Certificate for #5086 ⟨a, b | aaa=bb, abbb=a⟩

Back:⟨a, b | aaa=bb, abbb=a⟩

Completion settings:

[1] bb=aaa

Axiom: aaa=bb.

Flip LHS and RHS.

Defines rule #4.

Referenced by [2], [3], [5].

[2] aaaab=a

Axiom: abbb=a.

Reduce LHS:

[1]a(bb)b
⇒ aaaab

Referenced by [4].

[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], [5], [6].

[4] abaaa=a

Simplify [2] aaaab=a.

Reduce LHS:

[3]a(aaab)
⇒ abaaa

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

[5] ab=aaaaaaa

Overlap of [4] abaaa=a with [3] aaab=baaa:

ab aaa aaab

Critical pair: abbaaa=ab.

Reduce LHS:

[1]a(bb)aaa
⇒ aaaaaaa

Flip LHS and RHS.

Defines rule #3.

Referenced by [7].

[6] baaaaaa=aaa

Overlap of [3] aaab=baaa with [4] abaaa=a:

aa ab abaaa

Critical pair: aaa=baaaaaa.

Flip LHS and RHS.

Referenced by [8].

[7] aaaaaaaaaa=a

Overlap of [4] abaaa=a with [5] ab=aaaaaaa:

abaaa ab

Critical pair: aaaaaaaaaa=a.

Defines rule #1.

Referenced by [8].

[8] ba=aaaaaaa

Overlap of [6] baaaaaa=aaa with [7] aaaaaaaaaa=a:

b aaaaaa aaaaaaaaaa

Critical pair: ba=aaaaaaa.

Defines rule #2.