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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313554
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
n105.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
11.6514 seconds
cpu usage
38.7076
user time
36.2576
system time
2.45007
max virtual memory
1.9028804E7
max residence set size
4637804.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
38.36/11.57 WORST_CASE(Omega(n^1), O(n^1)) 38.61/11.59 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 38.61/11.59 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 38.61/11.59 38.61/11.59 38.61/11.59 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 38.61/11.59 38.61/11.59 (0) CpxTRS 38.61/11.59 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 38.61/11.59 (2) CpxWeightedTrs 38.61/11.59 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 38.61/11.59 (4) CpxTypedWeightedTrs 38.61/11.59 (5) CompletionProof [UPPER BOUND(ID), 2 ms] 38.61/11.59 (6) CpxTypedWeightedCompleteTrs 38.61/11.59 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 38.61/11.59 (8) CpxRNTS 38.61/11.59 (9) CompleteCoflocoProof [FINISHED, 504 ms] 38.61/11.59 (10) BOUNDS(1, n^1) 38.61/11.59 (11) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 38.61/11.59 (12) CpxTRS 38.61/11.59 (13) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 38.61/11.59 (14) typed CpxTrs 38.61/11.59 (15) OrderProof [LOWER BOUND(ID), 0 ms] 38.61/11.59 (16) typed CpxTrs 38.61/11.59 (17) RewriteLemmaProof [LOWER BOUND(ID), 291 ms] 38.61/11.59 (18) BEST 38.61/11.59 (19) proven lower bound 38.61/11.59 (20) LowerBoundPropagationProof [FINISHED, 0 ms] 38.61/11.59 (21) BOUNDS(n^1, INF) 38.61/11.59 (22) typed CpxTrs 38.61/11.59 (23) RewriteLemmaProof [LOWER BOUND(ID), 56 ms] 38.61/11.59 (24) typed CpxTrs 38.61/11.59 38.61/11.59 38.61/11.59 ---------------------------------------- 38.61/11.59 38.61/11.59 (0) 38.61/11.59 Obligation: 38.61/11.59 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 38.61/11.59 38.61/11.59 38.61/11.59 The TRS R consists of the following rules: 38.61/11.59 38.61/11.59 le(0, y) -> true 38.61/11.59 le(s(x), 0) -> false 38.61/11.59 le(s(x), s(y)) -> le(x, y) 38.61/11.59 minus(x, 0) -> x 38.61/11.59 minus(s(x), s(y)) -> minus(x, y) 38.61/11.59 mod(0, y) -> 0 38.61/11.59 mod(s(x), 0) -> 0 38.61/11.59 mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y)) 38.61/11.59 if_mod(true, x, y) -> mod(minus(x, y), y) 38.61/11.59 if_mod(false, s(x), s(y)) -> s(x) 38.61/11.59 38.61/11.59 S is empty. 38.61/11.59 Rewrite Strategy: INNERMOST 38.61/11.59 ---------------------------------------- 38.61/11.59 38.61/11.59 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 38.61/11.59 Transformed relative TRS to weighted TRS 38.61/11.59 ---------------------------------------- 38.61/11.59 38.61/11.59 (2) 38.61/11.59 Obligation: 38.61/11.59 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 38.61/11.59 38.61/11.59 38.61/11.59 The TRS R consists of the following rules: 38.61/11.59 38.61/11.59 le(0, y) -> true [1] 38.61/11.59 le(s(x), 0) -> false [1] 38.61/11.59 le(s(x), s(y)) -> le(x, y) [1] 38.61/11.59 minus(x, 0) -> x [1] 38.61/11.59 minus(s(x), s(y)) -> minus(x, y) [1] 38.61/11.59 mod(0, y) -> 0 [1] 38.61/11.59 mod(s(x), 0) -> 0 [1] 38.61/11.59 mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y)) [1] 38.61/11.59 if_mod(true, x, y) -> mod(minus(x, y), y) [1] 38.61/11.59 if_mod(false, s(x), s(y)) -> s(x) [1] 38.61/11.59 38.61/11.59 Rewrite Strategy: INNERMOST 38.61/11.59 ---------------------------------------- 38.61/11.59 38.61/11.59 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 38.61/11.59 Infered types. 38.61/11.59 ---------------------------------------- 38.61/11.59 38.61/11.59 (4) 38.61/11.59 Obligation: 38.61/11.59 Runtime Complexity Weighted TRS with Types. 38.61/11.59 The TRS R consists of the following rules: 38.61/11.59 38.61/11.59 le(0, y) -> true [1] 38.61/11.59 le(s(x), 0) -> false [1] 38.61/11.59 le(s(x), s(y)) -> le(x, y) [1] 38.61/11.59 minus(x, 0) -> x [1] 38.61/11.59 minus(s(x), s(y)) -> minus(x, y) [1] 38.61/11.59 mod(0, y) -> 0 [1] 38.61/11.59 mod(s(x), 0) -> 0 [1] 38.61/11.59 mod(s(x), s(y)) -> if_mod(le(y, x), s(x), s(y)) [1]
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