MAYBE * Step 1: Failure MAYBE + Considered Problem: - Strict TRS: 'add('0(),y) -> y 'add('neg('s('0())),y) -> 'pred(y) 'add('neg('s('s(x))),y) -> 'pred('add('pos('s(x)),y)) 'add('pos('s('0())),y) -> 'succ(y) 'add('pos('s('s(x))),y) -> 'succ('add('pos('s(x)),y)) 'mult('0(),'0()) -> '0() 'mult('0(),'neg(y)) -> '0() 'mult('0(),'pos(y)) -> '0() 'mult('neg(x),'0()) -> '0() 'mult('neg(x),'neg(y)) -> 'pos('natmult(x,y)) 'mult('neg(x),'pos(y)) -> 'neg('natmult(x,y)) 'mult('pos(x),'0()) -> '0() 'mult('pos(x),'neg(y)) -> 'neg('natmult(x,y)) 'mult('pos(x),'pos(y)) -> 'pos('natmult(x,y)) 'natadd('0(),y) -> y 'natadd('s(x),y) -> 's('natadd(x,y)) 'natmult('0(),y) -> '0() 'natmult('s(x),y) -> 'natadd(y,'natmult(x,y)) 'pred('0()) -> 'neg('s('0())) 'pred('neg('s(x))) -> 'neg('s('s(x))) 'pred('pos('s('0()))) -> '0() 'pred('pos('s('s(x)))) -> 'pos('s(x)) 'succ('0()) -> 'pos('s('0())) 'succ('neg('s('0()))) -> '0() 'succ('neg('s('s(x)))) -> 'neg('s(x)) 'succ('pos('s(x))) -> 'pos('s('s(x))) add(x,y) -> 'add(x,y) computeLine(line,m,acc) -> computeLine'1(line,acc,m) computeLine'1(dd(x,xs),acc,m) -> computeLine'2(m,acc,x,xs) computeLine'1(nil(),acc,m) -> acc computeLine'2(dd(l,ls),acc,x,xs) -> computeLine(xs,ls,lineMult(x,l,acc)) computeLine'2(nil(),acc,x,xs) -> nil() lineMult(n,l1,l2) -> lineMult'1(l1,l2,n) lineMult'1(dd(x,xs),l2,n) -> lineMult'2(l2,n,x,xs) lineMult'1(nil(),l2,n) -> nil() lineMult'2(dd(y,ys),n,x,xs) -> dd(add(mult(x,n),y),lineMult(n,xs,ys)) lineMult'2(nil(),n,x,xs) -> dd(mult(x,n),lineMult(n,xs,nil())) matrixMult(m1,m2) -> matrixMult'1(m1,m2) matrixMult'1(dd(l,ls),m2) -> dd(computeLine(l,m2,nil()),matrixMult(ls,m2)) matrixMult'1(nil(),m2) -> nil() mult(x,y) -> 'mult(x,y) - Signature: {'add/2,'mult/2,'natadd/2,'natmult/2,'pred/1,'succ/1,add/2,computeLine/3,computeLine'1/3,computeLine'2/4 ,lineMult/3,lineMult'1/3,lineMult'2/4,matrixMult/2,matrixMult'1/2,mult/2} / {'0/0,'neg/1,'pos/1,'s/1,dd/2 ,nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {'add,'mult,'natadd,'natmult,'pred,'succ,add,computeLine ,computeLine'1,computeLine'2,lineMult,lineMult'1,lineMult'2,matrixMult,matrixMult'1 ,mult} and constructors {'0,'neg,'pos,'s,dd,nil} + Applied Processor: EmptyProcessor + Details: The problem is still open. MAYBE