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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308332
details
property
value
status
complete
benchmark
Ex6_15_AEL02_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n133.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
11.5463 seconds
cpu usage
39.6376
user time
37.575
system time
2.06259
max virtual memory
3.8436452E7
max residence set size
4179568.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
39.31/11.48 WORST_CASE(Omega(n^1), O(n^1)) 39.51/11.51 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 39.51/11.51 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 39.51/11.51 39.51/11.51 39.51/11.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 39.51/11.51 39.51/11.51 (0) CpxTRS 39.51/11.51 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 39.51/11.51 (2) CpxTRS 39.51/11.51 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 39.51/11.51 (4) CpxTRS 39.51/11.51 (5) CpxTrsMatchBoundsTAProof [FINISHED, 373 ms] 39.51/11.51 (6) BOUNDS(1, n^1) 39.51/11.51 (7) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 39.51/11.51 (8) TRS for Loop Detection 39.51/11.51 (9) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 39.51/11.51 (10) BEST 39.51/11.51 (11) proven lower bound 39.51/11.51 (12) LowerBoundPropagationProof [FINISHED, 0 ms] 39.51/11.51 (13) BOUNDS(n^1, INF) 39.51/11.51 (14) TRS for Loop Detection 39.51/11.51 39.51/11.51 39.51/11.51 ---------------------------------------- 39.51/11.51 39.51/11.51 (0) 39.51/11.51 Obligation: 39.51/11.51 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 39.51/11.51 39.51/11.51 39.51/11.51 The TRS R consists of the following rules: 39.51/11.51 39.51/11.51 active(sel(s(X), cons(Y, Z))) -> mark(sel(X, Z)) 39.51/11.51 active(sel(0, cons(X, Z))) -> mark(X) 39.51/11.51 active(first(0, Z)) -> mark(nil) 39.51/11.51 active(first(s(X), cons(Y, Z))) -> mark(cons(Y, first(X, Z))) 39.51/11.51 active(from(X)) -> mark(cons(X, from(s(X)))) 39.51/11.51 active(sel1(s(X), cons(Y, Z))) -> mark(sel1(X, Z)) 39.51/11.51 active(sel1(0, cons(X, Z))) -> mark(quote(X)) 39.51/11.51 active(first1(0, Z)) -> mark(nil1) 39.51/11.51 active(first1(s(X), cons(Y, Z))) -> mark(cons1(quote(Y), first1(X, Z))) 39.51/11.51 active(quote(0)) -> mark(01) 39.51/11.51 active(quote1(cons(X, Z))) -> mark(cons1(quote(X), quote1(Z))) 39.51/11.51 active(quote1(nil)) -> mark(nil1) 39.51/11.51 active(quote(s(X))) -> mark(s1(quote(X))) 39.51/11.51 active(quote(sel(X, Z))) -> mark(sel1(X, Z)) 39.51/11.51 active(quote1(first(X, Z))) -> mark(first1(X, Z)) 39.51/11.51 active(unquote(01)) -> mark(0) 39.51/11.51 active(unquote(s1(X))) -> mark(s(unquote(X))) 39.51/11.51 active(unquote1(nil1)) -> mark(nil) 39.51/11.51 active(unquote1(cons1(X, Z))) -> mark(fcons(unquote(X), unquote1(Z))) 39.51/11.51 active(fcons(X, Z)) -> mark(cons(X, Z)) 39.51/11.51 active(sel(X1, X2)) -> sel(active(X1), X2) 39.51/11.51 active(sel(X1, X2)) -> sel(X1, active(X2)) 39.51/11.51 active(s(X)) -> s(active(X)) 39.51/11.51 active(cons(X1, X2)) -> cons(active(X1), X2) 39.51/11.51 active(first(X1, X2)) -> first(active(X1), X2) 39.51/11.51 active(first(X1, X2)) -> first(X1, active(X2)) 39.51/11.51 active(from(X)) -> from(active(X)) 39.51/11.51 active(sel1(X1, X2)) -> sel1(active(X1), X2) 39.51/11.51 active(sel1(X1, X2)) -> sel1(X1, active(X2)) 39.51/11.51 active(first1(X1, X2)) -> first1(active(X1), X2) 39.51/11.51 active(first1(X1, X2)) -> first1(X1, active(X2)) 39.51/11.51 active(cons1(X1, X2)) -> cons1(active(X1), X2) 39.51/11.51 active(cons1(X1, X2)) -> cons1(X1, active(X2)) 39.51/11.51 active(s1(X)) -> s1(active(X)) 39.51/11.51 active(unquote(X)) -> unquote(active(X)) 39.51/11.51 active(unquote1(X)) -> unquote1(active(X)) 39.51/11.51 active(fcons(X1, X2)) -> fcons(active(X1), X2) 39.51/11.51 active(fcons(X1, X2)) -> fcons(X1, active(X2)) 39.51/11.51 sel(mark(X1), X2) -> mark(sel(X1, X2)) 39.51/11.51 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 39.51/11.51 s(mark(X)) -> mark(s(X)) 39.51/11.51 cons(mark(X1), X2) -> mark(cons(X1, X2)) 39.51/11.51 first(mark(X1), X2) -> mark(first(X1, X2)) 39.51/11.51 first(X1, mark(X2)) -> mark(first(X1, X2)) 39.51/11.51 from(mark(X)) -> mark(from(X)) 39.51/11.51 sel1(mark(X1), X2) -> mark(sel1(X1, X2)) 39.51/11.51 sel1(X1, mark(X2)) -> mark(sel1(X1, X2)) 39.51/11.51 first1(mark(X1), X2) -> mark(first1(X1, X2)) 39.51/11.51 first1(X1, mark(X2)) -> mark(first1(X1, X2)) 39.51/11.51 cons1(mark(X1), X2) -> mark(cons1(X1, X2)) 39.51/11.51 cons1(X1, mark(X2)) -> mark(cons1(X1, X2)) 39.51/11.51 s1(mark(X)) -> mark(s1(X)) 39.51/11.51 unquote(mark(X)) -> mark(unquote(X)) 39.51/11.51 unquote1(mark(X)) -> mark(unquote1(X)) 39.51/11.51 fcons(mark(X1), X2) -> mark(fcons(X1, X2)) 39.51/11.51 fcons(X1, mark(X2)) -> mark(fcons(X1, X2)) 39.51/11.51 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 39.51/11.51 proper(s(X)) -> s(proper(X)) 39.51/11.51 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 39.51/11.51 proper(0) -> ok(0) 39.51/11.51 proper(first(X1, X2)) -> first(proper(X1), proper(X2)) 39.51/11.51 proper(nil) -> ok(nil) 39.51/11.51 proper(from(X)) -> from(proper(X)) 39.51/11.51 proper(sel1(X1, X2)) -> sel1(proper(X1), proper(X2)) 39.51/11.51 proper(quote(X)) -> quote(proper(X)) 39.51/11.51 proper(first1(X1, X2)) -> first1(proper(X1), proper(X2)) 39.51/11.51 proper(nil1) -> ok(nil1)
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