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Runtime_Complexity_Full_Rewriting 2019-04-01 06.11 pair #433308166
details
property
value
status
complete
benchmark
OvConsOS_nosorts_noand_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n044.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
294.492 seconds
cpu usage
1127.22
user time
1112.68
system time
14.5347
max virtual memory
3.8304824E7
max residence set size
1.5073772E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
1115.90/291.59 WORST_CASE(Omega(n^1), ?) 1126.86/294.37 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 1126.86/294.37 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1126.86/294.37 1126.86/294.37 1126.86/294.37 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1126.86/294.37 1126.86/294.37 (0) CpxTRS 1126.86/294.37 (1) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] 1126.86/294.37 (2) CpxTRS 1126.86/294.37 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1126.86/294.37 (4) typed CpxTrs 1126.86/294.37 (5) OrderProof [LOWER BOUND(ID), 0 ms] 1126.86/294.37 (6) typed CpxTrs 1126.86/294.37 (7) RewriteLemmaProof [LOWER BOUND(ID), 569 ms] 1126.86/294.37 (8) BEST 1126.86/294.37 (9) proven lower bound 1126.86/294.37 (10) LowerBoundPropagationProof [FINISHED, 0 ms] 1126.86/294.37 (11) BOUNDS(n^1, INF) 1126.86/294.37 (12) typed CpxTrs 1126.86/294.37 (13) RewriteLemmaProof [LOWER BOUND(ID), 133 ms] 1126.86/294.37 (14) typed CpxTrs 1126.86/294.37 (15) RewriteLemmaProof [LOWER BOUND(ID), 75 ms] 1126.86/294.37 (16) typed CpxTrs 1126.86/294.37 (17) RewriteLemmaProof [LOWER BOUND(ID), 63 ms] 1126.86/294.37 (18) typed CpxTrs 1126.86/294.37 (19) RewriteLemmaProof [LOWER BOUND(ID), 37 ms] 1126.86/294.37 (20) typed CpxTrs 1126.86/294.37 (21) RewriteLemmaProof [LOWER BOUND(ID), 141 ms] 1126.86/294.37 (22) typed CpxTrs 1126.86/294.37 (23) RewriteLemmaProof [LOWER BOUND(ID), 115 ms] 1126.86/294.37 (24) typed CpxTrs 1126.86/294.37 (25) RewriteLemmaProof [LOWER BOUND(ID), 113 ms] 1126.86/294.37 (26) typed CpxTrs 1126.86/294.37 (27) RewriteLemmaProof [LOWER BOUND(ID), 206 ms] 1126.86/294.37 (28) typed CpxTrs 1126.86/294.37 1126.86/294.37 1126.86/294.37 ---------------------------------------- 1126.86/294.37 1126.86/294.37 (0) 1126.86/294.37 Obligation: 1126.86/294.37 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). 1126.86/294.37 1126.86/294.37 1126.86/294.37 The TRS R consists of the following rules: 1126.86/294.37 1126.86/294.37 active(zeros) -> mark(cons(0, zeros)) 1126.86/294.37 active(U11(tt, L)) -> mark(U12(tt, L)) 1126.86/294.37 active(U12(tt, L)) -> mark(s(length(L))) 1126.86/294.37 active(U21(tt, IL, M, N)) -> mark(U22(tt, IL, M, N)) 1126.86/294.37 active(U22(tt, IL, M, N)) -> mark(U23(tt, IL, M, N)) 1126.86/294.37 active(U23(tt, IL, M, N)) -> mark(cons(N, take(M, IL))) 1126.86/294.37 active(length(nil)) -> mark(0) 1126.86/294.37 active(length(cons(N, L))) -> mark(U11(tt, L)) 1126.86/294.37 active(take(0, IL)) -> mark(nil) 1126.86/294.37 active(take(s(M), cons(N, IL))) -> mark(U21(tt, IL, M, N)) 1126.86/294.37 active(cons(X1, X2)) -> cons(active(X1), X2) 1126.86/294.37 active(U11(X1, X2)) -> U11(active(X1), X2) 1126.86/294.37 active(U12(X1, X2)) -> U12(active(X1), X2) 1126.86/294.37 active(s(X)) -> s(active(X)) 1126.86/294.37 active(length(X)) -> length(active(X)) 1126.86/294.37 active(U21(X1, X2, X3, X4)) -> U21(active(X1), X2, X3, X4) 1126.86/294.37 active(U22(X1, X2, X3, X4)) -> U22(active(X1), X2, X3, X4) 1126.86/294.37 active(U23(X1, X2, X3, X4)) -> U23(active(X1), X2, X3, X4) 1126.86/294.37 active(take(X1, X2)) -> take(active(X1), X2) 1126.86/294.37 active(take(X1, X2)) -> take(X1, active(X2)) 1126.86/294.37 cons(mark(X1), X2) -> mark(cons(X1, X2)) 1126.86/294.37 U11(mark(X1), X2) -> mark(U11(X1, X2)) 1126.86/294.37 U12(mark(X1), X2) -> mark(U12(X1, X2)) 1126.86/294.37 s(mark(X)) -> mark(s(X)) 1126.86/294.37 length(mark(X)) -> mark(length(X)) 1126.86/294.37 U21(mark(X1), X2, X3, X4) -> mark(U21(X1, X2, X3, X4)) 1126.86/294.37 U22(mark(X1), X2, X3, X4) -> mark(U22(X1, X2, X3, X4)) 1126.86/294.37 U23(mark(X1), X2, X3, X4) -> mark(U23(X1, X2, X3, X4)) 1126.86/294.37 take(mark(X1), X2) -> mark(take(X1, X2)) 1126.86/294.37 take(X1, mark(X2)) -> mark(take(X1, X2)) 1126.86/294.37 proper(zeros) -> ok(zeros) 1126.86/294.37 proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) 1126.86/294.37 proper(0) -> ok(0) 1126.86/294.37 proper(U11(X1, X2)) -> U11(proper(X1), proper(X2)) 1126.86/294.37 proper(tt) -> ok(tt) 1126.86/294.37 proper(U12(X1, X2)) -> U12(proper(X1), proper(X2)) 1126.86/294.37 proper(s(X)) -> s(proper(X)) 1126.86/294.37 proper(length(X)) -> length(proper(X)) 1126.86/294.37 proper(U21(X1, X2, X3, X4)) -> U21(proper(X1), proper(X2), proper(X3), proper(X4)) 1126.86/294.37 proper(U22(X1, X2, X3, X4)) -> U22(proper(X1), proper(X2), proper(X3), proper(X4)) 1126.86/294.37 proper(U23(X1, X2, X3, X4)) -> U23(proper(X1), proper(X2), proper(X3), proper(X4)) 1126.86/294.37 proper(take(X1, X2)) -> take(proper(X1), proper(X2)) 1126.86/294.37 proper(nil) -> ok(nil) 1126.86/294.37 cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) 1126.86/294.37 U11(ok(X1), ok(X2)) -> ok(U11(X1, X2)) 1126.86/294.37 U12(ok(X1), ok(X2)) -> ok(U12(X1, X2)) 1126.86/294.37 s(ok(X)) -> ok(s(X)) 1126.86/294.37 length(ok(X)) -> ok(length(X)) 1126.86/294.37 U21(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U21(X1, X2, X3, X4)) 1126.86/294.37 U22(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U22(X1, X2, X3, X4)) 1126.86/294.37 U23(ok(X1), ok(X2), ok(X3), ok(X4)) -> ok(U23(X1, X2, X3, X4)) 1126.86/294.37 take(ok(X1), ok(X2)) -> ok(take(X1, X2)) 1126.86/294.37 top(mark(X)) -> top(proper(X))
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