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


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<?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 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><funapp><name>mark</name><arg><funapp><name>odds</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__odds</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>head</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__head</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__tail</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__nats</name></funapp></lhs><rhs><funapp><name>nats</name></funapp></rhs></rule><rule><lhs><funapp><name>a__incr</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__pairs</name></funapp></lhs><rhs><funapp><name>pairs</name></funapp></rhs></rule><rule><lhs><funapp><name>a__odds</name></funapp></lhs><rhs><funapp><name>odds</name></funapp></rhs></rule><rule><lhs><funapp><name>a__head</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>head</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__tail</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>tail</name><arg><var>X</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a__nats</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>cons</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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>incr</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nats</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__pairs</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>odds</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__odds</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__incr</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mark</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a__tail</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>pairs</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>head</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a__head</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tail</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>a__nats</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__pairs</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>odds</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__odds</name></funapp></lhs><rhs><funapp><name>a__incr</name><arg><funapp><name>a__pairs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__incr</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>incr</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__tail</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>nats</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__nats</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__incr</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>pairs</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__pairs</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>odds</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__odds</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__tail</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__nats</name></funapp></lhs><rhs><funapp><name>nats</name></funapp></rhs></rule><rule><lhs><funapp><name>a__incr</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__pairs</name></funapp></lhs><rhs><funapp><name>pairs</name></funapp></rhs></rule><rule><lhs><funapp><name>a__odds</name></funapp></lhs><rhs><funapp><name>odds</name></funapp></rhs></rule><rule><lhs><funapp><name>a__head</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>head</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__tail</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>tail</name><arg><var>X</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a__nats</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>cons</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>incr</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nats</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__pairs</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>odds</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__odds</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__incr</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mark</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a__tail</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>pairs</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tail</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a__head</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>head</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>a__nats</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__pairs</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>odds</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__odds</name></funapp></lhs><rhs><funapp><name>a__incr</name><arg><funapp><name>a__pairs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__incr</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>incr</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__tail</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>mark</name><arg><var>XS</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>nats</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__nats</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__incr</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>pairs</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__pairs</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>odds</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__odds</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__tail</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__nats</name></funapp></lhs><rhs><funapp><name>nats</name></funapp></rhs></rule><rule><lhs><funapp><name>a__incr</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__pairs</name></funapp></lhs><rhs><funapp><name>pairs</name></funapp></rhs></rule><rule><lhs><funapp><name>a__odds</name></funapp></lhs><rhs><funapp><name>odds</name></funapp></rhs></rule><rule><lhs><funapp><name>a__tail</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>tail</name><arg><var>X</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a__nats</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>cons</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>incr</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nats</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__pairs</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>odds</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__odds</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__incr</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mark</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>a__tail</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>pairs</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tail</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>a__nats</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__pairs</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>odds</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__odds</name></funapp></lhs><rhs><funapp><name>a__incr</name><arg><funapp><name>a__pairs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__incr</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>incr</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>nats</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__nats</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__incr</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>pairs</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__pairs</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>odds</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__odds</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>tail</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__tail</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__nats</name></funapp></lhs><rhs><funapp><name>nats</name></funapp></rhs></rule><rule><lhs><funapp><name>a__incr</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__pairs</name></funapp></lhs><rhs><funapp><name>pairs</name></funapp></rhs></rule><rule><lhs><funapp><name>a__odds</name></funapp></lhs><rhs><funapp><name>odds</name></funapp></rhs></rule><rule><lhs><funapp><name>a__tail</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>tail</name><arg><var>X</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a__nats</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>cons</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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>incr</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nats</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__pairs</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>odds</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__odds</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__incr</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mark</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>pairs</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>tail</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a__tail</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>a__nats</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__pairs</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>odds</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__odds</name></funapp></lhs><rhs><funapp><name>a__incr</name><arg><funapp><name>a__pairs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__incr</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>incr</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>nats</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__nats</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__incr</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>pairs</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__pairs</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>odds</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__odds</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__nats</name></funapp></lhs><rhs><funapp><name>nats</name></funapp></rhs></rule><rule><lhs><funapp><name>a__incr</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__pairs</name></funapp></lhs><rhs><funapp><name>pairs</name></funapp></rhs></rule><rule><lhs><funapp><name>a__odds</name></funapp></lhs><rhs><funapp><name>odds</name></funapp></rhs></rule><rule><lhs><funapp><name>a__tail</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>tail</name><arg><var>X</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a__nats</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>cons</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>incr</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nats</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__pairs</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>odds</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__odds</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__incr</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mark</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>pairs</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__tail</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>tail</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></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>a__nats</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__pairs</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>odds</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__odds</name></funapp></lhs><rhs><funapp><name>a__incr</name><arg><funapp><name>a__pairs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__incr</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>incr</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>nats</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__nats</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__incr</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>pairs</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__pairs</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>odds</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__odds</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__nats</name></funapp></lhs><rhs><funapp><name>nats</name></funapp></rhs></rule><rule><lhs><funapp><name>a__incr</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__pairs</name></funapp></lhs><rhs><funapp><name>pairs</name></funapp></rhs></rule><rule><lhs><funapp><name>a__odds</name></funapp></lhs><rhs><funapp><name>odds</name></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a__nats</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>cons</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>incr</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>nats</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__pairs</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>odds</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__odds</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__incr</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mark</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>pairs</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>a__nats</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__pairs</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>odds</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__odds</name></funapp></lhs><rhs><funapp><name>a__incr</name><arg><funapp><name>a__pairs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__incr</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>incr</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>nats</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__nats</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__incr</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>pairs</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__pairs</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>odds</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__odds</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__incr</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__pairs</name></funapp></lhs><rhs><funapp><name>pairs</name></funapp></rhs></rule><rule><lhs><funapp><name>a__odds</name></funapp></lhs><rhs><funapp><name>odds</name></funapp></rhs></rule></rules></trs><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>a__odds</name></sharp></funapp></lhs><rhs><funapp><sharp><name>a__incr</name></sharp><arg><funapp><name>a__pairs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__odds</name></sharp></funapp></lhs><rhs><funapp><sharp><name>a__pairs</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__incr</name></sharp><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>nats</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__nats</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__incr</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>pairs</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__pairs</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>odds</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__odds</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>a__incr</name></sharp><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__incr</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>odds</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__odds</name></sharp></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__odds</name></sharp></funapp></lhs><rhs><funapp><sharp><name>a__incr</name></sharp><arg><funapp><name>a__pairs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a__nats</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>cons</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>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>incr</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>nats</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__pairs</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>odds</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__odds</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>a__incr</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><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>mark</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>pairs</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>a__incr</name></sharp><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><sharp><name>mark</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>a__odds</name></sharp><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>a__incr</name></sharp><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__incr</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__odds</name></sharp></funapp></lhs><rhs><funapp><sharp><name>a__incr</name></sharp><arg><funapp><name>a__pairs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>a__nats</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>nats</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__pairs</name></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>incr</name><arg><funapp><name>odds</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__odds</name></funapp></lhs><rhs><funapp><name>a__incr</name><arg><funapp><name>a__pairs</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__incr</name><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></arg><arg><funapp><name>incr</name><arg><var>XS</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>nats</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__nats</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>a__incr</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>pairs</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__pairs</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>odds</name></funapp></arg></funapp></lhs><rhs><funapp><name>a__odds</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><funapp><name>mark</name><arg><var>X1</var></arg></funapp></arg><arg><var>X2</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>0</name></funapp></rhs></rule><rule><lhs><funapp><name>mark</name><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__incr</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>incr</name><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>a__pairs</name></funapp></lhs><rhs><funapp><name>pairs</name></funapp></rhs></rule><rule><lhs><funapp><name>a__odds</name></funapp></lhs><rhs><funapp><name>odds</name></funapp></rhs></rule></rules></trs><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>a__odds</name></sharp></funapp></lhs><rhs><funapp><sharp><name>a__incr</name></sharp><arg><funapp><name>a__pairs</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__incr</name></sharp><arg><funapp><name>mark</name><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>a__incr</name></sharp><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>incr</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>s</name><arg><var>X</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>a__incr</name></sharp><arity>1</arity><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></interpret><interpret><name>mark</name><arity>1</arity><polynomial><variable>1</variable></polynomial></interpret><interpret><name>nats</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>a__nats</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>incr</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>a__incr</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>pairs</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>a__pairs</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>odds</name><arity>0</arity><polynomial><coefficient><integer>1</integer></coefficient></polynomial></interpret><interpret><name>a__odds</name><arity>0</arity><polynomial><coefficient><integer>1</integer></coefficient></polynomial></interpret><interpret><name>cons</name><arity>2</arity><polynomial><variable>1</variable></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></sum></polynomial></interpret><interpret><sharp><name>mark</name></sharp><arity>1</arity><polynomial><variable>1</variable></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>a__incr</name></sharp><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule></rules></dps><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>a__incr</name></sharp><arg><funapp><name>cons</name><arg><var>X</var></arg><arg><var>XS</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><monoRedPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>cons</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>mark</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule></rules></dps><trs><rules/></trs><usableRules><rules/></usableRules><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>cons</name><arg><var>X1</var></arg><arg><var>X2</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>mark</name></sharp><arg><var>X1</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></monoRedPairUrProc></dpProof></component></depGraphProc></dpProof></redPairProc></dpProof></component></depGraphProc></dpProof></monoRedPairProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>a__odds</name></sharp></funapp></lhs><rhs><funapp><sharp><name>a__pairs</name></sharp></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>nats</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__nats</name></sharp></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>mark</name></sharp><arg><funapp><name>pairs</name></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>a__pairs</name></sharp></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty
</version><strategy>Statistics for single proof: 100.00 % (15 real / 0 unknown / 0 assumptions / 15 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem>