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Runtime Complexity: TRS pair #487111282
details
property
value
status
complete
benchmark
Liveness6.3.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n140.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
7.92177 seconds
cpu usage
27.1389
user time
25.6229
system time
1.51597
max virtual memory
1.934216E7
max residence set size
4087592.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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) DependencyGraphProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (6) CpxTRS (7) CpxTrsMatchBoundsProof [FINISHED, 0 ms] (8) BOUNDS(1, n^1) (9) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (10) TRS for Loop Detection (11) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (12) BEST (13) proven lower bound (14) LowerBoundPropagationProof [FINISHED, 0 ms] (15) BOUNDS(n^1, INF) (16) 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: rec(rec(x)) -> sent(rec(x)) rec(sent(x)) -> sent(rec(x)) rec(no(x)) -> sent(rec(x)) rec(bot) -> up(sent(bot)) rec(up(x)) -> up(rec(x)) sent(up(x)) -> up(sent(x)) no(up(x)) -> up(no(x)) top(rec(up(x))) -> top(check(rec(x))) top(sent(up(x))) -> top(check(rec(x))) top(no(up(x))) -> top(check(rec(x))) check(up(x)) -> up(check(x)) check(sent(x)) -> sent(check(x)) check(rec(x)) -> rec(check(x)) check(no(x)) -> no(check(x)) check(no(x)) -> no(x) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) DependencyGraphProof (UPPER BOUND(ID)) The following rules are not reachable from basic terms in the dependency graph and can be removed: top(rec(up(x))) -> top(check(rec(x))) top(sent(up(x))) -> top(check(rec(x))) top(no(up(x))) -> top(check(rec(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: rec(rec(x)) -> sent(rec(x)) rec(sent(x)) -> sent(rec(x)) rec(no(x)) -> sent(rec(x)) rec(bot) -> up(sent(bot)) rec(up(x)) -> up(rec(x)) sent(up(x)) -> up(sent(x)) no(up(x)) -> up(no(x)) check(up(x)) -> up(check(x)) check(sent(x)) -> sent(check(x)) check(rec(x)) -> rec(check(x)) check(no(x)) -> no(check(x)) check(no(x)) -> no(x) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) NestedDefinedSymbolProof (UPPER BOUND(ID)) The TRS does not nest defined symbols. Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: rec(rec(x)) -> sent(rec(x)) rec(sent(x)) -> sent(rec(x)) rec(no(x)) -> sent(rec(x)) check(sent(x)) -> sent(check(x)) check(rec(x)) -> rec(check(x)) check(no(x)) -> no(check(x)) check(no(x)) -> no(x) ----------------------------------------
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