//p-1+(1/2)(p+1)gcd(p-1,4)
<a,b|baaaa,pa-wbab-baaa,pb-xbaaab,class=5>(all x, x~x' if x^4=x'^4 mod p)(p=1 mod 4)
<a,b|baaaa,pa-wbab-wbaaa,pb-xbaaab,babb+baaab,class=5>(all x, x~x' if x^4=x'^4 mod p)(p=1 mod 4)
<a,b|baaaa,pa-wbab-baaa,pb-xbaaab,class=5>(all x, x~-x)(p=3 mod 4)
<a,b|baaab,pa-wbab-baaa,pb-xbaaaa,class=5>(all x)
<a,b|baaab,pa-wbab-wbaaa,pb-xbaaaa,baab+baaaa,class=5>(all x)(p=1 mod 4)
<a,b|baaab,pa-wbab-baaa-xbaaaa,pb+(2*z)baaaa,class=5>(x ne 0, x~x' if x^4=x'^4 mod p, z=w^-1)(p=1 mod 4)
<a,b|baaab,pa-wbab-wbaaa-xbaaaa,pb+(2*w)baaaa,baab+baaaa,class=5>(x ne 0, x~x' if x^4=x'^4 mod p)(p=1 mod 4)
<a,b|baaab,pa-wbab-baaa-xbaaaa,pb+(2*z)baaaa,class=5>(x ne 0, x~-x, z=w^-1)(p=3 mod 4)
