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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313893
details
property
value
status
complete
benchmark
19.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n063.star.cs.uiowa.edu
space
Beerendonk_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
295.921 seconds
cpu usage
1160.38
user time
1147.83
system time
12.5498
max virtual memory
5.7095692E7
max residence set size
1.5112176E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1143.13/291.51 WORST_CASE(Omega(n^1), O(n^2)) 1159.94/295.76 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1159.94/295.76 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1159.94/295.76 1159.94/295.76 1159.94/295.76 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1159.94/295.76 1159.94/295.76 (0) CpxTRS 1159.94/295.76 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1159.94/295.76 (2) CpxWeightedTrs 1159.94/295.76 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1159.94/295.76 (4) CpxTypedWeightedTrs 1159.94/295.76 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1159.94/295.76 (6) CpxTypedWeightedCompleteTrs 1159.94/295.76 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 1159.94/295.76 (8) CpxTypedWeightedCompleteTrs 1159.94/295.76 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 7 ms] 1159.94/295.76 (10) CpxRNTS 1159.94/295.76 (11) InliningProof [UPPER BOUND(ID), 630 ms] 1159.94/295.76 (12) CpxRNTS 1159.94/295.76 (13) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 1159.94/295.76 (14) CpxRNTS 1159.94/295.76 (15) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 0 ms] 1159.94/295.76 (16) CpxRNTS 1159.94/295.76 (17) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1159.94/295.76 (18) CpxRNTS 1159.94/295.76 (19) IntTrsBoundProof [UPPER BOUND(ID), 102 ms] 1159.94/295.76 (20) CpxRNTS 1159.94/295.76 (21) IntTrsBoundProof [UPPER BOUND(ID), 6 ms] 1159.94/295.76 (22) CpxRNTS 1159.94/295.76 (23) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1159.94/295.76 (24) CpxRNTS 1159.94/295.76 (25) IntTrsBoundProof [UPPER BOUND(ID), 324 ms] 1159.94/295.76 (26) CpxRNTS 1159.94/295.76 (27) IntTrsBoundProof [UPPER BOUND(ID), 176 ms] 1159.94/295.76 (28) CpxRNTS 1159.94/295.76 (29) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1159.94/295.76 (30) CpxRNTS 1159.94/295.76 (31) IntTrsBoundProof [UPPER BOUND(ID), 255 ms] 1159.94/295.76 (32) CpxRNTS 1159.94/295.76 (33) IntTrsBoundProof [UPPER BOUND(ID), 85 ms] 1159.94/295.76 (34) CpxRNTS 1159.94/295.76 (35) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1159.94/295.76 (36) CpxRNTS 1159.94/295.76 (37) IntTrsBoundProof [UPPER BOUND(ID), 5112 ms] 1159.94/295.76 (38) CpxRNTS 1159.94/295.76 (39) IntTrsBoundProof [UPPER BOUND(ID), 2087 ms] 1159.94/295.76 (40) CpxRNTS 1159.94/295.76 (41) FinalProof [FINISHED, 0 ms] 1159.94/295.76 (42) BOUNDS(1, n^2) 1159.94/295.76 (43) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1159.94/295.76 (44) TRS for Loop Detection 1159.94/295.76 (45) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1159.94/295.76 (46) BEST 1159.94/295.76 (47) proven lower bound 1159.94/295.76 (48) LowerBoundPropagationProof [FINISHED, 0 ms] 1159.94/295.76 (49) BOUNDS(n^1, INF) 1159.94/295.76 (50) TRS for Loop Detection 1159.94/295.76 1159.94/295.76 1159.94/295.76 ---------------------------------------- 1159.94/295.76 1159.94/295.76 (0) 1159.94/295.76 Obligation: 1159.94/295.76 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1159.94/295.76 1159.94/295.76 1159.94/295.76 The TRS R consists of the following rules: 1159.94/295.76 1159.94/295.76 cond1(true, x, y, z) -> cond2(gr(x, 0), x, y, z) 1159.94/295.76 cond2(true, x, y, z) -> cond1(or(gr(x, z), gr(y, z)), p(x), y, z) 1159.94/295.76 cond2(false, x, y, z) -> cond3(gr(y, 0), x, y, z) 1159.94/295.76 cond3(true, x, y, z) -> cond1(or(gr(x, z), gr(y, z)), x, p(y), z) 1159.94/295.76 cond3(false, x, y, z) -> cond1(or(gr(x, z), gr(y, z)), x, y, z) 1159.94/295.76 gr(0, x) -> false 1159.94/295.76 gr(s(x), 0) -> true 1159.94/295.76 gr(s(x), s(y)) -> gr(x, y) 1159.94/295.76 or(false, false) -> false 1159.94/295.76 or(true, x) -> true 1159.94/295.76 or(x, true) -> true 1159.94/295.76 p(0) -> 0 1159.94/295.76 p(s(x)) -> x 1159.94/295.76 1159.94/295.76 S is empty. 1159.94/295.76 Rewrite Strategy: INNERMOST 1159.94/295.76 ---------------------------------------- 1159.94/295.76 1159.94/295.76 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1159.94/295.76 Transformed relative TRS to weighted TRS 1159.94/295.76 ---------------------------------------- 1159.94/295.76 1159.94/295.76 (2) 1159.94/295.76 Obligation: 1159.94/295.76 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1159.94/295.76 1159.94/295.76 1159.94/295.76 The TRS R consists of the following rules: 1159.94/295.76 1159.94/295.76 cond1(true, x, y, z) -> cond2(gr(x, 0), x, y, z) [1] 1159.94/295.76 cond2(true, x, y, z) -> cond1(or(gr(x, z), gr(y, z)), p(x), y, z) [1]
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