Certificate for #7152 ⟨a, b | bb=aa, abab=aa⟩

Back:⟨a, b | bb=aa, abab=aa⟩

Completion settings:

[1] bb=aa

Axiom: bb=aa.

Defines rule #1.

Referenced by [3], [4], [5], [6].

[2] abab=aa

Axiom: abab=aa.

Defines rule #3.

Referenced by [4], [5], [6].

[3] baa=aab

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

b b bb

Critical pair: baa=aab.

Defines rule #2.

Referenced by [4], [5], [6].

[4] aaaba=aab

Overlap of [2] abab=aa with [1] bb=aa:

aba b bb

Critical pair: abaaa=aab.

Reduce LHS:

[3]a(baa)a
⇒ aaaba

Defines rule #4.

Referenced by [6].

[5] aaaaab=aaba

Overlap of [3] baa=aab with [2] abab=aa:

ba a abab

Critical pair: baaa=aabbab.

Reduce LHS:

[3](baa)a
⇒ aaba

Reduce RHS:

[1]aa(bb)ab
⇒ aaaaab

Flip LHS and RHS.

Defines rule #5.

[6] aaaaaaa=aaa

Overlap of [3] baa=aab with [4] aaaba=aab:

ba a aaaba

Critical pair: baaab=aabaaba.

Reduce LHS:

[3](baa)ab
[2]⇒ a(abab)
⇒ aaa

Reduce RHS:

[3]aa(baa)ba
[1]⇒ aaaa(bb)a
⇒ aaaaaaa

Flip LHS and RHS.

Defines rule #6.