Certificate for #12196 ⟨a, b | aaaa=bb, aaab=a⟩

Back:⟨a, b | aaaa=bb, aaab=a⟩

Completion settings:

[1] bb=aaaa

Axiom: aaaa=bb.

Flip LHS and RHS.

Defines rule #4.

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

[2] aaab=a

Axiom: aaab=a.

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

[3] baaaa=aa

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

b b bb

Critical pair: baaaa=aaaab.

Reduce RHS:

[2]a(aaab)
⇒ aa

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

[4] ab=aaaaaaa

Overlap of [2] aaab=a with [1] bb=aaaa:

aaa b bb

Critical pair: aaaaaaa=ab.

Flip LHS and RHS.

Defines rule #3.

[5] baa=aaaaaaaa

Overlap of [1] bb=aaaa with [3] baaaa=aa:

b b baaaa

Critical pair: baa=aaaaaaaa.

Referenced by [6].

[6] aaaaaaaaa=a

Overlap of [3] baaaa=aa with [2] aaab=a:

baa aa aaab

Critical pair: baaa=aaab.

Reduce LHS:

[5](baa)a
⇒ aaaaaaaaa

Reduce RHS:

[2](aaab)
⇒ a

Defines rule #1.

Referenced by [7].

[7] ba=aaaaaaa

Overlap of [3] baaaa=aa with [6] aaaaaaaaa=a:

b aaaa aaaaaaaaa

Critical pair: ba=aaaaaaa.

Defines rule #2.