YES(?,O(1))

We are left with following problem, upon which TcT provides the
certificate YES(?,O(1)).

Strict Trs:
  { not(x) -> xor(x, true())
  , implies(x, y) -> xor(and(x, y), xor(x, true()))
  , or(x, y) -> xor(and(x, y), xor(x, y))
  , =(x, y) -> xor(x, xor(y, true())) }
Obligation:
  innermost runtime complexity
Answer:
  YES(?,O(1))

The input was oriented with the instance of 'Small Polynomial Path
Order (PS)' as induced by the safe mapping

 safe(not) = {1}, safe(xor) = {1, 2}, safe(true) = {},
 safe(implies) = {}, safe(and) = {1, 2}, safe(or) = {},
 safe(=) = {1}

and precedence

 not > implies, or > implies, = > implies, not ~ or, not ~ =,
 or ~ = .

Following symbols are considered recursive:

 {}

The recursion depth is 0.

For your convenience, here are the satisfied ordering constraints:

         not(; x) > xor(; x,  true())                      
                                                           
  implies(x,  y;) > xor(; and(; x,  y),  xor(; x,  true()))
                                                           
       or(x,  y;) > xor(; and(; x,  y),  xor(; x,  y))     
                                                           
          =(y; x) > xor(; x,  xor(; y,  true()))           
                                                           

Hurray, we answered YES(?,O(1))