Certificate for #7153 ⟨a, b | bb=aa, abab=ab⟩

Back:⟨a, b | bb=aa, abab=ab⟩

Completion settings:

[1] bb=aa

Axiom: bb=aa.

Defines rule #1.

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

[2] abab=ab

Axiom: abab=ab.

Defines rule #3.

Referenced by [4], [5].

[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=aaa

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

aba b bb

Critical pair: abaaa=abb.

Reduce LHS:

[3]a(baa)a
⇒ aaaba

Reduce RHS:

[1]a(bb)
⇒ aaa

Defines rule #4.

Referenced by [6].

[5] aaaaab=aaaa

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

ba a abab

Critical pair: baab=aabbab.

Reduce LHS:

[3](baa)b
[1]⇒ aa(bb)
⇒ aaaa

Reduce RHS:

[1]aa(bb)ab
⇒ aaaaab

Flip LHS and RHS.

Defines rule #5.

[6] aaaaaaa=aaaab

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

ba a aaaba

Critical pair: baaaa=aabaaba.

Reduce LHS:

[3](baa)aa
[3]⇒ aa(baa)
⇒ aaaab

Reduce RHS:

[3]aa(baa)ba
[1]⇒ aaaa(bb)a
⇒ aaaaaaa

Flip LHS and RHS.

Defines rule #6.