage
22.9451
user time
21.451
system time
1.49412
max virtual memory
1.9014296E7
max residence set size
3669656.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
WORST_CASE(Omega(n^1), O(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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsMatchBoundsTAProof [FINISHED, 72 ms] (6) BOUNDS(1, n^1) (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 464 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 148 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 123 ms] (22) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: active(eq(0, 0)) -> mark(true) active(eq(s(X), s(Y))) -> mark(eq(X, Y)) active(eq(X, Y)) -> mark(false) active(inf(X)) -> mark(cons(X, inf(s(X)))) active(take(0, X)) -> mark(nil) active(take(s(X), cons(Y, L))) -> mark(cons(Y, take(X, L))) active(length(nil)) -> mark(0) active(length(cons(X, L))) -> mark(s(length(L))) active(inf(X)) -> inf(active(X)) active(take(X1, X2)) -> take(active(X1), X2) active(take(X1, X2)) -> take(X1, active(X2)) active(length(X)) -> length(active(X)) inf(mark(X)) -> mark(inf(X)) take(mark(X1), X2) -> mark(take(X1, X2)) take(X1, mark(X2)) -> mark(take(X1, X2)) length(mark(X)) -> mark(length(X)) proper(eq(X1, X2)) -> eq(proper(X1), proper(X2)) proper(0) -> ok(0) proper(true) -> ok(true) proper(s(X)) -> s(proper(X)) proper(false) -> ok(false) proper(inf(X)) -> inf(proper(X)) proper(cons(any(X1), X2)) -> cons(any(any(proper(X1))), any(proper(X2))) proper(take(X1, X2)) -> take(proper(X1), proper(X2)) proper(nil) -> ok(nil) proper(length(X)) -> length(proper(X)) eq(ok(X1), ok(X2)) -> ok(eq(X1, X2)) s(ok(X)) -> ok(s(X)) inf(ok(X)) -> ok(inf(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) take(ok(X1), ok(X2)) -> ok(take(X1, X2)) length(ok(X)) -> ok(length(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) any(X) -> s(X) any(proper(X)) -> any(any(any(X))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The following defined symbols can occur below the 0th argument of top: proper, active The following defined symbols can occur below the 0th argument of proper: proper, active The following defined symbols can occur below the 0th argument of active: proper, active Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: active(eq(0, 0)) -> mark(true) active(eq(s(X), s(Y))) -> mark(eq(X, Y)) active(eq(X, Y)) -> mark(false) active(inf(X)) -> mark(cons(X, inf(s(X)))) active(take(0, X)) -> mark(nil) active(take(s(X), cons(Y, L))) -> mark(cons(Y, take(X, L))) active(length(nil)) -> mark(0) active(length(cons(X, L))) -> mark(s(length(L))) active(inf(X)) -> inf(active(X)) active(take(X1, X2)) -> take(active(X1), X2) active(take(X1, X2)) -> take(X1, active(X2)) active(length(X)) -> length(active(X))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to Runtime Complexity: TRS