details

property	value
status	complete
benchmark	strmatch.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n041.star.cs.uiowa.edu
space	Frederiksen_Others

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	8.01786398888 seconds
cpu usage	28.464161243
max memory	3.166769152E9

stage attributes

key	value
certification-result	CERTIFIED
output-size	185753
starexec-result	WORST_CASE(?,O(n^2))
certification-time	0.1

output

/export/starexec/sandbox2/solver/bin/starexec_run_certified /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- 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" xsi:noNamespaceSchemaLocation="cpf.xsd"><input><complexityInput><trsInput><trs><rules><rule><lhs><funapp><name>prefix</name><arg><funapp><name>Cons</name><arg><var>x'</var></arg><arg><var>xs'</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>!EQ</name><arg><var>x'</var></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>prefix</name><arg><var>xs'</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>domatch</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>n</var></arg></funapp></lhs><rhs><funapp><name>Nil</name></funapp></rhs></rule><rule><lhs><funapp><name>domatch</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>n</var></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>n</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>prefix</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>prefix</name><arg><funapp><name>Nil</name></funapp></arg><arg><var>cs</var></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>domatch</name><arg><var>patcs</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>n</var></arg></funapp></lhs><rhs><funapp><name>domatch[Ite]</name><arg><funapp><name>prefix</name><arg><var>patcs</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></arg><arg><var>patcs</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>n</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>eqNatList</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>eqNatList[Ite]</name><arg><funapp><name>!EQ</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>y</var></arg><arg><var>ys</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>eqNatList</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>eqNatList</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>eqNatList</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>strmatch</name><arg><var>patstr</var></arg><arg><var>str</var></arg></funapp></lhs><rhs><funapp><name>domatch</name><arg><var>patstr</var></arg><arg><var>str</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></rhs></rule></rules></trs><strategy><innermost/></strategy><relativeRules><rules><rule><lhs><funapp><name>and</name><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>!EQ</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>S</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>domatch[Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><var>patcs</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>n</var></arg></funapp></lhs><rhs><funapp><name>domatch</name><arg><var>patcs</var></arg><arg><var>xs</var></arg><arg><funapp><name>Cons</name><arg><var>n</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>domatch[Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>patcs</var></arg><arg><funapp><name>Cons</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>n</var></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>n</var></arg><arg><funapp><name>domatch</name><arg><var>patcs</var></arg><arg><var>xs</var></arg><arg><funapp><name>Cons</name><arg><var>n</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>eqNatList[Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><var>y</var></arg><arg><var>ys</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>eqNatList[Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>y</var></arg><arg><var>ys</var></arg><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></lhs><rhs><funapp><name>eqNatList</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></rhs></rule></rules></relativeRules></trsInput><runtimeComplexity><signature><symbol><name>Cons</name><arity>2</arity></symbol><symbol><name>Nil</name><arity>0</arity></symbol><symbol><name>False</name><arity>0</arity></symbol><symbol><name>True</name><arity>0</arity></symbol><symbol><name>S</name><arity>1</arity></symbol><symbol><name>0</name><arity>0</arity></symbol></signature><signature><symbol><name>prefix</name><arity>2</arity></symbol><symbol><name>domatch</name><arity>3</arity></symbol><symbol><name>eqNatList</name><arity>2</arity></symbol><symbol><name>notEmpty</name><arity>1</arity></symbol><symbol><name>strmatch</name><arity>2</arity></symbol><symbol><name>and</name><arity>2</arity></symbol><symbol><name>!EQ</name><arity>2</arity></symbol><symbol><name>domatch[Ite]</name><arity>4</arity></symbol><symbol><name>eqNatList[Ite]</name><arity>5</arity></symbol></signature></runtimeComplexity><polynomial>2</polynomial></complexityInput></input><cpfVersion>2.1</cpfVersion><proof><complexityProof><dtTransformation><strictDTs><ruleWithDT><rule><lhs><funapp><name>prefix</name><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><name>prefix</name><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c12</name><arg><funapp><sharp><name>and</name></sharp><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><name>prefix</name><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><sharp><name>prefix</name></sharp><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>prefix</name><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c13</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>prefix</name><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c14</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>domatch</name><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>Nil</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c15</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>domatch</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>z0</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c16</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>domatch</name><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>domatch[Ite]</name><arg><funapp><name>prefix</name><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c17</name><arg><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>prefix</name><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></arg><arg><funapp><sharp><name>prefix</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>eqNatList</name><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>eqNatList[Ite]</name><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z2</var></arg><arg><var>z3</var></arg><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c18</name><arg><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z2</var></arg><arg><var>z3</var></arg><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>eqNatList</name><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c19</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>eqNatList</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c20</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>eqNatList</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c21</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c22</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c23</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>strmatch</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>domatch</name><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>strmatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c24</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></rhs></rule></ruleWithDT></strictDTs><weakDTs><ruleWithDT><rule><lhs><funapp><name>and</name><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>c</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>and</name><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>c1</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>and</name><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>c2</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>and</name><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>c3</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c4</name><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c5</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c6</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>!EQ</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c7</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>domatch[Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>domatch</name><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c8</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>domatch[Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>domatch</name><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c9</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>eqNatList[Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c10</name></funapp></rhs></rule></ruleWithDT><ruleWithDT><rule><lhs><funapp><name>eqNatList[Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>eqNatList</name><arg><var>z3</var></arg><arg><var>z1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c11</name><arg><funapp><sharp><name>eqNatList</name></sharp><arg><var>z3</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule></ruleWithDT></weakDTs><innermostLhss><funapp><sharp><name>and</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp><funapp><sharp><name>and</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp><funapp><sharp><name>and</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp><funapp><sharp><name>and</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>z1</var></arg></funapp></arg></funapp><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg></funapp><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z2</var></arg></funapp><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Nil</name></funapp></arg></funapp><funapp><sharp><name>strmatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></innermostLhss><complexityProof><usableRules><nonUsableRules><rules><rule><lhs><funapp><name>domatch[Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>domatch</name><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>domatch[Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>domatch</name><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>eqNatList[Ite]</name><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>eqNatList[Ite]</name><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>eqNatList</name><arg><var>z3</var></arg><arg><var>z1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>domatch</name><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>Nil</name></funapp></rhs></rule><rule><lhs><funapp><name>domatch</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>Cons</name><arg><var>z0</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>domatch</name><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>domatch[Ite]</name><arg><funapp><name>prefix</name><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>eqNatList</name><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>eqNatList[Ite]</name><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z2</var></arg><arg><var>z3</var></arg><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>eqNatList</name><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>eqNatList</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>eqNatList</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>True</name></funapp></rhs></rule><rule><lhs><funapp><name>notEmpty</name><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>False</name></funapp></rhs></rule><rule><lhs><funapp><name>strmatch</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>domatch</name><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></rhs></rule></rules></nonUsableRules><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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c2</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c3</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c4</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>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>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>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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c11</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>c12</name><arity>3</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c13</name><arity>0</arity><polynomial><sum><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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></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>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>c18</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>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>!EQ</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prefix</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>and</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>!EQ</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>domatch[Ite]</name></sharp><arity>4</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>eqNatList[Ite]</name></sharp><arity>5</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>prefix</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>domatch</name></sharp><arity>3</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>eqNatList</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>notEmpty</name></sharp><arity>1</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>strmatch</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><name>S</name><arity>1</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><name>0</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>False</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>True</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Cons</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></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>domatch</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c15</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c22</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c23</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>strmatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c24</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>c</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>c1</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>c2</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>c3</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c4</name><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c5</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c6</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c7</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c8</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c9</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c10</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c11</name><arg><funapp><sharp><name>eqNatList</name></sharp><arg><var>z3</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c12</name><arg><funapp><sharp><name>and</name></sharp><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><name>prefix</name><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><sharp><name>prefix</name></sharp><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c13</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c14</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c15</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c16</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c17</name><arg><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>prefix</name><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></arg><arg><funapp><sharp><name>prefix</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c18</name><arg><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z2</var></arg><arg><var>z3</var></arg><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c19</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c20</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c21</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c22</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c23</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>strmatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c24</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c2</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c3</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c4</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>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>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>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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c11</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>c12</name><arity>3</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c13</name><arity>0</arity><polynomial><sum><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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></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>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>c18</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>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>!EQ</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prefix</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>and</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>!EQ</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>domatch[Ite]</name></sharp><arity>4</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>eqNatList[Ite]</name></sharp><arity>5</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>prefix</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>domatch</name></sharp><arity>3</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>eqNatList</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>notEmpty</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>strmatch</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><name>S</name><arity>1</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><name>0</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>False</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>True</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Cons</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Nil</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c16</name></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>c</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>c1</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>c2</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>c3</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c4</name><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c5</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c6</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c7</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c8</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c9</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c10</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c11</name><arg><funapp><sharp><name>eqNatList</name></sharp><arg><var>z3</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c12</name><arg><funapp><sharp><name>and</name></sharp><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><name>prefix</name><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><sharp><name>prefix</name></sharp><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c13</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c14</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c15</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c16</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c17</name><arg><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>prefix</name><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></arg><arg><funapp><sharp><name>prefix</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c18</name><arg><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z2</var></arg><arg><var>z3</var></arg><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c19</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c20</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c21</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c22</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c23</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>strmatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c24</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c2</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c3</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c4</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>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>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>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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c11</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>c12</name><arity>3</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c13</name><arity>0</arity><polynomial><sum><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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></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>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>c18</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>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>!EQ</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prefix</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>and</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>!EQ</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>domatch[Ite]</name></sharp><arity>4</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>eqNatList[Ite]</name></sharp><arity>5</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>prefix</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>domatch</name></sharp><arity>3</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>eqNatList</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>notEmpty</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>strmatch</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><name>S</name><arity>1</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><name>0</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>False</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>True</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Cons</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></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>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c19</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c20</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c21</name></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>c</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>c1</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>c2</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>c3</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c4</name><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c5</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c6</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c7</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c8</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c9</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c10</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c11</name><arg><funapp><sharp><name>eqNatList</name></sharp><arg><var>z3</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c12</name><arg><funapp><sharp><name>and</name></sharp><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><name>prefix</name><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><sharp><name>prefix</name></sharp><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c13</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c14</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c15</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c16</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c17</name><arg><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>prefix</name><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></arg><arg><funapp><sharp><name>prefix</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c18</name><arg><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z2</var></arg><arg><var>z3</var></arg><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c19</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c20</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c21</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c22</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c23</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>strmatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c24</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c2</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c3</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c4</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>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>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>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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c11</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>c12</name><arity>3</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c13</name><arity>0</arity><polynomial><sum><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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></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>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>c18</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>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>!EQ</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prefix</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>and</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>!EQ</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>domatch[Ite]</name></sharp><arity>4</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>eqNatList[Ite]</name></sharp><arity>5</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>prefix</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>domatch</name></sharp><arity>3</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>eqNatList</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>notEmpty</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>strmatch</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><name>S</name><arity>1</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><name>0</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>False</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>True</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Cons</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>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>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c13</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c14</name></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>c</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>c1</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>c2</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>c3</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c4</name><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c5</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c6</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c7</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c8</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c9</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c10</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c11</name><arg><funapp><sharp><name>eqNatList</name></sharp><arg><var>z3</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c12</name><arg><funapp><sharp><name>and</name></sharp><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><name>prefix</name><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><sharp><name>prefix</name></sharp><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c13</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c14</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c15</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c16</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c17</name><arg><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>prefix</name><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></arg><arg><funapp><sharp><name>prefix</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c18</name><arg><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z2</var></arg><arg><var>z3</var></arg><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c19</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c20</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c21</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c22</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c23</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>strmatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c24</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c2</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c3</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c4</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>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>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>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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c11</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>c12</name><arity>3</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c13</name><arity>0</arity><polynomial><sum><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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></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>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>c18</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>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>!EQ</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prefix</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>and</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>!EQ</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>domatch[Ite]</name></sharp><arity>4</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>eqNatList[Ite]</name></sharp><arity>5</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>prefix</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>domatch</name></sharp><arity>3</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>eqNatList</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>notEmpty</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>strmatch</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><name>S</name><arity>1</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><name>0</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>False</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>True</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Cons</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>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>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c18</name><arg><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z2</var></arg><arg><var>z3</var></arg><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>c</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>c1</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>c2</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>c3</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c4</name><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c5</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c6</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c7</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c8</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c9</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c10</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c11</name><arg><funapp><sharp><name>eqNatList</name></sharp><arg><var>z3</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c12</name><arg><funapp><sharp><name>and</name></sharp><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><name>prefix</name><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><sharp><name>prefix</name></sharp><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c13</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c14</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c15</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c16</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c17</name><arg><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>prefix</name><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></arg><arg><funapp><sharp><name>prefix</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c18</name><arg><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z2</var></arg><arg><var>z3</var></arg><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c19</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c20</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c21</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c22</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c23</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>strmatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c24</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c2</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c3</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c4</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>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>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>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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c11</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>c12</name><arity>3</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c13</name><arity>0</arity><polynomial><sum><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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></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>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>c18</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>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>!EQ</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prefix</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>and</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>!EQ</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>domatch[Ite]</name></sharp><arity>4</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>eqNatList[Ite]</name></sharp><arity>5</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>prefix</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>domatch</name></sharp><arity>3</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>eqNatList</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>notEmpty</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>strmatch</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><name>S</name><arity>1</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><name>0</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>False</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>True</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Cons</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>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>domatch</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c17</name><arg><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>prefix</name><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></arg><arg><funapp><sharp><name>prefix</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>c</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>c1</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>c2</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>c3</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c4</name><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c5</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c6</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c7</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c8</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c9</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c10</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c11</name><arg><funapp><sharp><name>eqNatList</name></sharp><arg><var>z3</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c12</name><arg><funapp><sharp><name>and</name></sharp><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><name>prefix</name><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><sharp><name>prefix</name></sharp><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c13</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c14</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c15</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c16</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c17</name><arg><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>prefix</name><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></arg><arg><funapp><sharp><name>prefix</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c18</name><arg><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z2</var></arg><arg><var>z3</var></arg><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c19</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c20</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c21</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c22</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c23</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>strmatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c24</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c2</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c3</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c4</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>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>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>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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c11</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>c12</name><arity>3</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c13</name><arity>0</arity><polynomial><sum><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>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></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>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>c18</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>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>!EQ</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>prefix</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>and</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>!EQ</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>domatch[Ite]</name></sharp><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</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>3</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>eqNatList[Ite]</name></sharp><arity>5</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>prefix</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>domatch</name></sharp><arity>3</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>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>eqNatList</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>notEmpty</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>strmatch</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>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><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><name>S</name><arity>1</arity><polynomial><sum><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>2</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>False</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>True</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>Cons</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>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c12</name><arg><funapp><sharp><name>and</name></sharp><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><name>prefix</name><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><sharp><name>prefix</name></sharp><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>c</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>False</name></funapp></arg></funapp></lhs><rhs><funapp><name>c1</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>c2</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><funapp><name>True</name></funapp></arg></funapp></lhs><rhs><funapp><name>c3</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>S</name><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c4</name><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c5</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>S</name><arg><var>z0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c6</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>!EQ</name></sharp><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>c7</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c8</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c9</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg><arg><funapp><name>Cons</name><arg><var>z3</var></arg><arg><funapp><name>Cons</name><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>False</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c10</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>True</name></funapp></arg><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c11</name><arg><funapp><sharp><name>eqNatList</name></sharp><arg><var>z3</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c12</name><arg><funapp><sharp><name>and</name></sharp><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><name>prefix</name><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></arg><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><funapp><sharp><name>prefix</name></sharp><arg><var>z1</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c13</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>prefix</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c14</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z2</var></arg></funapp></lhs><rhs><funapp><name>c15</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg><arg><var>z0</var></arg></funapp></lhs><rhs><funapp><name>c16</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></lhs><rhs><funapp><name>c17</name><arg><funapp><sharp><name>domatch[Ite]</name></sharp><arg><funapp><name>prefix</name><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z3</var></arg></funapp></arg><arg><funapp><sharp><name>prefix</name></sharp><arg><var>z0</var></arg><arg><funapp><name>Cons</name><arg><var>z1</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Cons</name><arg><var>z2</var></arg><arg><var>z3</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c18</name><arg><funapp><sharp><name>eqNatList[Ite]</name></sharp><arg><funapp><name>!EQ</name><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg><arg><var>z2</var></arg><arg><var>z3</var></arg><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><sharp><name>!EQ</name></sharp><arg><var>z0</var></arg><arg><var>z2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c19</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c20</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>eqNatList</name></sharp><arg><funapp><name>Nil</name></funapp></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c21</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Cons</name><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>c22</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>notEmpty</name></sharp><arg><funapp><name>Nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>c23</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>strmatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg></funapp></lhs><rhs><funapp><name>c24</name><arg><funapp><sharp><name>domatch</name></sharp><arg><var>z0</var></arg><arg><var>z1</var></arg><arg><funapp><name>Nil</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><complexityProof><rIsEmpty/></complexityProof></ruleShifting></complexityProof></ruleShifting></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: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (10 real / 0 unknown / 0 assumptions / 10 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> popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Runti Compl Inner Rewri certi 34749