output.txt

Starting...
<< Received >> Rules:
<< Received >> Rules:() + () = ()()                                      => [combine]
((())) + () = ((())())                              => [absorb-right]
() + ((())) = (()(()))                              => [absorb-left]
(())(()) + () = (())(()())                          => [combined-absorb-right]
() + (())(()) = (()())(())                          => [combined-absorb-left]
(())(()) + ((())) = ((())(())(()))                  => [absorb-combined-right]
((())) + (())(()) = ((())(())(()))                  => [absorb-combined-left]
() + (()) + ((())) = (()()) + ((())) = ((()())(())) => [left-associative]

Example: 
(()) + () = () + (()) = (()())

Let's start with a warmup.
(()) + (()()) = ???

>
<< Equation: (()) + (()())
<< Solution: (())(()()) 

<< Received >> Correct!
<< Received >> Correct!Okay, now we're cookin!
(()()()) + ()() + (()) = ???

>
<< Equation: (()()()) + ()() + (())
<< Solution: (()()()()())(()) 

<< Received >> Correct!
<< Received >> Correct!Alright see if you can get this one.
(()()) + (((()())()())()) + (()()()()()()()()) + (()) + ()()() = ???

>
<< Equation: (()()) + (((()())()())()) + (()()()()()()()()) + (()) + ()()()
<< Solution: ((()())((()())()())()(()()()()()()()())(())()()()) 

<< Received >> Correct!
<< Received >> Correct!This one's a little bigger!
(()) + (()()()) + (()()()()()()()()) + () + (()(())) + (((()())()())()) + (((()())()())()) + (()()()()()()()()) + (()()) + ()() = ???

>
<< Equation: (()) + (()()()) + (()()()()()()()()) + () + (()(())) + (((()())()())()) + (((()())()())()) + (()()()()()()()()) + (()()) + ()()
<< Solution: (((())(()()())(()()()()()()()()())()(()))((()())()())())(((()())()())()(()()()()()()()())(()())()()) 

<< Received >> Correct!
<< Received >> Correct!Ha. No more messin around. Final Round.
((()())()(())(()()())(()()()()()()()())) + ((())()()()(()()())) + ((()(())()()())((()(())((()))(((())))()()))()) + (()()()()()()()()()) + (((()()()()()()()()())()(((()()())()())()()))()(())((()))(((())))((((()))))) + (((()()())(())())()(((()()())()())()())) + (()()(())(())(()()())) + (((()())()(((()()())()())()()))((()(())((()))(((())))()()))()) + (((())())(()()()(())()())((((()))))(((())))((()))(())()) + (()()()) + ((()()()()()()()()()()()())((()())()())()) + ((()()()()()()()()()()())()(())((()))(((())))((((()))))) + ((()()(())()()())()(((()()())()())()())) + (((())())((()(())((()))(((())))()()))()) + ((()()()())((((()))))(((())))((()))(())()) + ((()()()()()(((()()())()())()()))((((()))))(((())))((()))(())()) + ((()()()()(((()()())()())()()))((()(())((()))(((())))()()))()) + ((()()()())((()())()())()) + ()()()() + ((()())(())()(())((()))(((())))((((()))))) + ((()()()()((()())()())())((()(())((()))(((())))()()))()) + ((()()()()()()())()(((()()())()())()())) + (((()()()()()()()())()()()(())()())()(((()()())()())()())) + ((()()()()()()(())()())()(())((()))(((())))((((()))))) + ((()())()(()))((())()(())) + (((()())()(())()())()(((()()())()())()())) + (()()()()()()) + (()()(())(()()())(()()()()()()()())) + ((()()())()(())(()()()()()()()())) + ((()())(())()()()(()()()()()()()())) + (((()())()(()))(()()()(())()())((()(())((()))(((())))()()))()) + ((()()()()()()(())()())((()(())((()))(((())
<< Received >> Correct!Ha. No more messin around. Final Round.
((()())()(())(()()())(()()()()()()()())) + ((())()()()(()()())) + ((()(())()()())((()(())((()))(((())))()()))()) + (()()()()()()()()()) + (((()()()()()()()()())()(((()()())()())()()))()(())((()))(((())))((((()))))) + (((()()())(())())()(((()()())()())()())) + (()()(())(())(()()())) + (((()())()(((()()())()())()()))((()(())((()))(((())))()()))()) + (((())())(()()()(())()())((((()))))(((())))((()))(())()) + (()()()) + ((()()()()()()()()()()()())((()())()())()) + ((()()()()()()()()()()())()(())((()))(((())))((((()))))) + ((()()(())()()())()(((()()())()())()())) + (((())())((()(())((()))(((())))()()))()) + ((()()()())((((()))))(((())))((()))(())()) + ((()()()()()(((()()())()())()()))((((()))))(((())))((()))(())()) + ((()()()()(((()()())()())()()))((()(())((()))(((())))()()))()) + ((()()()())((()())()())()) + ()()()() + ((()())(())()(())((()))(((())))((((()))))) + ((()()()()((()())()())())((()(())((()))(((())))()()))()) + ((()()()()()()())()(((()()())()())()())) + (((()()()()()()()())()()()(())()())()(((()()())()())()())) + ((()()()()()()(())()())()(())((()))(((())))((((()))))) + ((()())()(()))((())()(())) + (((()())()(())()())()(((()()())()())()())) + (()()()()()()) + (()()(())(()()())(()()()()()()()())) + ((()()())()(())(()()()()()()()())) + ((()())(())()()()(()()()()()()()())) + (((()())()(()))(()()()(())()())((()(())((()))(((())))()()))()) + ((()()()()()()(())()())((()(())((()))(((())))()()))()) + ((()()()()()()()()()())()(((()()())()())()())) + (((())()(((()()())()())()()))((((()))))(((())))((()))(())()) + (((()(()))()(((()()())()())()()))((()(())((()))(((())))()()))()) + ((()()()()()())()()()(())()()) + ((()()()()()()()()()())()()()(())()()) + ((()()(()))((())())()(((()()())()())()())) + ((()(()))((())())((()())()())()) + ((()()()()(())()())((()(())((()))(((())))()()))()) + (((()()()()()()()()())()()()(())()())()(())((()))(((())))((((()))))) + ((()())()(())()()(()()()()()()()())) + ((()()())((()(())((()))(((())))()()))()(()(())((()))(((())))((((())))))) + ((())()(()()()()()()()()))(()()()(())()()) + (((()())(())()()())((()())()())()) + ((()()()()())()()()(())()()) + (((()())()(()))((())())()(())((()))(((())))((((()))))) + ((()()()())()(((()()())()())()())) + (((())((()())()())())((()(())((()))(((())))()()))()) + (((())()(()()()))()(())((()))(((())))((((()))))) = ???

>
<< Equation: ((()())()(())(()()())(()()()()()()()())) + ((())()()()(()()())) + ((()(())()()())((()(())((()))(((())))()()))()) + (()()()()()()()()()) + (((()()()()()()()()())()(((()()())()())()()))()(())((()))(((())))((((()))))) + (((()()())(())())()(((()()())()())()())) + (()()(())(())(()()())) + (((()())()(((()()())()())()()))((()(())((()))(((())))()()))()) + (((())())(()()()(())()())((((()))))(((())))((()))(())()) + (()()()) + ((()()()()()()()()()()()())((()())()())()) + ((()()()()()()()()()()())()(())((()))(((())))((((()))))) + ((()()(())()()())()(((()()())()())()())) + (((())())((()(())((()))(((())))()()))()) + ((()()()())((((()))))(((())))((()))(())()) + ((()()()()()(((()()())()())()()))((((()))))(((())))((()))(())()) + ((()()()()(((()()())()())()()))((()(())((()))(((())))()()))()) + ((()()()())((()())()())()) + ()()()() + ((()())(())()(())((()))(((())))((((()))))) + ((()()()()((()())()())())((()(())((()))(((())))()()))()) + ((()()()()()()())()(((()()())()())()())) + (((()()()()()()()())()()()(())()())()(((()()())()())()())) + ((()()()()()()(())()())()(())((()))(((())))((((()))))) + ((()())()(()))((())()(())) + (((()())()(())()())()(((()()())()())()())) + (()()()()()()) + (()()(())(()()())(()()()()()()()())) + ((()()())()(())(()()()()()()()())) + ((()())(())()()()(()()()()()()()())) + (((()())()(()))(()()()(())()())((()(())((()))(((())))()()))()) + ((()()()()()()(())()())((()(())((()))(((())))()()))()) + ((()()()()()()()()()())()(((()()())()())()())) + (((())()(((()()())()())()()))((((()))))(((())))((()))(())()) + (((()(()))()(((()()())()())()()))((()(())((()))(((())))()()))()) + ((()()()()()())()()()(())()()) + ((()()()()()()()()()())()()()(())()()) + ((()()(()))((())())()(((()()())()())()())) + ((()(()))((())())((()())()())()) + ((()()()()(())()())((()(())((()))(((())))()()))()) + (((()()()()()()()()())()()()(())()())()(())((()))(((())))((((()))))) + ((()())()(())()()(()()()()()()()())) + ((()()())((()(())((()))(((())))()()))()(()(())((()))(((())))((((())))))) + ((())()(()()()()()()()()))(()()()(())()()) + (((()())(())()()())((()())()())()) + ((()()()()())()()()(())()()) + (((()())()(()))((())())()(())((()))(((())))((((()))))) + ((()()()())()(((()()())()())()())) + (((())((()())()())())((()(())((()))(((())))()()))()) + (((())()(()()()))()(())((()))(((())))((((())))))
<< Solution: (((()())()(())(()()())(()()()()()()()()))((())()()()(()()()))(()(())()()())((()(())((()))(((())))()()))()(()()()()()()()()())(((()()()()()()()()())()(((()()())()())()()))()(())((()))(((())))((((())))))(((()()())(())())()(((()()())()())()()))(()()(())(())(()()())))(((()())()(((()()())()())()()))((()(())((()))(((())))()()))()(((())())(()()()(())()())((((()))))(((())))((()))(())())(()()())((()()()()()()()()()()()())((()())()())())((()()()()()()()()()()())()(())((()))(((())))((((())))))((()()(())()()())()(((()()())()())()())))(((())())((()(())((()))(((())))()()))()((()()()())((((()))))(((())))((()))(())())((()()()()()(((()()())()())()()))((((()))))(((())))((()))(())()))((()()()()(((()()())()())()()))((()(())((()))(((())))()()))()((()()()())((()())()())())()()()()((()())(())()(())((()))(((())))((((()))))))((()()()()((()())()())())((()(())((()))(((())))()()))()((()()()()()()())()(((()()())()())()()))(((()()()()()()()())()()()(())()())()(((()()())()())()()))((()()()()()()(())()())()(())((()))(((())))((((())))))((()())()(()))((())()(()))(((()())()(())()())()(((()()())()())()()))(()()()()()())(()()(())(()()())(()()()()()()()()))((()()())()(())(()()()()()()()()))((()())(())()()()(()()()()()()()())))(((()())()(()))(()()()(())()())((()(())((()))(((())))()()))())((()()()()()()(())()())((()(())((()))(((())))()()))()((()()()()()()()()()())()(((()()())()())()()))(((())()(((()()())()())()()))((((()))))(((())))((()))(())()))(((()(()))()(((()()())()())()()))((()(())((()))(((())))()()))()((()()()()()())()()()(())()())((()()()()()()()()()())()()()(())()())((()()(()))((())())()(((()()())()())()()))((()(()))((())())((()())()())()))((()()()()(())()())((()(())((()))(((())))()()))()(((()()()()()()()()())()()()(())()())()(())((()))(((())))((((())))))((()())()(())()()(()()()()()()()())))((()()())((()(())((()))(((())))()()))()(()(())((()))(((())))((((())))))((())()(()()()()()()()()))(()()()(())()())(((()())(())()()())((()())()())())((()()()()())()()()(())()())(((()())()(()))((())())()(())((()))(((())))((((())))))((()()()())()(((()()())()())()())))(((())((()())()())())((()(())((()))(((())))()()))()(((())()(()()()))()(())((()))(((())))((((())))))) 

<< Received >> Correct!
<< Received >> Correct!Congratulations, here's your flag: picoCTF{5cr1pt1nG_l1k3_4_pRo_0466cdd7}