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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313729
details
property
value
status
complete
benchmark
thiemann11.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n071.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.911 seconds
cpu usage
1124.45
user time
1104.56
system time
19.8915
max virtual memory
5.6605336E7
max residence set size
1.4887752E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^2))
output
1124.13/291.78 WORST_CASE(Omega(n^1), O(n^2)) 1124.27/291.83 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1124.27/291.83 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1124.27/291.83 1124.27/291.83 1124.27/291.83 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1124.27/291.83 1124.27/291.83 (0) CpxTRS 1124.27/291.83 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1124.27/291.83 (2) CpxWeightedTrs 1124.27/291.83 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1124.27/291.83 (4) CpxTypedWeightedTrs 1124.27/291.83 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1124.27/291.83 (6) CpxTypedWeightedCompleteTrs 1124.27/291.83 (7) NarrowingProof [BOTH BOUNDS(ID, ID), 0 ms] 1124.27/291.83 (8) CpxTypedWeightedCompleteTrs 1124.27/291.83 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1124.27/291.83 (10) CpxRNTS 1124.27/291.83 (11) SimplificationProof [BOTH BOUNDS(ID, ID), 0 ms] 1124.27/291.83 (12) CpxRNTS 1124.27/291.83 (13) CpxRntsAnalysisOrderProof [BOTH BOUNDS(ID, ID), 3 ms] 1124.27/291.83 (14) CpxRNTS 1124.27/291.83 (15) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1124.27/291.83 (16) CpxRNTS 1124.27/291.83 (17) IntTrsBoundProof [UPPER BOUND(ID), 222 ms] 1124.27/291.83 (18) CpxRNTS 1124.27/291.83 (19) IntTrsBoundProof [UPPER BOUND(ID), 98 ms] 1124.27/291.83 (20) CpxRNTS 1124.27/291.83 (21) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1124.27/291.83 (22) CpxRNTS 1124.27/291.83 (23) IntTrsBoundProof [UPPER BOUND(ID), 354 ms] 1124.27/291.83 (24) CpxRNTS 1124.27/291.83 (25) IntTrsBoundProof [UPPER BOUND(ID), 135 ms] 1124.27/291.83 (26) CpxRNTS 1124.27/291.83 (27) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1124.27/291.83 (28) CpxRNTS 1124.27/291.83 (29) IntTrsBoundProof [UPPER BOUND(ID), 360 ms] 1124.27/291.83 (30) CpxRNTS 1124.27/291.83 (31) IntTrsBoundProof [UPPER BOUND(ID), 155 ms] 1124.27/291.83 (32) CpxRNTS 1124.27/291.83 (33) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1124.27/291.83 (34) CpxRNTS 1124.27/291.83 (35) IntTrsBoundProof [UPPER BOUND(ID), 97 ms] 1124.27/291.83 (36) CpxRNTS 1124.27/291.83 (37) IntTrsBoundProof [UPPER BOUND(ID), 12 ms] 1124.27/291.83 (38) CpxRNTS 1124.27/291.83 (39) ResultPropagationProof [UPPER BOUND(ID), 0 ms] 1124.27/291.83 (40) CpxRNTS 1124.27/291.83 (41) IntTrsBoundProof [UPPER BOUND(ID), 4253 ms] 1124.27/291.83 (42) CpxRNTS 1124.27/291.83 (43) IntTrsBoundProof [UPPER BOUND(ID), 1373 ms] 1124.27/291.83 (44) CpxRNTS 1124.27/291.83 (45) FinalProof [FINISHED, 0 ms] 1124.27/291.83 (46) BOUNDS(1, n^2) 1124.27/291.83 (47) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1124.27/291.83 (48) TRS for Loop Detection 1124.27/291.83 (49) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1124.27/291.83 (50) BEST 1124.27/291.83 (51) proven lower bound 1124.27/291.83 (52) LowerBoundPropagationProof [FINISHED, 0 ms] 1124.27/291.83 (53) BOUNDS(n^1, INF) 1124.27/291.83 (54) TRS for Loop Detection 1124.27/291.83 1124.27/291.83 1124.27/291.83 ---------------------------------------- 1124.27/291.83 1124.27/291.83 (0) 1124.27/291.83 Obligation: 1124.27/291.83 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1124.27/291.83 1124.27/291.83 1124.27/291.83 The TRS R consists of the following rules: 1124.27/291.83 1124.27/291.83 le(0, y) -> true 1124.27/291.83 le(s(x), 0) -> false 1124.27/291.83 le(s(x), s(y)) -> le(x, y) 1124.27/291.83 zero(0) -> true 1124.27/291.83 zero(s(x)) -> false 1124.27/291.83 id(0) -> 0 1124.27/291.83 id(s(x)) -> s(id(x)) 1124.27/291.83 minus(x, 0) -> x 1124.27/291.83 minus(s(x), s(y)) -> minus(x, y) 1124.27/291.83 mod(x, y) -> if_mod(zero(x), zero(y), le(y, x), id(x), id(y)) 1124.27/291.83 if_mod(true, b1, b2, x, y) -> 0 1124.27/291.83 if_mod(false, b1, b2, x, y) -> if2(b1, b2, x, y) 1124.27/291.83 if2(true, b2, x, y) -> 0 1124.27/291.83 if2(false, b2, x, y) -> if3(b2, x, y) 1124.27/291.83 if3(true, x, y) -> mod(minus(x, y), s(y)) 1124.27/291.83 if3(false, x, y) -> x 1124.27/291.83 1124.27/291.83 S is empty. 1124.27/291.83 Rewrite Strategy: INNERMOST 1124.27/291.83 ---------------------------------------- 1124.27/291.83 1124.27/291.83 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1124.27/291.83 Transformed relative TRS to weighted TRS 1124.27/291.83 ---------------------------------------- 1124.27/291.83 1124.27/291.83 (2) 1124.27/291.83 Obligation:
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