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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308301
details
property
value
status
complete
benchmark
Ex4_Zan97_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.568 seconds
cpu usage
324.889
user time
322.574
system time
2.31503
max virtual memory
1.8279384E7
max residence set size
5814792.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
324.77/291.52 WORST_CASE(Omega(n^1), ?) 324.77/291.53 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 324.77/291.53 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 324.77/291.53 324.77/291.53 324.77/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 324.77/291.53 324.77/291.53 (0) CpxTRS 324.77/291.53 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 324.77/291.53 (2) CpxTRS 324.77/291.53 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 324.77/291.53 (4) typed CpxTrs 324.77/291.53 (5) OrderProof [LOWER BOUND(ID), 0 ms] 324.77/291.53 (6) typed CpxTrs 324.77/291.53 (7) RewriteLemmaProof [LOWER BOUND(ID), 316 ms] 324.77/291.53 (8) BEST 324.77/291.53 (9) proven lower bound 324.77/291.53 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 324.77/291.53 (11) BOUNDS(n^1, INF) 324.77/291.53 (12) typed CpxTrs 324.77/291.53 324.77/291.53 324.77/291.53 ---------------------------------------- 324.77/291.53 324.77/291.53 (0) 324.77/291.53 Obligation: 324.77/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 324.77/291.53 324.77/291.53 324.77/291.53 The TRS R consists of the following rules: 324.77/291.53 324.77/291.53 f(X) -> cons(X, n__f(g(X))) 324.77/291.53 g(0) -> s(0) 324.77/291.53 g(s(X)) -> s(s(g(X))) 324.77/291.53 sel(0, cons(X, Y)) -> X 324.77/291.53 sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) 324.77/291.53 f(X) -> n__f(X) 324.77/291.53 activate(n__f(X)) -> f(X) 324.77/291.53 activate(X) -> X 324.77/291.53 324.77/291.53 S is empty. 324.77/291.53 Rewrite Strategy: FULL 324.77/291.53 ---------------------------------------- 324.77/291.53 324.77/291.53 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 324.77/291.53 Renamed function symbols to avoid clashes with predefined symbol. 324.77/291.53 ---------------------------------------- 324.77/291.53 324.77/291.53 (2) 324.77/291.53 Obligation: 324.77/291.53 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 324.77/291.53 324.77/291.53 324.77/291.53 The TRS R consists of the following rules: 324.77/291.53 324.77/291.53 f(X) -> cons(X, n__f(g(X))) 324.77/291.53 g(0') -> s(0') 324.77/291.53 g(s(X)) -> s(s(g(X))) 324.77/291.53 sel(0', cons(X, Y)) -> X 324.77/291.53 sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) 324.77/291.53 f(X) -> n__f(X) 324.77/291.53 activate(n__f(X)) -> f(X) 324.77/291.53 activate(X) -> X 324.77/291.53 324.77/291.53 S is empty. 324.77/291.53 Rewrite Strategy: FULL 324.77/291.53 ---------------------------------------- 324.77/291.53 324.77/291.53 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 324.77/291.53 Infered types. 324.77/291.53 ---------------------------------------- 324.77/291.53 324.77/291.53 (4) 324.77/291.53 Obligation: 324.77/291.53 TRS: 324.77/291.53 Rules: 324.77/291.53 f(X) -> cons(X, n__f(g(X))) 324.77/291.53 g(0') -> s(0') 324.77/291.53 g(s(X)) -> s(s(g(X))) 324.77/291.53 sel(0', cons(X, Y)) -> X 324.77/291.53 sel(s(X), cons(Y, Z)) -> sel(X, activate(Z)) 324.77/291.53 f(X) -> n__f(X) 324.77/291.53 activate(n__f(X)) -> f(X) 324.77/291.53 activate(X) -> X 324.77/291.53 324.77/291.53 Types: 324.77/291.53 f :: 0':s -> n__f:cons 324.77/291.53 cons :: 0':s -> n__f:cons -> n__f:cons 324.77/291.53 n__f :: 0':s -> n__f:cons 324.77/291.53 g :: 0':s -> 0':s 324.77/291.53 0' :: 0':s 324.77/291.53 s :: 0':s -> 0':s 324.77/291.53 sel :: 0':s -> n__f:cons -> 0':s 324.77/291.53 activate :: n__f:cons -> n__f:cons 324.77/291.53 hole_n__f:cons1_0 :: n__f:cons 324.77/291.53 hole_0':s2_0 :: 0':s 324.77/291.53 gen_n__f:cons3_0 :: Nat -> n__f:cons 324.77/291.53 gen_0':s4_0 :: Nat -> 0':s 324.77/291.53 324.77/291.53 ----------------------------------------
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