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Deriv Compl Full Rewri 33144 pair #381922257
details
property
value
status
complete
benchmark
#3.17a.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n052.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
222.753782988 seconds
cpu usage
371.053867617
max memory
3.13399296E9
stage attributes
key
value
output-size
15925
starexec-result
WORST_CASE(?,O(n^6))
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^6)) * Step 1: DecomposeCP WORST_CASE(?,O(n^6)) + Considered Problem: - Strict TRS: app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) app(nil(),k) -> k plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) pred(cons(s(x),nil())) -> cons(x,nil()) sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k))))) sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l)) sum(cons(x,nil())) -> cons(x,nil()) sum(plus(cons(0(),x),cons(y,l))) -> pred(sum(cons(s(x),cons(y,l)))) - Signature: {app/2,plus/2,pred/1,sum/1} / {0/0,cons/2,nil/0,s/1} - Obligation: derivational complexity wrt. signature {0,app,cons,nil,plus,pred,s,sum} + Applied Processor: DecomposeCP {onSelectionCP_ = any strict-rules, withBoundCP_ = RelativeComp, withCP_ = NaturalMI {miDimension = 2, miDegree = 2, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Nothing}} + Details: We first use the processor NaturalMI {miDimension = 2, miDegree = 2, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Nothing} to orient following rules strictly: app(l,nil()) -> l app(nil(),k) -> k plus(0(),y) -> y pred(cons(s(x),nil())) -> cons(x,nil()) sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k))))) sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l)) The Processor induces the complexity certificate TIME (?,O(n^2)) SPACE(?,?) Observe that weak rules from Problem (R) are non-size-increasing. Once the complexity of (R) has been assessed, it suffices to consider only rules whose complexity has not been estimated in (R) resulting in the following Problem (S). Overall the certificate is obtained by composition. Problem (S) - Strict TRS: app(cons(x,l),k) -> cons(x,app(l,k)) plus(s(x),y) -> s(plus(x,y)) sum(cons(x,nil())) -> cons(x,nil()) sum(plus(cons(0(),x),cons(y,l))) -> pred(sum(cons(s(x),cons(y,l)))) - Signature: {app/2,plus/2,pred/1,sum/1} / {0/0,cons/2,nil/0,s/1} - Obligation: derivational complexity wrt. signature {0,app,cons,nil,plus,pred,s,sum} ** Step 1.a:1: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) app(nil(),k) -> k plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) pred(cons(s(x),nil())) -> cons(x,nil()) sum(app(l,cons(x,cons(y,k)))) -> sum(app(l,sum(cons(x,cons(y,k))))) sum(cons(x,cons(y,l))) -> sum(cons(plus(x,y),l)) sum(cons(x,nil())) -> cons(x,nil()) sum(plus(cons(0(),x),cons(y,l))) -> pred(sum(cons(s(x),cons(y,l)))) - Signature: {app/2,plus/2,pred/1,sum/1} / {0/0,cons/2,nil/0,s/1} - Obligation: derivational complexity wrt. signature {0,app,cons,nil,plus,pred,s,sum} + Applied Processor: NaturalMI {miDimension = 2, miDegree = 2, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Just first alternative for decompose on 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) = [1] [2] p(app) = [1 0] x1 + [1 1] x2 + [2] [0 1] [0 1] [0] p(cons) = [1 1] x1 + [1 0] x2 + [1] [0 0] [0 1] [1] p(nil) = [1] [0] p(plus) = [1 1] x1 + [1 0] x2 + [0] [0 0] [0 1] [0] p(pred) = [1 2] x1 + [2] [0 0] [1] p(s) = [1 0] x1 + [0] [0 1] [0] p(sum) = [1 0] x1 + [0] [0 0] [1] Following rules are strictly oriented: app(l,nil()) = [1 0] l + [3] [0 1] [0] > [1 0] l + [0] [0 1] [0] = l
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