details

property	value
status	complete
benchmark	Ex6_Luc98_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n145.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	10.8566 seconds
cpu usage	22.8602
user time	21.2821
system time	1.57807
max virtual memory	1.93411E7
max residence set size	3930492.0

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/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 73 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), 424 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), 132 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 107 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 89 ms] (24) 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(first(0, X)) -> mark(nil) active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))) active(from(X)) -> mark(cons(X, from(s(X)))) active(first(X1, X2)) -> first(active(X1), X2) active(first(X1, X2)) -> first(X1, active(X2)) active(s(X)) -> s(active(X)) active(cons(X1, X2)) -> cons(active(X1), X2) active(from(X)) -> from(active(X)) first(mark(X1), X2) -> mark(first(X1, X2)) first(X1, mark(X2)) -> mark(first(X1, X2)) s(mark(X)) -> mark(s(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) from(mark(X)) -> mark(from(X)) proper(first(X1, X2)) -> first(proper(X1), proper(X2)) proper(0) -> ok(0) proper(nil) -> ok(nil) proper(s(X)) -> s(proper(X)) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(from(X)) -> from(proper(X)) first(ok(X1), ok(X2)) -> ok(first(X1, X2)) s(ok(X)) -> ok(s(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) from(ok(X)) -> ok(from(X)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(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(first(0, X)) -> mark(nil) active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))) active(from(X)) -> mark(cons(X, from(s(X)))) active(first(X1, X2)) -> first(active(X1), X2) active(first(X1, X2)) -> first(X1, active(X2)) active(s(X)) -> s(active(X)) active(cons(X1, X2)) -> cons(active(X1), X2) active(from(X)) -> from(active(X)) proper(first(X1, X2)) -> first(proper(X1), proper(X2)) proper(s(X)) -> s(proper(X)) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(from(X)) -> from(proper(X)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Runtime Complexity: TRS