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e>half</name><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>s</name><arg><funapp><name>half</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><realScc>true</realScc><arcs><forwardArc>1</forwardArc><forwardArc>2</forwardArc><forwardArc>3</forwardArc></arcs><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><arctic><domain><integers/></domain></arctic></domain><degree>1</degree></polynomial></type><interpret><sharp><name>s</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>i</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>half</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>g</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>f</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>p</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>-1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>0</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules><rule><lhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>s</name><arg><funapp><name>half</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>s</name><arg><funapp><name>p</name><arg><funapp><name>p</name><arg><funapp><name>half</name><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><usableRules><rules><rule><lhs><funapp><name>s</name><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule><rule><lhs><funapp><name>s</name><arg><funapp><name>p</name><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>p</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>g</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>half</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>p</name><arg><funapp><name>p</name><arg><funapp><name>half</name><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>g</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>half</name><arg><funapp><name>s</name><arg><funapp><name>i</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>i</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>p</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><redPairUrProc><orderingConstraintProof><redPair><interpretation><type><polynomial><domain><arctic><domain><integers/></domain></arctic></domain><degree>1</degree></polynomial></type><interpret><sharp><name>s</name></sharp><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>0</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>-16</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>i</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>5</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>5</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>half</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>-4</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>g</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>f</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>3</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>s</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>2</integer></coefficient></polynomial></sum></polynomial></interpret><interpret><name>p</name><arity>1</arity><polynomial><sum><polynomial><product><polynomial><coefficient><integer>-1</integer></coefficient></polynomial><polynomial><variable>1</variable></polynomial></product></polynomial><polynomial><coefficient><integer>1</integer></coefficient></polynomial></sum></polynomial></interpret></interpretation></redPair></orderingConstraintProof><dps><rules/></dps><usableRules><rules><rule><lhs><funapp><name>s</name><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><var>x1</var></rhs></rule><rule><lhs><funapp><name>s</name><arg><funapp><name>p</name><arg><funapp><name>p</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>p</name><arg><var>x1</var></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>g</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>half</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><name>s</name><arg><funapp><name>s</name><arg><funapp><name>p</name><arg><funapp><name>p</name><arg><funapp><name>half</name><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>g</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>half</name><arg><funapp><name>s</name><arg><funapp><name>i</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></rhs></rule><rule><lhs><funapp><name>i</name><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><name>p</name><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></usableRules><dpProof><pIsEmpty/></dpProof></redPairUrProc></dpProof></redPairUrProc></dpProof></component><component><dps><rules><rule><lhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>s</name><arg><funapp><name>half</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>p</name><arg><funapp><name>p</name><arg><funapp><name>half</name><arg><funapp><name>s</name><arg><var>x1</var></arg></funapp></arg></funapp></arg></funapp></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs/></component><component><dps><rules><rule><lhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>g</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs/></component><component><dps><rules><rule><lhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>f</name><arg><var>x1</var></arg></funapp></arg></funapp></lhs><rhs><funapp><sharp><name>g</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs><forwardArc>1</forwardArc><forwardArc>2</forwardArc></arcs></component><component><dps><rules><rule><lhs><funapp><sharp><name>g</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>s</name></sharp><arg><funapp><name>i</name><arg><var>x1</var></arg></funapp></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs/></component><component><dps><rules><rule><lhs><funapp><sharp><name>g</name></sharp><arg><var>x1</var></arg></funapp></lhs><rhs><funapp><sharp><name>i</name></sharp><arg><var>x1</var></arg></funapp></rhs></rule></rules></dps><realScc>false</realScc><arcs/></component></depGraphProc></dpProof></dpTrans></trsTerminationProof></stringReversal></trsTerminationProof></proof><origin><proofOrigin><tool><name>ttt2</name><version>ttt2 1.18 [hg: 65024290f751]</version><strategy>((if standard then var else fail) | con | (if srs then ((sleep -t 25?;rlab;(((( (if srs then arctic -dim 1 -ib 4 -ob 5 else fail) || (if srs then arctic -dim 2 -ib 2 -ob 3 else fail) || (if srs then arctic -dim 3 -ib 1 -ob 2 else fail) || (if srs then arctic -dim 3 -ib 2 -ob 2 else fail) || matrix -dim 1 -ib 5 -ob 8 || matrix -dim 2 -ib 3 -ob 4 || matrix -dim 3 -ib 2 -ob 3 || matrix -dim 3 -ib 1 -ob 2 || matrix -dim 4 -ib 1 -ob 2 || matrix -dim 5 -ib 1 -ob 1 || kbo -ib 3 -ob 4 || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( matrix -dp -ur -dim 1 -ib 3 -ob 5 || matrix -dp -ur -dim 1 -ib 3 -ob 8 -rat 2 -db 1 || matrix -dp -ur -dim 1 -ib 4 -ob 10 -rat 4 -db 1 || matrix -dp -ur -dim 2 -ib 2 -ob 3 || matrix -dp -ur -dim 2 -ib 3 -ob 4 -rat 2 -db 0 || matrix -dp -ur -dim 3 -ib 1 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 -rat 2 -db 0 || matrix -dp -ur -dim 4 -ib 1 -ob 2 || lpo -ur -af || (arctic -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))! || (( unfold || fail)*[7])!)[299])! || ((((( (if srs then arctic -dim 1 -ib 4 -ob 5 else fail) || (if srs then arctic -dim 2 -ib 2 -ob 3 else fail) || (if srs then arctic -dim 3 -ib 1 -ob 2 else fail) || (if srs then arctic -dim 3 -ib 2 -ob 2 else fail) || matrix -dim 1 -ib 5 -ob 8 || matrix -dim 2 -ib 3 -ob 4 || matrix -dim 3 -ib 2 -ob 3 || matrix -dim 3 -ib 1 -ob 2 || matrix -dim 4 -ib 1 -ob 2 || matrix -dim 5 -ib 1 -ob 1 || kbo -ib 3 -ob 4 || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( matrix -dp -ur -dim 1 -ib 3 -ob 5 || matrix -dp -ur -dim 1 -ib 3 -ob 8 -rat 2 -db 1 || matrix -dp -ur -dim 1 -ib 4 -ob 10 -rat 4 -db 1 || matrix -dp -ur -dim 2 -ib 2 -ob 3 || matrix -dp -ur -dim 2 -ib 3 -ob 4 -rat 2 -db 0 || matrix -dp -ur -dim 3 -ib 1 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 -rat 2 -db 0 || matrix -dp -ur -dim 4 -ib 1 -ob 2 || lpo -ur -af || (arctic -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))! || (( unfold || fail)*[7])!)[299])! || (rev?;((( (if srs then arctic -dim 1 -ib 4 -ob 5 else fail) || (if srs then arctic -dim 2 -ib 2 -ob 3 else fail) || (if srs then arctic -dim 3 -ib 1 -ob 2 else fail) || (if srs then arctic -dim 3 -ib 2 -ob 2 else fail) || matrix -dim 1 -ib 5 -ob 8 || matrix -dim 2 -ib 3 -ob 4 || matrix -dim 3 -ib 2 -ob 3 || matrix -dim 3 -ib 1 -ob 2 || matrix -dim 4 -ib 1 -ob 2 || matrix -dim 5 -ib 1 -ob 1 || kbo -ib 3 -ob 4 || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( matrix -dp -ur -dim 1 -ib 3 -ob 5 || matrix -dp -ur -dim 1 -ib 3 -ob 8 -rat 2 -db 1 || matrix -dp -ur -dim 1 -ib 4 -ob 10 -rat 4 -db 1 || matrix -dp -ur -dim 2 -ib 2 -ob 3 || matrix -dp -ur -dim 2 -ib 3 -ob 4 -rat 2 -db 0 || matrix -dp -ur -dim 3 -ib 1 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 -rat 2 -db 0 || matrix -dp -ur -dim 4 -ib 1 -ob 2 || lpo -ur -af || (arctic -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))![299])! ) else ((((( (if srs then arctic -dim 1 -ib 4 -ob 5 else fail) || (if srs then arctic -dim 2 -ib 2 -ob 3 else fail) || (if srs then arctic -dim 3 -ib 1 -ob 2 else fail) || (if srs then arctic -dim 3 -ib 2 -ob 2 else fail) || matrix -dim 1 -ib 5 -ob 8 || matrix -dim 2 -ib 3 -ob 4 || matrix -dim 3 -ib 2 -ob 3 || matrix -dim 3 -ib 1 -ob 2 || matrix -dim 4 -ib 1 -ob 2 || matrix -dim 5 -ib 1 -ob 1 || kbo -ib 3 -ob 4 || fail)[5]*);((dp;(edg -gtcap -nl[1.0]?;(sccs | ((sc || sc -rec -defs || sc -mulex -defs) || sct || {ur?;( matrix -dp -ur -dim 1 -ib 3 -ob 5 || matrix -dp -ur -dim 1 -ib 3 -ob 8 -rat 2 -db 1 || matrix -dp -ur -dim 1 -ib 4 -ob 10 -rat 4 -db 1 || matrix -dp -ur -dim 2 -ib 2 -ob 3 || matrix -dp -ur -dim 2 -ib 3 -ob 4 -rat 2 -db 0 || matrix -dp -ur -dim 3 -ib 1 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 || matrix -dp -ur -dim 3 -ib 2 -ob 3 -rat 2 -db 0 || matrix -dp -ur -dim 4 -ib 1 -ob 2 || lpo -ur -af || (arctic -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || (arctic -bz -dp -ur -dim 1 -ib 4 -ob 3[25] | arctic -bz -dp -ur -dim 2 -ib 2 -ob 2[28] | arctic -bz -dp -ur -dim 3 -ib 1 -ob 1[28] | arctic -bz -dp -ur -dim 4 -ib 1 -ob 1[28] | fail) || fail) } restore) )*[29])) || (bounds -cert || fail;(bounds -rfc -qc))))! || (( unfold || fail)*[7])!)[299])))</strategy></tool></proofOrigin></origin></certificationProblem>