YES Problem: g(A()) -> A() g(B()) -> A() g(B()) -> B() g(C()) -> A() g(C()) -> B() g(C()) -> C() foldB(t,0()) -> t foldB(t,s(n)) -> f(foldB(t,n),B()) foldC(t,0()) -> t foldC(t,s(n)) -> f(foldC(t,n),C()) f(t,x) -> f'(t,g(x)) f'(triple(a,b,c),C()) -> triple(a,b,s(c)) f'(triple(a,b,c),B()) -> f(triple(a,b,c),A()) f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b)) f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c) Proof: Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [0] [f''](x0) = [0 0 0]x0 + [1] [1 0 0] [1], [1 0 0] [1 0 1] [1 0 1] [0] [triple](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [1 0 0]x2 + [1] [0 0 0] [0 0 0] [0 0 0] [0], [1 0 0] [1 0 0] [0] [f'](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [0] [1 0 0] [0 0 0] [1], [1 0 0] [1 0 1] [foldC](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [1 1 1] [1 0 1] , [1 0 0] [1 0 0] [0] [f](x0, x1) = [0 1 0]x0 + [0 0 1]x1 + [0] [1 0 0] [0 0 1] [1], [1 0 0] [0] [s](x0) = [0 0 0]x0 + [0] [0 0 1] [1], [1 0 1] [1 0 1] [foldB](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [1 0 1] [1 0 1] , [0] [0] = [0] [0], [1] [C] = [0] [0], [1] [B] = [0] [0], [1 0 0] [0] [g](x0) = [0 0 0]x0 + [1] [1 0 0] [0], [0] [A] = [0] [0] orientation: [0] [0] g(A()) = [1] >= [0] = A() [0] [0] [1] [0] g(B()) = [1] >= [0] = A() [1] [0] [1] [1] g(B()) = [1] >= [0] = B() [1] [0] [1] [0] g(C()) = [1] >= [0] = A() [1] [0] [1] [1] g(C()) = [1] >= [0] = B() [1] [0] [1] [1] g(C()) = [1] >= [0] = C() [1] [0] [1 0 1] foldB(t,0()) = [0 1 0]t >= t = t [1 0 1] [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [1] foldB(t,s(n)) = [0 0 0]n + [0 1 0]t + [0] >= [0 0 0]n + [0 1 0]t + [0] = f(foldB(t,n),B()) [1 0 1] [1 0 1] [1] [1 0 1] [1 0 1] [1] [1 0 0] foldC(t,0()) = [0 1 0]t >= t = t [1 1 1] [1 0 1] [1 0 0] [1] [1 0 1] [1 0 0] [1] foldC(t,s(n)) = [0 0 0]n + [0 1 0]t + [0] >= [0 0 0]n + [0 1 0]t + [0] = f(foldC(t,n),C()) [1 0 1] [1 1 1] [1] [1 0 1] [1 0 0] [1] [1 0 0] [1 0 0] [0] [1 0 0] [1 0 0] [0] f(t,x) = [0 1 0]t + [0 0 1]x + [0] >= [0 1 0]t + [0 0 0]x + [0] = f'(t,g(x)) [1 0 0] [0 0 1] [1] [1 0 0] [0 0 0] [1] [1 0 0] [1 0 1] [1 0 1] [1] [1 0 0] [1 0 1] [1 0 1] [1] f'(triple(a,b,c),C()) = [0 0 0]a + [0 0 0]b + [1 0 0]c + [1] >= [0 0 0]a + [0 0 0]b + [1 0 0]c + [1] = triple(a,b,s(c)) [1 0 0] [1 0 1] [1 0 1] [1] [0 0 0] [0 0 0] [0 0 0] [0] [1 0 0] [1 0 1] [1 0 1] [1] [1 0 0] [1 0 1] [1 0 1] [0] f'(triple(a,b,c),B()) = [0 0 0]a + [0 0 0]b + [1 0 0]c + [1] >= [0 0 0]a + [0 0 0]b + [1 0 0]c + [1] = f(triple(a,b,c),A()) [1 0 0] [1 0 1] [1 0 1] [1] [1 0 0] [1 0 1] [1 0 1] [1] [1 0 0] [1 0 1] [1 0 1] [0] [1 0 0] [1 0 1] [1 0 1] [0] f'(triple(a,b,c),A()) = [0 0 0]a + [0 0 0]b + [1 0 0]c + [1] >= [0 0 0]a + [0 0 0]b + [0 0 0]c + [1] = f''(foldB(triple(s(a),0(),c),b)) [1 0 0] [1 0 1] [1 0 1] [1] [1 0 0] [1 0 1] [1 0 1] [1] [1 0 0] [1 0 1] [1 0 1] [0] [1 0 0] [1 0 1] [1 0 1] [0] f''(triple(a,b,c)) = [0 0 0]a + [0 0 0]b + [0 0 0]c + [1] >= [0 0 0]a + [0 0 0]b + [0 0 0]c + [1] = foldC(triple(a,b,0()),c) [1 0 0] [1 0 1] [1 0 1] [1] [1 0 0] [1 0 1] [1 0 1] [1] problem: g(A()) -> A() g(B()) -> B() g(C()) -> B() g(C()) -> C() foldB(t,0()) -> t foldB(t,s(n)) -> f(foldB(t,n),B()) foldC(t,0()) -> t foldC(t,s(n)) -> f(foldC(t,n),C()) f(t,x) -> f'(t,g(x)) f'(triple(a,b,c),C()) -> triple(a,b,s(c)) f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b)) f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [f''](x0) = [0 1 0]x0 [0 0 0] , [1 0 1] [1 0 0] [1 0 1] [1] [triple](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 1 0]x2 + [1] [0 0 0] [0 0 0] [0 0 0] [0], [1 0 0] [1 0 0] [f'](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [0 0 0] [0 1 0] , [1 0 0] [foldC](x0, x1) = x0 + [0 0 0]x1 [0 0 0] , [1 0 0] [1 1 1] [f](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [0 0 0] [1 1 1] , [1 0 0] [s](x0) = [0 0 0]x0 [0 0 1] , [1 0 0] [1 0 0] [foldB](x0, x1) = [0 1 0]x0 + [0 0 0]x1 [0 1 1] [1 0 0] , [0] [0] = [0] [0], [0] [C] = [0] [0], [0] [B] = [0] [0], [1 0 1] [0] [g](x0) = [0 0 1]x0 + [0] [0 0 0] [1], [0] [A] = [0] [1] orientation: [1] [0] g(A()) = [1] >= [0] = A() [1] [1] [0] [0] g(B()) = [0] >= [0] = B() [1] [0] [0] [0] g(C()) = [0] >= [0] = B() [1] [0] [0] [0] g(C()) = [0] >= [0] = C() [1] [0] [1 0 0] foldB(t,0()) = [0 1 0]t >= t = t [0 1 1] [1 0 0] [1 0 0] [1 0 0] [1 0 0] foldB(t,s(n)) = [0 0 0]n + [0 1 0]t >= [0 0 0]n + [0 1 0]t = f(foldB(t,n),B()) [1 0 0] [0 1 1] [0 0 0] [0 0 0] foldC(t,0()) = t >= t = t [1 0 0] [1 0 0] [1 0 0] foldC(t,s(n)) = [0 0 0]n + t >= [0 0 0]n + [0 1 0]t = f(foldC(t,n),C()) [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 1 1] [1 0 0] [1 0 1] f(t,x) = [0 1 0]t + [0 0 0]x >= [0 1 0]t + [0 0 0]x = f'(t,g(x)) [0 0 0] [1 1 1] [0 0 0] [0 0 1] [1 0 1] [1 0 0] [1 0 1] [1] [1 0 1] [1 0 0] [1 0 1] [1] f'(triple(a,b,c),C()) = [0 0 0]a + [0 0 0]b + [0 1 0]c + [1] >= [0 0 0]a + [0 0 0]b + [0 0 0]c + [1] = triple(a,b,s(c)) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 0] [1 0 1] [1] [1 0 1] [1 0 0] [1 0 1] [1] f'(triple(a,b,c),A()) = [0 0 0]a + [0 0 0]b + [0 1 0]c + [1] >= [0 0 0]a + [0 0 0]b + [0 1 0]c + [1] = f''(foldB(triple(s(a),0(),c),b)) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [0] [1 0 1] [1 0 0] [1 0 1] [1] [1 0 1] [1 0 0] [1 0 0] [1] f''(triple(a,b,c)) = [0 0 0]a + [0 0 0]b + [0 1 0]c + [1] >= [0 0 0]a + [0 0 0]b + [0 0 0]c + [1] = foldC(triple(a,b,0()),c) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [0] problem: g(B()) -> B() g(C()) -> B() g(C()) -> C() foldB(t,0()) -> t foldB(t,s(n)) -> f(foldB(t,n),B()) foldC(t,0()) -> t foldC(t,s(n)) -> f(foldC(t,n),C()) f(t,x) -> f'(t,g(x)) f'(triple(a,b,c),C()) -> triple(a,b,s(c)) f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b)) f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c) Matrix Interpretation Processor: dim=1 interpretation: [f''](x0) = x0 + 1, [triple](x0, x1, x2) = x0 + x1 + x2 + 3, [f'](x0, x1) = x0 + x1 + 6, [foldC](x0, x1) = x0 + x1, [f](x0, x1) = x0 + x1 + 6, [s](x0) = x0 + 7, [foldB](x0, x1) = x0 + x1 + 4, [0] = 1, [C] = 1, [B] = 1, [g](x0) = x0, [A] = 7 orientation: g(B()) = 1 >= 1 = B() g(C()) = 1 >= 1 = B() g(C()) = 1 >= 1 = C() foldB(t,0()) = t + 5 >= t = t foldB(t,s(n)) = n + t + 11 >= n + t + 11 = f(foldB(t,n),B()) foldC(t,0()) = t + 1 >= t = t foldC(t,s(n)) = n + t + 7 >= n + t + 7 = f(foldC(t,n),C()) f(t,x) = t + x + 6 >= t + x + 6 = f'(t,g(x)) f'(triple(a,b,c),C()) = a + b + c + 10 >= a + b + c + 10 = triple(a,b,s(c)) f'(triple(a,b,c),A()) = a + b + c + 16 >= a + b + c + 16 = f''(foldB(triple(s(a),0(),c),b)) f''(triple(a,b,c)) = a + b + c + 4 >= a + b + c + 4 = foldC(triple(a,b,0()),c) problem: g(B()) -> B() g(C()) -> B() g(C()) -> C() foldB(t,s(n)) -> f(foldB(t,n),B()) foldC(t,s(n)) -> f(foldC(t,n),C()) f(t,x) -> f'(t,g(x)) f'(triple(a,b,c),C()) -> triple(a,b,s(c)) f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b)) f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [f''](x0) = [0 0 0]x0 [0 0 1] , [1 1 1] [1 0 1] [1 0 0] [0] [triple](x0, x1, x2) = [0 0 0]x0 + [0 1 0]x1 + [0 0 0]x2 + [1] [1 1 0] [1 1 0] [1 1 1] [0], [1 1 0] [1 1 0] [0] [f'](x0, x1) = [0 1 0]x0 + [0 0 1]x1 + [0] [0 0 1] [0 0 0] [1], [1 0 0] [1 0 0] [foldC](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [1 0 0] , [1 1 0] [1 1 1] [1] [f](x0, x1) = [0 1 0]x0 + [0 1 0]x1 + [0] [0 1 1] [0 0 0] [1], [1 0 0] [1] [s](x0) = [0 0 0]x0 + [0] [0 1 0] [0], [1 0 0] [1 0 0] [foldB](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [1 0 0] [1 0 0] , [0] [0] = [0] [0], [0] [C] = [0] [0], [0] [B] = [0] [0], [1 0 0] [1] [g](x0) = [0 0 1]x0 + [0] [0 1 0] [0], [0] [A] = [0] [0] orientation: [1] [0] g(B()) = [0] >= [0] = B() [0] [0] [1] [0] g(C()) = [0] >= [0] = B() [0] [0] [1] [0] g(C()) = [0] >= [0] = C() [0] [0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] foldB(t,s(n)) = [0 0 0]n + [0 0 0]t + [0] >= [0 0 0]n + [0 0 0]t + [0] = f(foldB(t,n),B()) [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1] foldC(t,s(n)) = [0 0 0]n + [0 0 0]t + [0] >= [0 0 0]n + [0 0 0]t + [0] = f(foldC(t,n),C()) [1 0 0] [0 0 0] [1] [1 0 0] [0 0 0] [1] [1 1 0] [1 1 1] [1] [1 1 0] [1 0 1] [1] f(t,x) = [0 1 0]t + [0 1 0]x + [0] >= [0 1 0]t + [0 1 0]x + [0] = f'(t,g(x)) [0 1 1] [0 0 0] [1] [0 0 1] [0 0 0] [1] [1 1 1] [1 1 1] [1 0 0] [1] [1 1 1] [1 0 1] [1 0 0] [1] f'(triple(a,b,c),C()) = [0 0 0]a + [0 1 0]b + [0 0 0]c + [1] >= [0 0 0]a + [0 1 0]b + [0 0 0]c + [1] = triple(a,b,s(c)) [1 1 0] [1 1 0] [1 1 1] [1] [1 1 0] [1 1 0] [1 1 0] [1] [1 1 1] [1 1 1] [1 0 0] [1] [1 1 0] [1 0 0] [1 0 0] [1] f'(triple(a,b,c),A()) = [0 0 0]a + [0 1 0]b + [0 0 0]c + [1] >= [0 0 0]a + [0 0 0]b + [0 0 0]c + [0] = f''(foldB(triple(s(a),0(),c),b)) [1 1 0] [1 1 0] [1 1 1] [1] [1 1 0] [1 0 0] [1 0 0] [1] [1 1 1] [1 0 1] [1 0 0] [1 1 1] [1 0 1] [1 0 0] f''(triple(a,b,c)) = [0 0 0]a + [0 0 0]b + [0 0 0]c >= [0 0 0]a + [0 0 0]b + [0 0 0]c = foldC(triple(a,b,0()),c) [1 1 0] [1 1 0] [1 1 1] [0 0 0] [0 0 0] [1 0 0] problem: foldB(t,s(n)) -> f(foldB(t,n),B()) foldC(t,s(n)) -> f(foldC(t,n),C()) f(t,x) -> f'(t,g(x)) f'(triple(a,b,c),C()) -> triple(a,b,s(c)) f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b)) f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c) Matrix Interpretation Processor: dim=3 interpretation: [1 1 1] [f''](x0) = [0 0 1]x0 [0 0 0] , [1 0 0] [1 1 1] [1 0 0] [1] [triple](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 1]x2 + [0] [0 0 0] [0 0 0] [0 1 0] [0], [1 0 0] [1 0 0] [f'](x0, x1) = [0 0 1]x0 + [0 0 0]x1 [0 1 0] [0 0 1] , [1 0 1] [1 1 1] [foldC](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 1 0] [1 0 0] [f](x0, x1) = [0 0 1]x0 + [0 0 0]x1 [0 1 1] [0 0 0] , [1 0 0] [0] [s](x0) = [0 0 1]x0 + [1] [0 1 0] [0], [1 0 0] [1 1 1] [foldB](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [0] = [0] [0], [0] [C] = [0] [1], [0] [B] = [0] [0], [1 0 0] [g](x0) = [0 0 0]x0 [0 0 0] , [0] [A] = [0] [1] orientation: [1 1 1] [1 0 0] [1] [1 1 1] [1 0 0] foldB(t,s(n)) = [0 0 0]n + [0 0 0]t + [0] >= [0 0 0]n + [0 0 0]t = f(foldB(t,n),B()) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 1 1] [1 0 1] [1] [1 1 1] [1 0 1] foldC(t,s(n)) = [0 0 0]n + [0 0 0]t + [0] >= [0 0 0]n + [0 0 0]t = f(foldC(t,n),C()) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [1 1 0] [1 0 0] [1 0 0] [1 0 0] f(t,x) = [0 0 1]t + [0 0 0]x >= [0 0 1]t + [0 0 0]x = f'(t,g(x)) [0 1 1] [0 0 0] [0 1 0] [0 0 0] [1 0 0] [1 1 1] [1] [1 0 0] [1 1 1] [1] f'(triple(a,b,c),C()) = [0 0 0]a + [0 0 0]b + c + [0] >= [0 0 0]a + [0 0 0]b + c + [0] = triple(a,b,s(c)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [1] [1 0 0] [1 1 1] [1] [1 0 0] [1 1 1] [1 0 0] [1] f'(triple(a,b,c),A()) = [0 0 0]a + [0 0 0]b + c + [0] >= [0 0 0]a + [0 0 0]b + [0 0 0]c + [0] = f''(foldB(triple(s(a),0(),c),b)) [0 0 0] [0 0 0] [1] [0 0 0] [0 0 0] [0 0 0] [0] [1 0 0] [1 1 1] [1 1 1] [1] [1 0 0] [1 1 1] [1 1 1] [1] f''(triple(a,b,c)) = [0 0 0]a + [0 0 0]b + [0 1 0]c + [0] >= [0 0 0]a + [0 0 0]b + [0 0 0]c + [0] = foldC(triple(a,b,0()),c) [0 0 0] [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0 0 0] [0] problem: f(t,x) -> f'(t,g(x)) f'(triple(a,b,c),C()) -> triple(a,b,s(c)) f'(triple(a,b,c),A()) -> f''(foldB(triple(s(a),0(),c),b)) f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [f''](x0) = [1 0 0]x0 [0 0 1] , [1 1 0] [1 1 0] [1 1 0] [triple](x0, x1, x2) = [0 0 0]x0 + [1 1 0]x1 + [0 0 0]x2 [1 0 0] [1 1 0] [1 0 0] , [1 0 0] [1 1 1] [f'](x0, x1) = [1 0 0]x0 + [0 0 0]x1 [1 0 0] [0 1 0] , [1 0 0] [1 1 0] [foldC](x0, x1) = [1 0 0]x0 + [1 1 0]x1 [0 1 0] [1 0 0] , [1 0 0] [1 0 0] [f](x0, x1) = [1 0 0]x0 + [0 0 0]x1 [1 0 0] [0 0 0] , [1 1 0] [s](x0) = [0 0 0]x0 [0 0 0] , [1 0 0] [1 1 0] [foldB](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [1 0 0] [1 1 0] , [0] [0] = [0] [0], [0] [C] = [0] [1], [1 0 0] [g](x0) = [0 0 0]x0 [0 0 0] , [0] [A] = [1] [0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] f(t,x) = [1 0 0]t + [0 0 0]x >= [1 0 0]t + [0 0 0]x = f'(t,g(x)) [1 0 0] [0 0 0] [1 0 0] [0 0 0] [1 1 0] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [1 1 0] f'(triple(a,b,c),C()) = [1 1 0]a + [1 1 0]b + [1 1 0]c + [0] >= [0 0 0]a + [1 1 0]b + [0 0 0]c = triple(a,b,s(c)) [1 1 0] [1 1 0] [1 1 0] [0] [1 0 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [1 1 0] f'(triple(a,b,c),A()) = [1 1 0]a + [1 1 0]b + [1 1 0]c + [0] >= [1 1 0]a + [1 1 0]b + [1 1 0]c = f''(foldB(triple(s(a),0(),c),b)) [1 1 0] [1 1 0] [1 1 0] [1] [1 1 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] [1 1 0] f''(triple(a,b,c)) = [1 1 0]a + [1 1 0]b + [1 1 0]c >= [1 1 0]a + [1 1 0]b + [1 1 0]c = foldC(triple(a,b,0()),c) [1 0 0] [1 1 0] [1 0 0] [0 0 0] [1 1 0] [1 0 0] problem: f(t,x) -> f'(t,g(x)) f''(triple(a,b,c)) -> foldC(triple(a,b,0()),c) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1] [f''](x0) = [0 0 0]x0 + [0] [0 1 0] [0], [1 0 0] [1 0 0] [1 0 0] [triple](x0, x1, x2) = [0 0 0]x0 + [0 1 0]x1 + [0 0 0]x2 [0 0 0] [0 1 0] [0 0 0] , [1 0 0] [1 0 0] [f'](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [foldC](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 1] [0 0 0] , [1 0 0] [1 0 0] [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [0] [0] = [0] [0], [1 0 0] [g](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 0] [1 0 0] [1 0 0] [1 0 0] f(t,x) = [0 0 0]t + [0 0 0]x >= [0 0 0]t + [0 0 0]x = f'(t,g(x)) [0 0 0] [0 0 0] [0 0 0] [0 0 0] [1 0 0] [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] [1 0 0] f''(triple(a,b,c)) = [0 0 0]a + [0 0 0]b + [0 0 0]c + [0] >= [0 0 0]a + [0 0 0]b + [0 0 0]c = foldC(triple(a,b,0()),c) [0 0 0] [0 1 0] [0 0 0] [0] [0 0 0] [0 1 0] [0 0 0] problem: f(t,x) -> f'(t,g(x)) Matrix Interpretation Processor: dim=3 interpretation: [1 0 0] [1 0 0] [f'](x0, x1) = [0 0 0]x0 + [0 0 0]x1 [0 0 0] [0 0 0] , [1 0 0] [1 0 0] [1] [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0] [0 0 0] [0 0 0] [0], [1 0 0] [g](x0) = [0 0 0]x0 [0 0 0] orientation: [1 0 0] [1 0 0] [1] [1 0 0] [1 0 0] f(t,x) = [0 0 0]t + [0 0 0]x + [0] >= [0 0 0]t + [0 0 0]x = f'(t,g(x)) [0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] problem: Qed