Certificate for #7057 ⟨a, b | ab=aa, aaaa=bb⟩

Back:⟨a, b | ab=aa, aaaa=bb⟩

Completion settings:

[1] ab=aa

Axiom: ab=aa.

Defines rule #3.

Referenced by [3], [4].

[2] bb=aaaa

Axiom: aaaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [3], [4], [5].

[3] aaaaa=aaa

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

a b bb

Critical pair: aaaaa=aab.

Reduce RHS:

[1]a(ab)
⇒ aaa

Defines rule #1.

Referenced by [4], [5].

[4] baaaa=aaa

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

b b bb

Critical pair: baaaa=aaaab.

Reduce RHS:

[1]aaa(ab)
[3]⇒ (aaaaa)
⇒ aaa

Referenced by [5].

[5] baaa=aaaa

Overlap of [2] bb=aaaa with [4] baaaa=aaa:

b b baaaa

Critical pair: baaa=aaaaaaaa.

Reduce RHS:

[3](aaaaa)aaa
[3]⇒ (aaaaa)a
⇒ aaaa

Defines rule #2.