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Runti Compl Full Rewri 10127 pair #381903795
details
property
value
status
complete
benchmark
Ex4_7_56_Bor03_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n056.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
complexity
runtime (wallclock)
8.4059278965 seconds
cpu usage
23.800835033
max memory
4.153266176E9
stage attributes
key
value
output-size
23077
starexec-result
WORST_CASE(Omega(n^1), O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_complexity /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^1)) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). (0) CpxTRS (1) NestedDefinedSymbolProof [UPPER BOUND(ID), 0 ms] (2) CpxTRS (3) RelTrsToTrsProof [UPPER BOUND(ID), 0 ms] (4) CpxTRS (5) CpxTrsMatchBoundsTAProof [FINISHED, 72 ms] (6) BOUNDS(1, n^1) (7) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (8) CpxTRS (9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (10) typed CpxTrs (11) OrderProof [LOWER BOUND(ID), 0 ms] (12) typed CpxTrs (13) RewriteLemmaProof [LOWER BOUND(ID), 451 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 145 ms] (20) typed CpxTrs (21) RewriteLemmaProof [LOWER BOUND(ID), 121 ms] (22) typed CpxTrs (23) RewriteLemmaProof [LOWER BOUND(ID), 91 ms] (24) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(n^1, n^1). The TRS R consists of the following rules: active(from(X)) -> mark(cons(X, from(s(X)))) active(after(0, XS)) -> mark(XS) active(after(s(N), cons(X, XS))) -> mark(after(N, XS)) active(from(X)) -> from(active(X)) active(cons(X1, X2)) -> cons(active(X1), X2) active(s(X)) -> s(active(X)) active(after(X1, X2)) -> after(active(X1), X2) active(after(X1, X2)) -> after(X1, active(X2)) from(mark(X)) -> mark(from(X)) cons(mark(X1), X2) -> mark(cons(X1, X2)) s(mark(X)) -> mark(s(X)) after(mark(X1), X2) -> mark(after(X1, X2)) after(X1, mark(X2)) -> mark(after(X1, X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(s(X)) -> s(proper(X)) proper(after(X1, X2)) -> after(proper(X1), proper(X2)) proper(0) -> ok(0) from(ok(X)) -> ok(from(X)) cons(ok(X1), ok(X2)) -> ok(cons(X1, X2)) s(ok(X)) -> ok(s(X)) after(ok(X1), ok(X2)) -> ok(after(X1, X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) S is empty. Rewrite Strategy: FULL ---------------------------------------- (1) NestedDefinedSymbolProof (UPPER BOUND(ID)) The following defined symbols can occur below the 0th argument of top: proper, active The following defined symbols can occur below the 0th argument of proper: proper, active The following defined symbols can occur below the 0th argument of active: proper, active Hence, the left-hand sides of the following rules are not basic-reachable and can be removed: active(from(X)) -> mark(cons(X, from(s(X)))) active(after(0, XS)) -> mark(XS) active(after(s(N), cons(X, XS))) -> mark(after(N, XS)) active(from(X)) -> from(active(X)) active(cons(X1, X2)) -> cons(active(X1), X2) active(s(X)) -> s(active(X)) active(after(X1, X2)) -> after(active(X1), X2) active(after(X1, X2)) -> after(X1, active(X2)) proper(from(X)) -> from(proper(X)) proper(cons(X1, X2)) -> cons(proper(X1), proper(X2)) proper(s(X)) -> s(proper(X)) proper(after(X1, X2)) -> after(proper(X1), proper(X2)) ---------------------------------------- (2)
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