details

property	value
status	complete
benchmark	MYNAT_nokinds-noand_Z.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n020.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	4.12295508385 seconds
cpu usage	9.696686628
max memory	6.77548032E8

stage attributes

key	value
certification-result	CERTIFIED
output-size	48431
starexec-result	YES
certification-time	0.1

output

/export/starexec/sandbox/solver/bin/starexec_run_certified /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES <?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>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U12</name><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U12</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U21</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U31</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U32</name><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U32</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>U41</name><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U51</name><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>U52</name><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U52</name><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>plus</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U61</name><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>U71</name><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>U72</name><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>U72</name><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><funapp><name>x</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><funapp><name>n__0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><funapp><name>n__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U11</name><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U21</name><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><funapp><name>n__x</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U31</name><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>N</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>U41</name><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>N</var></arg><arg><funapp><name>s</name><arg><var>M</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U51</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>x</name><arg><var>N</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>U61</name><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>x</name><arg><var>N</var></arg><arg><funapp><name>s</name><arg><var>M</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>U71</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>0</name></funapp></lhs><rhs><funapp><name>n__0</name></funapp></rhs></rule><rule><lhs><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__s</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>x</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__x</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__x</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>x</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><var>X</var></arg></funapp></lhs><rhs><var>X</var></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>U12</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>U32</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>M</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>M</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>U72</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>M</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U72</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>x</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U72</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>x</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U72</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U72</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>M</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__x</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__x</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__x</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__x</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><var>N</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><var>N</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><var>N</var></arg><arg><funapp><name>s</name><arg><var>M</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><var>N</var></arg><arg><funapp><name>s</name><arg><var>M</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><var>M</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>x</name></sharp><arg><var>N</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>x</name></sharp><arg><var>N</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>x</name></sharp><arg><var>N</var></arg><arg><funapp><name>s</name><arg><var>M</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>x</name></sharp><arg><var>N</var></arg><arg><funapp><name>s</name><arg><var>M</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><var>M</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__x</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>x</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__plus</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><var>N</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__x</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>x</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>x</name></sharp><arg><var>N</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__x</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__x</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__x</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__x</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>x</name></sharp><arg><var>N</var></arg><arg><funapp><name>s</name><arg><var>M</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>U72</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U72</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>x</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><var>N</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><var>N</var></arg><arg><funapp><name>s</name><arg><var>M</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>plus</name></sharp><arg><var>N</var></arg><arg><funapp><name>s</name><arg><var>M</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><var>M</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>M</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>M</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U72</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>x</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>x</name></sharp><arg><var>N</var></arg><arg><funapp><name>s</name><arg><var>M</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><var>M</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U72</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U72</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>M</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>M</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><redPairProc><orderingConstraintProof><redPair><pathOrder><statusPrecedence><statusPrecedenceEntry><name>tt</name><arity>0</arity><precedence>3</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>n__plus</name><arity>2</arity><precedence>4</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>isNat</name><arity>1</arity><precedence>3</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><sharp><name>plus</name></sharp><arity>2</arity><precedence>0</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>0</name><arity>0</arity><precedence>3</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>n__x</name><arity>2</arity><precedence>5</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><sharp><name>x</name></sharp><arity>2</arity><precedence>5</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>n__s</name><arity>1</arity><precedence>1</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><sharp><name>U31</name></sharp><arity>2</arity><precedence>5</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>s</name><arity>1</arity><precedence>1</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><sharp><name>U71</name></sharp><arity>3</arity><precedence>5</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><sharp><name>U72</name></sharp><arity>3</arity><precedence>5</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>x</name><arity>2</arity><precedence>5</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><sharp><name>U51</name></sharp><arity>3</arity><precedence>0</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><sharp><name>U52</name></sharp><arity>3</arity><precedence>0</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>n__0</name><arity>0</arity><precedence>3</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>plus</name><arity>2</arity><precedence>4</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>U41</name><arity>2</arity><precedence>4</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>U71</name><arity>3</arity><precedence>5</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>U72</name><arity>3</arity><precedence>5</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>U61</name><arity>1</arity><precedence>2</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>U51</name><arity>3</arity><precedence>4</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>U32</name><arity>1</arity><precedence>3</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>U52</name><arity>3</arity><precedence>4</precedence><lex/></statusPrecedenceEntry></statusPrecedence><argumentFilter><argumentFilterEntry><sharp><name>U11</name></sharp><arity>2</arity><collapsing>2</collapsing></argumentFilterEntry><argumentFilterEntry><name>tt</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><sharp><name>isNat</name></sharp><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>activate</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>n__plus</name><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>isNat</name><arity>1</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><sharp><name>activate</name></sharp><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>plus</name></sharp><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>0</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><sharp><name>U41</name></sharp><arity>2</arity><collapsing>2</collapsing></argumentFilterEntry><argumentFilterEntry><name>n__x</name><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>x</name></sharp><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>n__s</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>U31</name></sharp><arity>2</arity><nonCollapsing><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>s</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>U71</name></sharp><arity>3</arity><nonCollapsing><position>2</position><position>3</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>U72</name></sharp><arity>3</arity><nonCollapsing><position>2</position><position>3</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>x</name><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>U51</name></sharp><arity>3</arity><nonCollapsing><position>2</position><position>3</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><sharp><name>U52</name></sharp><arity>3</arity><nonCollapsing><position>2</position><position>3</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>n__0</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>plus</name><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>U41</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>U71</name><arity>3</arity><nonCollapsing><position>2</position><position>3</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>U72</name><arity>3</arity><nonCollapsing><position>2</position><position>3</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>U11</name><arity>2</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>U21</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>U31</name><arity>2</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>U61</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>U51</name><arity>3</arity><nonCollapsing><position>2</position><position>3</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>U32</name><arity>1</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>U12</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>U52</name><arity>3</arity><nonCollapsing><position>2</position><position>3</position><position>1</position></nonCollapsing></argumentFilterEntry></argumentFilter></pathOrder></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__x</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>x</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>U72</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V2</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U41</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U51</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__x</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>x</name></sharp><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U71</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>U72</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>plus</name></sharp><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></redPairProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>x</name></sharp><arg><var>N</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>U12</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>U32</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U52</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>plus</name><arg><funapp><name>activate</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>M</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>U61</name></sharp><arg><funapp><name>tt</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>isNat</name></sharp><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>isNat</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>0</name></sharp></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (4 real / 0 unknown / 0 assumptions / 4 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