details

property	value
status	complete
benchmark	cime4.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n069.star.cs.uiowa.edu
space	Secret_05_TRS

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rci_cert
runtime (wallclock)	0.520797014236 seconds
cpu usage	2.283843352
max memory	5.9871232E7

stage attributes

key	value
certification-result	CERTIFIED
output-size	29007
starexec-result	WORST_CASE(?,O(n^0))
certification-time	0.0

output

/export/starexec/sandbox/solver/bin/starexec_run_tct_rci_cert /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(1)) <?xml version="1.0" encoding="UTF-8"?> <?xml-stylesheet type="text/xsl" href="cpfHTML.xsl"?> <certificationProblem xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" 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><funapp><name>k</name><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>k</name><arg><funapp><name>b</name></funapp></arg></funapp></arg><arg><var>X</var></arg></funapp><funapp><sharp><name>g</name></sharp><arg><var>X</var></arg></funapp><funapp><sharp><name>h</name></sharp><arg><funapp><name>d</name></funapp></arg></funapp><funapp><sharp><name>h</name></sharp><arg><funapp><name>d</name></funapp></arg></funapp><funapp><sharp><name>u</name></sharp><arg><funapp><name>d</name></funapp></arg><arg><funapp><name>c</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg></funapp></innermostLhss><complexityProof><usableRules><nonUsableRules><rules><rule><lhs><funapp><name>f</name><arg><funapp><name>k</name><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>k</name><arg><funapp><name>b</name></funapp></arg></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>f</name><arg><var>X</var></arg><arg><var>X</var></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>g</name><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>u</name><arg><funapp><name>h</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>h</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>u</name><arg><funapp><name>d</name></funapp></arg><arg><funapp><name>c</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>k</name><arg><var>Y</var></arg></funapp></rhs></rule></rules></nonUsableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>13</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>b</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>12</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>c</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>d</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>8</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>f</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>g</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>h</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>9</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>k</name><arity>1</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>u</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>8</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>f</name></sharp><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>9</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>g</name></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>6</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>h</name></sharp><arity>1</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><sharp><name>u</name></sharp><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>c1</name><arity>1</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>c2</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c3</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>c4</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>c5</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>k</name><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>k</name><arg><funapp><name>b</name></funapp></arg></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><funapp><sharp><name>f</name></sharp><arg><var>X</var></arg><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>k</name><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>k</name><arg><funapp><name>b</name></funapp></arg></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><funapp><sharp><name>f</name></sharp><arg><var>X</var></arg><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>g</name></sharp><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>c2</name><arg><funapp><sharp><name>u</name></sharp><arg><funapp><name>h</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>h</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><funapp><sharp><name>h</name></sharp><arg><var>X</var></arg></funapp></arg><arg><funapp><sharp><name>h</name></sharp><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>h</name></sharp><arg><funapp><name>d</name></funapp></arg></funapp></lhs><rhs><funapp><name>c3</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>h</name></sharp><arg><funapp><name>d</name></funapp></arg></funapp></lhs><rhs><funapp><name>c4</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>u</name></sharp><arg><funapp><name>d</name></funapp></arg><arg><funapp><name>c</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>c5</name></funapp></rhs></rule></rules></usableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>b</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>c</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>d</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>f</name><arity>3</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>g</name><arity>1</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>h</name><arity>1</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>k</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>u</name><arity>3</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><sharp><name>f</name></sharp><arity>3</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><sharp><name>g</name></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>h</name></sharp><arity>1</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><sharp><name>u</name></sharp><arity>3</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>c1</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>c2</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></sum></polynomial></interpret><interpret><name>c3</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>c4</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>c5</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><sharp><name>g</name></sharp><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>c2</name><arg><funapp><sharp><name>u</name></sharp><arg><funapp><name>h</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>h</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><funapp><sharp><name>h</name></sharp><arg><var>X</var></arg></funapp></arg><arg><funapp><sharp><name>h</name></sharp><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>k</name><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>k</name><arg><funapp><name>b</name></funapp></arg></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><funapp><sharp><name>f</name></sharp><arg><var>X</var></arg><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>g</name></sharp><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>c2</name><arg><funapp><sharp><name>u</name></sharp><arg><funapp><name>h</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>h</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><funapp><sharp><name>h</name></sharp><arg><var>X</var></arg></funapp></arg><arg><funapp><sharp><name>h</name></sharp><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>h</name></sharp><arg><funapp><name>d</name></funapp></arg></funapp></lhs><rhs><funapp><name>c3</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>h</name></sharp><arg><funapp><name>d</name></funapp></arg></funapp></lhs><rhs><funapp><name>c4</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>u</name></sharp><arg><funapp><name>d</name></funapp></arg><arg><funapp><name>c</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>c5</name></funapp></rhs></rule></rules></usableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>b</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>c</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>14</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>d</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>f</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>g</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>h</name><arity>1</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>k</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>f</name></sharp><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>g</name></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>12</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>h</name></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>u</name></sharp><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>8</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>c1</name><arity>1</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>c2</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></sum></polynomial></interpret><interpret><name>c3</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>c4</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>c5</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><sharp><name>u</name></sharp><arg><funapp><name>d</name></funapp></arg><arg><funapp><name>c</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>c5</name></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>k</name><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>k</name><arg><funapp><name>b</name></funapp></arg></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><funapp><sharp><name>f</name></sharp><arg><var>X</var></arg><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>g</name></sharp><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>c2</name><arg><funapp><sharp><name>u</name></sharp><arg><funapp><name>h</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>h</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><funapp><sharp><name>h</name></sharp><arg><var>X</var></arg></funapp></arg><arg><funapp><sharp><name>h</name></sharp><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>h</name></sharp><arg><funapp><name>d</name></funapp></arg></funapp></lhs><rhs><funapp><name>c3</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>h</name></sharp><arg><funapp><name>d</name></funapp></arg></funapp></lhs><rhs><funapp><name>c4</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>u</name></sharp><arg><funapp><name>d</name></funapp></arg><arg><funapp><name>c</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>c5</name></funapp></rhs></rule></rules></usableRules><complexityProof><ruleShifting><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>a</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>5</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>b</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>8</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>c</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>d</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>f</name><arity>3</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>g</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>h</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>k</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>u</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>f</name></sharp><arity>3</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><sharp><name>g</name></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>12</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>h</name></sharp><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>5</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>u</name></sharp><arity>3</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>c1</name><arity>1</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret><interpret><name>c2</name><arity>3</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>3</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>c3</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>c4</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>c5</name><arity>0</arity><polynomial><coefficient><integer>0</integer></coefficient></polynomial></interpret></interpretation></redPair></orderingConstraintProof><trs><rules><rule><lhs><funapp><sharp><name>h</name></sharp><arg><funapp><name>d</name></funapp></arg></funapp></lhs><rhs><funapp><name>c3</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>h</name></sharp><arg><funapp><name>d</name></funapp></arg></funapp></lhs><rhs><funapp><name>c4</name></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><sharp><name>f</name></sharp><arg><funapp><name>k</name><arg><funapp><name>a</name></funapp></arg></funapp></arg><arg><funapp><name>k</name><arg><funapp><name>b</name></funapp></arg></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>c1</name><arg><funapp><sharp><name>f</name></sharp><arg><var>X</var></arg><arg><var>X</var></arg><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>g</name></sharp><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>c2</name><arg><funapp><sharp><name>u</name></sharp><arg><funapp><name>h</name><arg><var>X</var></arg></funapp></arg><arg><funapp><name>h</name><arg><var>X</var></arg></funapp></arg><arg><var>X</var></arg></funapp></arg><arg><funapp><sharp><name>h</name></sharp><arg><var>X</var></arg></funapp></arg><arg><funapp><sharp><name>h</name></sharp><arg><var>X</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>h</name></sharp><arg><funapp><name>d</name></funapp></arg></funapp></lhs><rhs><funapp><name>c3</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>h</name></sharp><arg><funapp><name>d</name></funapp></arg></funapp></lhs><rhs><funapp><name>c4</name></funapp></rhs></rule><rule><lhs><funapp><sharp><name>u</name></sharp><arg><funapp><name>d</name></funapp></arg><arg><funapp><name>c</name><arg><var>Y</var></arg></funapp></arg><arg><var>X</var></arg></funapp></lhs><rhs><funapp><name>c5</name></funapp></rhs></rule></rules></usableRules><complexityProof><rIsEmpty/></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></ruleShifting></complexityProof></usableRules></complexityProof></dtTransformation></complexityProof></proof><origin><proofOrigin><tool><name>TcT</name><version/></tool></proofOrigin></origin></certificationProblem> 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