Certificate for #4180 ⟨a, b | baa=abb, bba=a⟩

Back:⟨a, b | baa=abb, bba=a⟩

Completion settings:

[1] baa=abb

Axiom: baa=abb.

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

[2] bba=a

Axiom: bba=a.

Defines rule #2.

Referenced by [3], [4], [5], [6].

[3] aa=babb

Overlap of [2] bba=a with [1] baa=abb:

b ba baa

Critical pair: babb=aa.

Flip LHS and RHS.

Defines rule #3.

Referenced by [4].

[4] ababb=abb

Overlap of [3] aa=babb with [3] aa=babb:

a a aa

Critical pair: ababb=babba.

Reduce RHS:

[2]ba(bba)
[1]⇒ (baa)
⇒ abb

Defines rule #4.

Referenced by [5], [6].

[5] abbbb=abb

Overlap of [1] baa=abb with [4] ababb=abb:

ba a ababb

Critical pair: baabb=abbbabb.

Reduce LHS:

[1](baa)bb
⇒ abbbb

Reduce RHS:

[2]ab(bba)bb
[4]⇒ (ababb)
⇒ abb

Defines rule #1.

[6] ababa=aba

Overlap of [4] ababb=abb with [2] bba=a:

abab b bba

Critical pair: ababa=abbba.

Reduce RHS:

[2]ab(bba)
⇒ aba

Defines rule #5.