/export/starexec/sandbox/solver/bin/starexec_run_certified /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(?, O(n^2))
<?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 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ifting><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>c</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c2</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c3</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c4</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c5</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c6</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c7</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c8</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c9</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c10</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c11</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c12</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c13</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c14</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c15</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c16</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c17</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c18</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c19</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c20</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c21</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c22</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c23</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c24</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c25</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c26</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c27</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c28</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c29</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c30</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#add</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#succ</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#natmult</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#add</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#mult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#natmult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#pred</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#succ</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>*</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>dyade</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>dyade#1</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>mult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>mult#1</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#0</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#pos</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#neg</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>::</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><sharp><name>dyade#1</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c27</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult#1</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c30</name></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><funapp><sharp><name>#pred</name></sharp><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c2</name><arg><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c3</name><arg><funapp><sharp><name>#succ</name></sharp><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c4</name><arg><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c5</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c6</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c7</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c8</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c9</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c10</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c11</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c12</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c13</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#natmult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c14</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#natmult</name></sharp><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c15</name><arg><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>#natmult</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c16</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c17</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c18</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c19</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c20</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c21</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c22</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c23</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c24</name><arg><funapp><sharp><name>#mult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dyade</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c25</name><arg><funapp><sharp><name>dyade#1</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dyade#1</name></sharp><arg><funapp><name>::</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c26</name><arg><funapp><sharp><name>mult</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><sharp><name>dyade</name></sharp><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dyade#1</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c27</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c28</name><arg><funapp><sharp><name>mult#1</name></sharp><arg><var>z1</var></arg><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult#1</name></sharp><arg><funapp><name>::</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c29</name><arg><funapp><sharp><name>*</name></sharp><arg><var>z2</var></arg><arg><var>z0</var></arg></funapp></arg><arg><funapp><sharp><name>mult</name></sharp><arg><var>z2</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult#1</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c30</name></funapp></rhs></rule></rules></usableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>c</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c2</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c3</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c4</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c5</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c6</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c7</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c8</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c9</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c10</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c11</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c12</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c13</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c14</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c15</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c16</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c17</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c18</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c19</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c20</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c21</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c22</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c23</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c24</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c25</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c26</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c27</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c28</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c29</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c30</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#add</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#succ</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#natmult</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#add</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#mult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#natmult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#pred</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#succ</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>*</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>dyade</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>dyade#1</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>mult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>mult#1</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#0</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#pos</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#neg</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>::</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><sharp><name>dyade#1</name></sharp><arg><funapp><name>::</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c26</name><arg><funapp><sharp><name>mult</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><sharp><name>dyade</name></sharp><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><funapp><sharp><name>#pred</name></sharp><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c2</name><arg><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c3</name><arg><funapp><sharp><name>#succ</name></sharp><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c4</name><arg><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c5</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c6</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c7</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c8</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c9</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c10</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c11</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c12</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c13</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#natmult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c14</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#natmult</name></sharp><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c15</name><arg><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>#natmult</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c16</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c17</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c18</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c19</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c20</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c21</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c22</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c23</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c24</name><arg><funapp><sharp><name>#mult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dyade</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c25</name><arg><funapp><sharp><name>dyade#1</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dyade#1</name></sharp><arg><funapp><name>::</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c26</name><arg><funapp><sharp><name>mult</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><sharp><name>dyade</name></sharp><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dyade#1</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c27</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c28</name><arg><funapp><sharp><name>mult#1</name></sharp><arg><var>z1</var></arg><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult#1</name></sharp><arg><funapp><name>::</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c29</name><arg><funapp><sharp><name>*</name></sharp><arg><var>z2</var></arg><arg><var>z0</var></arg></funapp></arg><arg><funapp><sharp><name>mult</name></sharp><arg><var>z2</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult#1</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c30</name></funapp></rhs></rule></rules></usableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>c</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c2</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c3</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c4</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c5</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c6</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c7</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c8</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c9</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c10</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c11</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c12</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c13</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c14</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c15</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c16</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c17</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c18</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c19</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c20</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c21</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c22</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c23</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c24</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c25</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c26</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c27</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c28</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c29</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c30</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#add</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#succ</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#natmult</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#add</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#mult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#natmult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#pred</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#succ</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>*</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>dyade</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>dyade#1</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>mult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>mult#1</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#0</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#pos</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#neg</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>::</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><sharp><name>dyade</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c25</name><arg><funapp><sharp><name>dyade#1</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><funapp><sharp><name>#pred</name></sharp><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c2</name><arg><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c3</name><arg><funapp><sharp><name>#succ</name></sharp><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c4</name><arg><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c5</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c6</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c7</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c8</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c9</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c10</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c11</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c12</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c13</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#natmult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c14</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#natmult</name></sharp><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c15</name><arg><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>#natmult</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c16</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c17</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c18</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c19</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c20</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c21</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c22</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c23</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c24</name><arg><funapp><sharp><name>#mult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dyade</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c25</name><arg><funapp><sharp><name>dyade#1</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dyade#1</name></sharp><arg><funapp><name>::</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c26</name><arg><funapp><sharp><name>mult</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><sharp><name>dyade</name></sharp><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dyade#1</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c27</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c28</name><arg><funapp><sharp><name>mult#1</name></sharp><arg><var>z1</var></arg><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult#1</name></sharp><arg><funapp><name>::</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c29</name><arg><funapp><sharp><name>*</name></sharp><arg><var>z2</var></arg><arg><var>z0</var></arg></funapp></arg><arg><funapp><sharp><name>mult</name></sharp><arg><var>z2</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult#1</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c30</name></funapp></rhs></rule></rules></usableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>2</degree></polynomial></type><interpret><name>c</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c2</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c3</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c4</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c5</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c6</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c7</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c8</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c9</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c10</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c11</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c12</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c13</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c14</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c15</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c16</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c17</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c18</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c19</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c20</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c21</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c22</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c23</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c24</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c25</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c26</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c27</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c28</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c29</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c30</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#add</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#succ</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#natmult</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#add</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#mult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#natmult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#pred</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#succ</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>*</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>dyade</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>dyade#1</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>mult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>mult#1</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#0</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#pos</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#neg</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>::</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><sharp><name>*</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c24</name><arg><funapp><sharp><name>#mult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult#1</name></sharp><arg><funapp><name>::</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c29</name><arg><funapp><sharp><name>*</name></sharp><arg><var>z2</var></arg><arg><var>z0</var></arg></funapp></arg><arg><funapp><sharp><name>mult</name></sharp><arg><var>z2</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><funapp><sharp><name>#pred</name></sharp><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c2</name><arg><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c3</name><arg><funapp><sharp><name>#succ</name></sharp><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c4</name><arg><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c5</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c6</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c7</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c8</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c9</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c10</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c11</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c12</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c13</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#natmult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c14</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#natmult</name></sharp><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c15</name><arg><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>#natmult</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c16</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c17</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c18</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c19</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c20</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c21</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c22</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c23</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c24</name><arg><funapp><sharp><name>#mult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dyade</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c25</name><arg><funapp><sharp><name>dyade#1</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dyade#1</name></sharp><arg><funapp><name>::</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c26</name><arg><funapp><sharp><name>mult</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><sharp><name>dyade</name></sharp><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dyade#1</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c27</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c28</name><arg><funapp><sharp><name>mult#1</name></sharp><arg><var>z1</var></arg><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult#1</name></sharp><arg><funapp><name>::</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c29</name><arg><funapp><sharp><name>*</name></sharp><arg><var>z2</var></arg><arg><var>z0</var></arg></funapp></arg><arg><funapp><sharp><name>mult</name></sharp><arg><var>z2</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult#1</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c30</name></funapp></rhs></rule></rules></usableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>2</degree></polynomial></type><interpret><name>c</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c1</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c2</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c3</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c4</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c5</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c6</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c7</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c8</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c9</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c10</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c11</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c12</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c13</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c14</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c15</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c16</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c17</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c18</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c19</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c20</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c21</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c22</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c23</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c24</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c25</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c26</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c27</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c28</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c29</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c30</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#add</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#succ</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#natmult</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#add</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#mult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#natmult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#pred</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>#succ</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>*</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>dyade</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>dyade#1</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>mult</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>mult#1</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#0</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#pos</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#neg</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>::</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c28</name><arg><funapp><sharp><name>mult#1</name></sharp><arg><var>z1</var></arg><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><funapp><sharp><name>#pred</name></sharp><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c2</name><arg><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c3</name><arg><funapp><sharp><name>#succ</name></sharp><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c4</name><arg><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c5</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c6</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c7</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c8</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c9</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#neg</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c10</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c11</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c12</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#mult</name></sharp><arg><funapp><name>#pos</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c13</name><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#natmult</name></sharp><arg><funapp><name>#0</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c14</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#natmult</name></sharp><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c15</name><arg><funapp><sharp><name>#add</name></sharp><arg><funapp><name>#pos</name><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>#natmult</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>#natmult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c16</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c17</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c18</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#pred</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c19</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c20</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c21</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c22</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>#succ</name></sharp><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>z0</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c23</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c24</name><arg><funapp><sharp><name>#mult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dyade</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c25</name><arg><funapp><sharp><name>dyade#1</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dyade#1</name></sharp><arg><funapp><name>::</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c26</name><arg><funapp><sharp><name>mult</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><sharp><name>dyade</name></sharp><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>dyade#1</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c27</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c28</name><arg><funapp><sharp><name>mult#1</name></sharp><arg><var>z1</var></arg><arg><var>z0</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult#1</name></sharp><arg><funapp><name>::</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c29</name><arg><funapp><sharp><name>*</name></sharp><arg><var>z2</var></arg><arg><var>z0</var></arg></funapp></arg><arg><funapp><sharp><name>mult</name></sharp><arg><var>z2</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult#1</name></sharp><arg><funapp><name>nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c30</name></funapp></rhs></rule></rules></usableRules><complexityProof><rIsEmpty/></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></usableRules></complexityProof></dtTransformation></complexityProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty
</version><strategy>Statistics for single proof: 100.00 % (8 real / 0 unknown / 0 assumptions / 8 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem>