Certificate for #16052 ⟨a, b | aaa=bb, aaba=aa⟩

Back:⟨a, b | aaa=bb, aaba=aa⟩

Completion settings:

[1] bb=aaa

Axiom: aaa=bb.

Flip LHS and RHS.

Defines rule #5.

Referenced by [3], [5].

[2] aaba=aa

Axiom: aaba=aa.

Defines rule #3.

Referenced by [4], [7].

[3] aaab=baaa

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

b b bb

Critical pair: baaa=aaab.

Flip LHS and RHS.

Referenced by [4], [6].

[4] baaaa=aaa

Overlap of [2] aaba=aa with [2] aaba=aa:

aab a aaba

Critical pair: aabaa=aaaba.

Reduce LHS:

[2](aaba)a
⇒ aaa

Reduce RHS:

[3](aaab)a
⇒ baaaa

Flip LHS and RHS.

Referenced by [5].

[5] baaa=aaaaaaa

Overlap of [1] bb=aaa with [4] baaaa=aaa:

b b baaaa

Critical pair: baaa=aaaaaaa.

Defines rule #2.

Referenced by [6].

[6] aaab=aaaaaaa

Simplify [3] aaab=baaa.

Reduce RHS:

[5](baaa)
⇒ aaaaaaa

Defines rule #4.

Referenced by [7].

[7] aaaaaaaa=aaa

Overlap of [6] aaab=aaaaaaa with [2] aaba=aa:

a aab aaba

Critical pair: aaa=aaaaaaaa.

Flip LHS and RHS.

Defines rule #1.