YES
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napp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>bot</name></funapp></lhs><rhs><funapp><name>new</name><arg><funapp><name>bot</name></funapp></arg></funapp></rhs></rule></rules></relativeRules></trsInput></input><cpfVersion>2.1</cpfVersion><proof><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>top</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>north</name><arity>4</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><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>old</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>east</name><arity>4</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><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>new</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>south</name><arity>4</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><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>west</name><arity>4</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><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>bot</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>bot</name></funapp></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>bot</name></funapp></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>bot</name></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>bot</name></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>bot</name></funapp></lhs><rhs><funapp><name>new</name><arg><funapp><name>bot</name></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><integers/></domain><dimension>2</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><name>top</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>north</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>new</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>old</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>east</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>south</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>west</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>bot</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>bot</name></funapp></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>bot</name></funapp></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>bot</name></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>bot</name></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>bot</name></funapp></lhs><rhs><funapp><name>new</name><arg><funapp><name>bot</name></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><integers/></domain><dimension>2</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><name>top</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>north</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>new</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>old</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>east</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>south</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>west</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>bot</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>bot</name></funapp></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>bot</name></funapp></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>bot</name></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>bot</name></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>bot</name></funapp></lhs><rhs><funapp><name>new</name><arg><funapp><name>bot</name></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><integers/></domain><dimension>2</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><name>top</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>north</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>new</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>old</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>east</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>south</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>west</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>bot</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>bot</name></funapp></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>bot</name></funapp></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>bot</name></funapp></lhs><rhs><funapp><name>new</name><arg><funapp><name>bot</name></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><integers/></domain><dimension>2</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><name>top</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>north</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>new</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>old</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>east</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>south</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>west</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>bot</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>bot</name></funapp></lhs><rhs><funapp><name>new</name><arg><funapp><name>bot</name></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><integers/></domain><dimension>2</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><name>top</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>north</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>new</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>old</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>east</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>south</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>west</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>bot</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>bot</name></funapp></lhs><rhs><funapp><name>new</name><arg><funapp><name>bot</name></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><integers/></domain><dimension>2</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><name>top</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>north</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>new</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>old</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>east</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>south</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>west</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>bot</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>old</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>bot</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>bot</name></funapp></lhs><rhs><funapp><name>new</name><arg><funapp><name>bot</name></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><integers/></domain><dimension>2</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><name>top</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>north</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>new</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>old</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>east</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>south</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>west</name><arity>4</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>bot</name><arity>0</arity><polynomial><sum><polynomial><product><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>bot</name></funapp></lhs><rhs><funapp><name>new</name><arg><funapp><name>bot</name></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>top</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>north</name><arity>4</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>new</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>old</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>east</name><arity>4</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>south</name><arity>4</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>west</name><arity>4</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><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>bot</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><funapp><name>bot</name></funapp></arg><arg><var>s</var></arg><arg><funapp><name>old</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>bot</name></funapp></lhs><rhs><funapp><name>new</name><arg><funapp><name>bot</name></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>top</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>north</name><arity>4</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>new</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>old</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>east</name><arity>4</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>south</name><arity>4</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><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>bot</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>west</name><arity>4</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><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><funapp><name>bot</name></funapp></arg><arg><funapp><name>old</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>bot</name></funapp></lhs><rhs><funapp><name>new</name><arg><funapp><name>bot</name></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>top</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>north</name><arity>4</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>new</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>old</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>east</name><arity>4</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><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>bot</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>south</name><arity>4</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><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>west</name><arity>4</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><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>4</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules/></trs><trs><rules><rule><lhs><funapp><name>top</name><arg><funapp><name>north</name><arg><funapp><name>new</name><arg><var>n</var></arg></funapp></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>north</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><funapp><name>new</name><arg><var>e</var></arg></funapp></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>east</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><funapp><name>new</name><arg><var>s</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>south</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><funapp><name>new</name><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>top</name><arg><funapp><name>west</name><arg><var>n</var></arg><arg><var>e</var></arg><arg><var>s</var></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>bot</name></funapp></lhs><rhs><funapp><name>new</name><arg><funapp><name>bot</name></funapp></arg></funapp></rhs></rule></rules></trs><relativeTerminationProof><rIsEmpty/></relativeTerminationProof></ruleRemoval></relativeTerminationProof></ruleRemoval></relativeTerminationProof></ruleRemoval></relativeTerminationProof></ruleRemoval></relativeTerminationProof></ruleRemoval></relativeTerminationProof></ruleRemoval></relativeTerminationProof></ruleRemoval></relativeTerminationProof></ruleRemoval></relativeTerminationProof></ruleRemoval></relativeTerminationProof></ruleRemoval></relativeTerminationProof></ruleRemoval></relativeTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
</version><strategy>Statistics for single proof: 100.00 % (12 real / 0 unknown / 0 assumptions / 12 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem>