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<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked="sum"><NAME>Marked_sum</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>-</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>avg</NAME></SYMBOL><SYMBOL arity="2" unmarked="+"><NAME>Marked_+</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>++</NAME></SYMBOL><SYMBOL arity="2" unmarked="quot"><NAME>Marked_quot</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>:</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>length</NAME></SYMBOL><SYMBOL arity="2" unmarked="-"><NAME>Marked_-</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="1" unmarked="hd"><NAME>Marked_hd</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>sum</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>hd</NAME></SYMBOL><SYMBOL arity="2" unmarked="++"><NAME>Marked_++</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="1" unmarked="avg"><NAME>Marked_avg</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>nil</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>quot</NAME></SYMBOL><SYMBOL arity="1" unmarked="length"><NAME>Marked_length</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>+</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>ys</VAR><VAR>xs</VAR><VAR>z</VAR><VAR>y</VAR><VAR>x</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>+(0,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>+(s(x),y)</LHS><RHS>s(+(x,y))</RHS></RULE><RULE><LHS>++(nil,ys)</LHS><RHS>ys</RHS></RULE><RULE><LHS>++(:(x,xs),ys)</LHS><RHS>:(x,++(xs,ys))</RHS></RULE><RULE><LHS>sum(:(x,nil))</LHS><RHS>:(x,nil)</RHS></RULE><RULE><LHS>sum(:(x,:(y,xs)))</LHS><RHS>sum(:(+(x,y),xs))</RHS></RULE><RULE><LHS>sum(++(xs,:(x,:(y,ys))))</LHS><RHS>sum(++(xs,sum(:(x,:(y,ys)))))</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS>quot(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>quot(s(x),s(y))</LHS><RHS>s(quot(-(x,y),s(y)))</RHS></RULE><RULE><LHS>length(nil)</LHS><RHS>0</RHS></RULE><RULE><LHS>length(:(x,xs))</LHS><RHS>s(length(xs))</RHS></RULE><RULE><LHS>hd(:(x,xs))</LHS><RHS>x</RHS></RULE><RULE><LHS>avg(xs)</LHS><RHS>quot(hd(sum(xs)),length(xs))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>+(0,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>+(s(x),y)</LHS><RHS>s(+(x,y))</RHS></RULE><RULE><LHS>++(nil,ys)</LHS><RHS>ys</RHS></RULE><RULE><LHS>++(:(x,xs),ys)</LHS><RHS>:(x,++(xs,ys))</RHS></RULE><RULE><LHS>sum(:(x,nil))</LHS><RHS>:(x,nil)</RHS></RULE><RULE><LHS>sum(:(x,:(y,xs)))</LHS><RHS>sum(:(+(x,y),xs))</RHS></RULE><RULE><LHS>sum(++(xs,:(x,:(y,ys))))</LHS><RHS>sum(++(xs,sum(:(x,:(y,ys)))))</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS>quot(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>quot(s(x),s(y))</LHS><RHS>s(quot(-(x,y),s(y)))</RHS></RULE><RULE><LHS>length(nil)</LHS><RHS>0</RHS></RULE><RULE><LHS>length(:(x,xs))</LHS><RHS>s(length(xs))</RHS></RULE><RULE><LHS>hd(:(x,xs))</LHS><RHS>x</RHS></RULE><RULE><LHS>avg(xs)</LHS><RHS>quot(hd(sum(xs)),length(xs))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_+(s(x),y)</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_++(:(x,xs),ys)</LHS><RHS>Marked_++(xs,ys)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_sum(:(x,:(y,xs)))</LHS><RHS>Marked_sum(:(+(x,y),xs))</RHS></DPRULE><DPRULE num="3"><LHS>Marked_sum(:(x,:(y,xs)))</LHS><RHS>Marked_+(x,y)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_sum(++(xs,:(x,:(y,ys))))</LHS><RHS>Marked_sum(++(xs,sum(:(x,:(y,ys)))))</RHS></DPRULE><DPRULE num="5"><LHS>Marked_sum(++(xs,:(x,:(y,ys))))</LHS><RHS>Marked_++(xs,sum(:(x,:(y,ys))))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_sum(++(xs,:(x,:(y,ys))))</LHS><RHS>Marked_sum(:(x,:(y,ys)))</RHS></DPRULE><DPRULE num="7"><LHS>Marked_-(s(x),s(y))</LHS><RHS>Marked_-(x,y)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_quot(s(x),s(y))</LHS><RHS>Marked_quot(-(x,y),s(y))</RHS></DPRULE><DPRULE num="9"><LHS>Marked_quot(s(x),s(y))</LHS><RHS>Marked_-(x,y)</RHS></DPRULE><DPRULE num="10"><LHS>Marked_length(:(x,xs))</LHS><RHS>Marked_length(xs)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_avg(xs)</LHS><RHS>Marked_quot(hd(sum(xs)),length(xs))</RHS></DPRULE><DPRULE num="12"><LHS>Marked_avg(xs)</LHS><RHS>Marked_hd(sum(xs))</RHS></DPRULE><DPRULE num="13"><LHS>Marked_avg(xs)</LHS><RHS>Marked_sum(xs)</RHS></DPRULE><DPRULE num="14"><LHS>Marked_avg(xs)</LHS><RHS>Marked_length(xs)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="14"/></NONSCC><SCC num="1"><NODE ref="10"/></SCC><NONSCC num="2"><NODE ref="13"/></NONSCC><NONSCC num="3"><NODE ref="6"/></NONSCC><NONSCC num="4"><NODE ref="5"/></NONSCC><SCC num="5"><NODE ref="4"/></SCC><NONSCC num="6"><NODE ref="3"/></NONSCC><SCC num="7"><NODE ref="2"/></SCC><NONSCC num="8"><NODE ref="12"/></NONSCC><NONSCC num="9"><NODE ref="11"/></NONSCC><NONSCC num="10"><NODE ref="9"/></NONSCC><SCC num="11"><NODE ref="8"/></SCC><SCC num="12"><NODE ref="7"/></SCC><SCC num="13"><NODE ref="1"/></SCC><SCC num="14"><NODE ref="0"/></SCC></CCLIST><EDGE end="1" start="0"/><EDGE end="7" start="2"/><EDGE end="6" start="2"/><EDGE end="5" start="2"/><EDGE end="4" start="2"/><EDGE end="3" start="2"/><EDGE end="7" start="3"/><EDGE end="6" start="3"/><EDGE end="13" start="4"/><EDGE end="7" start="5"/><EDGE end="6" start="5"/><EDGE end="4" start="5"/><EDGE end="3" start="5"/><EDGE end="14" start="6"/><EDGE end="6" start="7"/><EDGE end="11" start="9"/><EDGE end="10" start="9"/><EDGE end="12" start="10"/><EDGE end="10" start="11"/></DAG></CRITERION><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>+(0,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>+(s(x),y)</LHS><RHS>s(+(x,y))</RHS></RULE><RULE><LHS>++(nil,ys)</LHS><RHS>ys</RHS></RULE><RULE><LHS>++(:(x,xs),ys)</LHS><RHS>:(x,++(xs,ys))</RHS></RULE><RULE><LHS>sum(:(x,nil))</LHS><RHS>:(x,nil)</RHS></RULE><RULE><LHS>sum(:(x,:(y,xs)))</LHS><RHS>sum(:(+(x,y),xs))</RHS></RULE><RULE><LHS>sum(++(xs,:(x,:(y,ys))))</LHS><RHS>sum(++(xs,sum(:(x,:(y,ys)))))</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS>quot(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>quot(s(x),s(y))</LHS><RHS>s(quot(-(x,y),s(y)))</RHS></RULE><RULE><LHS>length(nil)</LHS><RHS>0</RHS></RULE><RULE><LHS>length(:(x,xs))</LHS><RHS>s(length(xs))</RHS></RULE><RULE><LHS>hd(:(x,xs))</LHS><RHS>x</RHS></RULE><RULE><LHS>avg(xs)</LHS><RHS>quot(hd(sum(xs)),length(xs))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_quot(s(x),s(y))</LHS><RHS>Marked_quot(-(x,y),s(y))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>+</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>quot</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>hd</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>sum</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>length</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>:</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_quot</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>++</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>avg</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>-</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING></CRITERION></PROPERTY><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>+(0,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>+(s(x),y)</LHS><RHS>s(+(x,y))</RHS></RULE><RULE><LHS>++(nil,ys)</LHS><RHS>ys</RHS></RULE><RULE><LHS>++(:(x,xs),ys)</LHS><RHS>:(x,++(xs,ys))</RHS></RULE><RULE><LHS>sum(:(x,nil))</LHS><RHS>:(x,nil)</RHS></RULE><RULE><LHS>sum(:(x,:(y,xs)))</LHS><RHS>sum(:(+(x,y),xs))</RHS></RULE><RULE><LHS>sum(++(xs,:(x,:(y,ys))))</LHS><RHS>sum(++(xs,sum(:(x,:(y,ys)))))</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS>quot(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>quot(s(x),s(y))</LHS><RHS>s(quot(-(x,y),s(y)))</RHS></RULE><RULE><LHS>length(nil)</LHS><RHS>0</RHS></RULE><RULE><LHS>length(:(x,xs))</LHS><RHS>s(length(xs))</RHS></RULE><RULE><LHS>hd(:(x,xs))</LHS><RHS>x</RHS></RULE><RULE><LHS>avg(xs)</LHS><RHS>quot(hd(sum(xs)),length(xs))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_-(s(x),s(y))</LHS><RHS>Marked_-(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>+</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>quot</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>hd</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>sum</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_-</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>length</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>:</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>++</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>avg</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>-</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING></CRITERION></PROPERTY><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>+(0,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>+(s(x),y)</LHS><RHS>s(+(x,y))</RHS></RULE><RULE><LHS>++(nil,ys)</LHS><RHS>ys</RHS></RULE><RULE><LHS>++(:(x,xs),ys)</LHS><RHS>:(x,++(xs,ys))</RHS></RULE><RULE><LHS>sum(:(x,nil))</LHS><RHS>:(x,nil)</RHS></RULE><RULE><LHS>sum(:(x,:(y,xs)))</LHS><RHS>sum(:(+(x,y),xs))</RHS></RULE><RULE><LHS>sum(++(xs,:(x,:(y,ys))))</LHS><RHS>sum(++(xs,sum(:(x,:(y,ys)))))</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS>quot(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>quot(s(x),s(y))</LHS><RHS>s(quot(-(x,y),s(y)))</RHS></RULE><RULE><LHS>length(nil)</LHS><RHS>0</RHS></RULE><RULE><LHS>length(:(x,xs))</LHS><RHS>s(length(xs))</RHS></RULE><RULE><LHS>hd(:(x,xs))</LHS><RHS>x</RHS></RULE><RULE><LHS>avg(xs)</LHS><RHS>quot(hd(sum(xs)),length(xs))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_sum(++(xs,:(x,:(y,ys))))</LHS><RHS>Marked_sum(++(xs,sum(:(x,:(y,ys)))))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING numstrictcol="1" size="3" type="matrix"><POLYSYMB><SYMBOL><NAME>+</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>1</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>1</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>1</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>quot</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>1</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>1</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>1</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>1</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>hd</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>1</INT><INT>1</INT></COLUMN><COLUMN><INT>1</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>sum</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>1</INT><INT>1</INT><INT>1</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>length</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>:</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>1</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>1</INT><INT>1</INT><INT>1</INT></COLUMN><COLUMN><INT>1</INT><INT>1</INT><INT>1</INT></COLUMN><COLUMN><INT>1</INT><INT>1</INT><INT>1</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>1</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>1</INT><INT>0</INT><INT>1</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>++</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>1</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>1</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>1</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>1</INT><INT>1</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>1</INT><INT>0</INT></COLUMN><COLUMN><INT>1</INT><INT>1</INT><INT>1</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>avg</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>1</INT><INT>1</INT><INT>1</INT></COLUMN><COLUMN><INT>0</INT><INT>1</INT><INT>1</INT></COLUMN><COLUMN><INT>1</INT><INT>1</INT><INT>1</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>-</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>1</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>1</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>1</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_sum</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>1</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><MATRIX><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN><COLUMN><INT>0</INT><INT>0</INT><INT>0</INT></COLUMN></MATRIX></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING></CRITERION></PROPERTY><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>+(0,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>+(s(x),y)</LHS><RHS>s(+(x,y))</RHS></RULE><RULE><LHS>++(nil,ys)</LHS><RHS>ys</RHS></RULE><RULE><LHS>++(:(x,xs),ys)</LHS><RHS>:(x,++(xs,ys))</RHS></RULE><RULE><LHS>sum(:(x,nil))</LHS><RHS>:(x,nil)</RHS></RULE><RULE><LHS>sum(:(x,:(y,xs)))</LHS><RHS>sum(:(+(x,y),xs))</RHS></RULE><RULE><LHS>sum(++(xs,:(x,:(y,ys))))</LHS><RHS>sum(++(xs,sum(:(x,:(y,ys)))))</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS>quot(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>quot(s(x),s(y))</LHS><RHS>s(quot(-(x,y),s(y)))</RHS></RULE><RULE><LHS>length(nil)</LHS><RHS>0</RHS></RULE><RULE><LHS>length(:(x,xs))</LHS><RHS>s(length(xs))</RHS></RULE><RULE><LHS>hd(:(x,xs))</LHS><RHS>x</RHS></RULE><RULE><LHS>avg(xs)</LHS><RHS>quot(hd(sum(xs)),length(xs))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_++(:(x,xs),ys)</LHS><RHS>Marked_++(xs,ys)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>+</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>quot</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_++</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>hd</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>sum</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>length</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>:</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>++</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>avg</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>-</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING></CRITERION></PROPERTY><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>+(0,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>+(s(x),y)</LHS><RHS>s(+(x,y))</RHS></RULE><RULE><LHS>++(nil,ys)</LHS><RHS>ys</RHS></RULE><RULE><LHS>++(:(x,xs),ys)</LHS><RHS>:(x,++(xs,ys))</RHS></RULE><RULE><LHS>sum(:(x,nil))</LHS><RHS>:(x,nil)</RHS></RULE><RULE><LHS>sum(:(x,:(y,xs)))</LHS><RHS>sum(:(+(x,y),xs))</RHS></RULE><RULE><LHS>sum(++(xs,:(x,:(y,ys))))</LHS><RHS>sum(++(xs,sum(:(x,:(y,ys)))))</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS>quot(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>quot(s(x),s(y))</LHS><RHS>s(quot(-(x,y),s(y)))</RHS></RULE><RULE><LHS>length(nil)</LHS><RHS>0</RHS></RULE><RULE><LHS>length(:(x,xs))</LHS><RHS>s(length(xs))</RHS></RULE><RULE><LHS>hd(:(x,xs))</LHS><RHS>x</RHS></RULE><RULE><LHS>avg(xs)</LHS><RHS>quot(hd(sum(xs)),length(xs))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_sum(:(x,:(y,xs)))</LHS><RHS>Marked_sum(:(+(x,y),xs))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>+</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>quot</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>hd</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>sum</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>length</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>:</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>++</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>avg</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>-</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_sum</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING></CRITERION></PROPERTY><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>+(0,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>+(s(x),y)</LHS><RHS>s(+(x,y))</RHS></RULE><RULE><LHS>++(nil,ys)</LHS><RHS>ys</RHS></RULE><RULE><LHS>++(:(x,xs),ys)</LHS><RHS>:(x,++(xs,ys))</RHS></RULE><RULE><LHS>sum(:(x,nil))</LHS><RHS>:(x,nil)</RHS></RULE><RULE><LHS>sum(:(x,:(y,xs)))</LHS><RHS>sum(:(+(x,y),xs))</RHS></RULE><RULE><LHS>sum(++(xs,:(x,:(y,ys))))</LHS><RHS>sum(++(xs,sum(:(x,:(y,ys)))))</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS>quot(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>quot(s(x),s(y))</LHS><RHS>s(quot(-(x,y),s(y)))</RHS></RULE><RULE><LHS>length(nil)</LHS><RHS>0</RHS></RULE><RULE><LHS>length(:(x,xs))</LHS><RHS>s(length(xs))</RHS></RULE><RULE><LHS>hd(:(x,xs))</LHS><RHS>x</RHS></RULE><RULE><LHS>avg(xs)</LHS><RHS>quot(hd(sum(xs)),length(xs))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_+(s(x),y)</LHS><RHS>Marked_+(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>+</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>quot</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>hd</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>sum</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>length</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>:</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>++</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_+</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>avg</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>-</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING></CRITERION></PROPERTY><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>+(0,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>+(s(x),y)</LHS><RHS>s(+(x,y))</RHS></RULE><RULE><LHS>++(nil,ys)</LHS><RHS>ys</RHS></RULE><RULE><LHS>++(:(x,xs),ys)</LHS><RHS>:(x,++(xs,ys))</RHS></RULE><RULE><LHS>sum(:(x,nil))</LHS><RHS>:(x,nil)</RHS></RULE><RULE><LHS>sum(:(x,:(y,xs)))</LHS><RHS>sum(:(+(x,y),xs))</RHS></RULE><RULE><LHS>sum(++(xs,:(x,:(y,ys))))</LHS><RHS>sum(++(xs,sum(:(x,:(y,ys)))))</RHS></RULE><RULE><LHS>-(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>-(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>-(s(x),s(y))</LHS><RHS>-(x,y)</RHS></RULE><RULE><LHS>quot(0,s(y))</LHS><RHS>0</RHS></RULE><RULE><LHS>quot(s(x),s(y))</LHS><RHS>s(quot(-(x,y),s(y)))</RHS></RULE><RULE><LHS>length(nil)</LHS><RHS>0</RHS></RULE><RULE><LHS>length(:(x,xs))</LHS><RHS>s(length(xs))</RHS></RULE><RULE><LHS>hd(:(x,xs))</LHS><RHS>x</RHS></RULE><RULE><LHS>avg(xs)</LHS><RHS>quot(hd(sum(xs)),length(xs))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_length(:(x,xs))</LHS><RHS>Marked_length(xs)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>+</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_length</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>3</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>quot</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>nil</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>s</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>hd</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>sum</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>0</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>length</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>:</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>++</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>2</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="1"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>avg</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></MONOME></POLYNOMIAL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>-</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF><ARG degree="1" num="0"/></MONOME></POLYNOMIAL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></SUMPOLY></POLYNOMIAL></POLYSYMB></ORDERING></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROOF>
