YES Problem: a__zeros() -> cons(0(),zeros()) a__tail(cons(X,XS)) -> mark(XS) mark(zeros()) -> a__zeros() mark(tail(X)) -> a__tail(mark(X)) mark(cons(X1,X2)) -> cons(mark(X1),X2) mark(0()) -> 0() a__zeros() -> zeros() a__tail(X) -> tail(X) Proof: Matrix Interpretation Processor: dim=1 interpretation: [tail](x0) = x0 + 2, [mark](x0) = 4x0 + 2, [a__tail](x0) = x0 + 6, [cons](x0, x1) = x0 + 6x1, [zeros] = 0, [0] = 2, [a__zeros] = 2 orientation: a__zeros() = 2 >= 2 = cons(0(),zeros()) a__tail(cons(X,XS)) = X + 6XS + 6 >= 4XS + 2 = mark(XS) mark(zeros()) = 2 >= 2 = a__zeros() mark(tail(X)) = 4X + 10 >= 4X + 8 = a__tail(mark(X)) mark(cons(X1,X2)) = 4X1 + 24X2 + 2 >= 4X1 + 6X2 + 2 = cons(mark(X1),X2) mark(0()) = 10 >= 2 = 0() a__zeros() = 2 >= 0 = zeros() a__tail(X) = X + 6 >= X + 2 = tail(X) problem: a__zeros() -> cons(0(),zeros()) mark(zeros()) -> a__zeros() mark(cons(X1,X2)) -> cons(mark(X1),X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [mark](x0) = [0 0 0]x0 [0 0 0] , [1 0 1] [1 0 0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [zeros] = [0] [1], [0] [0] = [0] [0], [1] [a__zeros] = [0] [0] orientation: [1] [0] a__zeros() = [0] >= [0] = cons(0(),zeros()) [0] [0] [1] [1] mark(zeros()) = [0] >= [0] = a__zeros() [0] [0] [1 0 1] [1 0 0] [1 0 1] [1 0 0] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(mark(X1),X2) [0 0 0] [0 0 0] [0 0 0] [0 0 0] problem: mark(zeros()) -> a__zeros() mark(cons(X1,X2)) -> cons(mark(X1),X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1] [mark](x0) = [0 1 0]x0 + [0] [0 1 1] [0], [1 0 0] [1 0 1] [0] [cons](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1] [1 0 0] [0 0 0] [0], [0] [zeros] = [0] [0], [0] [a__zeros] = [0] [0] orientation: [1] [0] mark(zeros()) = [0] >= [0] = a__zeros() [0] [0] [1 0 0] [1 0 1] [1] [1 0 0] [1 0 1] [1] mark(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 + [1] >= [0 0 0]X1 + [0 0 0]X2 + [1] = cons(mark(X1),X2) [1 0 0] [0 0 0] [1] [1 0 0] [0 0 0] [1] problem: mark(cons(X1,X2)) -> cons(mark(X1),X2) Matrix Interpretation Processor: dim=3 interpretation: [1 0 1] [mark](x0) = [0 0 1]x0 [0 1 0] , [1 0 1] [1 0 0] [0] [cons](x0, x1) = [0 0 1]x0 + [0 0 0]x1 + [1] [0 1 0] [0 0 0] [1] orientation: [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] [0] mark(cons(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 + [1] >= [0 1 0]X1 + [0 0 0]X2 + [1] = cons(mark(X1),X2) [0 0 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] problem: Qed