details

property	value
status	complete
benchmark	Hamming.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n028.star.cs.uiowa.edu
space	Applicative_05

run statistics

property	value
solver	AProVE21
configuration	certified
runtime (wallclock)	3.08190488815 seconds
cpu usage	8.495242215
max memory	6.0633088E8

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	NO
certification-time	0.36

output

/export/starexec/sandbox2/solver/bin/starexec_run_certified /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- NO <?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><trsInput><trs><rules><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>if</name></funapp></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><var>xs</var></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>if</name></funapp></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><var>ys</var></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>lt</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>lt</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>lt</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>lt</name></funapp></arg><arg><var>y</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>app</name><arg><funapp><name>app</name><arg><funapp><name>eq</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>eq</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>eq</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>merge</name></funapp></arg><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><var>xs</var></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>merge</name></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><var>ys</var></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>merge</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>y</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>if</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>lt</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>merge</name></funapp></arg><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>y</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>if</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>eq</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>merge</name></funapp></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>merge</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><funapp><name>app</name><arg><var>f</var></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>mult</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>mult</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>plus</name></funapp></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>mult</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>plus</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>plus</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>plus</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>list1</name></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>mult</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>hamming</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>list2</name></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>mult</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>hamming</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>list3</name></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>mult</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>hamming</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>hamming</name></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>merge</name></funapp></arg><arg><funapp><name>list1</name></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>merge</name></funapp></arg><arg><funapp><name>list2</name></funapp></arg></funapp></arg><arg><funapp><name>list3</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsNonterminationProof><uncurry><uncurryInformation><name>app</name><uncurriedSymbols><uncurriedSymbolEntry><name>if</name><arity>0</arity><name>if</name><name>if1</name><name>if2</name><name>if3</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>true</name><arity>0</arity><name>true</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>false</name><arity>0</arity><name>false</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>lt</name><arity>0</arity><name>lt</name><name>lt1</name><name>lt2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>s</name><arity>0</arity><name>s</name><name>s1</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>0</name><arity>0</arity><name>0</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>eq</name><arity>0</arity><name>eq</name><name>eq1</name><name>eq2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>merge</name><arity>0</arity><name>merge</name><name>merge1</name><name>merge2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>nil</name><arity>0</arity><name>nil</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>cons</name><arity>0</arity><name>cons</name><name>cons1</name><name>cons2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>map</name><arity>0</arity><name>map</name><name>map1</name><name>map2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>mult</name><arity>0</arity><name>mult</name><name>mult1</name><name>mult2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>plus</name><arity>0</arity><name>plus</name><name>plus1</name><name>plus2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>list1</name><arity>0</arity><name>list1</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>hamming</name><arity>0</arity><name>hamming</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>list2</name><arity>0</arity><name>list2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>list3</name><arity>0</arity><name>list3</name></uncurriedSymbolEntry></uncurriedSymbols><uncurryRules><rules><rule><lhs><funapp><name>app</name><arg><funapp><name>if</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>if1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>if2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>lt</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>lt1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>lt1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>lt2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>eq</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>eq1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>eq1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>eq2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>merge</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>merge1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>merge1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>merge2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>mult</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>mult1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>mult1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>mult2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>plus</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>plus1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>plus1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>plus2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></uncurryRules><etaRules><rules/></etaRules></uncurryInformation><trs><rules><rule><lhs><funapp><name>if3</name><arg><funapp><name>true</name></funapp></arg><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><var>xs</var></rhs></rule><rule><lhs><funapp><name>if3</name><arg><funapp><name>false</name></funapp></arg><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><var>ys</var></rhs></rule><rule><lhs><funapp><name>lt2</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>lt2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>lt2</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>lt2</name><arg><var>y</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq2</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>eq2</name><arg><funapp><name>s1</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>eq2</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>merge2</name><arg><var>xs</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><var>xs</var></rhs></rule><rule><lhs><funapp><name>merge2</name><arg><funapp><name>nil</name></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><var>ys</var></rhs></rule><rule><lhs><funapp><name>merge2</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>if3</name><arg><funapp><name>lt2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>merge2</name><arg><var>xs</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>if3</name><arg><funapp><name>eq2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>merge2</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><funapp><name>merge2</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>map2</name><arg><var>f</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>map2</name><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><funapp><name>app</name><arg><var>f</var></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>map2</name><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult2</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>mult2</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>plus2</name><arg><var>y</var></arg><arg><funapp><name>mult2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus2</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>plus2</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><funapp><name>plus2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>list1</name></funapp></lhs><rhs><funapp><name>map2</name><arg><funapp><name>mult1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>hamming</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>list2</name></funapp></lhs><rhs><funapp><name>map2</name><arg><funapp><name>mult1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>hamming</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>list3</name></funapp></lhs><rhs><funapp><name>map2</name><arg><funapp><name>mult1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>hamming</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>hamming</name></funapp></lhs><rhs><funapp><name>cons2</name><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>merge2</name><arg><funapp><name>list1</name></funapp></arg><arg><funapp><name>merge2</name><arg><funapp><name>list2</name></funapp></arg><arg><funapp><name>list3</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>if</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>if1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>if2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>lt</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>lt1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>lt1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>lt2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>eq</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>eq1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>eq1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>eq2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>merge</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>merge1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>merge1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>merge2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>mult</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>mult1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>mult1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>mult2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>plus</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>plus1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>plus1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>plus2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></trs><trsNonterminationProof><innermostLhssIncrease><innermostLhss><funapp><name>if3</name><arg><funapp><name>true</name></funapp></arg><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp><funapp><name>if3</name><arg><funapp><name>false</name></funapp></arg><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp><funapp><name>lt2</name><arg><funapp><name>s1</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>x1</var></arg></funapp></arg></funapp><funapp><name>lt2</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s1</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>lt2</name><arg><var>x0</var></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>eq2</name><arg><var>x0</var></arg><arg><var>x0</var></arg></funapp><funapp><name>eq2</name><arg><funapp><name>s1</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>eq2</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s1</name><arg><var>x0</var></arg></funapp></arg></funapp><funapp><name>merge2</name><arg><var>x0</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp><funapp><name>merge2</name><arg><funapp><name>nil</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>merge2</name><arg><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></arg></funapp><funapp><name>map2</name><arg><var>x0</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp><funapp><name>map2</name><arg><var>x0</var></arg><arg><funapp><name>cons2</name><arg><var>x1</var></arg><arg><var>x2</var></arg></funapp></arg></funapp><funapp><name>mult2</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>mult2</name><arg><funapp><name>s1</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp><funapp><name>plus2</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>plus2</name><arg><funapp><name>s1</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp><funapp><name>list1</name></funapp><funapp><name>list2</name></funapp><funapp><name>list3</name></funapp><funapp><name>hamming</name></funapp><funapp><name>app</name><arg><funapp><name>if</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>app</name><arg><funapp><name>if1</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp><funapp><name>app</name><arg><funapp><name>if2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>x2</var></arg></funapp><funapp><name>app</name><arg><funapp><name>lt</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>app</name><arg><funapp><name>lt1</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>app</name><arg><funapp><name>eq</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>app</name><arg><funapp><name>eq1</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp><funapp><name>app</name><arg><funapp><name>merge</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>app</name><arg><funapp><name>merge1</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>app</name><arg><funapp><name>cons1</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>app</name><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp><funapp><name>app</name><arg><funapp><name>mult</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>app</name><arg><funapp><name>mult1</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp><funapp><name>app</name><arg><funapp><name>plus</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>app</name><arg><funapp><name>plus1</name><arg><var>x0</var></arg></funapp></arg><arg><var>x1</var></arg></funapp></innermostLhss><trsNonterminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>lt2</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>lt2</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>merge2</name></sharp><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>if3</name></sharp><arg><funapp><name>lt2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>merge2</name><arg><var>xs</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>if3</name><arg><funapp><name>eq2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>merge2</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><funapp><name>merge2</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>merge2</name></sharp><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>lt2</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>merge2</name></sharp><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>merge2</name></sharp><arg><var>xs</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>merge2</name></sharp><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>if3</name></sharp><arg><funapp><name>eq2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>merge2</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><funapp><name>merge2</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>merge2</name></sharp><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq2</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>merge2</name></sharp><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>merge2</name></sharp><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>merge2</name></sharp><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>merge2</name></sharp><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>app</name></sharp><arg><var>f</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult2</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus2</name></sharp><arg><var>y</var></arg><arg><funapp><name>mult2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mult2</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult2</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus2</name></sharp><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus2</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>list1</name></sharp></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><funapp><name>mult1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>hamming</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>list1</name></sharp></funapp></lhs><rhs><funapp><sharp><name>hamming</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>list2</name></sharp></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><funapp><name>mult1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>hamming</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>list2</name></sharp></funapp></lhs><rhs><funapp><sharp><name>hamming</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>list3</name></sharp></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><funapp><name>mult1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>hamming</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>list3</name></sharp></funapp></lhs><rhs><funapp><sharp><name>hamming</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>hamming</name></sharp></funapp></lhs><rhs><funapp><sharp><name>merge2</name></sharp><arg><funapp><name>list1</name></funapp></arg><arg><funapp><name>merge2</name><arg><funapp><name>list2</name></funapp></arg><arg><funapp><name>list3</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>hamming</name></sharp></funapp></lhs><rhs><funapp><sharp><name>list1</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>hamming</name></sharp></funapp></lhs><rhs><funapp><sharp><name>merge2</name></sharp><arg><funapp><name>list2</name></funapp></arg><arg><funapp><name>list3</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>hamming</name></sharp></funapp></lhs><rhs><funapp><sharp><name>list2</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>hamming</name></sharp></funapp></lhs><rhs><funapp><sharp><name>list3</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>if2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>if3</name></sharp><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>lt1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>lt2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>eq1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>eq2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>merge1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>merge2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>map2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>mult1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>mult2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>app</name></sharp><arg><funapp><name>plus1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus2</name></sharp><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpNonterminationProof><dpRuleRemoval><dps><rules><rule><lhs><funapp><sharp><name>hamming</name></sharp></funapp></lhs><rhs><funapp><sharp><name>list1</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>list1</name></sharp></funapp></lhs><rhs><funapp><sharp><name>hamming</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>hamming</name></sharp></funapp></lhs><rhs><funapp><sharp><name>list2</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>list2</name></sharp></funapp></lhs><rhs><funapp><sharp><name>hamming</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>hamming</name></sharp></funapp></lhs><rhs><funapp><sharp><name>list3</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>list3</name></sharp></funapp></lhs><rhs><funapp><sharp><name>hamming</name></sharp></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>if3</name><arg><funapp><name>true</name></funapp></arg><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><var>xs</var></rhs></rule><rule><lhs><funapp><name>if3</name><arg><funapp><name>false</name></funapp></arg><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></lhs><rhs><var>ys</var></rhs></rule><rule><lhs><funapp><name>lt2</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>lt2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>lt2</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>lt2</name><arg><var>y</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>eq2</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>eq2</name><arg><funapp><name>s1</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>eq2</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>merge2</name><arg><var>xs</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><var>xs</var></rhs></rule><rule><lhs><funapp><name>merge2</name><arg><funapp><name>nil</name></funapp></arg><arg><var>ys</var></arg></funapp></lhs><rhs><var>ys</var></rhs></rule><rule><lhs><funapp><name>merge2</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>if3</name><arg><funapp><name>lt2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>merge2</name><arg><var>xs</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>if3</name><arg><funapp><name>eq2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><funapp><name>merge2</name><arg><var>xs</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><funapp><name>merge2</name><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>map2</name><arg><var>f</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>map2</name><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><funapp><name>app</name><arg><var>f</var></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>map2</name><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult2</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>mult2</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>plus2</name><arg><var>y</var></arg><arg><funapp><name>mult2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus2</name><arg><funapp><name>0</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>plus2</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><funapp><name>plus2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>list1</name></funapp></lhs><rhs><funapp><name>map2</name><arg><funapp><name>mult1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>hamming</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>list2</name></funapp></lhs><rhs><funapp><name>map2</name><arg><funapp><name>mult1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>hamming</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>list3</name></funapp></lhs><rhs><funapp><name>map2</name><arg><funapp><name>mult1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>hamming</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>hamming</name></funapp></lhs><rhs><funapp><name>cons2</name><arg><funapp><name>s1</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>merge2</name><arg><funapp><name>list1</name></funapp></arg><arg><funapp><name>merge2</name><arg><funapp><name>list2</name></funapp></arg><arg><funapp><name>list3</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>if</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>if1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>if2</name><arg><var>x0</var></arg><arg><var>x1</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if3</name><arg><var>x0</var></arg><arg><var>x1</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>lt</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>lt1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>lt1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>lt2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>eq</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>eq1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>eq1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>eq2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>merge</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>merge1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>merge1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>merge2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>mult</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>mult1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>mult1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>mult2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>plus</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>plus1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>plus1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>plus2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></trs><dpNonterminationProof><dpRuleRemoval><dps><rules><rule><lhs><funapp><sharp><name>hamming</name></sharp></funapp></lhs><rhs><funapp><sharp><name>list1</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>list1</name></sharp></funapp></lhs><rhs><funapp><sharp><name>hamming</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>hamming</name></sharp></funapp></lhs><rhs><funapp><sharp><name>list2</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>list2</name></sharp></funapp></lhs><rhs><funapp><sharp><name>hamming</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>hamming</name></sharp></funapp></lhs><rhs><funapp><sharp><name>list3</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>list3</name></sharp></funapp></lhs><rhs><funapp><sharp><name>hamming</name></sharp></funapp></rhs></rule></rules></dps><trs><rules/></trs><dpNonterminationProof><innermostLhssRemovalProc><innermostLhss/><dpNonterminationProof><loop><rewriteSequence><startTerm><funapp><sharp><name>list1</name></sharp></funapp></startTerm><rewriteStep><positionInTerm/><rule><lhs><funapp><sharp><name>list1</name></sharp></funapp></lhs><rhs><funapp><sharp><name>hamming</name></sharp></funapp></rhs></rule><funapp><sharp><name>hamming</name></sharp></funapp></rewriteStep><rewriteStep><positionInTerm/><rule><lhs><funapp><sharp><name>hamming</name></sharp></funapp></lhs><rhs><funapp><sharp><name>list1</name></sharp></funapp></rhs></rule><funapp><sharp><name>list1</name></sharp></funapp></rewriteStep></rewriteSequence><substitution/><box/></loop></dpNonterminationProof></innermostLhssRemovalProc></dpNonterminationProof></dpRuleRemoval></dpNonterminationProof></dpRuleRemoval></dpNonterminationProof></dpTrans></trsNonterminationProof></innermostLhssIncrease></trsNonterminationProof></uncurry></trsNonterminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished </version><strategy>Statistics for single proof: 100.00 % (7 real / 0 unknown / 0 assumptions / 7 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 TRS Standard Certified