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Runtime Complexity: TRS pair #487110884
details
property
value
status
complete
benchmark
aprove5.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.605 seconds
cpu usage
1103.93
user time
1093.12
system time
10.8097
max virtual memory
1.9454188E7
max residence set size
1.1166944E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
WORST_CASE(Omega(n^1), O(n^3)) 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTRS (5) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxWeightedTrs (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTypedWeightedTrs (9) CompletionProof [UPPER BOUND(ID), 0 ms] (10) CpxTypedWeightedCompleteTrs (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 538 ms] (14) BOUNDS(1, n^3) (15) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (16) TRS for Loop Detection (17) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (18) BEST (19) proven lower bound (20) LowerBoundPropagationProof [FINISHED, 0 ms] (21) BOUNDS(n^1, INF) (22) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: minus(x, 0) -> x minus(0, y) -> 0 minus(s(x), s(y)) -> minus(p(s(x)), p(s(y))) minus(x, plus(y, z)) -> minus(minus(x, y), z) p(s(s(x))) -> s(p(s(x))) p(0) -> s(s(0)) div(s(x), s(y)) -> s(div(minus(x, y), s(y))) div(plus(x, y), z) -> plus(div(x, z), div(y, z)) plus(0, y) -> y plus(s(x), y) -> s(plus(y, minus(s(x), s(0)))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The following defined symbols can occur below the 0th argument of minus: p, minus The following defined symbols can occur below the 1th argument of minus: p The following defined symbols can occur below the 0th argument of p: p The following defined symbols can occur below the 0th argument of plus: p, minus The following defined symbols can occur below the 1th argument of plus: p, minus The following defined symbols can occur below the 0th argument of div: p, minus Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: minus(x, plus(y, z)) -> minus(minus(x, y), z) div(plus(x, y), z) -> plus(div(x, z), div(y, z)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(1, n^3). The TRS R consists of the following rules: minus(x, 0) -> x minus(0, y) -> 0 minus(s(x), s(y)) -> minus(p(s(x)), p(s(y))) p(s(s(x))) -> s(p(s(x))) p(0) -> s(s(0)) div(s(x), s(y)) -> s(div(minus(x, y), s(y))) plus(0, y) -> y plus(s(x), y) -> s(plus(y, minus(s(x), s(0)))) S is empty. Rewrite Strategy: FULL ---------------------------------------- (3) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. The duplicating contexts are: div(s(x), s([])) The defined contexts are: minus([], x1) minus(x0, [])
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