/export/starexec/sandbox/solver/bin/starexec_run_certified /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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><name>or</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>x</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>and</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>x</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></dps><extensions><rules><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></a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napp><sharp><name>not</name></sharp><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>not</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>not</name></sharp><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>not</name></sharp><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>not</name></sharp><arg><var>y</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>eq</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>eq</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>neq</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>neq</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>eq</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>not</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>or</name><arg><funapp><name>not</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>not</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>not</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>not</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>neq</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>false</name></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><funapp><name>and</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><funapp><name>true</name></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></trs><usableRules><rules/></usableRules><acDPTerminationProof><acTrivialProc/></acDPTerminationProof></acMonoRedPairProc></acDPTerminationProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>not</name></sharp><arg><funapp><name>eq</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>neq</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>not</name></sharp><arg><funapp><name>neq</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>eq</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>not</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>not</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>not</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>not</name></sharp><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>not</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>not</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>x</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>and</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>x</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>x</var></arg><arg><funapp><name>or</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>or</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><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><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>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></sum></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>x</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>x</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><funapp><name>true</name></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><funapp><name>and</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>or</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>false</name></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>and</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>or</name></sharp><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></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>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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></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>1</variable></polynomial><polynomial><variable>2</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></sum></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>true</name></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><funapp><name>true</name></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><funapp><name>and</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>or</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>false</name></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>and</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>or</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><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>2</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></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>1</variable></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>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>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>and</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>false</name></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><funapp><name>true</name></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><funapp><name>and</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>or</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>and</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acTrivialProc/></acDPTerminationProof></acRedPairProc></acDPTerminationProof></acRedPairProc></acDPTerminationProof></acRedPairProc></acDPTerminationProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>or</name></sharp><arg><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc></component><component><dps><rules><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><var>x</var></arg><arg><funapp><name>and</name><arg><var>y</var></arg><arg><var>z</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><sharp><name>and</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>2</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>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>or</name><arity>2</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>2</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>2</variable></polynomial></product></polynomial></sum></polynomial></interpret><interpret><name>true</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>false</name><arity>0</arity><polynomial><sum><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>false</name></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><var>y</var></arg><arg><var>z</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>and</name></sharp><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><sharp><name>and</name></sharp><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></dps><trs><rules><rule><lhs><funapp><name>eq</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>eq</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>neq</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>neq</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>eq</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>not</name><arg><var>x</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>or</name><arg><funapp><name>not</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>not</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>not</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>not</name><arg><var>x</var></arg></funapp></arg><arg><funapp><name>not</name><arg><var>y</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>neq</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><funapp><name>true</name></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>false</name></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><funapp><name>and</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>z</var></arg></funapp></arg><arg><funapp><name>or</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><funapp><name>true</name></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>or</name><arg><funapp><name>or</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>or</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule></rules></trs><usableRules><rules><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><funapp><name>false</name></funapp></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>true</name></funapp></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>or</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></lhs><rhs><var>x</var></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>false</name></funapp></arg></funapp></lhs><rhs><funapp><name>false</name></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>x</var></arg></funapp></arg><arg><var>ext</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>ext</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>and</name><arg><funapp><name>and</name><arg><var>x</var></arg><arg><var>y</var></arg></funapp></arg><arg><var>z</var></arg></funapp></lhs><rhs><funapp><name>and</name><arg><var>x</var></arg><arg><funapp><name>and</name><arg><var>y</var></arg><arg><var>z</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><acDPTerminationProof><acTrivialProc/></acDPTerminationProof></acMonoRedPairProc></acDPTerminationProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>eq</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>eq</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acTrivialProc/></acDPTerminationProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>neq</name></sharp><arg><var>x</var></arg><arg><var>y</var></arg></funapp></lhs><rhs><funapp><sharp><name>neq</name></sharp><arg><var>y</var></arg><arg><var>x</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><acDPTerminationProof><acTrivialProc/></acDPTerminationProof></component></acDepGraphProc></acDPTerminationProof></acDependencyPairs></acTerminationProof></proof><origin><proofOrigin><tool><name>AProVE</name><version>AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished
</version><strategy>Statistics for single proof: 100.00 % (12 real / 0 unknown / 0 assumptions / 12 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>