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Derivational Complexity: TRS pair #487103828
details
property
value
status
complete
benchmark
OvConsOS_nosorts-noand_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n150.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
rcdcRelativeAlsoLower
runtime (wallclock)
139.091 seconds
cpu usage
538.799
user time
528.87
system time
9.92875
max virtual memory
3.800956E7
max residence set size
1.464362E7
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(INF, INF).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), 558 ms] (4) CpxRelTRS (5) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (6) TRS for Loop Detection (7) DecreasingLoopProof [LOWER BOUND(ID), 64 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, 37.1 s] (14) BOUNDS(INF, INF) ---------------------------------------- (0) Obligation: The Derivational Complexity (full) of the given DCpxTrs could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: zeros -> cons(0, n__zeros) U11(tt, L) -> U12(tt, activate(L)) U12(tt, L) -> s(length(activate(L))) U21(tt, IL, M, N) -> U22(tt, activate(IL), activate(M), activate(N)) U22(tt, IL, M, N) -> U23(tt, activate(IL), activate(M), activate(N)) U23(tt, IL, M, N) -> cons(activate(N), n__take(activate(M), activate(IL))) length(nil) -> 0 length(cons(N, L)) -> U11(tt, activate(L)) take(0, IL) -> nil take(s(M), cons(N, IL)) -> U21(tt, activate(IL), M, N) zeros -> n__zeros take(X1, X2) -> n__take(X1, X2) activate(n__zeros) -> zeros activate(n__take(X1, X2)) -> take(X1, X2) activate(X) -> X S is empty. Rewrite Strategy: FULL ---------------------------------------- (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(n__zeros) -> n__zeros encArg(tt) -> tt encArg(s(x_1)) -> s(encArg(x_1)) encArg(n__take(x_1, x_2)) -> n__take(encArg(x_1), encArg(x_2)) encArg(nil) -> nil encArg(cons_zeros) -> zeros encArg(cons_U11(x_1, x_2)) -> U11(encArg(x_1), encArg(x_2)) encArg(cons_U12(x_1, x_2)) -> U12(encArg(x_1), encArg(x_2)) encArg(cons_U21(x_1, x_2, x_3, x_4)) -> U21(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U22(x_1, x_2, x_3, x_4)) -> U22(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_U23(x_1, x_2, x_3, x_4)) -> U23(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encArg(cons_length(x_1)) -> length(encArg(x_1)) encArg(cons_take(x_1, x_2)) -> take(encArg(x_1), encArg(x_2)) encArg(cons_activate(x_1)) -> activate(encArg(x_1)) encode_zeros -> zeros encode_cons(x_1, x_2) -> cons(encArg(x_1), encArg(x_2)) encode_0 -> 0 encode_n__zeros -> n__zeros encode_U11(x_1, x_2) -> U11(encArg(x_1), encArg(x_2)) encode_tt -> tt encode_U12(x_1, x_2) -> U12(encArg(x_1), encArg(x_2)) encode_activate(x_1) -> activate(encArg(x_1)) encode_s(x_1) -> s(encArg(x_1)) encode_length(x_1) -> length(encArg(x_1)) encode_U21(x_1, x_2, x_3, x_4) -> U21(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U22(x_1, x_2, x_3, x_4) -> U22(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_U23(x_1, x_2, x_3, x_4) -> U23(encArg(x_1), encArg(x_2), encArg(x_3), encArg(x_4)) encode_n__take(x_1, x_2) -> n__take(encArg(x_1), encArg(x_2)) encode_nil -> nil encode_take(x_1, x_2) -> take(encArg(x_1), encArg(x_2)) ---------------------------------------- (2) Obligation: The Runtime Complexity (full) of the given CpxRelTRS could be proven to be BOUNDS(INF, INF). The TRS R consists of the following rules: zeros -> cons(0, n__zeros)
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