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Derivational Complexity: TRS Innermost pair #487108290
details
property
value
status
complete
benchmark
Ex1_GL02a_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
291.63 seconds
cpu usage
1142.52
user time
1130.16
system time
12.3614
max virtual memory
3.79455E7
max residence set size
1.5122096E7
stage attributes
key
value
starexec-result
WORST_CASE(Omega(n^1), ?)
output
WORST_CASE(Omega(n^1), ?) proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 431 ms] (4) CpxRelTRS (5) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxRelTRS (7) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (8) typed CpxTrs (9) OrderProof [LOWER BOUND(ID), 0 ms] (10) typed CpxTrs (11) RewriteLemmaProof [LOWER BOUND(ID), 300 ms] (12) BEST (13) proven lower bound (14) LowerBoundPropagationProof [FINISHED, 0 ms] (15) BOUNDS(n^1, INF) (16) typed CpxTrs (17) RewriteLemmaProof [LOWER BOUND(ID), 9456 ms] (18) BOUNDS(1, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: a__eq(0, 0) -> true a__eq(s(X), s(Y)) -> a__eq(X, Y) a__eq(X, Y) -> false a__inf(X) -> cons(X, inf(s(X))) a__take(0, X) -> nil a__take(s(X), cons(Y, L)) -> cons(Y, take(X, L)) a__length(nil) -> 0 a__length(cons(X, L)) -> s(length(L)) mark(eq(X1, X2)) -> a__eq(X1, X2) mark(inf(X)) -> a__inf(mark(X)) mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) mark(length(X)) -> a__length(mark(X)) mark(0) -> 0 mark(true) -> true mark(s(X)) -> s(X) mark(false) -> false mark(cons(X1, X2)) -> cons(X1, X2) mark(nil) -> nil a__eq(X1, X2) -> eq(X1, X2) a__inf(X) -> inf(X) a__take(X1, X2) -> take(X1, X2) a__length(X) -> length(X) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID)) The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem: encArg(0) -> 0 encArg(true) -> true encArg(s(x_1)) -> s(encArg(x_1)) encArg(false) -> false encArg(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(inf(x_1)) -> inf(encArg(x_1)) encArg(nil) -> nil encArg(take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(length(x_1)) -> length(encArg(x_1)) encArg(eq(x_1, x_2)) -> eq(encArg(x_1), encArg(x_2)) encArg(cons_a__eq(x_1, x_2)) -> a__eq(encArg(x_1), encArg(x_2)) encArg(cons_a__inf(x_1)) -> a__inf(encArg(x_1)) encArg(cons_a__take(x_1, x_2)) -> a__take(encArg(x_1), encArg(x_2)) encArg(cons_a__length(x_1)) -> a__length(encArg(x_1)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encode_a__eq(x_1, x_2) -> a__eq(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_true -> true encode_s(x_1) -> s(encArg(x_1)) encode_false -> false encode_a__inf(x_1) -> a__inf(encArg(x_1)) encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_inf(x_1) -> inf(encArg(x_1)) encode_a__take(x_1, x_2) -> a__take(encArg(x_1), encArg(x_2)) encode_nil -> nil encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) encode_a__length(x_1) -> a__length(encArg(x_1)) encode_length(x_1) -> length(encArg(x_1)) encode_mark(x_1) -> mark(encArg(x_1)) encode_eq(x_1, x_2) -> eq(encArg(x_1), encArg(x_2)) ----------------------------------------
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