details

property	value
status	complete
benchmark	beans.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n150.star.cs.uiowa.edu
space	Mixed_TRS

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	2.24425 seconds
cpu usage	5.0117
user time	4.76126
system time	0.250439
max virtual memory	1.859176E7
max residence set size	342728.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	0.25
bare-result	YES

output

<?xml version="1.0" encoding="UTF-8" standalone="no"?><?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?><certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="cpf.xsd"><input><trsInput><trs><rules><rule><lhs><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>L</name><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>L</name><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>L</name></sharp><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>L</name></sharp><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>L</name></sharp><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>L</name></sharp><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>L</name></sharp><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>L</name></sharp><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>L</name></sharp><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></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>f</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>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>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>L</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>L</name></sharp><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>L</name></sharp><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><redPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>L</name></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>-1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></sum></polynomial></interpret><interpret><name>f</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>-1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></sum></polynomial></interpret><interpret><name>nil</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><dpProof><pIsEmpty/></dpProof></redPairProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>L</name></sharp><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>L</name></sharp><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>L</name></sharp><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></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>f</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>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>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>f</name></sharp><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></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><monoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>f</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>s</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>nil</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>0</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>f</name></sharp><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></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><trs><rules><rule><lhs><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>f</name><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>f</name><arg><var>z</var></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>f</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>f</name><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><var>z</var></arg></funapp></arg><arg><var>w</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs><dpProof><pIsEmpty/></dpProof></monoRedPairProc></dpProof></monoRedPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><var>y</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><var>x</var></arg><arg><funapp><name>f</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (8 real / 0 unknown / 0 assumptions / 8 total proof steps)</strategy><url>http://aprove.informatik.rwth-aachen.de</url></tool><toolUser><firstName>John</firstName><lastName>Doe</lastName></toolUser></proofOrigin><inputOrigin/></origin></certificationProblem> popout

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