Certificate for #16148 ⟨a, b | aab=ab, aaaa=bb⟩

Back:⟨a, b | aab=ab, aaaa=bb⟩

Completion settings:

[1] aab=ab

Axiom: aab=ab.

Referenced by [3], [5].

[2] aaaa=bb

Axiom: aaaa=bb.

Defines rule #4.

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

[3] ab=bbb

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

aa aa aab

Critical pair: aaab=bbb.

Reduce LHS:

[1]a(aab)
[1]⇒ (aab)
⇒ ab

Defines rule #2.

Referenced by [4], [5].

[4] bba=bbbb

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

a aaa aaaa

Critical pair: abb=bba.

Reduce LHS:

[3](ab)b
⇒ bbbb

Flip LHS and RHS.

Defines rule #3.

[5] bbbbb=bbb

Overlap of [2] aaaa=bb with [3] ab=bbb:

aaa a ab

Critical pair: aaabbb=bbb.

Reduce LHS:

[1]a(aab)bb
[1]⇒ (aab)bb
[3]⇒ (ab)bb
⇒ bbbbb

Defines rule #1.