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Runti Compl Full Rewri 10127 pair #381902593
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
n057.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.513790131 seconds
cpu usage
1112.17391822
max memory
1.1818708992E10
stage attributes
key
value
output-size
23317
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox/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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) RcToIrcProof [BOTH BOUNDS(ID, ID), 17 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), 3 ms] (12) CpxRNTS (13) CompleteCoflocoProof [FINISHED, 562 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:
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