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Deriv Compl Full Rewri 33144 pair #381922007
details
property
value
status
complete
benchmark
ExIntrod_GM04_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n051.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
58.394961834 seconds
cpu usage
219.837358352
max memory
4.0880128E8
stage attributes
key
value
output-size
93089
starexec-result
WORST_CASE(?,O(n^3))
output
/export/starexec/sandbox/solver/bin/starexec_run_tct_dc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^3)) * Step 1: NaturalMI WORST_CASE(?,O(n^3)) + Considered Problem: - Strict TRS: a__adx(X) -> adx(X) a__adx(cons(X,Y)) -> a__incr(cons(X,adx(Y))) a__hd(X) -> hd(X) a__hd(cons(X,Y)) -> mark(X) a__incr(X) -> incr(X) a__incr(cons(X,Y)) -> cons(s(X),incr(Y)) a__nats() -> a__adx(a__zeros()) a__nats() -> nats() a__tl(X) -> tl(X) a__tl(cons(X,Y)) -> mark(Y) a__zeros() -> cons(0(),zeros()) a__zeros() -> zeros() mark(0()) -> 0() mark(adx(X)) -> a__adx(mark(X)) mark(cons(X1,X2)) -> cons(X1,X2) mark(hd(X)) -> a__hd(mark(X)) mark(incr(X)) -> a__incr(mark(X)) mark(nats()) -> a__nats() mark(s(X)) -> s(X) mark(tl(X)) -> a__tl(mark(X)) mark(zeros()) -> a__zeros() - Signature: {a__adx/1,a__hd/1,a__incr/1,a__nats/0,a__tl/1,a__zeros/0,mark/1} / {0/0,adx/1,cons/2,hd/1,incr/1,nats/0,s/1 ,tl/1,zeros/0} - Obligation: derivational complexity wrt. signature {0,a__adx,a__hd,a__incr,a__nats,a__tl,a__zeros,adx,cons,hd,incr,mark ,nats,s,tl,zeros} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Just any strict-rules} + Details: We apply a matrix interpretation of kind triangular matrix interpretation: Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [0] p(a__adx) = [1] x1 + [0] p(a__hd) = [1] x1 + [1] p(a__incr) = [1] x1 + [0] p(a__nats) = [1] p(a__tl) = [1] x1 + [4] p(a__zeros) = [1] p(adx) = [1] x1 + [0] p(cons) = [1] x1 + [1] x2 + [0] p(hd) = [1] x1 + [1] p(incr) = [1] x1 + [0] p(mark) = [1] x1 + [0] p(nats) = [1] p(s) = [1] x1 + [0] p(tl) = [1] x1 + [4] p(zeros) = [1] Following rules are strictly oriented: a__hd(cons(X,Y)) = [1] X + [1] Y + [1] > [1] X + [0] = mark(X) a__tl(cons(X,Y)) = [1] X + [1] Y + [4] > [1] Y + [0] = mark(Y) Following rules are (at-least) weakly oriented: a__adx(X) = [1] X + [0] >= [1] X + [0] = adx(X) a__adx(cons(X,Y)) = [1] X + [1] Y + [0] >= [1] X + [1] Y + [0] = a__incr(cons(X,adx(Y))) a__hd(X) = [1] X + [1] >= [1] X + [1] = hd(X) a__incr(X) = [1] X + [0] >= [1] X + [0] = incr(X) a__incr(cons(X,Y)) = [1] X + [1] Y + [0] >= [1] X + [1] Y + [0] = cons(s(X),incr(Y)) a__nats() = [1] >= [1] = a__adx(a__zeros()) a__nats() = [1] >= [1] = nats()
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