Certificate for #15526 ⟨a, b | aaa=bb, ababb=b⟩

Back:⟨a, b | aaa=bb, ababb=b⟩

Completion settings:

[1] bb=aaa

Axiom: aaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [2], [3], [7].

[2] abaaaa=b

Axiom: ababb=b.

Reduce LHS:

[1]aba(bb)
⇒ abaaaa

Referenced by [4], [5], [6], [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], [7].

[4] aab=baaaaaaa

Overlap of [3] aaab=baaa with [2] abaaaa=b:

aa ab abaaaa

Critical pair: aab=baaaaaaa.

Referenced by [5].

[5] ab=baaaaaaaaaaa

Overlap of [4] aab=baaaaaaa with [2] abaaaa=b:

a ab abaaaa

Critical pair: ab=baaaaaaaaaaa.

Defines rule #3.

Referenced by [6], [7].

[6] baaaaaaaaaaaaaaa=b

Overlap of [2] abaaaa=b with [5] ab=baaaaaaaaaaa:

abaaaa ab

Critical pair: baaaaaaaaaaaaaaa=b.

Defines rule #2.

[7] aaaaaaaaaaaaaaaaaa=aaa

Overlap of [2] abaaaa=b with [5] ab=baaaaaaaaaaa:

abaaa a ab

Critical pair: abaaabaaaaaaaaaaa=bb.

Reduce LHS:

[3]ab(aaab)aaaaaaaaaaa
[1]⇒ a(bb)aaaaaaaaaaaaaa
⇒ aaaaaaaaaaaaaaaaaa

Reduce RHS:

[1](bb)
⇒ aaa

Defines rule #1.