<?xml version="1.0" encoding="UTF-8"?>
<!DOCTYPE PROOF SYSTEM "http://a3pat.ensiie.fr/pub/a3pat.dtd">
<PROOF><SIGNATURE><SYMBOLLIST><SYMBOL arity="1" unmarked="quicksort"><NAME>Marked_quicksort</NAME></SYMBOL><SYMBOL arity="2" unmarked="minus"><NAME>Marked_minus</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>app</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>if_low</NAME></SYMBOL><SYMBOL arity="3" unmarked="if_high"><NAME>Marked_if_high</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>quot</NAME></SYMBOL><SYMBOL arity="3" unmarked=""><NAME>if_high</NAME></SYMBOL><SYMBOL arity="3" unmarked="if_low"><NAME>Marked_if_low</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>le</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>add</NAME></SYMBOL><SYMBOL arity="2" unmarked="low"><NAME>Marked_low</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>0</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>quicksort</NAME></SYMBOL><SYMBOL arity="2" unmarked="quot"><NAME>Marked_quot</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>false</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>low</NAME></SYMBOL><SYMBOL arity="2" unmarked="high"><NAME>Marked_high</NAME></SYMBOL><SYMBOL arity="1" unmarked=""><NAME>s</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>high</NAME></SYMBOL><SYMBOL arity="2" unmarked="le"><NAME>Marked_le</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>true</NAME></SYMBOL><SYMBOL arity="0" unmarked=""><NAME>nil</NAME></SYMBOL><SYMBOL arity="2" unmarked="app"><NAME>Marked_app</NAME></SYMBOL><SYMBOL arity="2" unmarked=""><NAME>minus</NAME></SYMBOL></SYMBOLLIST><VARLIST><VAR>n</VAR><VAR>m</VAR><VAR>y</VAR><VAR>x</VAR></VARLIST></SIGNATURE><PROPERTY criterion="dp" prop="sntrs"><SYSTEM><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(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(minus(x,y),s(y)))</RHS></RULE><RULE><LHS>le(0,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(x),s(y))</LHS><RHS>le(x,y)</RHS></RULE><RULE><LHS>app(nil,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>app(add(n,x),y)</LHS><RHS>add(n,app(x,y))</RHS></RULE><RULE><LHS>low(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>low(n,add(m,x))</LHS><RHS>if_low(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_low(true,n,add(m,x))</LHS><RHS>add(m,low(n,x))</RHS></RULE><RULE><LHS>if_low(false,n,add(m,x))</LHS><RHS>low(n,x)</RHS></RULE><RULE><LHS>high(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>high(n,add(m,x))</LHS><RHS>if_high(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_high(true,n,add(m,x))</LHS><RHS>high(n,x)</RHS></RULE><RULE><LHS>if_high(false,n,add(m,x))</LHS><RHS>add(m,high(n,x))</RHS></RULE><RULE><LHS>quicksort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>quicksort(add(n,x))</LHS><RHS>app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))</RHS></RULE></REWSYS></SYSTEM><CRITERION/><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(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(minus(x,y),s(y)))</RHS></RULE><RULE><LHS>le(0,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(x),s(y))</LHS><RHS>le(x,y)</RHS></RULE><RULE><LHS>app(nil,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>app(add(n,x),y)</LHS><RHS>add(n,app(x,y))</RHS></RULE><RULE><LHS>low(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>low(n,add(m,x))</LHS><RHS>if_low(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_low(true,n,add(m,x))</LHS><RHS>add(m,low(n,x))</RHS></RULE><RULE><LHS>if_low(false,n,add(m,x))</LHS><RHS>low(n,x)</RHS></RULE><RULE><LHS>high(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>high(n,add(m,x))</LHS><RHS>if_high(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_high(true,n,add(m,x))</LHS><RHS>high(n,x)</RHS></RULE><RULE><LHS>if_high(false,n,add(m,x))</LHS><RHS>add(m,high(n,x))</RHS></RULE><RULE><LHS>quicksort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>quicksort(add(n,x))</LHS><RHS>app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_minus(s(x),s(y))</LHS><RHS>Marked_minus(x,y)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_quot(s(x),s(y))</LHS><RHS>Marked_quot(minus(x,y),s(y))</RHS></DPRULE><DPRULE num="2"><LHS>Marked_quot(s(x),s(y))</LHS><RHS>Marked_minus(x,y)</RHS></DPRULE><DPRULE num="3"><LHS>Marked_le(s(x),s(y))</LHS><RHS>Marked_le(x,y)</RHS></DPRULE><DPRULE num="4"><LHS>Marked_app(add(n,x),y)</LHS><RHS>Marked_app(x,y)</RHS></DPRULE><DPRULE num="5"><LHS>Marked_low(n,add(m,x))</LHS><RHS>Marked_if_low(le(m,n),n,add(m,x))</RHS></DPRULE><DPRULE num="6"><LHS>Marked_low(n,add(m,x))</LHS><RHS>Marked_le(m,n)</RHS></DPRULE><DPRULE num="7"><LHS>Marked_if_low(true,n,add(m,x))</LHS><RHS>Marked_low(n,x)</RHS></DPRULE><DPRULE num="8"><LHS>Marked_if_low(false,n,add(m,x))</LHS><RHS>Marked_low(n,x)</RHS></DPRULE><DPRULE num="9"><LHS>Marked_high(n,add(m,x))</LHS><RHS>Marked_if_high(le(m,n),n,add(m,x))</RHS></DPRULE><DPRULE num="10"><LHS>Marked_high(n,add(m,x))</LHS><RHS>Marked_le(m,n)</RHS></DPRULE><DPRULE num="11"><LHS>Marked_if_high(true,n,add(m,x))</LHS><RHS>Marked_high(n,x)</RHS></DPRULE><DPRULE num="12"><LHS>Marked_if_high(false,n,add(m,x))</LHS><RHS>Marked_high(n,x)</RHS></DPRULE><DPRULE num="13"><LHS>Marked_quicksort(add(n,x))</LHS><RHS>Marked_app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))</RHS></DPRULE><DPRULE num="14"><LHS>Marked_quicksort(add(n,x))</LHS><RHS>Marked_quicksort(low(n,x))</RHS></DPRULE><DPRULE num="15"><LHS>Marked_quicksort(add(n,x))</LHS><RHS>Marked_low(n,x)</RHS></DPRULE><DPRULE num="16"><LHS>Marked_quicksort(add(n,x))</LHS><RHS>Marked_quicksort(high(n,x))</RHS></DPRULE><DPRULE num="17"><LHS>Marked_quicksort(add(n,x))</LHS><RHS>Marked_high(n,x)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="17"/></NONSCC><NONSCC num="1"><NODE ref="10"/></NONSCC><SCC num="2"><NODE ref="9"/><NODE ref="11"/><NODE ref="12"/></SCC><SCC num="3"><NODE ref="14"/><NODE ref="16"/></SCC><NONSCC num="4"><NODE ref="15"/></NONSCC><NONSCC num="5"><NODE ref="13"/></NONSCC><NONSCC num="6"><NODE ref="6"/></NONSCC><SCC num="7"><NODE ref="5"/><NODE ref="7"/><NODE ref="8"/></SCC><SCC num="8"><NODE ref="4"/></SCC><SCC num="9"><NODE ref="3"/></SCC><NONSCC num="10"><NODE ref="2"/></NONSCC><SCC num="11"><NODE ref="0"/></SCC><SCC num="12"><NODE ref="1"/></SCC></CCLIST><EDGE end="2" start="0"/><EDGE end="1" start="0"/><EDGE end="9" start="1"/><EDGE end="1" start="2"/><EDGE end="5" start="3"/><EDGE end="4" start="3"/><EDGE end="0" start="3"/><EDGE end="7" start="4"/><EDGE end="6" start="4"/><EDGE end="8" start="5"/><EDGE end="9" start="6"/><EDGE end="6" start="7"/><EDGE end="11" start="10"/><EDGE end="10" start="12"/></DAG></CRITERION><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(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(minus(x,y),s(y)))</RHS></RULE><RULE><LHS>le(0,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(x),s(y))</LHS><RHS>le(x,y)</RHS></RULE><RULE><LHS>app(nil,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>app(add(n,x),y)</LHS><RHS>add(n,app(x,y))</RHS></RULE><RULE><LHS>low(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>low(n,add(m,x))</LHS><RHS>if_low(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_low(true,n,add(m,x))</LHS><RHS>add(m,low(n,x))</RHS></RULE><RULE><LHS>if_low(false,n,add(m,x))</LHS><RHS>low(n,x)</RHS></RULE><RULE><LHS>high(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>high(n,add(m,x))</LHS><RHS>if_high(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_high(true,n,add(m,x))</LHS><RHS>high(n,x)</RHS></RULE><RULE><LHS>if_high(false,n,add(m,x))</LHS><RHS>add(m,high(n,x))</RHS></RULE><RULE><LHS>quicksort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>quicksort(add(n,x))</LHS><RHS>app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_quot(s(x),s(y))</LHS><RHS>Marked_quot(minus(x,y),s(y))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="poly"><POLYSYMB><SYMBOL><NAME>minus</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>true</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>high</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>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>low</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>false</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>Marked_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>quicksort</NAME></SYMBOL><POLYNOMIAL><SUMPOLY><POLYNOMIAL><MONOME><COEF><INT>1</INT></COEF></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>add</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>le</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>if_high</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></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>if_low</NAME></SYMBOL><POLYNOMIAL><MONOME><COEF><INT>0</INT></COEF></MONOME></POLYNOMIAL></POLYSYMB><POLYSYMB><SYMBOL><NAME>app</NAME></SYMBOL><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></POLYSYMB></ORDERING></CRITERION></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(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(minus(x,y),s(y)))</RHS></RULE><RULE><LHS>le(0,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(x),s(y))</LHS><RHS>le(x,y)</RHS></RULE><RULE><LHS>app(nil,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>app(add(n,x),y)</LHS><RHS>add(n,app(x,y))</RHS></RULE><RULE><LHS>low(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>low(n,add(m,x))</LHS><RHS>if_low(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_low(true,n,add(m,x))</LHS><RHS>add(m,low(n,x))</RHS></RULE><RULE><LHS>if_low(false,n,add(m,x))</LHS><RHS>low(n,x)</RHS></RULE><RULE><LHS>high(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>high(n,add(m,x))</LHS><RHS>if_high(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_high(true,n,add(m,x))</LHS><RHS>high(n,x)</RHS></RULE><RULE><LHS>if_high(false,n,add(m,x))</LHS><RHS>add(m,high(n,x))</RHS></RULE><RULE><LHS>quicksort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>quicksort(add(n,x))</LHS><RHS>app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_minus(s(x),s(y))</LHS><RHS>Marked_minus(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_minus</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_minus(s(x),s(y))</LHS><RHS>Marked_minus(x,y)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(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(minus(x,y),s(y)))</RHS></RULE><RULE><LHS>le(0,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(x),s(y))</LHS><RHS>le(x,y)</RHS></RULE><RULE><LHS>app(nil,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>app(add(n,x),y)</LHS><RHS>add(n,app(x,y))</RHS></RULE><RULE><LHS>low(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>low(n,add(m,x))</LHS><RHS>if_low(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_low(true,n,add(m,x))</LHS><RHS>add(m,low(n,x))</RHS></RULE><RULE><LHS>if_low(false,n,add(m,x))</LHS><RHS>low(n,x)</RHS></RULE><RULE><LHS>high(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>high(n,add(m,x))</LHS><RHS>if_high(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_high(true,n,add(m,x))</LHS><RHS>high(n,x)</RHS></RULE><RULE><LHS>if_high(false,n,add(m,x))</LHS><RHS>add(m,high(n,x))</RHS></RULE><RULE><LHS>quicksort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>quicksort(add(n,x))</LHS><RHS>app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="ordering" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(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(minus(x,y),s(y)))</RHS></RULE><RULE><LHS>le(0,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(x),s(y))</LHS><RHS>le(x,y)</RHS></RULE><RULE><LHS>app(nil,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>app(add(n,x),y)</LHS><RHS>add(n,app(x,y))</RHS></RULE><RULE><LHS>low(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>low(n,add(m,x))</LHS><RHS>if_low(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_low(true,n,add(m,x))</LHS><RHS>add(m,low(n,x))</RHS></RULE><RULE><LHS>if_low(false,n,add(m,x))</LHS><RHS>low(n,x)</RHS></RULE><RULE><LHS>high(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>high(n,add(m,x))</LHS><RHS>if_high(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_high(true,n,add(m,x))</LHS><RHS>high(n,x)</RHS></RULE><RULE><LHS>if_high(false,n,add(m,x))</LHS><RHS>add(m,high(n,x))</RHS></RULE><RULE><LHS>quicksort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>quicksort(add(n,x))</LHS><RHS>app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_quicksort(add(n,x))</LHS><RHS>Marked_quicksort(low(n,x))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_quicksort(add(n,x))</LHS><RHS>Marked_quicksort(high(n,x))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><ORDERING type="rpo"><AFS><PROJARG num="2"><SYMBOL><NAME>if_low</NAME></SYMBOL></PROJARG><PROJARG num="2"><SYMBOL><NAME>if_high</NAME></SYMBOL></PROJARG><PROJARG num="1"><SYMBOL><NAME>low</NAME></SYMBOL></PROJARG><PROJARG num="1"><SYMBOL><NAME>high</NAME></SYMBOL></PROJARG><PROJARG num="0"><SYMBOL><NAME>minus</NAME></SYMBOL></PROJARG></AFS><STATUSLIST><STATUS status="lex"><SYMBOL><NAME>true</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>s</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>false</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>quicksort</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>add</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>le</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>quot</NAME></SYMBOL></STATUS><STATUS status="lex"><SYMBOL><NAME>app</NAME></SYMBOL></STATUS></STATUSLIST><PRECEDENCE><PREC><OLHS><SYMBOL><NAME>s</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>quot</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>true</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>le</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>false</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>le</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>app</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>quicksort</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>app</NAME></SYMBOL></ORHS></PREC><PREC><OLHS><SYMBOL><NAME>add</NAME></SYMBOL></OLHS><ORHS><SYMBOL><NAME>quicksort</NAME></SYMBOL></ORHS></PREC></PRECEDENCE><EQUIVALENCE/></ORDERING></CRITERION></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(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(minus(x,y),s(y)))</RHS></RULE><RULE><LHS>le(0,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(x),s(y))</LHS><RHS>le(x,y)</RHS></RULE><RULE><LHS>app(nil,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>app(add(n,x),y)</LHS><RHS>add(n,app(x,y))</RHS></RULE><RULE><LHS>low(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>low(n,add(m,x))</LHS><RHS>if_low(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_low(true,n,add(m,x))</LHS><RHS>add(m,low(n,x))</RHS></RULE><RULE><LHS>if_low(false,n,add(m,x))</LHS><RHS>low(n,x)</RHS></RULE><RULE><LHS>high(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>high(n,add(m,x))</LHS><RHS>if_high(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_high(true,n,add(m,x))</LHS><RHS>high(n,x)</RHS></RULE><RULE><LHS>if_high(false,n,add(m,x))</LHS><RHS>add(m,high(n,x))</RHS></RULE><RULE><LHS>quicksort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>quicksort(add(n,x))</LHS><RHS>app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_app(add(n,x),y)</LHS><RHS>Marked_app(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_app</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_app(add(n,x),y)</LHS><RHS>Marked_app(x,y)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(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(minus(x,y),s(y)))</RHS></RULE><RULE><LHS>le(0,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(x),s(y))</LHS><RHS>le(x,y)</RHS></RULE><RULE><LHS>app(nil,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>app(add(n,x),y)</LHS><RHS>add(n,app(x,y))</RHS></RULE><RULE><LHS>low(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>low(n,add(m,x))</LHS><RHS>if_low(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_low(true,n,add(m,x))</LHS><RHS>add(m,low(n,x))</RHS></RULE><RULE><LHS>if_low(false,n,add(m,x))</LHS><RHS>low(n,x)</RHS></RULE><RULE><LHS>high(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>high(n,add(m,x))</LHS><RHS>if_high(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_high(true,n,add(m,x))</LHS><RHS>high(n,x)</RHS></RULE><RULE><LHS>if_high(false,n,add(m,x))</LHS><RHS>add(m,high(n,x))</RHS></RULE><RULE><LHS>quicksort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>quicksort(add(n,x))</LHS><RHS>app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(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(minus(x,y),s(y)))</RHS></RULE><RULE><LHS>le(0,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(x),s(y))</LHS><RHS>le(x,y)</RHS></RULE><RULE><LHS>app(nil,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>app(add(n,x),y)</LHS><RHS>add(n,app(x,y))</RHS></RULE><RULE><LHS>low(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>low(n,add(m,x))</LHS><RHS>if_low(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_low(true,n,add(m,x))</LHS><RHS>add(m,low(n,x))</RHS></RULE><RULE><LHS>if_low(false,n,add(m,x))</LHS><RHS>low(n,x)</RHS></RULE><RULE><LHS>high(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>high(n,add(m,x))</LHS><RHS>if_high(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_high(true,n,add(m,x))</LHS><RHS>high(n,x)</RHS></RULE><RULE><LHS>if_high(false,n,add(m,x))</LHS><RHS>add(m,high(n,x))</RHS></RULE><RULE><LHS>quicksort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>quicksort(add(n,x))</LHS><RHS>app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_low(n,add(m,x))</LHS><RHS>Marked_if_low(le(m,n),n,add(m,x))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_if_low(true,n,add(m,x))</LHS><RHS>Marked_low(n,x)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_if_low(false,n,add(m,x))</LHS><RHS>Marked_low(n,x)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_if_low</NAME></SYMBOL><INT>3</INT></PROJ><PROJ><SYMBOL><NAME>Marked_low</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_if_low(false,n,add(m,x))</LHS><RHS>Marked_low(n,x)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_if_low(true,n,add(m,x))</LHS><RHS>Marked_low(n,x)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(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(minus(x,y),s(y)))</RHS></RULE><RULE><LHS>le(0,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(x),s(y))</LHS><RHS>le(x,y)</RHS></RULE><RULE><LHS>app(nil,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>app(add(n,x),y)</LHS><RHS>add(n,app(x,y))</RHS></RULE><RULE><LHS>low(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>low(n,add(m,x))</LHS><RHS>if_low(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_low(true,n,add(m,x))</LHS><RHS>add(m,low(n,x))</RHS></RULE><RULE><LHS>if_low(false,n,add(m,x))</LHS><RHS>low(n,x)</RHS></RULE><RULE><LHS>high(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>high(n,add(m,x))</LHS><RHS>if_high(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_high(true,n,add(m,x))</LHS><RHS>high(n,x)</RHS></RULE><RULE><LHS>if_high(false,n,add(m,x))</LHS><RHS>add(m,high(n,x))</RHS></RULE><RULE><LHS>quicksort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>quicksort(add(n,x))</LHS><RHS>app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_low(n,add(m,x))</LHS><RHS>Marked_if_low(le(m,n),n,add(m,x))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="0"/></NONSCC></CCLIST></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(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(minus(x,y),s(y)))</RHS></RULE><RULE><LHS>le(0,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(x),s(y))</LHS><RHS>le(x,y)</RHS></RULE><RULE><LHS>app(nil,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>app(add(n,x),y)</LHS><RHS>add(n,app(x,y))</RHS></RULE><RULE><LHS>low(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>low(n,add(m,x))</LHS><RHS>if_low(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_low(true,n,add(m,x))</LHS><RHS>add(m,low(n,x))</RHS></RULE><RULE><LHS>if_low(false,n,add(m,x))</LHS><RHS>low(n,x)</RHS></RULE><RULE><LHS>high(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>high(n,add(m,x))</LHS><RHS>if_high(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_high(true,n,add(m,x))</LHS><RHS>high(n,x)</RHS></RULE><RULE><LHS>if_high(false,n,add(m,x))</LHS><RHS>add(m,high(n,x))</RHS></RULE><RULE><LHS>quicksort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>quicksort(add(n,x))</LHS><RHS>app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_high(n,add(m,x))</LHS><RHS>Marked_if_high(le(m,n),n,add(m,x))</RHS></DPRULE><DPRULE num="1"><LHS>Marked_if_high(true,n,add(m,x))</LHS><RHS>Marked_high(n,x)</RHS></DPRULE><DPRULE num="2"><LHS>Marked_if_high(false,n,add(m,x))</LHS><RHS>Marked_high(n,x)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_if_high</NAME></SYMBOL><INT>3</INT></PROJ><PROJ><SYMBOL><NAME>Marked_high</NAME></SYMBOL><INT>2</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_if_high(false,n,add(m,x))</LHS><RHS>Marked_high(n,x)</RHS></DPRULE><DPRULE num="1"><LHS>Marked_if_high(true,n,add(m,x))</LHS><RHS>Marked_high(n,x)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(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(minus(x,y),s(y)))</RHS></RULE><RULE><LHS>le(0,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(x),s(y))</LHS><RHS>le(x,y)</RHS></RULE><RULE><LHS>app(nil,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>app(add(n,x),y)</LHS><RHS>add(n,app(x,y))</RHS></RULE><RULE><LHS>low(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>low(n,add(m,x))</LHS><RHS>if_low(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_low(true,n,add(m,x))</LHS><RHS>add(m,low(n,x))</RHS></RULE><RULE><LHS>if_low(false,n,add(m,x))</LHS><RHS>low(n,x)</RHS></RULE><RULE><LHS>high(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>high(n,add(m,x))</LHS><RHS>if_high(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_high(true,n,add(m,x))</LHS><RHS>high(n,x)</RHS></RULE><RULE><LHS>if_high(false,n,add(m,x))</LHS><RHS>add(m,high(n,x))</RHS></RULE><RULE><LHS>quicksort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>quicksort(add(n,x))</LHS><RHS>app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_high(n,add(m,x))</LHS><RHS>Marked_if_high(le(m,n),n,add(m,x))</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST><NONSCC num="0"><NODE ref="0"/></NONSCC></CCLIST></DAG></CRITERION></PROPERTY></PROPERTY><PROPERTY criterion="sterm" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(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(minus(x,y),s(y)))</RHS></RULE><RULE><LHS>le(0,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(x),s(y))</LHS><RHS>le(x,y)</RHS></RULE><RULE><LHS>app(nil,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>app(add(n,x),y)</LHS><RHS>add(n,app(x,y))</RHS></RULE><RULE><LHS>low(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>low(n,add(m,x))</LHS><RHS>if_low(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_low(true,n,add(m,x))</LHS><RHS>add(m,low(n,x))</RHS></RULE><RULE><LHS>if_low(false,n,add(m,x))</LHS><RHS>low(n,x)</RHS></RULE><RULE><LHS>high(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>high(n,add(m,x))</LHS><RHS>if_high(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_high(true,n,add(m,x))</LHS><RHS>high(n,x)</RHS></RULE><RULE><LHS>if_high(false,n,add(m,x))</LHS><RHS>add(m,high(n,x))</RHS></RULE><RULE><LHS>quicksort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>quicksort(add(n,x))</LHS><RHS>app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))</RHS></RULE></REWSYS><DPLIST><DPRULE num="0"><LHS>Marked_le(s(x),s(y))</LHS><RHS>Marked_le(x,y)</RHS></DPRULE></DPLIST></DPSYS></SYSTEM><PROJECTION><PROJ><SYMBOL><NAME>Marked_le</NAME></SYMBOL><INT>1</INT></PROJ></PROJECTION><STRICTPAIRS><DPLIST><DPRULE num="0"><LHS>Marked_le(s(x),s(y))</LHS><RHS>Marked_le(x,y)</RHS></DPRULE></DPLIST></STRICTPAIRS><PROPERTY criterion="weakgraph" prop="sndp"><SYSTEM><DPSYS><REWSYS><RULE><LHS>minus(x,0)</LHS><RHS>x</RHS></RULE><RULE><LHS>minus(s(x),s(y))</LHS><RHS>minus(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(minus(x,y),s(y)))</RHS></RULE><RULE><LHS>le(0,y)</LHS><RHS>true</RHS></RULE><RULE><LHS>le(s(x),0)</LHS><RHS>false</RHS></RULE><RULE><LHS>le(s(x),s(y))</LHS><RHS>le(x,y)</RHS></RULE><RULE><LHS>app(nil,y)</LHS><RHS>y</RHS></RULE><RULE><LHS>app(add(n,x),y)</LHS><RHS>add(n,app(x,y))</RHS></RULE><RULE><LHS>low(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>low(n,add(m,x))</LHS><RHS>if_low(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_low(true,n,add(m,x))</LHS><RHS>add(m,low(n,x))</RHS></RULE><RULE><LHS>if_low(false,n,add(m,x))</LHS><RHS>low(n,x)</RHS></RULE><RULE><LHS>high(n,nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>high(n,add(m,x))</LHS><RHS>if_high(le(m,n),n,add(m,x))</RHS></RULE><RULE><LHS>if_high(true,n,add(m,x))</LHS><RHS>high(n,x)</RHS></RULE><RULE><LHS>if_high(false,n,add(m,x))</LHS><RHS>add(m,high(n,x))</RHS></RULE><RULE><LHS>quicksort(nil)</LHS><RHS>nil</RHS></RULE><RULE><LHS>quicksort(add(n,x))</LHS><RHS>app(quicksort(low(n,x)),add(n,quicksort(high(n,x))))</RHS></RULE></REWSYS><DPLIST/></DPSYS></SYSTEM><CRITERION><DAG approx="simpl"><CCLIST/></DAG></CRITERION></PROPERTY></PROPERTY></PROPERTY></PROPERTY></PROOF>
