MAYBE Problem: app(nil(),y) -> y app(add(n,x),y) -> add(n,app(x,y)) reverse(nil()) -> nil() reverse(add(n,x)) -> app(reverse(x),add(n,nil())) shuffle(nil()) -> nil() shuffle(add(n,x)) -> add(n,shuffle(reverse(x))) Proof: Complexity Transformation Processor: strict: app(nil(),y) -> y app(add(n,x),y) -> add(n,app(x,y)) reverse(nil()) -> nil() reverse(add(n,x)) -> app(reverse(x),add(n,nil())) shuffle(nil()) -> nil() shuffle(add(n,x)) -> add(n,shuffle(reverse(x))) weak: Matrix Interpretation Processor: dimension: 1 max_matrix: 1 interpretation: [shuffle](x0) = x0, [reverse](x0) = x0 + 1, [add](x0, x1) = x0 + x1, [app](x0, x1) = x0 + x1, [nil] = 0 orientation: app(nil(),y) = y >= y = y app(add(n,x),y) = n + x + y >= n + x + y = add(n,app(x,y)) reverse(nil()) = 1 >= 0 = nil() reverse(add(n,x)) = n + x + 1 >= n + x + 1 = app(reverse(x),add(n,nil())) shuffle(nil()) = 0 >= 0 = nil() shuffle(add(n,x)) = n + x >= n + x + 1 = add(n,shuffle(reverse(x))) problem: strict: app(nil(),y) -> y app(add(n,x),y) -> add(n,app(x,y)) reverse(add(n,x)) -> app(reverse(x),add(n,nil())) shuffle(nil()) -> nil() shuffle(add(n,x)) -> add(n,shuffle(reverse(x))) weak: reverse(nil()) -> nil() Matrix Interpretation Processor: dimension: 1 max_matrix: 1 interpretation: [shuffle](x0) = x0, [reverse](x0) = x0, [add](x0, x1) = x0 + x1 + 1, [app](x0, x1) = x0 + x1 + 1, [nil] = 1 orientation: app(nil(),y) = y + 2 >= y = y app(add(n,x),y) = n + x + y + 2 >= n + x + y + 2 = add(n,app(x,y)) reverse(add(n,x)) = n + x + 1 >= n + x + 3 = app(reverse(x),add(n,nil())) shuffle(nil()) = 1 >= 1 = nil() shuffle(add(n,x)) = n + x + 1 >= n + x + 1 = add(n,shuffle(reverse(x))) reverse(nil()) = 1 >= 1 = nil() problem: strict: app(add(n,x),y) -> add(n,app(x,y)) reverse(add(n,x)) -> app(reverse(x),add(n,nil())) shuffle(nil()) -> nil() shuffle(add(n,x)) -> add(n,shuffle(reverse(x))) weak: app(nil(),y) -> y reverse(nil()) -> nil() Matrix Interpretation Processor: dimension: 1 max_matrix: 1 interpretation: [shuffle](x0) = x0 + 1, [reverse](x0) = x0, [add](x0, x1) = x0 + x1, [app](x0, x1) = x0 + x1, [nil] = 0 orientation: app(add(n,x),y) = n + x + y >= n + x + y = add(n,app(x,y)) reverse(add(n,x)) = n + x >= n + x = app(reverse(x),add(n,nil())) shuffle(nil()) = 1 >= 0 = nil() shuffle(add(n,x)) = n + x + 1 >= n + x + 1 = add(n,shuffle(reverse(x))) app(nil(),y) = y >= y = y reverse(nil()) = 0 >= 0 = nil() problem: strict: app(add(n,x),y) -> add(n,app(x,y)) reverse(add(n,x)) -> app(reverse(x),add(n,nil())) shuffle(add(n,x)) -> add(n,shuffle(reverse(x))) weak: shuffle(nil()) -> nil() app(nil(),y) -> y reverse(nil()) -> nil() Matrix Interpretation Processor: dimension: 2 max_matrix: [1 1] [0 1] interpretation: [1 1] [shuffle](x0) = [0 1]x0, [reverse](x0) = x0, [1 1] [0] [add](x0, x1) = [0 0]x0 + x1 + [1], [app](x0, x1) = x0 + x1, [0] [nil] = [0] orientation: [1 1] [0] [1 1] [0] app(add(n,x),y) = [0 0]n + x + y + [1] >= [0 0]n + x + y + [1] = add(n,app(x,y)) [1 1] [0] [1 1] [0] reverse(add(n,x)) = [0 0]n + x + [1] >= [0 0]n + x + [1] = app(reverse(x),add(n,nil())) [1 1] [1 1] [1] [1 1] [1 1] [0] shuffle(add(n,x)) = [0 0]n + [0 1]x + [1] >= [0 0]n + [0 1]x + [1] = add(n,shuffle(reverse(x))) [0] [0] shuffle(nil()) = [0] >= [0] = nil() app(nil(),y) = y >= y = y [0] [0] reverse(nil()) = [0] >= [0] = nil() problem: strict: app(add(n,x),y) -> add(n,app(x,y)) reverse(add(n,x)) -> app(reverse(x),add(n,nil())) weak: shuffle(add(n,x)) -> add(n,shuffle(reverse(x))) shuffle(nil()) -> nil() app(nil(),y) -> y reverse(nil()) -> nil() Open