details

property	value
status	complete
benchmark	Ex26_Luc03b_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n055.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	7.4998190403 seconds
cpu usage	24.7531548
max memory	4.311867392E9

stage attributes

key	value
output-size	15821
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 87 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(terms(N)) -> mark(cons(recip(sqr(N)), terms(s(N)))) active(sqr(0)) -> mark(0) active(sqr(s(X))) -> mark(s(add(sqr(X), dbl(X)))) active(dbl(0)) -> mark(0) active(dbl(s(X))) -> mark(s(s(dbl(X)))) active(add(0, X)) -> mark(X) active(add(s(X), Y)) -> mark(s(add(X, Y))) active(first(0, X)) -> mark(nil) active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))) active(terms(X)) -> terms(active(X)) active(cons(X1, X2)) -> cons(active(X1), X2) active(recip(X)) -> recip(active(X)) active(sqr(X)) -> sqr(active(X)) active(add(X1, X2)) -> add(active(X1), X2) active(add(X1, X2)) -> add(X1, active(X2)) active(dbl(X)) -> dbl(active(X)) active(first(X1, X2)) -> first(active(X1), X2) active(first(X1, X2)) -> first(X1, active(X2)) terms(mark(X)) -> mark(terms(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) recip(mark(X)) -> mark(recip(X)) sqr(mark(X)) -> mark(sqr(X)) add(mark(X1), X2) -> mark(add(X1, X2)) add(X1, mark(X2)) -> mark(add(X1, X2)) dbl(mark(X)) -> mark(dbl(X)) first(mark(X1), X2) -> mark(first(X1, X2)) first(X1, mark(X2)) -> mark(first(X1, X2)) proper(terms(X)) -> terms(proper(X)) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(recip(X)) -> recip(proper(X)) proper(sqr(X)) -> sqr(proper(X)) proper(s(X)) -> s(proper(X)) proper(0) -> ok(0) proper(add(X1, X2)) -> add(proper(X1), proper(X2)) proper(dbl(X)) -> dbl(proper(X)) proper(first(X1, X2)) -> first(proper(X1), proper(X2)) proper(nil) -> ok(nil) terms(ok(X)) -> ok(terms(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) recip(ok(X)) -> ok(recip(X)) sqr(ok(X)) -> ok(sqr(X)) s(ok(X)) -> ok(s(X)) add(ok(X1), ok(X2)) -> ok(add(X1, X2)) dbl(ok(X)) -> ok(dbl(X)) first(ok(X1), ok(X2)) -> ok(first(X1, X2)) 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(terms(N)) -> mark(cons(recip(sqr(N)), terms(s(N)))) active(sqr(0)) -> mark(0) active(sqr(s(X))) -> mark(s(add(sqr(X), dbl(X)))) popout

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

job log

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actions

all output return to Runti Compl Full Rewri 10127