details

property	value
status	complete
benchmark	thiemann23.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n140.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	2.70747 seconds
cpu usage	6.97596
user time	6.70279
system time	0.273174
max virtual memory	1.8533108E7
max residence set size	371632.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	0.28
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>digits</name></funapp></lhs><rhs><funapp><name>d</name><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>d</name><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>if</name><arg><funapp><name>le</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>cons</name><arg><var>x</var></arg><arg><funapp><name>d</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>if</name><arg><funapp><name>false</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>nil</name></funapp></rhs></rule><rule><lhs><funapp><name>le</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>le</name><arg><funapp><name>s</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>le</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>le</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></trs></trsInput></input><cpfVersion>2.1</cpfVersion><proof><trsTerminationProof><switchInnermost><wcrProof><joinableCriticalPairsBFS>10</joinableCriticalPairsBFS></wcrProof><trsTerminationProof><dpTrans><dps><rules><rule><lhs><funapp><sharp><name>digits</name></sharp></funapp></lhs><rhs><funapp><sharp><name>d</name></sharp><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>d</name></sharp><arg><var>x</var></arg></funapp></lhs><rhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>le</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>d</name></sharp><arg><var>x</var></arg></funapp></lhs><rhs><funapp><sharp><name>le</name></sharp><arg><var>x</var></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><sharp><name>d</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>le</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>le</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><markedSymbols>true</markedSymbols><dpProof><depGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>digits</name></sharp></funapp></lhs><rhs><funapp><sharp><name>d</name></sharp><arg><funapp><name>0</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><sharp><name>d</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>d</name></sharp><arg><var>x</var></arg></funapp></lhs><rhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>le</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules><rule><lhs><funapp><name>le</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>le</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>le</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>le</name><arg><funapp><name>s</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></rules></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss><funapp><name>le</name><arg><funapp><name>0</name></funapp></arg><arg><var>x0</var></arg></funapp><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x0</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></innermostLhss><dpProof><complexConstantRemovalProc><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp><ruleMap><ruleMapEntry><rule><lhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><sharp><name>d</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>x_removed</var></arg></funapp></lhs><rhs><funapp><name>D</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><var>x_removed</var></arg></funapp></rhs></rule></ruleMapEntry><ruleMapEntry><rule><lhs><funapp><sharp><name>d</name></sharp><arg><var>x</var></arg></funapp></lhs><rhs><funapp><sharp><name>if</name></sharp><arg><funapp><name>le</name><arg><var>x</var></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>D</name><arg><var>x</var></arg><arg><var>x_removed</var></arg></funapp></lhs><rhs><funapp><name>IF</name><arg><funapp><name>le</name><arg><var>x</var></arg><arg><var>x_removed</var></arg></funapp></arg><arg><var>x</var></arg><arg><var>x_removed</var></arg></funapp></rhs></rule></ruleMapEntry></ruleMap><dpProof><generalRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>c</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>-2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>D</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><polynomial><coefficient><integer>-1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>IF</name><arity>3</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>-1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>-1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial><polynomial><coefficient><integer>-1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></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><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>le</name><arity>2</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><name>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><strict><rules><rule><lhs><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>x_removed</var></arg></funapp></lhs><rhs><funapp><name>D</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><var>x_removed</var></arg></funapp></rhs></rule></rules></strict><bound><rules><rule><lhs><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x</var></arg><arg><var>x_removed</var></arg></funapp></lhs><rhs><funapp><name>D</name><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><var>x_removed</var></arg></funapp></rhs></rule></rules></bound><condRedPairProof><name>c</name><before>1</before><after>0</after><conditions><condition><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>le</name><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></arg><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp><rewrite/><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x4</var></arg><arg><var>x5</var></arg></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x4</var></arg><arg><var>x5</var></arg></funapp><nonStrict/><funapp><name>c</name></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><dpSequence><rules><rule><lhs><funapp><name>D</name><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></lhs><rhs><funapp><name>IF</name><arg><funapp><name>le</name><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></arg><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x4</var></arg><arg><var>x5</var></arg></funapp></lhs><rhs><funapp><name>D</name><arg><funapp><name>s</name><arg><var>x4</var></arg></funapp></arg><arg><var>x5</var></arg></funapp></rhs></rule></rules></dpSequence><conditionalConstraintProof><sameConstructor><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>le</name><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></arg><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp><rewrite/><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x4</var></arg><arg><var>x5</var></arg></funapp></constraint></conditionalConstraint><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>le</name><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><var>x2</var><rewrite/><var>x4</var></constraint></conditionalConstraint><conditionalConstraint><constraint><var>x3</var><rewrite/><var>x5</var></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x4</var></arg><arg><var>x5</var></arg></funapp><nonStrict/><funapp><name>c</name></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><conditionalConstraintProof><variableEquation><var>x4</var><var>x2</var><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>le</name><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><var>x3</var><rewrite/><var>x5</var></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x2</var></arg><arg><var>x5</var></arg></funapp><nonStrict/><funapp><name>c</name></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><conditionalConstraintProof><variableEquation><var>x5</var><var>x3</var><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>le</name><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp><nonStrict/><funapp><name>c</name></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><conditionalConstraintProof><induction><conditionalConstraint><constraint><funapp><name>le</name><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conjuncts/><ruleConstraintProofs><ruleConstraintProof><rule><lhs><funapp><name>le</name><arg><funapp><name>0</name></funapp></arg><arg><var>x12</var></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><subtermVarEntries/><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>true</name></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x12</var></arg></funapp><nonStrict/><funapp><name>c</name></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><conditionalConstraintProof><sameConstructor><conditionalConstraint><constraint><funapp><name>true</name></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x12</var></arg></funapp><nonStrict/><funapp><name>c</name></funapp></constraint></conditionalConstraint><conditionalConstraintProof><final/></conditionalConstraintProof></sameConstructor></conditionalConstraintProof></ruleConstraintProof><ruleConstraintProof><rule><lhs><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x14</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x13</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>le</name><arg><var>x14</var></arg><arg><var>x13</var></arg></funapp></rhs></rule><subtermVarEntries><subtermVarEntry><funapp><name>le</name><arg><var>x14</var></arg><arg><var>x13</var></arg></funapp></subtermVarEntry></subtermVarEntries><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>le</name><arg><var>x14</var></arg><arg><var>x13</var></arg></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>le</name><arg><var>x14</var></arg><arg><var>x13</var></arg></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x14</var></arg><arg><var>x13</var></arg></funapp><nonStrict/><funapp><name>c</name></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x14</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x13</var></arg></funapp></arg></funapp><nonStrict/><funapp><name>c</name></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><conditionalConstraintProof><simplifyCondition><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>le</name><arg><var>x14</var></arg><arg><var>x13</var></arg></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x14</var></arg><arg><var>x13</var></arg></funapp><nonStrict/><funapp><name>c</name></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><substitution/><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x14</var></arg><arg><var>x13</var></arg></funapp><nonStrict/><funapp><name>c</name></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x14</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x13</var></arg></funapp></arg></funapp><nonStrict/><funapp><name>c</name></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><conditionalConstraintProof><final/></conditionalConstraintProof></simplifyCondition></conditionalConstraintProof></ruleConstraintProof><ruleConstraintProof><rule><lhs><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x15</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><subtermVarEntries/><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>false</name></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x15</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><nonStrict/><funapp><name>c</name></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><conditionalConstraintProof><differentConstructor><conditionalConstraint><constraint><funapp><name>false</name></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint></differentConstructor></conditionalConstraintProof></ruleConstraintProof></ruleConstraintProofs></induction></conditionalConstraintProof></variableEquation></conditionalConstraintProof></variableEquation></conditionalConstraintProof></sameConstructor></conditionalConstraintProof></condition><condition><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>le</name><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></arg><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp><rewrite/><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x4</var></arg><arg><var>x5</var></arg></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x4</var></arg><arg><var>x5</var></arg></funapp><strict/><funapp><name>D</name><arg><funapp><name>s</name><arg><var>x4</var></arg></funapp></arg><arg><var>x5</var></arg></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><dpSequence><rules><rule><lhs><funapp><name>D</name><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></lhs><rhs><funapp><name>IF</name><arg><funapp><name>le</name><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></arg><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x4</var></arg><arg><var>x5</var></arg></funapp></lhs><rhs><funapp><name>D</name><arg><funapp><name>s</name><arg><var>x4</var></arg></funapp></arg><arg><var>x5</var></arg></funapp></rhs></rule></rules></dpSequence><conditionalConstraintProof><sameConstructor><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>le</name><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp></arg><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp><rewrite/><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x4</var></arg><arg><var>x5</var></arg></funapp></constraint></conditionalConstraint><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>le</name><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><var>x2</var><rewrite/><var>x4</var></constraint></conditionalConstraint><conditionalConstraint><constraint><var>x3</var><rewrite/><var>x5</var></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x4</var></arg><arg><var>x5</var></arg></funapp><strict/><funapp><name>D</name><arg><funapp><name>s</name><arg><var>x4</var></arg></funapp></arg><arg><var>x5</var></arg></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><conditionalConstraintProof><variableEquation><var>x4</var><var>x2</var><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>le</name><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><var>x3</var><rewrite/><var>x5</var></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x2</var></arg><arg><var>x5</var></arg></funapp><strict/><funapp><name>D</name><arg><funapp><name>s</name><arg><var>x2</var></arg></funapp></arg><arg><var>x5</var></arg></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><conditionalConstraintProof><variableEquation><var>x5</var><var>x3</var><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>le</name><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp><strict/><funapp><name>D</name><arg><funapp><name>s</name><arg><var>x2</var></arg></funapp></arg><arg><var>x3</var></arg></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><conditionalConstraintProof><induction><conditionalConstraint><constraint><funapp><name>le</name><arg><var>x2</var></arg><arg><var>x3</var></arg></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conjuncts/><ruleConstraintProofs><ruleConstraintProof><rule><lhs><funapp><name>le</name><arg><funapp><name>0</name></funapp></arg><arg><var>x12</var></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><subtermVarEntries/><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>true</name></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x12</var></arg></funapp><strict/><funapp><name>D</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x12</var></arg></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><conditionalConstraintProof><sameConstructor><conditionalConstraint><constraint><funapp><name>true</name></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>0</name></funapp></arg><arg><var>x12</var></arg></funapp><strict/><funapp><name>D</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg><arg><var>x12</var></arg></funapp></constraint></conditionalConstraint><conditionalConstraintProof><final/></conditionalConstraintProof></sameConstructor></conditionalConstraintProof></ruleConstraintProof><ruleConstraintProof><rule><lhs><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x14</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x13</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>le</name><arg><var>x14</var></arg><arg><var>x13</var></arg></funapp></rhs></rule><subtermVarEntries><subtermVarEntry><funapp><name>le</name><arg><var>x14</var></arg><arg><var>x13</var></arg></funapp></subtermVarEntry></subtermVarEntries><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>le</name><arg><var>x14</var></arg><arg><var>x13</var></arg></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>le</name><arg><var>x14</var></arg><arg><var>x13</var></arg></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x14</var></arg><arg><var>x13</var></arg></funapp><strict/><funapp><name>D</name><arg><funapp><name>s</name><arg><var>x14</var></arg></funapp></arg><arg><var>x13</var></arg></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x14</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x13</var></arg></funapp></arg></funapp><strict/><funapp><name>D</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x14</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x13</var></arg></funapp></arg></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><conditionalConstraintProof><simplifyCondition><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>le</name><arg><var>x14</var></arg><arg><var>x13</var></arg></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x14</var></arg><arg><var>x13</var></arg></funapp><strict/><funapp><name>D</name><arg><funapp><name>s</name><arg><var>x14</var></arg></funapp></arg><arg><var>x13</var></arg></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><substitution/><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x14</var></arg><arg><var>x13</var></arg></funapp><strict/><funapp><name>D</name><arg><funapp><name>s</name><arg><var>x14</var></arg></funapp></arg><arg><var>x13</var></arg></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x14</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x13</var></arg></funapp></arg></funapp><strict/><funapp><name>D</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x14</var></arg></funapp></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x13</var></arg></funapp></arg></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><conditionalConstraintProof><final/></conditionalConstraintProof></simplifyCondition></conditionalConstraintProof></ruleConstraintProof><ruleConstraintProof><rule><lhs><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x15</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><subtermVarEntries/><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>false</name></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><funapp><name>s</name><arg><var>x15</var></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp><strict/><funapp><name>D</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><var>x15</var></arg></funapp></arg></funapp></arg><arg><funapp><name>0</name></funapp></arg></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><conditionalConstraintProof><differentConstructor><conditionalConstraint><constraint><funapp><name>false</name></funapp><rewrite/><funapp><name>true</name></funapp></constraint></conditionalConstraint></differentConstructor></conditionalConstraintProof></ruleConstraintProof></ruleConstraintProofs></induction></conditionalConstraintProof></variableEquation></conditionalConstraintProof></variableEquation></conditionalConstraintProof></sameConstructor></conditionalConstraintProof></condition><condition><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>D</name><arg><funapp><name>s</name><arg><var>x6</var></arg></funapp></arg><arg><var>x7</var></arg></funapp><rewrite/><funapp><name>D</name><arg><var>x8</var></arg><arg><var>x9</var></arg></funapp></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>D</name><arg><var>x8</var></arg><arg><var>x9</var></arg></funapp><nonStrict/><funapp><name>IF</name><arg><funapp><name>le</name><arg><var>x8</var></arg><arg><var>x9</var></arg></funapp></arg><arg><var>x8</var></arg><arg><var>x9</var></arg></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><dpSequence><rules><rule><lhs><funapp><name>IF</name><arg><funapp><name>true</name></funapp></arg><arg><var>x6</var></arg><arg><var>x7</var></arg></funapp></lhs><rhs><funapp><name>D</name><arg><funapp><name>s</name><arg><var>x6</var></arg></funapp></arg><arg><var>x7</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>D</name><arg><var>x8</var></arg><arg><var>x9</var></arg></funapp></lhs><rhs><funapp><name>IF</name><arg><funapp><name>le</name><arg><var>x8</var></arg><arg><var>x9</var></arg></funapp></arg><arg><var>x8</var></arg><arg><var>x9</var></arg></funapp></rhs></rule></rules></dpSequence><conditionalConstraintProof><sameConstructor><conditionalConstraint><constraint><funapp><name>D</name><arg><funapp><name>s</name><arg><var>x6</var></arg></funapp></arg><arg><var>x7</var></arg></funapp><rewrite/><funapp><name>D</name><arg><var>x8</var></arg><arg><var>x9</var></arg></funapp></constraint></conditionalConstraint><conditionalConstraint><implication><conditionalConstraint><constraint><funapp><name>s</name><arg><var>x6</var></arg></funapp><rewrite/><var>x8</var></constraint></conditionalConstraint><conditionalConstraint><constraint><var>x7</var><rewrite/><var>x9</var></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>D</name><arg><var>x8</var></arg><arg><var>x9</var></arg></funapp><nonStrict/><funapp><name>IF</name><arg><funapp><name>le</name><arg><var>x8</var></arg><arg><var>x9</var></arg></funapp></arg><arg><var>x8</var></arg><arg><var>x9</var></arg></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><conditionalConstraintProof><variableEquation><var>x8</var><funapp><name>s</name><arg><var>x6</var></arg></funapp><conditionalConstraint><implication><conditionalConstraint><constraint><var>x7</var><rewrite/><var>x9</var></constraint></conditionalConstraint><conditionalConstraint><constraint><funapp><name>D</name><arg><funapp><name>s</name><arg><var>x6</var></arg></funapp></arg><arg><var>x9</var></arg></funapp><nonStrict/><funapp><name>IF</name><arg><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x6</var></arg></funapp></arg><arg><var>x9</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x6</var></arg></funapp></arg><arg><var>x9</var></arg></funapp></constraint></conditionalConstraint></implication></conditionalConstraint><conditionalConstraintProof><variableEquation><var>x9</var><var>x7</var><conditionalConstraint><constraint><funapp><name>D</name><arg><funapp><name>s</name><arg><var>x6</var></arg></funapp></arg><arg><var>x7</var></arg></funapp><nonStrict/><funapp><name>IF</name><arg><funapp><name>le</name><arg><funapp><name>s</name><arg><var>x6</var></arg></funapp></arg><arg><var>x7</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>x6</var></arg></funapp></arg><arg><var>x7</var></arg></funapp></constraint></conditionalConstraint><conditionalConstraintProof><final/></conditionalConstraintProof></variableEquation></conditionalConstraintProof></variableEquation></conditionalConstraintProof></sameConstructor></conditionalConstraintProof></condition></conditions></condRedPairProof><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><name>D</name><arg><var>x</var></arg><arg><var>x_removed</var></arg></funapp></lhs><rhs><funapp><name>IF</name><arg><funapp><name>le</name><arg><var>x</var></arg><arg><var>x_removed</var></arg></funapp></arg><arg><var>x</var></arg><arg><var>x_removed</var></arg></funapp></rhs></rule><edge><position>1</position><strict>false</strict><position>2</position></edge><edge><position>2</position><strict>false</strict><position>3</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></generalRedPairProc></dpProof></complexConstantRemovalProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>d</name></sharp><arg><var>x</var></arg></funapp></lhs><rhs><funapp><sharp><name>le</name></sharp><arg><var>x</var></arg><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>0</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>le</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>le</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><dpProof><usableRulesProc><usableRules><rules/></usableRules><dpProof><innermostLhssRemovalProc><innermostLhss/><dpProof><sizeChangeProc><subtermCriterion/><sizeChangeGraph><rule><lhs><funapp><sharp><name>le</name></sharp><arg><funapp><name>s</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>s</name><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>le</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><edge><position>1</position><strict>true</strict><position>1</position></edge><edge><position>2</position><strict>true</strict><position>2</position></edge></sizeChangeGraph></sizeChangeProc></dpProof></innermostLhssRemovalProc></dpProof></usableRulesProc></dpProof></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></switchInnermost></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 % (11 real / 0 unknown / 0 assumptions / 11 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