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Runti Compl Inner Rewri 22807 pair #381904441
details
property
value
status
complete
benchmark
clevermmult.raml.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n077.star.cs.uiowa.edu
space
raML
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rci
runtime (wallclock)
5.00361800194 seconds
cpu usage
19.614501431
max memory
1.21688064E8
stage attributes
key
value
output-size
141438
starexec-result
WORST_CASE(?,O(n^3))
output
/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^3)) * Step 1: Sum WORST_CASE(?,O(n^3)) + Considered Problem: - Strict TRS: *(@x,@y) -> #mult(@x,@y) +(@x,@y) -> #add(@x,@y) computeLine(@line,@m,@acc) -> computeLine#1(@line,@acc,@m) computeLine#1(::(@x,@xs),@acc,@m) -> computeLine#2(@m,@acc,@x,@xs) computeLine#1(nil(),@acc,@m) -> @acc computeLine#2(::(@l,@ls),@acc,@x,@xs) -> computeLine(@xs,@ls,lineMult(@x,@l,@acc)) computeLine#2(nil(),@acc,@x,@xs) -> nil() lineMult(@n,@l1,@l2) -> lineMult#1(@l1,@l2,@n) lineMult#1(::(@x,@xs),@l2,@n) -> lineMult#2(@l2,@n,@x,@xs) lineMult#1(nil(),@l2,@n) -> nil() lineMult#2(::(@y,@ys),@n,@x,@xs) -> ::(+(*(@x,@n),@y),lineMult(@n,@xs,@ys)) lineMult#2(nil(),@n,@x,@xs) -> ::(*(@x,@n),lineMult(@n,@xs,nil())) matrixMult(@m1,@m2) -> matrixMult#1(@m1,@m2) matrixMult#1(::(@l,@ls),@m2) -> ::(computeLine(@l,@m2,nil()),matrixMult(@ls,@m2)) matrixMult#1(nil(),@m2) -> nil() - Weak TRS: #add(#0(),@y) -> @y #add(#neg(#s(#0())),@y) -> #pred(@y) #add(#neg(#s(#s(@x))),@y) -> #pred(#add(#pos(#s(@x)),@y)) #add(#pos(#s(#0())),@y) -> #succ(@y) #add(#pos(#s(#s(@x))),@y) -> #succ(#add(#pos(#s(@x)),@y)) #mult(#0(),#0()) -> #0() #mult(#0(),#neg(@y)) -> #0() #mult(#0(),#pos(@y)) -> #0() #mult(#neg(@x),#0()) -> #0() #mult(#neg(@x),#neg(@y)) -> #pos(#natmult(@x,@y)) #mult(#neg(@x),#pos(@y)) -> #neg(#natmult(@x,@y)) #mult(#pos(@x),#0()) -> #0() #mult(#pos(@x),#neg(@y)) -> #neg(#natmult(@x,@y)) #mult(#pos(@x),#pos(@y)) -> #pos(#natmult(@x,@y)) #natmult(#0(),@y) -> #0() #natmult(#s(@x),@y) -> #add(#pos(@y),#natmult(@x,@y)) #pred(#0()) -> #neg(#s(#0())) #pred(#neg(#s(@x))) -> #neg(#s(#s(@x))) #pred(#pos(#s(#0()))) -> #0() #pred(#pos(#s(#s(@x)))) -> #pos(#s(@x)) #succ(#0()) -> #pos(#s(#0())) #succ(#neg(#s(#0()))) -> #0() #succ(#neg(#s(#s(@x)))) -> #neg(#s(@x)) #succ(#pos(#s(@x))) -> #pos(#s(#s(@x))) - Signature: {#add/2,#mult/2,#natmult/2,#pred/1,#succ/1,*/2,+/2,computeLine/3,computeLine#1/3,computeLine#2/4,lineMult/3 ,lineMult#1/3,lineMult#2/4,matrixMult/2,matrixMult#1/2} / {#0/0,#neg/1,#pos/1,#s/1,::/2,nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {#add,#mult,#natmult,#pred,#succ,*,+,computeLine ,computeLine#1,computeLine#2,lineMult,lineMult#1,lineMult#2,matrixMult,matrixMult#1} and constructors {#0 ,#neg,#pos,#s,::,nil} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DependencyPairs WORST_CASE(?,O(n^3)) + Considered Problem: - Strict TRS: *(@x,@y) -> #mult(@x,@y) +(@x,@y) -> #add(@x,@y) computeLine(@line,@m,@acc) -> computeLine#1(@line,@acc,@m) computeLine#1(::(@x,@xs),@acc,@m) -> computeLine#2(@m,@acc,@x,@xs) computeLine#1(nil(),@acc,@m) -> @acc computeLine#2(::(@l,@ls),@acc,@x,@xs) -> computeLine(@xs,@ls,lineMult(@x,@l,@acc)) computeLine#2(nil(),@acc,@x,@xs) -> nil() lineMult(@n,@l1,@l2) -> lineMult#1(@l1,@l2,@n) lineMult#1(::(@x,@xs),@l2,@n) -> lineMult#2(@l2,@n,@x,@xs) lineMult#1(nil(),@l2,@n) -> nil() lineMult#2(::(@y,@ys),@n,@x,@xs) -> ::(+(*(@x,@n),@y),lineMult(@n,@xs,@ys)) lineMult#2(nil(),@n,@x,@xs) -> ::(*(@x,@n),lineMult(@n,@xs,nil())) matrixMult(@m1,@m2) -> matrixMult#1(@m1,@m2) matrixMult#1(::(@l,@ls),@m2) -> ::(computeLine(@l,@m2,nil()),matrixMult(@ls,@m2)) matrixMult#1(nil(),@m2) -> nil() - Weak TRS: #add(#0(),@y) -> @y #add(#neg(#s(#0())),@y) -> #pred(@y) #add(#neg(#s(#s(@x))),@y) -> #pred(#add(#pos(#s(@x)),@y)) #add(#pos(#s(#0())),@y) -> #succ(@y) #add(#pos(#s(#s(@x))),@y) -> #succ(#add(#pos(#s(@x)),@y)) #mult(#0(),#0()) -> #0() #mult(#0(),#neg(@y)) -> #0() #mult(#0(),#pos(@y)) -> #0() #mult(#neg(@x),#0()) -> #0() #mult(#neg(@x),#neg(@y)) -> #pos(#natmult(@x,@y)) #mult(#neg(@x),#pos(@y)) -> #neg(#natmult(@x,@y)) #mult(#pos(@x),#0()) -> #0() #mult(#pos(@x),#neg(@y)) -> #neg(#natmult(@x,@y)) #mult(#pos(@x),#pos(@y)) -> #pos(#natmult(@x,@y)) #natmult(#0(),@y) -> #0() #natmult(#s(@x),@y) -> #add(#pos(@y),#natmult(@x,@y)) #pred(#0()) -> #neg(#s(#0())) #pred(#neg(#s(@x))) -> #neg(#s(#s(@x))) #pred(#pos(#s(#0()))) -> #0() #pred(#pos(#s(#s(@x)))) -> #pos(#s(@x))
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