details

property	value
status	complete
benchmark	TreeHeight.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n143.star.cs.uiowa.edu
space	Applicative_05

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	1.90842 seconds
cpu usage	4.58901
user time	4.37162
system time	0.21739
max virtual memory	1.85303E7
max residence set size	318240.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	0.18
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>app</name><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><funapp><name>app</name><arg><var>f</var></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>f</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>le</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>le</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>le</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>x</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>le</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>maxlist</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>y</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>if</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>le</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>maxlist</name></funapp></arg><arg><var>y</var></arg></funapp></arg><arg><var>ys</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>maxlist</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>height</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>node</name></funapp></arg><arg><var>x</var></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>maxlist</name></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><funapp><name>app</name><arg><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><funapp><name>height</name></funapp></arg></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><uncurry><uncurryInformation><name>app</name><uncurriedSymbols><uncurriedSymbolEntry><name>map</name><arity>0</arity><name>map</name><name>map1</name><name>map2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>nil</name><arity>0</arity><name>nil</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>cons</name><arity>0</arity><name>cons</name><name>cons1</name><name>cons2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>le</name><arity>0</arity><name>le</name><name>le1</name><name>le2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>0</name><arity>0</arity><name>0</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>true</name><arity>0</arity><name>true</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>s</name><arity>0</arity><name>s</name><name>s1</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>false</name><arity>0</arity><name>false</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>maxlist</name><arity>0</arity><name>maxlist</name><name>maxlist1</name><name>maxlist2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>if</name><arity>0</arity><name>if</name><name>if1</name><name>if2</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>height</name><arity>0</arity><name>height</name><name>height1</name></uncurriedSymbolEntry><uncurriedSymbolEntry><name>node</name><arity>0</arity><name>node</name><name>node1</name><name>node2</name></uncurriedSymbolEntry></uncurriedSymbols><uncurryRules><rules><rule><lhs><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>le</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>le1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>le1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>le2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>maxlist</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>maxlist1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>maxlist1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>maxlist2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>if</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>if1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>height</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>height1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>node</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>node1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>node1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>node2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></uncurryRules><etaRules><rules/></etaRules></uncurryInformation><trs><rules><rule><lhs><funapp><name>map2</name><arg><var>f</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>map2</name><arg><var>f</var></arg><arg><funapp><name>cons2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><funapp><name>app</name><arg><var>f</var></arg><arg><var>x</var></arg></funapp></arg><arg><funapp><name>map2</name><arg><var>f</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>le2</name><arg><funapp><name>0</name></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>le2</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>le2</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>le2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>maxlist2</name><arg><var>x</var></arg><arg><funapp><name>cons2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>if2</name><arg><funapp><name>le2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><funapp><name>maxlist2</name><arg><var>y</var></arg><arg><var>ys</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>maxlist2</name><arg><var>x</var></arg><arg><funapp><name>nil</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>height1</name><arg><funapp><name>node2</name><arg><var>x</var></arg><arg><var>xs</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><funapp><name>maxlist2</name><arg><funapp><name>0</name></funapp></arg><arg><funapp><name>map2</name><arg><funapp><name>height</name></funapp></arg><arg><var>xs</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>map</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>map1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>map2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>cons1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>cons2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>le</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>le1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>le1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>le2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>s</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>s1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>maxlist</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>maxlist1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>maxlist1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>maxlist2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>if</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>if1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>if2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>height</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>height1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>node</name></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>node1</name><arg><var>y1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>app</name><arg><funapp><name>node1</name><arg><var>x0</var></arg></funapp></arg><arg><var>y1</var></arg></funapp></lhs><rhs><funapp><name>node2</name><arg><var>x0</var></arg><arg><var>y1</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><pathOrder><statusPrecedence><statusPrecedenceEntry><name>map2</name><arity>2</arity><precedence>8</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>nil</name><arity>0</arity><precedence>0</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>cons2</name><arity>2</arity><precedence>2</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>app</name><arity>2</arity><precedence>8</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>le2</name><arity>2</arity><precedence>1</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>0</name><arity>0</arity><precedence>5</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>true</name><arity>0</arity><precedence>3</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>false</name><arity>0</arity><precedence>5</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>maxlist2</name><arity>2</arity><precedence>5</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>if2</name><arity>2</arity><precedence>4</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>height1</name><arity>1</arity><precedence>8</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>node2</name><arity>2</arity><precedence>5</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>height</name><arity>0</arity><precedence>5</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>map</name><arity>0</arity><precedence>9</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>map1</name><arity>1</arity><precedence>6</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>cons</name><arity>0</arity><precedence>10</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>cons1</name><arity>1</arity><precedence>7</precedence><lex/></statusPrecedenceEntry><statusPrecedenceEntry><name>le</name><arity>0</arity><precedence>11</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>s</name><arity>0</arity><precedence>12</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>maxlist</name><arity>0</arity><precedence>13</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>if</name><arity>0</arity><precedence>14</precedence><mul/></statusPrecedenceEntry><statusPrecedenceEntry><name>node</name><arity>0</arity><precedence>15</precedence><mul/></statusPrecedenceEntry></statusPrecedence><argumentFilter><argumentFilterEntry><name>map2</name><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>nil</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>cons2</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>app</name><arity>2</arity><nonCollapsing><position>2</position><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>le2</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>0</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>true</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>s1</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>false</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>maxlist2</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>if2</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>height1</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>node2</name><arity>2</arity><nonCollapsing><position>1</position><position>2</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>height</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>map</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>map1</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>cons</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>cons1</name><arity>1</arity><nonCollapsing><position>1</position></nonCollapsing></argumentFilterEntry><argumentFilterEntry><name>le</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>le1</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>s</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>maxlist</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>maxlist1</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>if</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>if1</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry><argumentFilterEntry><name>node</name><arity>0</arity><nonCollapsing/></argumentFilterEntry><argumentFilterEntry><name>node1</name><arity>1</arity><collapsing>1</collapsing></argumentFilterEntry></argumentFilter></pathOrder></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><name>le2</name><arg><funapp><name>s1</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s1</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>le2</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></trs><trsTerminationProof><ruleRemoval><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>le2</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>s1</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules/></trs><trsTerminationProof><rIsEmpty/></trsTerminationProof></ruleRemoval></trsTerminationProof></ruleRemoval></trsTerminationProof></uncurry></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 % (4 real / 0 unknown / 0 assumptions / 4 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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all output return to TRS Standard Certified