Problem:
rev(a()) -> a()
rev(b()) -> b()
rev(++(x,y)) -> ++(rev(y),rev(x))
rev(++(x,x)) -> rev(x)
Proof:
Complexity Transformation Processor:
strict:
rev(a()) -> a()
rev(b()) -> b()
rev(++(x,y)) -> ++(rev(y),rev(x))
rev(++(x,x)) -> rev(x)
weak:
Matrix Interpretation Processor:
dimension: 1
max_matrix:
1
interpretation:
[++](x0, x1) = x0 + x1 + 1,
[b] = 4,
[rev](x0) = x0 + 6,
[a] = 12
orientation:
rev(a()) = 18 >= 12 = a()
rev(b()) = 10 >= 4 = b()
rev(++(x,y)) = x + y + 7 >= x + y + 13 = ++(rev(y),rev(x))
rev(++(x,x)) = 2x + 7 >= x + 6 = rev(x)
problem:
strict:
rev(++(x,y)) -> ++(rev(y),rev(x))
weak:
rev(a()) -> a()
rev(b()) -> b()
rev(++(x,x)) -> rev(x)
Matrix Interpretation Processor:
dimension: 3
max_matrix:
[1 1 1]
[0 1 1]
[0 0 0]
interpretation:
[1 0 0] [1 0 1] [0]
[++](x0, x1) = [0 1 1]x0 + [0 1 1]x1 + [1]
[0 0 0] [0 0 0] [0],
[0]
[b] = [0]
[0],
[1 1 0]
[rev](x0) = [0 1 1]x0
[0 0 0] ,
[0]
[a] = [0]
[0]
orientation:
[1 1 1] [1 1 2] [1] [1 1 0] [1 1 0] [0]
rev(++(x,y)) = [0 1 1]x + [0 1 1]y + [1] >= [0 1 1]x + [0 1 1]y + [1] = ++(rev(y),rev(x))
[0 0 0] [0 0 0] [0] [0 0 0] [0 0 0] [0]
[0] [0]
rev(a()) = [0] >= [0] = a()
[0] [0]
[0] [0]
rev(b()) = [0] >= [0] = b()
[0] [0]
[2 2 3] [1] [1 1 0]
rev(++(x,x)) = [0 2 2]x + [1] >= [0 1 1]x = rev(x)
[0 0 0] [0] [0 0 0]
problem:
strict:
weak:
rev(++(x,y)) -> ++(rev(y),rev(x))
rev(a()) -> a()
rev(b()) -> b()
rev(++(x,x)) -> rev(x)
Qed