Certificate for #5342 ⟨a, b | aaa=bb, aba=aa⟩

Back:⟨a, b | aaa=bb, aba=aa⟩

Completion settings:

[1] bb=aaa

Axiom: aaa=bb.

Flip LHS and RHS.

Defines rule #5.

Referenced by [3], [4].

[2] aba=aa

Axiom: aba=aa.

Defines rule #3.

Referenced by [4], [5].

[3] aaab=baaa

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

b b bb

Critical pair: baaa=aaab.

Flip LHS and RHS.

Defines rule #4.

Referenced by [4], [5].

[4] aaaaaaa=aaaa

Overlap of [2] aba=aa with [3] aaab=baaa:

ab a aaab

Critical pair: abbaaa=aaaab.

Reduce LHS:

[1]a(bb)aaa
⇒ aaaaaaa

Reduce RHS:

[3]a(aaab)
[2]⇒ (aba)aa
⇒ aaaa

Defines rule #1.

[5] baaaa=aaaa

Overlap of [3] aaab=baaa with [2] aba=aa:

aa ab aba

Critical pair: aaaa=baaaa.

Flip LHS and RHS.

Defines rule #2.