details

property	value
status	complete
benchmark	PEANO_complete_FR.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n135.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2_cert
runtime (wallclock)	21.784553051 seconds
cpu usage	79.056221167
max memory	1.152888832E9

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	YES
certification-time	1.38

output

/export/starexec/sandbox2/solver/bin/starexec_run_ttt2_cert /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES <?xml version="1.0"?> <?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>V1</var></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>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>U12</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U13</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>U13</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><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U22</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>U22</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>N</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</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>and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>X</var></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>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></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>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</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>U31</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></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>U41</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></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>isNatKind</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__isNatKind</name><arg><var>X</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>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__isNat</name><arg><var>X</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><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__isNatKind</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNatKind</name><arg><var>X</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><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>X</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>V1</var></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>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></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>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>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>U12</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>U12</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>U12</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>U13</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>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><sharp><name>U22</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>U31</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>U41</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>U41</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>U41</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>U41</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>and</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</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__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>isNatKind</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>and</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></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>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></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__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__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</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>U21</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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>isNatKind</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>isNatKind</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>isNatKind</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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>and</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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>isNatKind</name></sharp><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</name></sharp><arg><funapp><name>activate</name><arg><var>V1</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>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</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>U31</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></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>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>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>and</name></sharp><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</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>and</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></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>U41</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</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>activate</name></sharp><arg><var>X2</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>activate</name></sharp><arg><var>X1</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><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__isNatKind</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</name></sharp><arg><var>X</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>activate</name></sharp><arg><var>X</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><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>isNatKind</name></sharp><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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>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>activate</name></sharp><arg><var>X2</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>activate</name></sharp><arg><var>X1</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><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</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>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>activate</name></sharp><arg><funapp><name>n__isNatKind</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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>activate</name></sharp><arg><funapp><name>n__s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><var>X</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>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>isNatKind</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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>isNatKind</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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>and</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></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>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></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>V1</var></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>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg><arg><var>V2</var></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__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</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>U21</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>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>U12</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>U12</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>plus</name></sharp><arg><var>N</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</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>U31</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U31</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>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>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>and</name></sharp><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</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>and</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></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>U41</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>M</var></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>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>U41</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>U41</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>true</realScc><arcs><forwardArc>1</forwardArc><forwardArc>2</forwardArc><forwardArc>3</forwardArc><forwardArc>4</forwardArc><forwardArc>5</forwardArc></arcs><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><arctic><domain><integers/></domain></arctic></domain><degree>1</degree></polynomial></type><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U12</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isNatKind</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>7</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isNat</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__isNatKind</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U11</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>6</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U21</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__isNat</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>and</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>activate</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U31</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U13</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>isNatKind</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>7</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>6</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>plus</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>7</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>6</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>isNat</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U12</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>6</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>6</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>7</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U41</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>activate</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>isNatKind</name></sharp><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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>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>activate</name></sharp><arg><var>X2</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>activate</name></sharp><arg><var>X1</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><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</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>V2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__isNatKind</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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>activate</name></sharp><arg><funapp><name>n__s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><var>X</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>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>isNatKind</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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>isNatKind</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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>and</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></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>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></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__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__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</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>U21</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>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>plus</name></sharp><arg><var>N</var></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>U31</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></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>s</name><arg><var>M</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></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>U41</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>M</var></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>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>U41</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>U41</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><usableRules><rules><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>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>U12</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U13</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>U13</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><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U22</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>U22</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>N</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</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>and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>X</var></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>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></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>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</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>U31</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></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>U41</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></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>isNatKind</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__isNatKind</name><arg><var>X</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>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__isNat</name><arg><var>X</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><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__isNatKind</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNatKind</name><arg><var>X</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><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>X</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></usableRules><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>isNatKind</name></sharp><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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>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>activate</name></sharp><arg><var>X2</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>activate</name></sharp><arg><var>X1</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><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</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>and</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__isNatKind</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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>activate</name></sharp><arg><funapp><name>n__s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><var>X</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__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>isNatKind</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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>isNatKind</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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>and</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</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>activate</name></sharp><arg><var>V1</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>isNatKind</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>U21</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>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>U41</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>M</var></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>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>U41</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>U41</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>true</realScc><arcs><forwardArc>1</forwardArc><forwardArc>3</forwardArc></arcs><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><arctic><domain><integers/></domain></arctic></domain><degree>1</degree></polynomial></type><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U12</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isNatKind</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isNat</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__isNatKind</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U21</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__isNat</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>and</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>activate</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U13</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>isNatKind</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>plus</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>isNat</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U41</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>activate</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>isNatKind</name></sharp><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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>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>activate</name></sharp><arg><var>X2</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><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</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>and</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__isNatKind</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</name></sharp><arg><var>X</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>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><var>X</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>isNatKind</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>and</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</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>activate</name></sharp><arg><var>V1</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>isNatKind</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>U21</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>V1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>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>U41</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>M</var></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>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>U41</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>U41</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><usableRules><rules><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>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>U12</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U13</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>U13</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><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U22</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>U22</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>N</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</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>and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>X</var></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>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></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>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</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>U31</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></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>U41</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></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>isNatKind</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__isNatKind</name><arg><var>X</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>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__isNat</name><arg><var>X</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><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__isNatKind</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNatKind</name><arg><var>X</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><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>X</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></usableRules><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><arctic><domain><integers/></domain></arctic></domain><degree>1</degree></polynomial></type><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U12</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isNatKind</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>6</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isNat</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__isNatKind</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U21</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__isNat</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>and</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>activate</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U13</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>isNatKind</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>plus</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>isNat</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U41</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>activate</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>isNatKind</name></sharp><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></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><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</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>and</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__isNatKind</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</name></sharp><arg><var>X</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>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>activate</name></sharp><arg><funapp><name>n__isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNat</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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>and</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</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>U21</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>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>U41</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>M</var></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>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><usableRules><rules><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>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>U12</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U13</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>U13</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><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U22</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>U22</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>N</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</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>and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>X</var></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>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></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>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</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>U31</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></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>U41</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></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>isNatKind</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__isNatKind</name><arg><var>X</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>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__isNat</name><arg><var>X</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><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__isNatKind</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNatKind</name><arg><var>X</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><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>X</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></usableRules><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><arctic><domain><integers/></domain></arctic></domain><degree>1</degree></polynomial></type><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U12</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isNatKind</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isNat</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__isNatKind</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U21</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__isNat</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>and</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>activate</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U13</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>isNatKind</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>plus</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>isNat</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U41</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>activate</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>isNatKind</name></sharp><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></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><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</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>and</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</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>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>isNatKind</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__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</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>U21</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>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>U41</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>M</var></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>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><usableRules><rules><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>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>U12</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U13</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>U13</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><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U22</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>U22</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>N</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</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>and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>X</var></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>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></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>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</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>U31</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></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>U41</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></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>isNatKind</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__isNatKind</name><arg><var>X</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>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__isNat</name><arg><var>X</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><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__isNatKind</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNatKind</name><arg><var>X</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><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>X</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></usableRules><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>U21</name></sharp><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs><forwardArc>1</forwardArc></arcs><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>5</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U12</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isNatKind</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>6</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>7</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isNat</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__isNatKind</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>6</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U21</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__isNat</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U13</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>5</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>5</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>isNat</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>6</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>5</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>5</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>activate</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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></rules></dps><usableRules><rules><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>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>U12</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U13</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>U13</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><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U22</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>U22</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>N</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</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>and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>X</var></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>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></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>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</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>U31</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></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>U41</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></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>isNatKind</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__isNatKind</name><arg><var>X</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>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__isNat</name><arg><var>X</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><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__isNatKind</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNatKind</name><arg><var>X</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><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>X</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></usableRules><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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></rules></dps><realScc>false</realScc><arcs/></component></depGraphProc></dpProof></redPairUrProc></dpProof></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>isNatKind</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc><forwardArc>2</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>isNatKind</name></sharp><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>isNatKind</name></sharp><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs><forwardArc>1</forwardArc></arcs><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><rationals><delta><rational><numerator>1</numerator><denominator>64</denominator></rational></delta></rationals></domain><degree>1</degree></polynomial></type><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U12</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isNatKind</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><rational><numerator>1</numerator><denominator>2</denominator></rational></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><rational><numerator>3</numerator><denominator>2</denominator></rational></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isNat</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><rational><numerator>5</numerator><denominator>2</denominator></rational></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__isNatKind</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><rational><numerator>1</numerator><denominator>2</denominator></rational></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__isNat</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><rational><numerator>5</numerator><denominator>2</denominator></rational></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U13</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><rational><numerator>1</numerator><denominator>2</denominator></rational></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>isNatKind</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><rational><numerator>1</numerator><denominator>2</denominator></rational></coefficient></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><rational><numerator>1</numerator><denominator>2</denominator></rational></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>activate</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><usableRules><rules><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>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>U12</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U13</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>U13</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><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U22</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>U22</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>N</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</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>and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>X</var></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>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></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>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</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>U31</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></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>U41</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></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>isNatKind</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__isNatKind</name><arg><var>X</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>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__isNat</name><arg><var>X</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><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__isNatKind</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNatKind</name><arg><var>X</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><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>X</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></usableRules><dpProof><pIsEmpty/></dpProof></redPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>isNatKind</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></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc></arcs></component><component><dps><rules><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><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</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>and</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</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>activate</name></sharp><arg><var>X</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>U41</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>M</var></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>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>true</realScc><arcs/><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><arctic><domain><integers/></domain></arctic></domain><degree>1</degree></polynomial></type><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U12</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isNatKind</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>6</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>12</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>6</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isNat</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__isNatKind</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__isNat</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>and</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>activate</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U13</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>4</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>plus</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><minusInfinity/></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>6</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U41</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><minusInfinity/></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>activate</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><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><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</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>activate</name></sharp><arg><var>X</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>U41</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>M</var></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>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><usableRules><rules/></usableRules><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><sharp><name>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc><forwardArc>2</forwardArc></arcs></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>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs><forwardArc>1</forwardArc></arcs><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><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>activate</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></component><component><dps><rules><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><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc></arcs></component><component><dps><rules><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>U41</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>M</var></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>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>true</realScc><arcs/><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U12</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isNatKind</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U31</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U11</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>isNat</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__isNatKind</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__isNat</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U13</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tt</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U22</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>plus</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__plus</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U41</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>n__0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>U21</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>U41</name></sharp><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>activate</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><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>U41</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>U11</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>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>U12</name><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><name>U13</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>U13</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><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><name>U22</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>U22</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>N</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>N</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>U41</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>and</name><arg><funapp><name>tt</name></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>activate</name><arg><var>X</var></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>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></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>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__0</name></funapp></arg></funapp></lhs><rhs><funapp><name>tt</name></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__plus</name><arg><var>V1</var></arg><arg><var>V2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNatKind</name><arg><funapp><name>n__s</name><arg><var>V1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</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>U31</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></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>U41</name><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></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>isNatKind</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__isNatKind</name><arg><var>X</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>and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></lhs><rhs><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>isNat</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>n__isNat</name><arg><var>X</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><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>X2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__isNatKind</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNatKind</name><arg><var>X</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><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__and</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>activate</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>activate</name><arg><funapp><name>n__isNat</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>isNat</name><arg><var>X</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></usableRules><dpProof><depGraphProc><component><dps><rules><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>U41</name></sharp><arg><funapp><name>and</name><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>M</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>M</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__and</name><arg><funapp><name>n__isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>M</var></arg><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs/></component></depGraphProc></dpProof></redPairUrProc></dpProof></component></depGraphProc></dpProof></redPairUrProc></dpProof></component></depGraphProc></dpProof></redPairUrProc></dpProof></redPairUrProc></dpProof></redPairUrProc></dpProof></component><component><dps><rules><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>and</name><arg><funapp><name>isNatKind</name><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V1</var></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>U11</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></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>V1</var></arg></funapp></arg></funapp></arg><arg><funapp><name>activate</name><arg><var>V2</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs/></component><component><dps><rules><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>U31</name></sharp><arg><funapp><name>and</name><arg><funapp><name>isNat</name><arg><var>N</var></arg></funapp></arg><arg><funapp><name>n__isNatKind</name><arg><var>N</var></arg></funapp></arg></funapp></arg><arg><var>N</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs/></component></depGraphProc></dpProof></redPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>U41</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><arcs/></component><component><dps><rules><rule><lhs><funapp><sharp><name>U12</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V2</var></arg></funapp></lhs><rhs><funapp><sharp><name>U13</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><arcs/></component><component><dps><rules><rule><lhs><funapp><sharp><name>U21</name></sharp><arg><funapp><name>tt</name></funapp></arg><arg><var>V1</var></arg></funapp></lhs><rhs><funapp><sharp><name>U22</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><arcs/></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><funapp><name>activate</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs/></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><arcs/></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></proof><origin><proofOrigin><tool><name>ttt2</name><version>ttt2 1.20 [hg: unknown]</version><strategy>((if standard then var else fail) | con | (if srs then ((sleep -t 25?;rlab;(((( (if srs then arctic -dim 1 -ib 4 -ob 5 else fail) || (if srs then arctic -dim 2 -ib 2 -ob 3 else fail) || (if srs then arctic -dim 3 -ib 1 -ob 2 else fail) || (if srs then arctic -dim 3 -ib 2 -ob 2 else fail) || matrix -dim 1 -ib 5 -ob 8 || matrix -dim 2 -ib 3 -ob 4 || matrix -dim 3 -ib 2 -ob 3 || matrix -dim 3 -ib 1 -ob 2 || matrix -dim 4 -ib 1 -ob 2 || matrix -dim 5 -ib 1 -ob 1 || kbo -ib 3 -ob 4 || wpo -msum -ib 3 -ob 4 -cpf || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( (wpo -cpf -dp -ur -sum -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -pol -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -max -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -msum -ib 3 -ob 3 [4] | wpo -cpf -dp -ur -mat -dim 2 -ib 3 -ob 3 [5] | wpo -cpf -dp -ur -mat -dim 3 -ib 3 -ob 3 [5] | wpo -cpf -dp -ur -ib 3 -ob 3 [9] | fail ) || matrix -dp -ur -dim 1 -ib 3 -ob 5 || matrix -dp -ur -dim 1 -ib 3 -ob 8 -rat 2 -db 1 || matrix -dp -ur -dim 1 -ib 4 -ob 10 -rat 4 -db 1 || matrix -dp -ur -dim 2 -ib 2 -ob 3 || matrix -dp -ur -dim 2 -ib 3 -ob 4 -rat 2 -db 0 || matrix -dp -ur -dim 3 -ib 1 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 -rat 2 -db 0 || matrix -dp -ur -dim 4 -ib 1 -ob 2 || lpo -ur -af || (arctic -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || fail) } restore) )*[29])) || (if standard then (bounds -cert || fail;(bounds -rfc -qc)) else fail)))! || (( unfold || fail)*[7])!)[299])! || ((((( (if srs then arctic -dim 1 -ib 4 -ob 5 else fail) || (if srs then arctic -dim 2 -ib 2 -ob 3 else fail) || (if srs then arctic -dim 3 -ib 1 -ob 2 else fail) || (if srs then arctic -dim 3 -ib 2 -ob 2 else fail) || matrix -dim 1 -ib 5 -ob 8 || matrix -dim 2 -ib 3 -ob 4 || matrix -dim 3 -ib 2 -ob 3 || matrix -dim 3 -ib 1 -ob 2 || matrix -dim 4 -ib 1 -ob 2 || matrix -dim 5 -ib 1 -ob 1 || kbo -ib 3 -ob 4 || wpo -msum -ib 3 -ob 4 -cpf || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( (wpo -cpf -dp -ur -sum -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -pol -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -max -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -msum -ib 3 -ob 3 [4] | wpo -cpf -dp -ur -mat -dim 2 -ib 3 -ob 3 [5] | wpo -cpf -dp -ur -mat -dim 3 -ib 3 -ob 3 [5] | wpo -cpf -dp -ur -ib 3 -ob 3 [9] | fail ) || matrix -dp -ur -dim 1 -ib 3 -ob 5 || matrix -dp -ur -dim 1 -ib 3 -ob 8 -rat 2 -db 1 || matrix -dp -ur -dim 1 -ib 4 -ob 10 -rat 4 -db 1 || matrix -dp -ur -dim 2 -ib 2 -ob 3 || matrix -dp -ur -dim 2 -ib 3 -ob 4 -rat 2 -db 0 || matrix -dp -ur -dim 3 -ib 1 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 -rat 2 -db 0 || matrix -dp -ur -dim 4 -ib 1 -ob 2 || lpo -ur -af || (arctic -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || fail) } restore) )*[29])) || (if standard then (bounds -cert || fail;(bounds -rfc -qc)) else fail)))! || (( unfold || fail)*[7])!)[299])! || (rev?;((( (if srs then arctic -dim 1 -ib 4 -ob 5 else fail) || (if srs then arctic -dim 2 -ib 2 -ob 3 else fail) || (if srs then arctic -dim 3 -ib 1 -ob 2 else fail) || (if srs then arctic -dim 3 -ib 2 -ob 2 else fail) || matrix -dim 1 -ib 5 -ob 8 || matrix -dim 2 -ib 3 -ob 4 || matrix -dim 3 -ib 2 -ob 3 || matrix -dim 3 -ib 1 -ob 2 || matrix -dim 4 -ib 1 -ob 2 || matrix -dim 5 -ib 1 -ob 1 || kbo -ib 3 -ob 4 || wpo -msum -ib 3 -ob 4 -cpf || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( (wpo -cpf -dp -ur -sum -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -pol -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -max -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -msum -ib 3 -ob 3 [4] | wpo -cpf -dp -ur -mat -dim 2 -ib 3 -ob 3 [5] | wpo -cpf -dp -ur -mat -dim 3 -ib 3 -ob 3 [5] | wpo -cpf -dp -ur -ib 3 -ob 3 [9] | fail ) || matrix -dp -ur -dim 1 -ib 3 -ob 5 || matrix -dp -ur -dim 1 -ib 3 -ob 8 -rat 2 -db 1 || matrix -dp -ur -dim 1 -ib 4 -ob 10 -rat 4 -db 1 || matrix -dp -ur -dim 2 -ib 2 -ob 3 || matrix -dp -ur -dim 2 -ib 3 -ob 4 -rat 2 -db 0 || matrix -dp -ur -dim 3 -ib 1 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 -rat 2 -db 0 || matrix -dp -ur -dim 4 -ib 1 -ob 2 || lpo -ur -af || (arctic -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || fail) } restore) )*[29])) || (if standard then (bounds -cert || fail;(bounds -rfc -qc)) else fail)))![299])! ) else ((((( (if srs then arctic -dim 1 -ib 4 -ob 5 else fail) || (if srs then arctic -dim 2 -ib 2 -ob 3 else fail) || (if srs then arctic -dim 3 -ib 1 -ob 2 else fail) || (if srs then arctic -dim 3 -ib 2 -ob 2 else fail) || matrix -dim 1 -ib 5 -ob 8 || matrix -dim 2 -ib 3 -ob 4 || matrix -dim 3 -ib 2 -ob 3 || matrix -dim 3 -ib 1 -ob 2 || matrix -dim 4 -ib 1 -ob 2 || matrix -dim 5 -ib 1 -ob 1 || kbo -ib 3 -ob 4 || wpo -msum -ib 3 -ob 4 -cpf || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( (wpo -cpf -dp -ur -sum -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -pol -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -max -ib 3 -ob 3 [3] | wpo -cpf -dp -ur -msum -ib 3 -ob 3 [4] | wpo -cpf -dp -ur -mat -dim 2 -ib 3 -ob 3 [5] | wpo -cpf -dp -ur -mat -dim 3 -ib 3 -ob 3 [5] | wpo -cpf -dp -ur -ib 3 -ob 3 [9] | fail ) || matrix -dp -ur -dim 1 -ib 3 -ob 5 || matrix -dp -ur -dim 1 -ib 3 -ob 8 -rat 2 -db 1 || matrix -dp -ur -dim 1 -ib 4 -ob 10 -rat 4 -db 1 || matrix -dp -ur -dim 2 -ib 2 -ob 3 || matrix -dp -ur -dim 2 -ib 3 -ob 4 -rat 2 -db 0 || matrix -dp -ur -dim 3 -ib 1 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 -rat 2 -db 0 || matrix -dp -ur -dim 4 -ib 1 -ob 2 || lpo -ur -af || (arctic -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || fail) } restore) )*[29])) || (if standard then (bounds -cert || fail;(bounds -rfc -qc)) else fail)))! || (( unfold || fail)*[7])!)[299])))</strategy></tool></proofOrigin></origin></certificationProblem> popout

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

job log

popout

actions

all output return to TRS Standard Certified