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Runtime Complexity: TRS pair #487110540
details
property
value
status
complete
benchmark
#4.30b.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n146.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
15.9566 seconds
cpu usage
50.7138
user time
48.9556
system time
1.75824
max virtual memory
3.7127688E7
max residence set size
4072176.0
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/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1).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) RcToIrcProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 1 ms] (4) CpxWeightedTrs (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTypedWeightedTrs (7) CompletionProof [UPPER BOUND(ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) CompleteCoflocoProof [FINISHED, 422 ms] (12) BOUNDS(1, n^1) (13) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (14) TRS for Loop Detection (15) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (16) BEST (17) proven lower bound (18) LowerBoundPropagationProof [FINISHED, 0 ms] (19) BOUNDS(n^1, INF) (20) 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: le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) mod(0, y) -> 0 mod(s(x), 0) -> 0 mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y)) if_mod(true, x, y) -> mod(minus(x, y), y) if_mod(false, s(x), s(y)) -> s(x) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) RcToIrcProof (BOTH BOUNDS(ID, ID)) Converted rc-obligation to irc-obligation. The duplicating contexts are: mod(s(x), s([])) mod(s([]), s(y)) if_mod(true, x, []) The defined contexts are: if_mod([], s(x1), s(x2)) mod([], x1) le(x0, []) if_mod(x0, s([]), s(x2)) minus([], x1) [] just represents basic- or constructor-terms in the following defined contexts: if_mod([], s(x1), s(x2)) mod([], x1) As the TRS is an overlay system and the defined contexts and the duplicating contexts don't overlap, we have rc = irc. ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(1, n^1). The TRS R consists of the following rules: le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) minus(x, 0) -> x minus(s(x), s(y)) -> minus(x, y) mod(0, y) -> 0 mod(s(x), 0) -> 0 mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y)) if_mod(true, x, y) -> mod(minus(x, y), y) if_mod(false, s(x), s(y)) -> s(x) S is empty. Rewrite Strategy: INNERMOST ----------------------------------------
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