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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313771
details
property
value
status
complete
benchmark
#3.5b.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n118.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
292.625 seconds
cpu usage
325.692
user time
322.647
system time
3.04516
max virtual memory
1.9146912E7
max residence set size
5172636.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^3))
output
325.56/292.56 WORST_CASE(Omega(n^1), O(n^3)) 325.56/292.58 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 325.56/292.58 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 325.56/292.58 325.56/292.58 325.56/292.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 325.56/292.58 325.56/292.58 (0) CpxTRS 325.56/292.58 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 325.56/292.58 (2) CpxWeightedTrs 325.56/292.58 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 325.56/292.58 (4) CpxTypedWeightedTrs 325.56/292.58 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 325.56/292.58 (6) CpxTypedWeightedCompleteTrs 325.56/292.58 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 325.56/292.58 (8) CpxTypedWeightedCompleteTrs 325.56/292.58 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 325.56/292.58 (10) CpxRNTS 325.56/292.58 (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 325.56/292.58 (12) CpxRNTS 325.56/292.58 (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 325.56/292.58 (14) CpxRNTS 325.56/292.58 (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 325.56/292.58 (16) CpxRNTS 325.56/292.58 (17) IntTrsBoundProof [UPPER BOUND(ID), 376 ms] 325.56/292.58 (18) CpxRNTS 325.56/292.58 (19) IntTrsBoundProof [UPPER BOUND(ID), 158 ms] 325.56/292.58 (20) CpxRNTS 325.56/292.58 (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 325.56/292.58 (22) CpxRNTS 325.56/292.58 (23) IntTrsBoundProof [UPPER BOUND(ID), 877 ms] 325.56/292.58 (24) CpxRNTS 325.56/292.58 (25) IntTrsBoundProof [UPPER BOUND(ID), 308 ms] 325.56/292.58 (26) CpxRNTS 325.56/292.58 (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 325.56/292.58 (28) CpxRNTS 325.56/292.58 (29) IntTrsBoundProof [UPPER BOUND(ID), 1323 ms] 325.56/292.58 (30) CpxRNTS 325.56/292.58 (31) IntTrsBoundProof [UPPER BOUND(ID), 92 ms] 325.56/292.58 (32) CpxRNTS 325.56/292.58 (33) FinalProof [FINISHED, 0 ms] 325.56/292.58 (34) BOUNDS(1, n^3) 325.56/292.58 (35) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 325.56/292.58 (36) TRS for Loop Detection 325.56/292.58 (37) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 325.56/292.58 (38) BEST 325.56/292.58 (39) proven lower bound 325.56/292.58 (40) LowerBoundPropagationProof [FINISHED, 0 ms] 325.56/292.58 (41) BOUNDS(n^1, INF) 325.56/292.58 (42) TRS for Loop Detection 325.56/292.58 325.56/292.58 325.56/292.58 ---------------------------------------- 325.56/292.58 325.56/292.58 (0) 325.56/292.58 Obligation: 325.56/292.58 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^3). 325.56/292.58 325.56/292.58 325.56/292.58 The TRS R consists of the following rules: 325.56/292.58 325.56/292.58 le(0, y) -> true 325.56/292.58 le(s(x), 0) -> false 325.56/292.58 le(s(x), s(y)) -> le(x, y) 325.56/292.58 minus(0, y) -> 0 325.56/292.58 minus(s(x), y) -> if_minus(le(s(x), y), s(x), y) 325.56/292.58 if_minus(true, s(x), y) -> 0 325.56/292.58 if_minus(false, s(x), y) -> s(minus(x, y)) 325.56/292.58 mod(0, y) -> 0 325.56/292.58 mod(s(x), 0) -> 0 325.56/292.58 mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y)) 325.56/292.58 if_mod(true, s(x), s(y)) -> mod(minus(x, y), s(y)) 325.56/292.58 if_mod(false, s(x), s(y)) -> s(x) 325.56/292.58 325.56/292.58 S is empty. 325.56/292.58 Rewrite Strategy: INNERMOST 325.56/292.58 ---------------------------------------- 325.56/292.58 325.56/292.58 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 325.56/292.58 Transformed relative TRS to weighted TRS 325.56/292.58 ---------------------------------------- 325.56/292.58 325.56/292.58 (2) 325.56/292.58 Obligation: 325.56/292.58 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). 325.56/292.58 325.56/292.58 325.56/292.58 The TRS R consists of the following rules: 325.56/292.58 325.56/292.58 le(0, y) -> true [1] 325.56/292.58 le(s(x), 0) -> false [1] 325.56/292.58 le(s(x), s(y)) -> le(x, y) [1] 325.56/292.58 minus(0, y) -> 0 [1] 325.56/292.58 minus(s(x), y) -> if_minus(le(s(x), y), s(x), y) [1] 325.56/292.58 if_minus(true, s(x), y) -> 0 [1] 325.56/292.58 if_minus(false, s(x), y) -> s(minus(x, y)) [1] 325.56/292.58 mod(0, y) -> 0 [1] 325.56/292.58 mod(s(x), 0) -> 0 [1] 325.56/292.58 mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y)) [1] 325.56/292.58 if_mod(true, s(x), s(y)) -> mod(minus(x, y), s(y)) [1]
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