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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313852
details
property
value
status
complete
benchmark
thetrickSize.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n174.star.cs.uiowa.edu
space
Frederiksen_Others
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
9.24445 seconds
cpu usage
31.6423
user time
29.8233
system time
1.81905
max virtual memory
3.811502E7
max residence set size
4194632.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
31.32/9.17 WORST_CASE(Omega(n^1), O(n^1)) 31.56/9.19 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 31.56/9.19 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 31.56/9.19 31.56/9.19 31.56/9.19 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). 31.56/9.19 31.56/9.19 (0) CpxRelTRS 31.56/9.19 (1) STerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 180 ms] 31.56/9.19 (2) CpxRelTRS 31.56/9.19 (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 31.56/9.19 (4) CpxWeightedTrs 31.56/9.19 (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 31.56/9.19 (6) CpxTypedWeightedTrs 31.56/9.19 (7) CompletionProof [UPPER BOUND(ID), 0 ms] 31.56/9.19 (8) CpxTypedWeightedCompleteTrs 31.56/9.19 (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 31.56/9.19 (10) CpxRNTS 31.56/9.19 (11) CompleteCoflocoProof [FINISHED, 539 ms] 31.56/9.19 (12) BOUNDS(1, n^1) 31.56/9.19 (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 31.56/9.19 (14) CpxRelTRS 31.56/9.19 (15) SlicingProof [LOWER BOUND(ID), 0 ms] 31.56/9.19 (16) CpxRelTRS 31.56/9.19 (17) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 31.56/9.19 (18) typed CpxTrs 31.56/9.19 (19) OrderProof [LOWER BOUND(ID), 0 ms] 31.56/9.19 (20) typed CpxTrs 31.56/9.19 (21) RewriteLemmaProof [LOWER BOUND(ID), 260 ms] 31.56/9.19 (22) BEST 31.56/9.19 (23) proven lower bound 31.56/9.19 (24) LowerBoundPropagationProof [FINISHED, 0 ms] 31.56/9.19 (25) BOUNDS(n^1, INF) 31.56/9.19 (26) typed CpxTrs 31.56/9.19 (27) RewriteLemmaProof [LOWER BOUND(ID), 71 ms] 31.56/9.19 (28) typed CpxTrs 31.56/9.19 (29) RewriteLemmaProof [LOWER BOUND(ID), 62 ms] 31.56/9.19 (30) BOUNDS(1, INF) 31.56/9.19 31.56/9.19 31.56/9.19 ---------------------------------------- 31.56/9.19 31.56/9.19 (0) 31.56/9.19 Obligation: 31.56/9.19 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). 31.56/9.19 31.56/9.19 31.56/9.19 The TRS R consists of the following rules: 31.56/9.19 31.56/9.19 lt0(Nil, Cons(x', xs)) -> True 31.56/9.19 lt0(Cons(x', xs'), Cons(x, xs)) -> lt0(xs', xs) 31.56/9.19 g(x, Nil) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))) 31.56/9.19 f(x, Nil) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))) 31.56/9.19 notEmpty(Cons(x, xs)) -> True 31.56/9.19 notEmpty(Nil) -> False 31.56/9.19 lt0(x, Nil) -> False 31.56/9.19 g(x, Cons(x', xs)) -> g[Ite][False][Ite](lt0(x, Cons(Nil, Nil)), x, Cons(x', xs)) 31.56/9.19 f(x, Cons(x', xs)) -> f[Ite][False][Ite](lt0(x, Cons(Nil, Nil)), x, Cons(x', xs)) 31.56/9.19 number4(n) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))) 31.56/9.19 goal(x, y) -> Cons(f(x, y), Cons(g(x, y), Nil)) 31.56/9.19 31.56/9.19 The (relative) TRS S consists of the following rules: 31.56/9.19 31.56/9.19 g[Ite][False][Ite](False, Cons(x, xs), y) -> g(xs, Cons(Cons(Nil, Nil), y)) 31.56/9.19 g[Ite][False][Ite](True, x', Cons(x, xs)) -> g(x', xs) 31.56/9.19 f[Ite][False][Ite](False, Cons(x, xs), y) -> f(xs, Cons(Cons(Nil, Nil), y)) 31.56/9.19 f[Ite][False][Ite](True, x', Cons(x, xs)) -> f(x', xs) 31.56/9.19 31.56/9.19 Rewrite Strategy: INNERMOST 31.56/9.19 ---------------------------------------- 31.56/9.19 31.56/9.19 (1) STerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) 31.56/9.19 proved termination of relative rules 31.56/9.19 ---------------------------------------- 31.56/9.19 31.56/9.19 (2) 31.56/9.19 Obligation: 31.56/9.19 The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^1). 31.56/9.19 31.56/9.19 31.56/9.19 The TRS R consists of the following rules: 31.56/9.19 31.56/9.19 lt0(Nil, Cons(x', xs)) -> True 31.56/9.19 lt0(Cons(x', xs'), Cons(x, xs)) -> lt0(xs', xs) 31.56/9.19 g(x, Nil) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))) 31.56/9.19 f(x, Nil) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))) 31.56/9.19 notEmpty(Cons(x, xs)) -> True 31.56/9.19 notEmpty(Nil) -> False 31.56/9.19 lt0(x, Nil) -> False 31.56/9.19 g(x, Cons(x', xs)) -> g[Ite][False][Ite](lt0(x, Cons(Nil, Nil)), x, Cons(x', xs)) 31.56/9.19 f(x, Cons(x', xs)) -> f[Ite][False][Ite](lt0(x, Cons(Nil, Nil)), x, Cons(x', xs)) 31.56/9.19 number4(n) -> Cons(Nil, Cons(Nil, Cons(Nil, Cons(Nil, Nil)))) 31.56/9.19 goal(x, y) -> Cons(f(x, y), Cons(g(x, y), Nil)) 31.56/9.19 31.56/9.19 The (relative) TRS S consists of the following rules: 31.56/9.19 31.56/9.19 g[Ite][False][Ite](False, Cons(x, xs), y) -> g(xs, Cons(Cons(Nil, Nil), y)) 31.56/9.19 g[Ite][False][Ite](True, x', Cons(x, xs)) -> g(x', xs) 31.56/9.19 f[Ite][False][Ite](False, Cons(x, xs), y) -> f(xs, Cons(Cons(Nil, Nil), y)) 31.56/9.19 f[Ite][False][Ite](True, x', Cons(x, xs)) -> f(x', xs)
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return to Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40