pp(n(x,y),z) = n(pp(x,z),pp(y,z))
pp(q(x,y),z) = q(pp(x,z),pp(y,z))
pp(x,n(y,z)) = n(pp(x,y),pp(x,z))
pp(x,q(y,z)) = q(pp(x,y),pp(x,z))
i(pp(x,y)) = pp(i(y),i(x))
pp(x,pp(y,z)) = pp(pp(x,y),z)
n(x,q(x,y)) = x
q(x,n(x,y)) = x
q(x,q(y,z)) = q(q(x,y),z)
n(x,n(y,z)) = n(n(x,y),z)
n(c,1) = 1
n(b,1) = 1
n(a,1) = 1
pp(i(x),x) = 1
i(i(x)) = x
pp(1,x) = x
i(1) = 1
n(x,x) = x
q(x,x) = x
q(x,y) = q(y,x)
n(x,y) = n(y,x)
!preorder n > q > i > pp > 1 > a > b > c
n(a,pp(a,b)) != a