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Runtime_Complexity_Innermost_Rewriting 2019-04-01 06.40 pair #433313515
details
property
value
status
complete
benchmark
Ex8_BLR02_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n151.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
291.513 seconds
cpu usage
530.038
user time
525.56
system time
4.47826
max virtual memory
1.9085848E7
max residence set size
5532124.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
529.87/291.45 WORST_CASE(Omega(n^1), ?) 529.87/291.46 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 529.87/291.46 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 529.87/291.46 529.87/291.46 529.87/291.46 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 529.87/291.46 529.87/291.46 (0) CpxTRS 529.87/291.46 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 529.87/291.46 (2) CpxTRS 529.87/291.46 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 529.87/291.46 (4) typed CpxTrs 529.87/291.46 (5) OrderProof [LOWER BOUND(ID), 0 ms] 529.87/291.46 (6) typed CpxTrs 529.87/291.46 (7) RewriteLemmaProof [LOWER BOUND(ID), 222 ms] 529.87/291.46 (8) BEST 529.87/291.46 (9) proven lower bound 529.87/291.46 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 529.87/291.46 (11) BOUNDS(n^1, INF) 529.87/291.46 (12) typed CpxTrs 529.87/291.46 (13) RewriteLemmaProof [LOWER BOUND(ID), 65 ms] 529.87/291.46 (14) BOUNDS(1, INF) 529.87/291.46 529.87/291.46 529.87/291.46 ---------------------------------------- 529.87/291.46 529.87/291.46 (0) 529.87/291.46 Obligation: 529.87/291.46 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 529.87/291.46 529.87/291.46 529.87/291.46 The TRS R consists of the following rules: 529.87/291.46 529.87/291.46 fib(N) -> sel(N, fib1(s(0), s(0))) 529.87/291.46 fib1(X, Y) -> cons(X, n__fib1(Y, add(X, Y))) 529.87/291.46 add(0, X) -> X 529.87/291.46 add(s(X), Y) -> s(add(X, Y)) 529.87/291.46 sel(0, cons(X, XS)) -> X 529.87/291.46 sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) 529.87/291.46 fib1(X1, X2) -> n__fib1(X1, X2) 529.87/291.46 activate(n__fib1(X1, X2)) -> fib1(X1, X2) 529.87/291.46 activate(X) -> X 529.87/291.46 529.87/291.46 S is empty. 529.87/291.46 Rewrite Strategy: INNERMOST 529.87/291.46 ---------------------------------------- 529.87/291.46 529.87/291.46 (1) RenamingProof (BOTH BOUNDS(ID, ID)) 529.87/291.46 Renamed function symbols to avoid clashes with predefined symbol. 529.87/291.46 ---------------------------------------- 529.87/291.46 529.87/291.46 (2) 529.87/291.46 Obligation: 529.87/291.46 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 529.87/291.46 529.87/291.46 529.87/291.46 The TRS R consists of the following rules: 529.87/291.46 529.87/291.46 fib(N) -> sel(N, fib1(s(0'), s(0'))) 529.87/291.46 fib1(X, Y) -> cons(X, n__fib1(Y, add(X, Y))) 529.87/291.46 add(0', X) -> X 529.87/291.46 add(s(X), Y) -> s(add(X, Y)) 529.87/291.46 sel(0', cons(X, XS)) -> X 529.87/291.46 sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) 529.87/291.46 fib1(X1, X2) -> n__fib1(X1, X2) 529.87/291.46 activate(n__fib1(X1, X2)) -> fib1(X1, X2) 529.87/291.46 activate(X) -> X 529.87/291.46 529.87/291.46 S is empty. 529.87/291.46 Rewrite Strategy: INNERMOST 529.87/291.46 ---------------------------------------- 529.87/291.46 529.87/291.46 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 529.87/291.46 Infered types. 529.87/291.46 ---------------------------------------- 529.87/291.46 529.87/291.46 (4) 529.87/291.46 Obligation: 529.87/291.46 Innermost TRS: 529.87/291.46 Rules: 529.87/291.46 fib(N) -> sel(N, fib1(s(0'), s(0'))) 529.87/291.46 fib1(X, Y) -> cons(X, n__fib1(Y, add(X, Y))) 529.87/291.46 add(0', X) -> X 529.87/291.46 add(s(X), Y) -> s(add(X, Y)) 529.87/291.46 sel(0', cons(X, XS)) -> X 529.87/291.46 sel(s(N), cons(X, XS)) -> sel(N, activate(XS)) 529.87/291.46 fib1(X1, X2) -> n__fib1(X1, X2) 529.87/291.46 activate(n__fib1(X1, X2)) -> fib1(X1, X2) 529.87/291.46 activate(X) -> X 529.87/291.46 529.87/291.46 Types: 529.87/291.46 fib :: 0':s -> 0':s 529.87/291.46 sel :: 0':s -> n__fib1:cons -> 0':s 529.87/291.46 fib1 :: 0':s -> 0':s -> n__fib1:cons 529.87/291.46 s :: 0':s -> 0':s 529.87/291.46 0' :: 0':s 529.87/291.46 cons :: 0':s -> n__fib1:cons -> n__fib1:cons 529.87/291.46 n__fib1 :: 0':s -> 0':s -> n__fib1:cons 529.87/291.46 add :: 0':s -> 0':s -> 0':s 529.87/291.46 activate :: n__fib1:cons -> n__fib1:cons
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