details

property	value
status	complete
benchmark	Liveness8.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n078.star.cs.uiowa.edu
space	AProVE_04

run statistics

property	value
solver	AProVE
configuration	complexity
runtime (wallclock)	291.590955019 seconds
cpu usage	1050.40438352
max memory	1.5139504128E10

stage attributes

key	value
output-size	8306
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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, 85 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(f(x)) -> mark(x) top(active(c)) -> top(mark(c)) top(mark(x)) -> top(check(x)) check(f(x)) -> f(check(x)) check(x) -> start(match(f(X), x)) match(f(x), f(y)) -> f(match(x, y)) match(X, x) -> proper(x) proper(c) -> ok(c) proper(f(x)) -> f(proper(x)) f(ok(x)) -> ok(f(x)) start(ok(x)) -> found(x) f(found(x)) -> found(f(x)) top(found(x)) -> top(active(x)) active(f(x)) -> f(active(x)) f(mark(x)) -> mark(f(x)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The following defined symbols can occur below the 0th argument of top: active, start, proper, top, f, check, match The following defined symbols can occur below the 0th argument of active: active, start, proper, top, f, check, match The following defined symbols can occur below the 0th argument of f: active, start, proper, top, f, check, match The following defined symbols can occur below the 0th argument of start: active, start, proper, top, f, check, match The following defined symbols can occur below the 0th argument of match: active, start, proper, top, f, check, match The following defined symbols can occur below the 0th argument of check: active, start, proper, top, f, check, match Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: match(f(x), f(y)) -> f(match(x, y)) proper(f(x)) -> f(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: active(f(x)) -> mark(x) top(active(c)) -> top(mark(c)) top(mark(x)) -> top(check(x)) check(f(x)) -> f(check(x)) check(x) -> start(match(f(X), x)) match(X, x) -> proper(x) proper(c) -> ok(c) f(ok(x)) -> ok(f(x)) start(ok(x)) -> found(x) f(found(x)) -> found(f(x)) top(found(x)) -> top(active(x)) active(f(x)) -> f(active(x)) f(mark(x)) -> mark(f(x)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) RelTrsToTrsProof (UPPER BOUND(ID)) transformed relative TRS to TRS popout

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

job log

popout

actions

all output return to Runti Compl Full Rewri 10127