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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308053
details
property
value
status
complete
benchmark
Ex7_BLR02_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n093.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.36313 seconds
cpu usage
28.5182
user time
26.9024
system time
1.61573
max virtual memory
5.5809652E7
max residence set size
3805020.0
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
28.07/8.14 WORST_CASE(Omega(n^1), O(n^1)) 28.07/8.15 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 28.07/8.15 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 28.07/8.15 28.07/8.15 28.07/8.15 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 28.07/8.15 28.07/8.15 (0) CpxTRS 28.07/8.15 (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] 28.07/8.15 (2) CpxTRS 28.07/8.15 (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] 28.07/8.15 (4) CpxTRS 28.07/8.15 (5) CpxTrsMatchBoundsTAProof [FINISHED, 102 ms] 28.07/8.15 (6) BOUNDS(1, n^1) 28.07/8.15 (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 28.07/8.15 (8) CpxTRS 28.07/8.15 (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 28.07/8.15 (10) typed CpxTrs 28.07/8.15 (11) OrderProof [LOWER BOUND(ID), 0 ms] 28.07/8.15 (12) typed CpxTrs 28.07/8.15 (13) RewriteLemmaProof [LOWER BOUND(ID), 484 ms] 28.07/8.15 (14) BEST 28.07/8.15 (15) proven lower bound 28.07/8.15 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 28.07/8.15 (17) BOUNDS(n^1, INF) 28.07/8.15 (18) typed CpxTrs 28.07/8.15 (19) RewriteLemmaProof [LOWER BOUND(ID), 131 ms] 28.07/8.15 (20) typed CpxTrs 28.07/8.15 (21) RewriteLemmaProof [LOWER BOUND(ID), 80 ms] 28.07/8.15 (22) typed CpxTrs 28.07/8.15 (23) RewriteLemmaProof [LOWER BOUND(ID), 94 ms] 28.07/8.15 (24) typed CpxTrs 28.07/8.15 (25) RewriteLemmaProof [LOWER BOUND(ID), 36 ms] 28.07/8.15 (26) typed CpxTrs 28.07/8.15 (27) RewriteLemmaProof [LOWER BOUND(ID), 92 ms] 28.07/8.15 (28) typed CpxTrs 28.07/8.15 (29) RewriteLemmaProof [LOWER BOUND(ID), 88 ms] 28.07/8.15 (30) typed CpxTrs 28.07/8.15 28.07/8.15 28.07/8.15 ---------------------------------------- 28.07/8.15 28.07/8.15 (0) 28.07/8.15 Obligation: 28.07/8.15 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). 28.07/8.15 28.07/8.15 28.07/8.15 The TRS R consists of the following rules: 28.07/8.15 28.07/8.15 active(from(X)) -> mark(cons(X, from(s(X)))) 28.07/8.15 active(head(cons(X, XS))) -> mark(X) 28.07/8.15 active(2nd(cons(X, XS))) -> mark(head(XS)) 28.07/8.15 active(take(0, XS)) -> mark(nil) 28.07/8.15 active(take(s(N), cons(X, XS))) -> mark(cons(X, take(N, XS))) 28.07/8.15 active(sel(0, cons(X, XS))) -> mark(X) 28.07/8.15 active(sel(s(N), cons(X, XS))) -> mark(sel(N, XS)) 28.07/8.15 active(from(X)) -> from(active(X)) 28.07/8.15 active(cons(X1, X2)) -> cons(active(X1), X2) 28.07/8.15 active(s(X)) -> s(active(X)) 28.07/8.15 active(head(X)) -> head(active(X)) 28.07/8.15 active(2nd(X)) -> 2nd(active(X)) 28.07/8.15 active(take(X1, X2)) -> take(active(X1), X2) 28.07/8.15 active(take(X1, X2)) -> take(X1, active(X2)) 28.07/8.15 active(sel(X1, X2)) -> sel(active(X1), X2) 28.07/8.15 active(sel(X1, X2)) -> sel(X1, active(X2)) 28.07/8.15 from(mark(X)) -> mark(from(X)) 28.07/8.15 cons(mark(X1), X2) -> mark(cons(X1, X2)) 28.07/8.15 s(mark(X)) -> mark(s(X)) 28.07/8.15 head(mark(X)) -> mark(head(X)) 28.07/8.15 2nd(mark(X)) -> mark(2nd(X)) 28.07/8.15 take(mark(X1), X2) -> mark(take(X1, X2)) 28.07/8.15 take(X1, mark(X2)) -> mark(take(X1, X2)) 28.07/8.15 sel(mark(X1), X2) -> mark(sel(X1, X2)) 28.07/8.15 sel(X1, mark(X2)) -> mark(sel(X1, X2)) 28.07/8.15 proper(from(X)) -> from(proper(X)) 28.07/8.15 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 28.07/8.15 proper(s(X)) -> s(proper(X)) 28.07/8.15 proper(head(X)) -> head(proper(X)) 28.07/8.15 proper(2nd(X)) -> 2nd(proper(X)) 28.07/8.15 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 28.07/8.15 proper(0) -> ok(0) 28.07/8.15 proper(nil) -> ok(nil) 28.07/8.15 proper(sel(X1, X2)) -> sel(proper(X1), proper(X2)) 28.07/8.15 from(ok(X)) -> ok(from(X)) 28.07/8.15 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 28.07/8.15 s(ok(X)) -> ok(s(X)) 28.07/8.15 head(ok(X)) -> ok(head(X)) 28.07/8.15 2nd(ok(X)) -> ok(2nd(X)) 28.07/8.15 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 28.07/8.15 sel(ok(X1), ok(X2)) -> ok(sel(X1, X2)) 28.07/8.15 top(mark(X)) -> top(proper(X)) 28.07/8.15 top(ok(X)) -> top(active(X)) 28.07/8.15 28.07/8.15 S is empty. 28.07/8.15 Rewrite Strategy: FULL 28.07/8.15 ---------------------------------------- 28.07/8.15 28.07/8.15 (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) 28.07/8.15 The following defined symbols can occur below the 0th argument of top: proper, active 28.07/8.15 The following defined symbols can occur below the 0th argument of proper: proper, active
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