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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313807
details
property
value
status
complete
benchmark
map0.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n019.star.cs.uiowa.edu
space
Frederiksen_Glenstrup
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
5.80279 seconds
cpu usage
19.5612
user time
17.9861
system time
1.57503
max virtual memory
3.8237852E7
max residence set size
4224824.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
19.23/5.72 WORST_CASE(Omega(n^1), O(n^1)) 19.23/5.73 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 19.23/5.73 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 19.23/5.73 19.23/5.73 19.23/5.73 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). 19.23/5.73 19.23/5.73 (0) CpxRelTRS 19.23/5.73 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 175 ms] 19.23/5.73 (2) CpxRelTRS 19.23/5.73 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 19.23/5.73 (4) CpxWeightedTrs 19.23/5.73 (5) CpxWeightedTrsRenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 19.23/5.73 (6) CpxWeightedTrs 19.23/5.73 (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 19.23/5.73 (8) CpxTypedWeightedTrs 19.23/5.73 (9) CompletionProof [UPPER BOUND(ID), 0 ms] 19.23/5.73 (10) CpxTypedWeightedCompleteTrs 19.23/5.73 (11) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 6 ms] 19.23/5.73 (12) CpxRNTS 19.23/5.73 (13) CompleteCoflocoProof [FINISHED, 214 ms] 19.23/5.73 (14) BOUNDS(1, n^1) 19.23/5.73 (15) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 19.23/5.73 (16) CpxRelTRS 19.23/5.73 (17) SlicingProof [LOWER BOUND(ID), 0 ms] 19.23/5.73 (18) CpxRelTRS 19.23/5.73 (19) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 19.23/5.73 (20) typed CpxTrs 19.23/5.73 (21) OrderProof [LOWER BOUND(ID), 6 ms] 19.23/5.73 (22) typed CpxTrs 19.23/5.73 (23) RewriteLemmaProof [LOWER BOUND(ID), 224 ms] 19.23/5.73 (24) BEST 19.23/5.73 (25) proven lower bound 19.23/5.73 (26) LowerBoundPropagationProof [FINISHED, 0 ms] 19.23/5.73 (27) BOUNDS(n^1, INF) 19.23/5.73 (28) typed CpxTrs 19.23/5.73 (29) RewriteLemmaProof [LOWER BOUND(ID), 1798 ms] 19.23/5.73 (30) typed CpxTrs 19.23/5.73 (31) RewriteLemmaProof [LOWER BOUND(ID), 50 ms] 19.23/5.73 (32) BOUNDS(1, INF) 19.23/5.73 19.23/5.73 19.23/5.73 ---------------------------------------- 19.23/5.73 19.23/5.73 (0) 19.23/5.73 Obligation: 19.23/5.73 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). 19.23/5.73 19.23/5.73 19.23/5.73 The TRS R consists of the following rules: 19.23/5.73 19.23/5.73 map(Cons(x, xs)) -> Cons(f(x), map(xs)) 19.23/5.73 map(Nil) -> Nil 19.23/5.73 goal(xs) -> map(xs) 19.23/5.73 f(x) -> *(x, x) 19.23/5.73 +Full(S(x), y) -> +Full(x, S(y)) 19.23/5.73 +Full(0, y) -> y 19.23/5.73 19.23/5.73 The (relative) TRS S consists of the following rules: 19.23/5.73 19.23/5.73 *(x, S(S(y))) -> +(x, *(x, S(y))) 19.23/5.73 *(x, S(0)) -> x 19.23/5.73 *(x, 0) -> 0 19.23/5.73 *(0, y) -> 0 19.23/5.73 19.23/5.73 Rewrite Strategy: INNERMOST 19.23/5.73 ---------------------------------------- 19.23/5.73 19.23/5.73 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 19.23/5.73 proved termination of relative rules 19.23/5.73 ---------------------------------------- 19.23/5.73 19.23/5.73 (2) 19.23/5.73 Obligation: 19.23/5.73 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). 19.23/5.73 19.23/5.73 19.23/5.73 The TRS R consists of the following rules: 19.23/5.73 19.23/5.73 map(Cons(x, xs)) -> Cons(f(x), map(xs)) 19.23/5.73 map(Nil) -> Nil 19.23/5.73 goal(xs) -> map(xs) 19.23/5.73 f(x) -> *(x, x) 19.23/5.73 +Full(S(x), y) -> +Full(x, S(y)) 19.23/5.73 +Full(0, y) -> y 19.23/5.73 19.23/5.73 The (relative) TRS S consists of the following rules: 19.23/5.73 19.23/5.73 *(x, S(S(y))) -> +(x, *(x, S(y))) 19.23/5.73 *(x, S(0)) -> x 19.23/5.73 *(x, 0) -> 0 19.23/5.73 *(0, y) -> 0 19.23/5.73 19.23/5.73 Rewrite Strategy: INNERMOST 19.23/5.73 ---------------------------------------- 19.23/5.73 19.23/5.73 (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 19.23/5.73 Transformed relative TRS to weighted TRS 19.23/5.73 ---------------------------------------- 19.23/5.73
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