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Derivational Complexity: TRS Innermost pair #487108394
details
property
value
status
complete
benchmark
OvConsOS_nosorts_noand_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n149.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
141.376 seconds
cpu usage
551.596
user time
542.104
system time
9.49198
max virtual memory
1.951698E7
max residence set size
1.4655E7
stage attributes
key
value
starexec-result
WORST_CASE(NON_POLY, ?)
output
WORST_CASE(NON_POLY, ?) proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(INF, INF). (0) DCpxTrs (1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxRelTRS (3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 894 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 2 ms] (8) BEST (9) proven lower bound (10) LowerBoundPropagationProof [FINISHED, 0 ms] (11) BOUNDS(n^1, INF) (12) TRS for Loop Detection (13) InfiniteLowerBoundProof [FINISHED, 39.5 s] (14) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: a__zeros -> cons(0, zeros) a__U11(tt, L) -> a__U12(tt, L) a__U12(tt, L) -> s(a__length(mark(L))) a__U21(tt, IL, M, N) -> a__U22(tt, IL, M, N) a__U22(tt, IL, M, N) -> a__U23(tt, IL, M, N) a__U23(tt, IL, M, N) -> cons(mark(N), take(M, IL)) a__length(nil) -> 0 a__length(cons(N, L)) -> a__U11(tt, L) a__take(0, IL) -> nil a__take(s(M), cons(N, IL)) -> a__U21(tt, IL, M, N) mark(zeros) -> a__zeros mark(U11(X1, X2)) -> a__U11(mark(X1), X2) mark(U12(X1, X2)) -> a__U12(mark(X1), X2) mark(length(X)) -> a__length(mark(X)) mark(U21(X1, X2, X3, X4)) -> a__U21(mark(X1), X2, X3, X4) mark(U22(X1, X2, X3, X4)) -> a__U22(mark(X1), X2, X3, X4) mark(U23(X1, X2, X3, X4)) -> a__U23(mark(X1), X2, X3, X4) mark(take(X1, X2)) -> a__take(mark(X1), mark(X2)) mark(cons(X1, X2)) -> cons(mark(X1), X2) mark(0) -> 0 mark(tt) -> tt mark(s(X)) -> s(mark(X)) mark(nil) -> nil a__zeros -> zeros a__U11(X1, X2) -> U11(X1, X2) a__U12(X1, X2) -> U12(X1, X2) a__length(X) -> length(X) a__U21(X1, X2, X3, X4) -> U21(X1, X2, X3, X4) a__U22(X1, X2, X3, X4) -> U22(X1, X2, X3, X4) a__U23(X1, X2, X3, X4) -> U23(X1, X2, X3, X4) a__take(X1, X2) -> take(X1, X2) 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(cons(x_1, x_2)) -> cons(encArg(x_1), encArg(x_2)) encArg(0) -> 0 encArg(zeros) -> zeros encArg(tt) -> tt encArg(s(x_1)) -> s(encArg(x_1)) encArg(take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(nil) -> nil encArg(U11(x_1, x_2)) -> U11(encArg(x_1), encArg(x_2)) encArg(U12(x_1, x_2)) -> U12(encArg(x_1), encArg(x_2)) encArg(length(x_1)) -> length(encArg(x_1)) encArg(U21(x_1, x_2, x_3, x_4)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(U22(x_1, x_2, x_3, x_4)) -> U22(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(U23(x_1, x_2, x_3, x_4)) -> U23(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_a__zeros) -> a__zeros encArg(cons_a__U11(x_1, x_2)) -> a__U11(encArg(x_1), encArg(x_2)) encArg(cons_a__U12(x_1, x_2)) -> a__U12(encArg(x_1), encArg(x_2)) encArg(cons_a__U21(x_1, x_2, x_3, x_4)) -> a__U21(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_a__U22(x_1, x_2, x_3, x_4)) -> a__U22(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_a__U23(x_1, x_2, x_3, x_4)) -> a__U23(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_a__length(x_1)) -> a__length(encArg(x_1)) encArg(cons_a__take(x_1, x_2)) -> a__take(encArg(x_1), encArg(x_2)) encArg(cons_mark(x_1)) -> mark(encArg(x_1)) encode_a__zeros -> a__zeros encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_zeros -> zeros encode_a__U11(x_1, x_2) -> a__U11(encArg(x_1), encArg(x_2)) encode_tt -> tt
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