details

property	value
status	complete
benchmark	Ex3_2_Luc97_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n053.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	8.46275019646 seconds
cpu usage	27.765641101
max memory	4.129808384E9

stage attributes

key	value
output-size	13343
starexec-result	WORST_CASE(Omega(n^1), O(n^1))

output

/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 29 ms] (6) BOUNDS(1, n^1) (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (8) TRS for Loop Detection (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (10) BEST (11) proven lower bound (12) LowerBoundPropagationProof [FINISHED, 0 ms] (13) BOUNDS(n^1, INF) (14) TRS for Loop Detection ---------------------------------------- (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(dbl(0)) -> mark(0) active(dbl(s(X))) -> mark(s(s(dbl(X)))) active(dbls(nil)) -> mark(nil) active(dbls(cons(X, Y))) -> mark(cons(dbl(X), dbls(Y))) active(sel(0, cons(X, Y))) -> mark(X) active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z)) active(indx(nil, X)) -> mark(nil) active(indx(cons(X, Y), Z)) -> mark(cons(sel(X, Z), indx(Y, Z))) active(from(X)) -> mark(cons(X, from(s(X)))) active(dbl(X)) -> dbl(active(X)) active(dbls(X)) -> dbls(active(X)) active(sel(X1, X2)) -> sel(active(X1), X2) active(sel(X1, X2)) -> sel(X1, active(X2)) active(indx(X1, X2)) -> indx(active(X1), X2) dbl(mark(X)) -> mark(dbl(X)) dbls(mark(X)) -> mark(dbls(X)) sel(mark(X1), X2) -> mark(sel(X1, X2)) sel(X1, mark(X2)) -> mark(sel(X1, X2)) indx(mark(X1), X2) -> mark(indx(X1, X2)) proper(dbl(X)) -> dbl(proper(X)) proper(0) -> ok(0) proper(s(X)) -> s(proper(X)) proper(dbls(X)) -> dbls(proper(X)) proper(nil) -> ok(nil) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) proper(indx(X1, X2)) -> indx(proper(X1), proper(X2)) proper(from(X)) -> from(proper(X)) dbl(ok(X)) -> ok(dbl(X)) s(ok(X)) -> ok(s(X)) dbls(ok(X)) -> ok(dbls(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) indx(ok(X1), ok(X2)) -> ok(indx(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(dbl(0)) -> mark(0) active(dbl(s(X))) -> mark(s(s(dbl(X)))) active(dbls(nil)) -> mark(nil) active(dbls(cons(X, Y))) -> mark(cons(dbl(X), dbls(Y))) active(sel(0, cons(X, Y))) -> mark(X) active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z)) active(indx(nil, X)) -> mark(nil) active(indx(cons(X, Y), Z)) -> mark(cons(sel(X, Z), indx(Y, Z))) active(from(X)) -> mark(cons(X, from(s(X)))) active(dbl(X)) -> dbl(active(X)) active(dbls(X)) -> dbls(active(X)) active(sel(X1, X2)) -> sel(active(X1), X2) active(sel(X1, X2)) -> sel(X1, active(X2)) popout

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

job log

popout

actions

all output return to Runti Compl Full Rewri 10127