Certificate for #15757 ⟨a, b | aab=bb, ababa=a⟩

Back:⟨a, b | aab=bb, ababa=a⟩

Completion settings:

[1] bb=aab

Axiom: aab=bb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [3].

[2] ababa=a

Axiom: ababa=a.

Defines rule #4.

Referenced by [4], [5].

[3] baab=aaaab

Overlap of [1] bb=aab with [1] bb=aab:

b b bb

Critical pair: baab=aabb.

Reduce RHS:

[1]aa(bb)
⇒ aaaab

Referenced by [4].

[4] baa=aaaa

Overlap of [3] baab=aaaab with [2] ababa=a:

ba ab ababa

Critical pair: baa=aaaababa.

Reduce RHS:

[2]aaa(ababa)
⇒ aaaa

Defines rule #2.

Referenced by [5].

[5] aaaaaaaa=aa

Overlap of [2] ababa=a with [4] baa=aaaa:

aba ba baa

Critical pair: abaaaaa=aa.

Reduce LHS:

[4]a(baa)aaa
⇒ aaaaaaaa

Defines rule #1.