/export/starexec/sandbox/solver/bin/starexec_run_tct_rci_cert /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(?,O(n^2))
<?xml version="1.0" encoding="UTF-8"?>
<?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?>
<certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 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var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#natmult</name><arg><funapp><name>#0</name></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#natmult</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></relativeRules></trsInput><runtimeComplexity><signature><symbol><name>#0</name><arity>0</arity></symbol><symbol><name>#neg</name><arity>1</arity></symbol><symbol><name>#pos</name><arity>1</arity></symbol><symbol><name>#s</name><arity>1</arity></symbol><symbol><name>::</name><arity>2</arity></symbol><symbol><name>nil</name><arity>0</arity></symbol></signature><signature><symbol><name>#add</name><arity>2</arity></symbol><symbol><name>#mult</name><arity>2</arity></symbol><symbol><name>#natmult</name><arity>2</arity></symbol><symbol><name>#pred</name><arity>1</arity></symbol><symbol><name>#succ</name><arity>1</arity></symbol><symbol><name>*</name><arity>2</arity></symbol><symbol><name>dyade</name><arity>2</arity></symbol><symbol><name>dyade#1</name><arity>2</arity></symbol><symbol><name>mult</name><arity>2</arity></symbol><symbol><name>mult#1</name><arity>2</arity></symbol></signature></runtimeComplexity><polynomial>2</polynomial></complexityInput></input><cpfVersion>2.2</cpfVersion><proof><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><naturals/></domain><dimension>1</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><name>#0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>#add</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>2</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#natmult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#neg</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#pos</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#pred</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#s</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#succ</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>*</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>::</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><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></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>dyade</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>dyade#1</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult#1</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>dyade#1</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>#add</name><arg><funapp><name>#0</name></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><var>@y</var></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#pred</name><arg><var>@y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#pred</name><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#succ</name><arg><var>@y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#succ</name><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#neg</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#neg</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#neg</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#neg</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#natmult</name><arg><funapp><name>#0</name></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#natmult</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>*</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#mult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>dyade</name><arg><var>@l1</var></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>dyade#1</name><arg><var>@l1</var></arg><arg><var>@l2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>dyade#1</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>::</name><arg><funapp><name>mult</name><arg><var>@x</var></arg><arg><var>@l2</var></arg></funapp></arg><arg><funapp><name>dyade</name><arg><var>@xs</var></arg><arg><var>@l2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>dyade#1</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><var>@n</var></arg><arg><var>@l</var></arg></funapp></lhs><rhs><funapp><name>mult#1</name><arg><var>@l</var></arg><arg><var>@n</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult#1</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@n</var></arg></funapp></lhs><rhs><funapp><name>::</name><arg><funapp><name>*</name><arg><var>@n</var></arg><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>mult</name><arg><var>@n</var></arg><arg><var>@xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult#1</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@n</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule></rules></usableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><naturals/></domain><dimension>2</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><name>#0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>#add</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</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>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</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>0</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></sum></polynomial></interpret><interpret><name>#natmult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</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>0</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></sum></polynomial></interpret><interpret><name>#neg</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></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>#pos</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></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>#pred</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></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>#s</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</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>#succ</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></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>*</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</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>0</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></sum></polynomial></interpret><interpret><name>::</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></coefficient></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>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></sum></polynomial></interpret><interpret><name>dyade</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>3</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>dyade#1</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</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>0</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></sum></polynomial></interpret><interpret><name>mult#1</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</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>0</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></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>dyade#1</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>::</name><arg><funapp><name>mult</name><arg><var>@x</var></arg><arg><var>@l2</var></arg></funapp></arg><arg><funapp><name>dyade</name><arg><var>@xs</var></arg><arg><var>@l2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult#1</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@n</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>#add</name><arg><funapp><name>#0</name></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><var>@y</var></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#pred</name><arg><var>@y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#pred</name><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#succ</name><arg><var>@y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#succ</name><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#neg</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#neg</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#neg</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#neg</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#natmult</name><arg><funapp><name>#0</name></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#natmult</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>*</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#mult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>dyade</name><arg><var>@l1</var></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>dyade#1</name><arg><var>@l1</var></arg><arg><var>@l2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>dyade#1</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>::</name><arg><funapp><name>mult</name><arg><var>@x</var></arg><arg><var>@l2</var></arg></funapp></arg><arg><funapp><name>dyade</name><arg><var>@xs</var></arg><arg><var>@l2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>dyade#1</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><var>@n</var></arg><arg><var>@l</var></arg></funapp></lhs><rhs><funapp><name>mult#1</name><arg><var>@l</var></arg><arg><var>@n</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult#1</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@n</var></arg></funapp></lhs><rhs><funapp><name>::</name><arg><funapp><name>*</name><arg><var>@n</var></arg><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>mult</name><arg><var>@n</var></arg><arg><var>@xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult#1</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@n</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule></rules></usableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><matrixInterpretation><domain><naturals/></domain><dimension>2</dimension><strictDimension>1</strictDimension></matrixInterpretation></type><interpret><name>#0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret><interpret><name>#add</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</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>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</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>0</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></sum></polynomial></interpret><interpret><name>#natmult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</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>0</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></sum></polynomial></interpret><interpret><name>#neg</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></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>#pos</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></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>#pred</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></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>#s</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>0</integer></coefficient></vector><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#succ</name><arity>1</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></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>*</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</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>0</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></sum></polynomial></interpret><interpret><name>::</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></coefficient></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>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></sum></polynomial></interpret><interpret><name>dyade</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>2</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</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>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>dyade#1</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>1</integer></coefficient><coefficient><integer>2</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</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>0</integer></coefficient><coefficient><integer>1</integer></coefficient></vector></matrix></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</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>0</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></sum></polynomial></interpret><interpret><name>mult#1</name><arity>2</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial><polynomial><product><polynomial><coefficient><matrix><vector><coefficient><integer>0</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>0</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></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><vector><coefficient><integer>0</integer></coefficient><coefficient><integer>0</integer></coefficient></vector></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>dyade</name><arg><var>@l1</var></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>dyade#1</name><arg><var>@l1</var></arg><arg><var>@l2</var></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>#add</name><arg><funapp><name>#0</name></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><var>@y</var></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#pred</name><arg><var>@y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#pred</name><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#succ</name><arg><var>@y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#succ</name><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#neg</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#neg</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#neg</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#neg</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#natmult</name><arg><funapp><name>#0</name></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#natmult</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>*</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#mult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>dyade</name><arg><var>@l1</var></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>dyade#1</name><arg><var>@l1</var></arg><arg><var>@l2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>dyade#1</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>::</name><arg><funapp><name>mult</name><arg><var>@x</var></arg><arg><var>@l2</var></arg></funapp></arg><arg><funapp><name>dyade</name><arg><var>@xs</var></arg><arg><var>@l2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>dyade#1</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><var>@n</var></arg><arg><var>@l</var></arg></funapp></lhs><rhs><funapp><name>mult#1</name><arg><var>@l</var></arg><arg><var>@n</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult#1</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@n</var></arg></funapp></lhs><rhs><funapp><name>::</name><arg><funapp><name>*</name><arg><var>@n</var></arg><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>mult</name><arg><var>@n</var></arg><arg><var>@xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult#1</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@n</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule></rules></usableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>2</degree></polynomial></type><interpret><name>#0</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>#add</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#mult</name><arity>2</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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#natmult</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#neg</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>#pos</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>#pred</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>#s</name><arity>1</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>#succ</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>*</name><arity>2</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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>::</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</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</int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unapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#neg</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#neg</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#natmult</name><arg><funapp><name>#0</name></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#natmult</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>*</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#mult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>dyade</name><arg><var>@l1</var></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>dyade#1</name><arg><var>@l1</var></arg><arg><var>@l2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>dyade#1</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>::</name><arg><funapp><name>mult</name><arg><var>@x</var></arg><arg><var>@l2</var></arg></funapp></arg><arg><funapp><name>dyade</name><arg><var>@xs</var></arg><arg><var>@l2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>dyade#1</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><var>@n</var></arg><arg><var>@l</var></arg></funapp></lhs><rhs><funapp><name>mult#1</name><arg><var>@l</var></arg><arg><var>@n</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult#1</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@n</var></arg></funapp></lhs><rhs><funapp><name>::</name><arg><funapp><name>*</name><arg><var>@n</var></arg><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>mult</name><arg><var>@n</var></arg><arg><var>@xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult#1</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@n</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule></rules></usableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>2</degree></polynomial></type><interpret><name>#0</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>#add</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#mult</name><arity>2</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>#natmult</name><arity>2</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>#neg</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>#pos</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>#pred</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>#s</name><arity>1</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>#succ</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>*</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>::</name><arity>2</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></sum></polynomial></interpret><interpret><name>dyade</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>dyade#1</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult#1</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>mult</name><arg><var>@n</var></arg><arg><var>@l</var></arg></funapp></lhs><rhs><funapp><name>mult#1</name><arg><var>@l</var></arg><arg><var>@n</var></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>#add</name><arg><funapp><name>#0</name></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><var>@y</var></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#pred</name><arg><var>@y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#pred</name><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#succ</name><arg><var>@y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#succ</name><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#neg</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#neg</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#neg</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#neg</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#natmult</name><arg><funapp><name>#0</name></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#natmult</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>*</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#mult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>dyade</name><arg><var>@l1</var></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>dyade#1</name><arg><var>@l1</var></arg><arg><var>@l2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>dyade#1</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>::</name><arg><funapp><name>mult</name><arg><var>@x</var></arg><arg><var>@l2</var></arg></funapp></arg><arg><funapp><name>dyade</name><arg><var>@xs</var></arg><arg><var>@l2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>dyade#1</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><var>@n</var></arg><arg><var>@l</var></arg></funapp></lhs><rhs><funapp><name>mult#1</name><arg><var>@l</var></arg><arg><var>@n</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult#1</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@n</var></arg></funapp></lhs><rhs><funapp><name>::</name><arg><funapp><name>*</name><arg><var>@n</var></arg><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>mult</name><arg><var>@n</var></arg><arg><var>@xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult#1</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@n</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule></rules></usableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>2</degree></polynomial></type><interpret><name>#0</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>#add</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#mult</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>#natmult</name><arity>2</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>#neg</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>#pos</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>#pred</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>#s</name><arity>1</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>#succ</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>*</name><arity>2</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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>::</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</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></sum></polynomial></interpret><interpret><name>dyade</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>dyade#1</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult</name><arity>2</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>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mult#1</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>*</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#mult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>#add</name><arg><funapp><name>#0</name></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><var>@y</var></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#pred</name><arg><var>@y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#pred</name><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#succ</name><arg><var>@y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#succ</name><arg><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#neg</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#0</name></funapp></arg><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#neg</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#neg</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#neg</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#neg</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#mult</name><arg><funapp><name>#pos</name><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#natmult</name><arg><funapp><name>#0</name></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#natmult</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#add</name><arg><funapp><name>#pos</name><arg><var>@y</var></arg></funapp></arg><arg><funapp><name>#natmult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#pred</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#0</name></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#0</name></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#0</name></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#neg</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>#succ</name><arg><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>#pos</name><arg><funapp><name>#s</name><arg><funapp><name>#s</name><arg><var>@x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>*</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></lhs><rhs><funapp><name>#mult</name><arg><var>@x</var></arg><arg><var>@y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>dyade</name><arg><var>@l1</var></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>dyade#1</name><arg><var>@l1</var></arg><arg><var>@l2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>dyade#1</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>::</name><arg><funapp><name>mult</name><arg><var>@x</var></arg><arg><var>@l2</var></arg></funapp></arg><arg><funapp><name>dyade</name><arg><var>@xs</var></arg><arg><var>@l2</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>dyade#1</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@l2</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>mult</name><arg><var>@n</var></arg><arg><var>@l</var></arg></funapp></lhs><rhs><funapp><name>mult#1</name><arg><var>@l</var></arg><arg><var>@n</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult#1</name><arg><funapp><name>::</name><arg><var>@x</var></arg><arg><var>@xs</var></arg></funapp></arg><arg><var>@n</var></arg></funapp></lhs><rhs><funapp><name>::</name><arg><funapp><name>*</name><arg><var>@n</var></arg><arg><var>@x</var></arg></funapp></arg><arg><funapp><name>mult</name><arg><var>@n</var></arg><arg><var>@xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mult#1</name><arg><funapp><name>nil</name></funapp></arg><arg><var>@n</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule></rules></usableRules><complexityProof><rIsEmpty/></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></proof><origin><proofOrigin><tool><name>TcT</name><version/></tool></proofOrigin></origin></certificationProblem>