Certificate for #1594 ⟨a, b | aaa=ab, bab=a⟩

Back:⟨a, b | aaa=ab, bab=a⟩

Completion settings:

[1] aaa=ab

Axiom: aaa=ab.

Defines rule #2.

Referenced by [4], [5].

[2] bab=a

Axiom: bab=a.

Referenced by [3], [5], [6].

[3] baa=aab

Overlap of [2] bab=a with [2] bab=a:

ba b bab

Critical pair: baa=aab.

Referenced by [5].

[4] aba=aab

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

a aa aaa

Critical pair: aab=aba.

Flip LHS and RHS.

Referenced by [5].

[5] abb=a

Overlap of [3] baa=aab with [1] aaa=ab:

b aa aaa

Critical pair: bab=aaba.

Reduce LHS:

[2](bab)
⇒ a

Reduce RHS:

[4]a(aba)
[1]⇒ (aaa)b
⇒ abb

Flip LHS and RHS.

Defines rule #3.

Referenced by [6].

[6] ba=ab

Overlap of [2] bab=a with [5] abb=a:

b ab abb

Critical pair: ba=ab.

Defines rule #1.