Case 1:
   P = a/b
   C = /c/d
   S = a/b

Case 2:
   P = /
   C = /a/b/c
   S = ../../..

Case 3:
   P = /a/b
   C = /a/c
   S = ../b

Case 4:
   P = /
   C = /
   S = .

Case 5:
   P = /x/y
   C = /x/y
   S = .

Case 6:
   P = /a/b/../c
   C = /a/d
   S = ../c

Case 7:
   P = /a/b
   C = /c/d
   S = ../../a/b

Case 8:
   P = /c/a/b
   C = /c/d
   S = ../a/b

Case 9:
   P = /c/d/a/b
   C = /c/d
   S = a/b