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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313761
details
property
value
status
complete
benchmark
#3.41.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n120.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.57711 seconds
cpu usage
18.4206
user time
16.9049
system time
1.51575
max virtual memory
1.9142788E7
max residence set size
4099612.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
18.29/5.52 WORST_CASE(Omega(n^1), O(n^1)) 18.35/5.53 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 18.35/5.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 18.35/5.53 18.35/5.53 18.35/5.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 18.35/5.53 18.35/5.53 (0) CpxTRS 18.35/5.53 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 18.35/5.53 (2) CpxWeightedTrs 18.35/5.53 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 18.35/5.53 (4) CpxTypedWeightedTrs 18.35/5.53 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 18.35/5.53 (6) CpxTypedWeightedCompleteTrs 18.35/5.53 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 18.35/5.53 (8) CpxRNTS 18.35/5.53 (9) CompleteCoflocoProof [FINISHED, 39 ms] 18.35/5.53 (10) BOUNDS(1, n^1) 18.35/5.53 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 18.35/5.53 (12) TRS for Loop Detection 18.35/5.53 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 18.35/5.53 (14) BEST 18.35/5.53 (15) proven lower bound 18.35/5.53 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 18.35/5.53 (17) BOUNDS(n^1, INF) 18.35/5.53 (18) TRS for Loop Detection 18.35/5.53 18.35/5.53 18.35/5.53 ---------------------------------------- 18.35/5.53 18.35/5.53 (0) 18.35/5.53 Obligation: 18.35/5.53 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 18.35/5.53 18.35/5.53 18.35/5.53 The TRS R consists of the following rules: 18.35/5.53 18.35/5.53 p(s(x)) -> x 18.35/5.53 fac(0) -> s(0) 18.35/5.53 fac(s(x)) -> times(s(x), fac(p(s(x)))) 18.35/5.53 18.35/5.53 S is empty. 18.35/5.53 Rewrite Strategy: INNERMOST 18.35/5.53 ---------------------------------------- 18.35/5.53 18.35/5.53 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 18.35/5.53 Transformed relative TRS to weighted TRS 18.35/5.53 ---------------------------------------- 18.35/5.53 18.35/5.53 (2) 18.35/5.53 Obligation: 18.35/5.53 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^1). 18.35/5.53 18.35/5.53 18.35/5.53 The TRS R consists of the following rules: 18.35/5.53 18.35/5.53 p(s(x)) -> x [1] 18.35/5.53 fac(0) -> s(0) [1] 18.35/5.53 fac(s(x)) -> times(s(x), fac(p(s(x)))) [1] 18.35/5.53 18.35/5.53 Rewrite Strategy: INNERMOST 18.35/5.53 ---------------------------------------- 18.35/5.53 18.35/5.53 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 18.35/5.53 Infered types. 18.35/5.53 ---------------------------------------- 18.35/5.53 18.35/5.53 (4) 18.35/5.53 Obligation: 18.35/5.53 Runtime Complexity Weighted TRS with Types. 18.35/5.53 The TRS R consists of the following rules: 18.35/5.53 18.35/5.53 p(s(x)) -> x [1] 18.35/5.53 fac(0) -> s(0) [1] 18.35/5.53 fac(s(x)) -> times(s(x), fac(p(s(x)))) [1] 18.35/5.53 18.35/5.53 The TRS has the following type information: 18.35/5.53 p :: s:0:times -> s:0:times 18.35/5.53 s :: s:0:times -> s:0:times 18.35/5.53 fac :: s:0:times -> s:0:times 18.35/5.53 0 :: s:0:times 18.35/5.53 times :: s:0:times -> s:0:times -> s:0:times 18.35/5.53 18.35/5.53 Rewrite Strategy: INNERMOST 18.35/5.53 ---------------------------------------- 18.35/5.53 18.35/5.53 (5) CompletionProof (UPPER BOUND(ID)) 18.35/5.53 The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: 18.35/5.53 18.35/5.53 p(v0) -> null_p [0] 18.35/5.53 fac(v0) -> null_fac [0] 18.35/5.53 18.35/5.53 And the following fresh constants: null_p, null_fac 18.35/5.53 18.35/5.53 ---------------------------------------- 18.35/5.53 18.35/5.53 (6) 18.35/5.53 Obligation: 18.35/5.53 Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: 18.35/5.53
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