Certificate for #3075 ⟨a, b | ab=a, aaaa=bb⟩

Back:⟨a, b | ab=a, aaaa=bb⟩

Completion settings:

[1] ab=a

Axiom: ab=a.

Defines rule #1.

Referenced by [3], [4].

[2] aaaa=bb

Axiom: aaaa=bb.

Defines rule #4.

Referenced by [3], [4].

[3] bbb=bb

Overlap of [2] aaaa=bb with [1] ab=a:

aaa a ab

Critical pair: aaaa=bbb.

Reduce LHS:

[2](aaaa)
⇒ bb

Flip LHS and RHS.

Defines rule #3.

Referenced by [5].

[4] bba=a

Overlap of [2] aaaa=bb with [2] aaaa=bb:

a aaa aaaa

Critical pair: abb=bba.

Reduce LHS:

[1](ab)b
[1]⇒ (ab)
⇒ a

Flip LHS and RHS.

Referenced by [5].

[5] ba=a

Overlap of [3] bbb=bb with [4] bba=a:

b bb bba

Critical pair: ba=bba.

Reduce RHS:

[4](bba)
⇒ a

Defines rule #2.