Runti Compl Inner Rewri 22807 pair #381904516

details

property	value
status	complete
benchmark	dyade.raml.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n042.star.cs.uiowa.edu
space	raML

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rci
runtime (wallclock)	4.33415102959 seconds
cpu usage	15.633031922
max memory	9.1492352E7

stage attributes

key	value
output-size	43908
starexec-result	WORST_CASE(?,O(n^2))

output

/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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WORST_CASE(?,O(n^2))
* Step 1: Sum WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            *(@x,@y) -> #mult(@x,@y)
            dyade(@l1,@l2) -> dyade#1(@l1,@l2)
            dyade#1(::(@x,@xs),@l2) -> ::(mult(@x,@l2),dyade(@xs,@l2))
            dyade#1(nil(),@l2) -> nil()
            mult(@n,@l) -> mult#1(@l,@n)
            mult#1(::(@x,@xs),@n) -> ::(*(@n,@x),mult(@n,@xs))
            mult#1(nil(),@n) -> 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,dyade/2,dyade#1/2,mult/2,mult#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,*,dyade,dyade#1,mult
            ,mult#1} and constructors {#0,#neg,#pos,#s,::,nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DependencyPairs WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            *(@x,@y) -> #mult(@x,@y)
            dyade(@l1,@l2) -> dyade#1(@l1,@l2)
            dyade#1(::(@x,@xs),@l2) -> ::(mult(@x,@l2),dyade(@xs,@l2))
            dyade#1(nil(),@l2) -> nil()
            mult(@n,@l) -> mult#1(@l,@n)
            mult#1(::(@x,@xs),@n) -> ::(*(@n,@x),mult(@n,@xs))
            mult#1(nil(),@n) -> 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,dyade/2,dyade#1/2,mult/2,mult#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,*,dyade,dyade#1,mult
            ,mult#1} and constructors {#0,#neg,#pos,#s,::,nil}
    + Applied Processor:
        DependencyPairs {dpKind_ = WIDP}
    + Details:
        We add the following weak innermost dependency pairs:
        
        Strict DPs
          *#(@x,@y) -> c_1(#mult#(@x,@y))

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