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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313315
details
property
value
status
complete
benchmark
tpa07.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n068.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
294.578 seconds
cpu usage
1115.66
user time
1103.25
system time
12.4095
max virtual memory
3.8175352E7
max residence set size
1.5046908E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^2), ?)
output
1103.75/291.53 WORST_CASE(Omega(n^2), ?) 1115.56/294.51 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1115.56/294.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1115.56/294.51 1115.56/294.51 1115.56/294.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1115.56/294.51 1115.56/294.51 (0) CpxTRS 1115.56/294.51 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1115.56/294.51 (2) CpxTRS 1115.56/294.51 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1115.56/294.51 (4) typed CpxTrs 1115.56/294.51 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1115.56/294.51 (6) typed CpxTrs 1115.56/294.51 (7) RewriteLemmaProof [LOWER BOUND(ID), 271 ms] 1115.56/294.51 (8) BEST 1115.56/294.51 (9) proven lower bound 1115.56/294.51 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1115.56/294.51 (11) BOUNDS(n^1, INF) 1115.56/294.51 (12) typed CpxTrs 1115.56/294.51 (13) RewriteLemmaProof [LOWER BOUND(ID), 27 ms] 1115.56/294.51 (14) typed CpxTrs 1115.56/294.51 (15) RewriteLemmaProof [LOWER BOUND(ID), 59 ms] 1115.56/294.51 (16) BEST 1115.56/294.51 (17) proven lower bound 1115.56/294.51 (18) LowerBoundPropagationProof [FINISHED, 0 ms] 1115.56/294.51 (19) BOUNDS(n^2, INF) 1115.56/294.51 (20) typed CpxTrs 1115.56/294.51 1115.56/294.51 1115.56/294.51 ---------------------------------------- 1115.56/294.51 1115.56/294.51 (0) 1115.56/294.51 Obligation: 1115.56/294.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1115.56/294.51 1115.56/294.51 1115.56/294.51 The TRS R consists of the following rules: 1115.56/294.51 1115.56/294.51 -(x, 0) -> x 1115.56/294.51 -(s(x), s(y)) -> -(x, y) 1115.56/294.51 +(0, y) -> y 1115.56/294.51 +(s(x), y) -> s(+(x, y)) 1115.56/294.51 *(x, 0) -> 0 1115.56/294.51 *(x, s(y)) -> +(x, *(x, y)) 1115.56/294.51 f(s(x), y) -> f(-(*(s(x), s(y)), s(*(s(x), y))), *(y, y)) 1115.56/294.51 1115.56/294.51 S is empty. 1115.56/294.51 Rewrite Strategy: INNERMOST 1115.56/294.51 ---------------------------------------- 1115.56/294.51 1115.56/294.51 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 1115.56/294.51 Renamed function symbols to avoid clashes with predefined symbol. 1115.56/294.51 ---------------------------------------- 1115.56/294.51 1115.56/294.51 (2) 1115.56/294.51 Obligation: 1115.56/294.51 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^2, INF). 1115.56/294.51 1115.56/294.51 1115.56/294.51 The TRS R consists of the following rules: 1115.56/294.51 1115.56/294.51 -(x, 0') -> x 1115.56/294.51 -(s(x), s(y)) -> -(x, y) 1115.56/294.51 +'(0', y) -> y 1115.56/294.51 +'(s(x), y) -> s(+'(x, y)) 1115.56/294.51 *'(x, 0') -> 0' 1115.56/294.51 *'(x, s(y)) -> +'(x, *'(x, y)) 1115.56/294.51 f(s(x), y) -> f(-(*'(s(x), s(y)), s(*'(s(x), y))), *'(y, y)) 1115.56/294.51 1115.56/294.51 S is empty. 1115.56/294.51 Rewrite Strategy: INNERMOST 1115.56/294.51 ---------------------------------------- 1115.56/294.51 1115.56/294.51 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1115.56/294.51 Infered types. 1115.56/294.51 ---------------------------------------- 1115.56/294.51 1115.56/294.51 (4) 1115.56/294.51 Obligation: 1115.56/294.51 Innermost TRS: 1115.56/294.51 Rules: 1115.56/294.51 -(x, 0') -> x 1115.56/294.51 -(s(x), s(y)) -> -(x, y) 1115.56/294.51 +'(0', y) -> y 1115.56/294.51 +'(s(x), y) -> s(+'(x, y)) 1115.56/294.51 *'(x, 0') -> 0' 1115.56/294.51 *'(x, s(y)) -> +'(x, *'(x, y)) 1115.56/294.51 f(s(x), y) -> f(-(*'(s(x), s(y)), s(*'(s(x), y))), *'(y, y)) 1115.56/294.51 1115.56/294.51 Types: 1115.56/294.51 - :: 0':s -> 0':s -> 0':s 1115.56/294.51 0' :: 0':s 1115.56/294.51 s :: 0':s -> 0':s 1115.56/294.51 +' :: 0':s -> 0':s -> 0':s 1115.56/294.51 *' :: 0':s -> 0':s -> 0':s 1115.56/294.51 f :: 0':s -> 0':s -> f 1115.56/294.51 hole_0':s1_0 :: 0':s 1115.56/294.51 hole_f2_0 :: f 1115.56/294.51 gen_0':s3_0 :: Nat -> 0':s
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