Certificate for #7105 ⟨a, b | ab=aa, bbaa=bb⟩

Back:⟨a, b | ab=aa, bbaa=bb⟩

Completion settings:

[1] aa=ab

Axiom: ab=aa.

Flip LHS and RHS.

Defines rule #1.

Referenced by [2], [3].

[2] bbab=bb

Axiom: bbaa=bb.

Reduce LHS:

[1]bb(aa)
⇒ bbab

Referenced by [4], [5].

[3] aba=abb

Overlap of [1] aa=ab with [1] aa=ab:

a a aa

Critical pair: aab=aba.

Reduce LHS:

[1](aa)b
⇒ abb

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

[4] bba=bbb

Overlap of [2] bbab=bb with [3] aba=abb:

bb ab aba

Critical pair: bbabb=bba.

Reduce LHS:

[2](bbab)b
⇒ bbb

Flip LHS and RHS.

Defines rule #2.

Referenced by [5].

[5] bbbb=bb

Overlap of [2] bbab=bb with [4] bba=bbb:

bbab bba

Critical pair: bbbb=bb.

Defines rule #4.