Certificate for #21086 ⟨a, b | bb=aa, aaaa=aba⟩

Back:⟨a, b | bb=aa, aaaa=aba⟩

Completion settings:

[1] bb=aa

Axiom: bb=aa.

Defines rule #5.

Referenced by [3], [4].

[2] aba=aaaa

Axiom: aaaa=aba.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4], [5].

[3] aab=baa

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

b b bb

Critical pair: baa=aab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [5].

[4] aaaaaaa=aaaaa

Overlap of [2] aba=aaaa with [3] aab=baa:

ab a aab

Critical pair: abbaa=aaaaab.

Reduce LHS:

[1]a(bb)aa
⇒ aaaaa

Reduce RHS:

[3]aaa(aab)
[3]⇒ a(aab)aa
[2]⇒ (aba)aaa
⇒ aaaaaaa

Flip LHS and RHS.

Defines rule #1.

[5] baaa=aaaaa

Overlap of [3] aab=baa with [2] aba=aaaa:

a ab aba

Critical pair: aaaaa=baaa.

Flip LHS and RHS.

Defines rule #2.