details

property	value
status	complete
benchmark	sequent_modulo.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	Mixed_AC

run statistics

property	value
solver	AProVE
configuration	certified
runtime (wallclock)	18.1633 seconds
cpu usage	27.8459
user time	26.7938
system time	1.05206
max virtual memory	1.8451048E7
max residence set size	2879488.0

stage attributes

key	value
certification-result	CERTIFIED
starexec-result	CERTIFIED YES
certification-time	2.66
bare-result	YES

output

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g></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sequent</name></sharp><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>virg</name></sharp><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg><arg><var>b</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sequent</name></sharp><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>virg</name></sharp><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg><arg><var>b</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sequent</name></sharp><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sequent</name></sharp><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg></funap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></funapp></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>virg</name><arg><funapp><name>virg</name><arg><funapp><name>emptyfset</name></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>virg</name><arg><var>a</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>virg</name><arg><funapp><name>virg</name><arg><var>a</var></arg><arg><var>a</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>virg</name><arg><var>a</var></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></extensions><acDPTerminationProof><acDepGraphProc><component><dps><rules><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>f</var></arg><arg><var>s</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>neg</name><arg><var>f</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>f</var></arg><arg><var>s</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>g</var></arg><arg><var>s</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>f</var></arg><arg><var>s</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>g</var></arg><arg><var>s</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>imp</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>f</var></arg><arg><var>s</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>imp</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>g</var></arg><arg><var>s</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>forall</name><arg><var>f</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>f</var></arg><arg><funapp><name>.</name><arg><funapp><name>1</name></funapp></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><funapp><name>shift</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>exists</name><arg><var>f</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>f</var></arg><arg><funapp><name>.</name><arg><funapp><name>1</name></funapp></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><funapp><name>shift</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><var>s</var></arg></funapp></arg><arg><var>t</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>f</var></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><var>t</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>substf</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>neg</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><interpret><name>or</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>imp</name><arity>2</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><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>forall</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>.</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>ron</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>shift</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>exists</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>substf</name><arity>2</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><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>id</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>substt</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>ef</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>neg</name><arg><var>f</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>f</var></arg><arg><var>s</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>g</var></arg><arg><var>s</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>f</var></arg><arg><var>s</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>imp</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>g</var></arg><arg><var>s</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>f</var></arg><arg><var>s</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>g</var></arg><arg><var>s</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>imp</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>f</var></arg><arg><var>s</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>forall</name><arg><var>f</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>f</var></arg><arg><funapp><name>.</name><arg><funapp><name>1</name></funapp></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><funapp><name>shift</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>exists</name><arg><var>f</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>f</var></arg><arg><funapp><name>.</name><arg><funapp><name>1</name></funapp></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><funapp><name>shift</name></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><var>s</var></arg></funapp></arg><arg><var>t</var></arg></funapp></lhs><rhs><funapp><sharp><name>substf</name></sharp><arg><var>f</var></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><var>t</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><usableRules><rules/></usableRules><acDPTerminationProof><acTrivialProc/></acDPTerminationProof></acRedPairProc></acDPTerminationProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>Pe</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>substt</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>forall</name><arg><var>f</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>ron</name></sharp><arg><var>s</var></arg><arg><funapp><name>shift</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>exists</name><arg><var>f</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>ron</name></sharp><arg><var>s</var></arg><arg><funapp><name>shift</name></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><var>s</var></arg></funapp></arg><arg><var>t</var></arg></funapp></lhs><rhs><funapp><sharp><name>ron</name></sharp><arg><var>s</var></arg><arg><var>t</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>substt</name></sharp><arg><funapp><name>substt</name><arg><var>x</var></arg><arg><var>s</var></arg></funapp></arg><arg><var>t</var></arg></funapp></lhs><rhs><funapp><sharp><name>substt</name></sharp><arg><var>x</var></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><var>t</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substt</name></sharp><arg><funapp><name>ef</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>substt</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substt</name></sharp><arg><funapp><name>substt</name><arg><var>x</var></arg><arg><var>s</var></arg></funapp></arg><arg><var>t</var></arg></funapp></lhs><rhs><funapp><sharp><name>ron</name></sharp><arg><var>s</var></arg><arg><var>t</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ron</name></sharp><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><var>t</var></arg></funapp></arg><arg><var>u</var></arg></funapp></lhs><rhs><funapp><sharp><name>ron</name></sharp><arg><var>s</var></arg><arg><funapp><name>ron</name><arg><var>t</var></arg><arg><var>u</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ron</name></sharp><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><var>t</var></arg></funapp></arg><arg><var>u</var></arg></funapp></lhs><rhs><funapp><sharp><name>ron</name></sharp><arg><var>t</var></arg><arg><var>u</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ron</name></sharp><arg><funapp><name>.</name><arg><var>x</var></arg><arg><var>s</var></arg></funapp></arg><arg><var>t</var></arg></funapp></lhs><rhs><funapp><sharp><name>substt</name></sharp><arg><var>x</var></arg><arg><var>t</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ron</name></sharp><arg><funapp><name>.</name><arg><var>x</var></arg><arg><var>s</var></arg></funapp></arg><arg><var>t</var></arg></funapp></lhs><rhs><funapp><sharp><name>ron</name></sharp><arg><var>s</var></arg><arg><var>t</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>ron</name></sharp><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>.</name><arity>2</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>substt</name></sharp><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>ron</name><arity>2</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><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>ef</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>substt</name><arity>2</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><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>1</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>shift</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>id</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>ron</name></sharp><arg><funapp><name>.</name><arg><var>x</var></arg><arg><var>s</var></arg></funapp></arg><arg><var>t</var></arg></funapp></lhs><rhs><funapp><sharp><name>substt</name></sharp><arg><var>x</var></arg><arg><var>t</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ron</name></sharp><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><var>t</var></arg></funapp></arg><arg><var>u</var></arg></funapp></lhs><rhs><funapp><sharp><name>ron</name></sharp><arg><var>t</var></arg><arg><var>u</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ron</name></sharp><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><var>t</var></arg></funapp></arg><arg><var>u</var></arg></funapp></lhs><rhs><funapp><sharp><name>ron</name></sharp><arg><var>s</var></arg><arg><funapp><name>ron</name><arg><var>t</var></arg><arg><var>u</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substt</name></sharp><arg><funapp><name>substt</name><arg><var>x</var></arg><arg><var>s</var></arg></funapp></arg><arg><var>t</var></arg></funapp></lhs><rhs><funapp><sharp><name>ron</name></sharp><arg><var>s</var></arg><arg><var>t</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>ron</name></sharp><arg><funapp><name>.</name><arg><var>x</var></arg><arg><var>s</var></arg></funapp></arg><arg><var>t</var></arg></funapp></lhs><rhs><funapp><sharp><name>ron</name></sharp><arg><var>s</var></arg><arg><var>t</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>substt</name></sharp><arg><funapp><name>substt</name><arg><var>x</var></arg><arg><var>s</var></arg></funapp></arg><arg><var>t</var></arg></funapp></lhs><rhs><funapp><sharp><name>substt</name></sharp><arg><var>x</var></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><var>t</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><usableRules><rules/></usableRules><acDPTerminationProof><acMonoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><sharp><name>substt</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</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>ef</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>substt</name></sharp><arg><funapp><name>ef</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>substt</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>substt</name><arg><funapp><name>ef</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>ef</name><arg><funapp><name>substt</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>substf</name><arg><funapp><name>Pe</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>Pe</name><arg><funapp><name>substt</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>substf</name><arg><funapp><name>neg</name><arg><var>f</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><name>neg</name><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><var>s</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>substf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>substf</name><arg><var>g</var></arg><arg><var>s</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>substf</name><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>substf</name><arg><var>g</var></arg><arg><var>s</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>substf</name><arg><funapp><name>imp</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><name>imp</name><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>substf</name><arg><var>g</var></arg><arg><var>s</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>substf</name><arg><funapp><name>forall</name><arg><var>f</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><name>forall</name><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><funapp><name>.</name><arg><funapp><name>1</name></funapp></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><funapp><name>shift</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>substf</name><arg><funapp><name>exists</name><arg><var>f</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><name>exists</name><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><funapp><name>.</name><arg><funapp><name>1</name></funapp></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><funapp><name>shift</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>substt</name><arg><var>x</var></arg><arg><funapp><name>id</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>substf</name><arg><var>f</var></arg><arg><funapp><name>id</name></funapp></arg></funapp></lhs><rhs><var>f</var></rhs></rule><rule><lhs><funapp><name>substt</name><arg><funapp><name>substt</name><arg><var>x</var></arg><arg><var>s</var></arg></funapp></arg><arg><var>t</var></arg></funapp></lhs><rhs><funapp><name>substt</name><arg><var>x</var></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><var>t</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>substf</name><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><var>s</var></arg></funapp></arg><arg><var>t</var></arg></funapp></lhs><rhs><funapp><name>substf</name><arg><var>f</var></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><var>t</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>substt</name><arg><funapp><name>1</name></funapp></arg><arg><funapp><name>.</name><arg><var>x</var></arg><arg><var>s</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>ron</name><arg><funapp><name>id</name></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><var>s</var></rhs></rule><rule><lhs><funapp><name>ron</name><arg><funapp><name>shift</name></funapp></arg><arg><funapp><name>.</name><arg><var>x</var></arg><arg><var>s</var></arg></funapp></arg></funapp></lhs><rhs><var>s</var></rhs></rule><rule><lhs><funapp><name>ron</name><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><var>t</var></arg></funapp></arg><arg><var>u</var></arg></funapp></lhs><rhs><funapp><name>ron</name><arg><var>s</var></arg><arg><funapp><name>ron</name><arg><var>t</var></arg><arg><var>u</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>ron</name><arg><funapp><name>.</name><arg><var>x</var></arg><arg><var>s</var></arg></funapp></arg><arg><var>t</var></arg></funapp></lhs><rhs><funapp><name>.</name><arg><funapp><name>substt</name><arg><var>x</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><var>t</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>ron</name><arg><var>s</var></arg><arg><funapp><name>id</name></funapp></arg></funapp></lhs><rhs><var>s</var></rhs></rule><rule><lhs><funapp><name>.</name><arg><funapp><name>1</name></funapp></arg><arg><funapp><name>shift</name></funapp></arg></funapp></lhs><rhs><funapp><name>id</name></funapp></rhs></rule><rule><lhs><funapp><name>.</name><arg><funapp><name>substt</name><arg><funapp><name>1</name></funapp></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>ron</name><arg><funapp><name>shift</name></funapp></arg><arg><var>s</var></arg></funapp></arg></funapp></lhs><rhs><var>s</var></rhs></rule><rule><lhs><funapp><name>virg</name><arg><funapp><name>emptyfset</name></funapp></arg><arg><var>a</var></arg></funapp></lhs><rhs><var>a</var></rhs></rule><rule><lhs><funapp><name>virg</name><arg><var>a</var></arg><arg><var>a</var></arg></funapp></lhs><rhs><var>a</var></rhs></rule><rule><lhs><funapp><name>*</name><arg><funapp><name>emptysset</name></funapp></arg><arg><var>a</var></arg></funapp></lhs><rhs><var>a</var></rhs></rule><rule><lhs><funapp><name>*</name><arg><var>a</var></arg><arg><var>a</var></arg></funapp></lhs><rhs><var>a</var></rhs></rule><rule><lhs><funapp><name>neg</name><arg><funapp><name>neg</name><arg><var>f</var></arg></funapp></arg></funapp></lhs><rhs><var>f</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>f</var></arg><arg><var>f</var></arg></funapp></lhs><rhs><var>f</var></rhs></rule><rule><lhs><funapp><name>or</name><arg><var>f</var></arg><arg><var>f</var></arg></funapp></lhs><rhs><var>f</var></rhs></rule><rule><lhs><funapp><name>imp</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><funapp><name>neg</name><arg><var>f</var></arg></funapp></arg><arg><var>g</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>exists</name><arg><var>f</var></arg></funapp></lhs><rhs><funapp><name>neg</name><arg><funapp><name>forall</name><arg><funapp><name>neg</name><arg><var>f</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><funapp><name>neg</name><arg><var>f</var></arg></funapp></arg></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>b</var></arg></funapp></lhs><rhs><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>sequent</name><arg><funapp><name>convf</name><arg><funapp><n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><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>substf</name><arg><var>g</var></arg><arg><var>s</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>substf</name><arg><var>g</var></arg><arg><var>s</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>imp</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>imp</name></sharp><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>substf</name><arg><var>g</var></arg><arg><var>s</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>forall</name><arg><var>f</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>.</name></sharp><arg><funapp><name>1</name></funapp></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><funapp><name>shift</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>substf</name></sharp><arg><funapp><name>exists</name><arg><var>f</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>exists</name></sharp><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><funapp><name>.</name><arg><funapp><name>1</name></funapp></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><funapp><name>shift</name></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>substf</name></sharp><arg><funapp><name>exists</name><arg><var>f</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><sharp><name>.</name></sharp><arg><funapp><name>1</name></funapp></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><funapp><name>shift</name></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>ron</name></sharp><arg><funapp><name>.</name><arg><var>x</var></arg><arg><var>s</var></arg></funapp></arg><arg><var>t</var></arg></funapp></lhs><rhs><funapp><sharp><name>.</name></sharp><arg><funapp><name>substt</name><arg><var>x</var></arg><arg><var>t</var></arg></funapp></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><var>t</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>imp</name></sharp><arg><var>f</var></arg><arg><var>g</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>neg</name><arg><var>f</var></arg></funapp></arg><arg><var>g</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>imp</name></sharp><arg><var>f</var></arg><arg><var>g</var></arg></funapp></lhs><rhs><funapp><sharp><name>neg</name></sharp><arg><var>f</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>exists</name></sharp><arg><var>f</var></arg></funapp></lhs><rhs><funapp><sharp><name>neg</name></sharp><arg><funapp><name>forall</name><arg><funapp><name>neg</name><arg><var>f</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>exists</name></sharp><arg><var>f</var></arg></funapp></lhs><rhs><funapp><sharp><name>neg</name></sharp><arg><var>f</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>convf</name><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>convf</name><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acMonoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>virg</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>sequent</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>convf</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>neg</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>emptyfset</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><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>or</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><sharp><name>convs</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>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>convf</name><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>convf</name><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>substt</name><arg><funapp><name>ef</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>ef</name><arg><funapp><name>substt</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>substf</name><arg><funapp><name>Pe</name><arg><var>x</var></arg></funapp></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>Pe</name><arg><funapp><name>substt</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>substf</name><arg><funapp><name>neg</name><arg><var>f</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><name>neg</name><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><var>s</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>substf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>substf</name><arg><var>g</var></arg><arg><var>s</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>substf</name><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>substf</name><arg><var>g</var></arg><arg><var>s</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>substf</name><arg><funapp><name>imp</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><name>imp</name><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><var>s</var></arg></funapp></arg><arg><funapp><name>substf</name><arg><var>g</var></arg><arg><var>s</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>substf</name><arg><funapp><name>forall</name><arg><var>f</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><name>forall</name><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><funapp><name>.</name><arg><funapp><name>1</name></funapp></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><funapp><name>shift</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>substf</name><arg><funapp><name>exists</name><arg><var>f</var></arg></funapp></arg><arg><var>s</var></arg></funapp></lhs><rhs><funapp><name>exists</name><arg><funapp><name>substf</name><arg><var>f</var></arg><arg><funapp><name>.</name><arg><funapp><name>1</name></funapp></arg><arg><funapp><name>ron</name><arg><var>s</var></arg><arg><funapp><name>shift</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>substt</name><arg><var>x</var></arg><arg><funapp><name>id</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>substf</name><arg><var>f</var></arg><arg><funapp><name>id</name></funapp></arg></funapp></lhs><rhs><var>f</var></rhs></rule><rule><lhs><funapp><name>substt</name><arg><funapp><name>substt</name><arg><var>x</var></arg><arg><var>s</var></arg></funapp></arg><arg><var>t</var></arg></funapp></lhs><rhs><funapp><name>substt</name><arg><var>x</var></a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var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>b</var></arg></funapp></lhs><rhs><funapp><sharp><name>sequent</name></sharp><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg><arg><var>a</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sequent</name></sharp><arg><funapp><name>convf</name><arg><funapp><name>and</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></lhs><rhs><funapp><sharp><name>sequent</name></sharp><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sequent</name></sharp><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sequent</name></sharp><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>sequent</name></sharp><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>sequent</name></sharp><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acMonoRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>1</degree></polynomial></type><interpret><name>virg</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>emptyfset</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><sharp><name>sequent</name></sharp><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>convf</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>neg</name><arity>1</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>or</name><arity>2</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><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><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><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>virg</name></sharp><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg><arg><var>a</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>virg</name></sharp><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg><arg><var>a</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>convs</name></sharp><arg><funapp><name>sequent</name><arg><funapp><name>convf</name><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>*</name><arg><var>a</var></arg><arg><var>a</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><var>a</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>*</name><arg><funapp><name>emptysset</name></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><var>a</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>*</name><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><var>f</var></arg><arg><var>a</var></arg></funapp></arg><arg><funapp><name>virg</name><arg><var>g</var></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><var>b</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>*</name><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><var>f</var></arg><arg><var>a</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></arg><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r></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>*</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><var>x</var></arg><arg><funapp><name>*</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>2</degree></polynomial></type><interpret><sharp><name>*</name></sharp><arity>2</arity><polynomial><sum><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>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>*</name><arity>2</arity><polynomial><sum><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>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>convs</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><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>sequent</name><arity>2</arity><polynomial><sum><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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>emptyfset</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>virg</name><arity>2</arity><polynomial><sum><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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>emptysset</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>convf</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>and</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>or</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>neg</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>*</name><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><funapp><name>emptyfset</name></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><var>f</var></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><funapp><name>emptyfset</name></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>*</name><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><var>f</var></arg><arg><var>a</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><var>b</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>*</name><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><var>f</var></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><var>b</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>*</name><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><var>f</var></arg><arg><var>a</var></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>emptyfset</name></funapp></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>emptyfset</name></funapp></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>*</name><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><funapp><name>emptyfset</name></funapp></arg><arg><funapp><name>emptyfset</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><funapp><name>emptyfset</name></funapp></arg><arg><funapp><name>emptyfset</name></funapp></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>*</name><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><funapp><name>virg</name><arg><var>f</var></arg><arg><var>a</var></arg></funapp></arg><arg><funapp><name>virg</name><arg><var>g</var></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><var>b</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funa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arg><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>convf</name><arg><funapp><name>or</name><arg><var>f</var></arg><arg><var>g</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><funapp><name>convf</name><arg><var>f</var></arg></funapp></arg><arg><funapp><name>convf</name><arg><var>g</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>virg</name><arg><funapp><name>virg</name><arg><var>a</var></arg><arg><var>a</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>virg</name><arg><var>a</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>virg</name><arg><funapp><name>virg</name><arg><funapp><name>emptyfset</name></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>virg</name><arg><var>a</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>virg</name><arg><funapp><name>emptyfset</name></funapp></arg><arg><var>a</var></arg></funapp></lhs><rhs><var>a</var></rhs></rule><rule><lhs><funapp><name>virg</name><arg><var>a</var></arg><arg><var>a</var></arg></funapp></lhs><rhs><var>a</var></rhs></rule><rule><lhs><funapp><name>*</name><arg><funapp><name>*</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>*</name><arg><var>x</var></arg><arg><funapp><name>*</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>*</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>*</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>virg</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>virg</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>virg</name><arg><funapp><name>virg</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>virg</name><arg><var>x</var></arg><arg><funapp><name>virg</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acRedPairProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><naturals/></domain><degree>2</degree></polynomial></type><interpret><sharp><name>*</name></sharp><arity>2</arity><polynomial><sum><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>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>*</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></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>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>emptysset</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>convs</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>sequent</name><arity>2</arity><polynomial><sum><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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>emptyfset</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>virg</name><arity>2</arity><polynomial><sum><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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>convf</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>neg</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>and</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>or</name><arity>2</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></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>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>*</name><arg><var>a</var></arg><arg><var>a</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><var>a</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>*</name><arg><funapp><name>emptysset</name></funapp></arg><arg><var>a</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><var>a</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>*</name></sharp><arg><funapp><name>*</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>*</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>*</name><arg><funapp><name>*</name><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><funapp><name>emptyfset</name></funapp></arg><arg><funapp><name>emptyfset</name></funapp></arg></funapp></arg></funapp></arg><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>*</name><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><funapp><name>emptyfset</name></funapp></arg><arg><funapp><name>emptyfset</name></funapp></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>*</name><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><funapp><name>emptyfset</name></funapp></arg><arg><var>b</var></arg></funapp></arg></funapp></arg><arg><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><var>a</var></arg><arg><funapp><name>virg</name><arg><var>f</var></arg><arg><var>b</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>convs</name><arg><funapp><name>sequent</name><arg><funapp><name>emptyfset</nam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><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>*</name><arg><funapp><name>*</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>*</name><arg><var>x</var></arg><arg><funapp><name>*</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>virg</name><arg><funapp><name>virg</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>virg</name><arg><var>x</var></arg><arg><funapp><name>virg</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acTrivialProc/></acDPTerminationProof></acMonoRedPairProc></acDPTerminationProof></acMonoRedPairProc></acDPTerminationProof></component></acDepGraphProc></acDPTerminationProof></acDependencyPairs></acTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty </version><strategy>Statistics for single proof: 100.00 % (17 real / 0 unknown / 0 assumptions / 17 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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