Certificate for #5186 ⟨a, b | aab=ba, bbba=a

Completion settings:

[1] aab=ba

Axiom: aab=ba.

Referenced by [3], [5], [7], [9], [11].

[2] bbba=a

Axiom: bbba=a.

Defines rule #3.

Referenced by [3], [4], [6], [8], [10].

[3] babba=aaa

Overlap of [1] aab=ba with [2] bbba=a:

aa b bbba

Critical pair: aaa=babba.

Flip LHS and RHS.

Referenced by [4].

[4] abba=bbaaa

Overlap of [2] bbba=a with [3] babba=aaa:

bb ba babba

Critical pair: bbaaa=abba.

Flip LHS and RHS.

Referenced by [5].

[5] baba=bbaaaaa

Overlap of [1] aab=ba with [4] abba=bbaaa:

a ab abba

Critical pair: abbaaa=baba.

Reduce LHS:

[4](abba)aa
bbaaaaa

Flip LHS and RHS.

Referenced by [6].

[6] aba=baaaaa

Overlap of [2] bbba=a with [5] baba=bbaaaaa:

bb ba baba

Critical pair: bbbbaaaaa=aba.

Reduce LHS:

[2]b(bbba)aaaa
baaaaa

Flip LHS and RHS.

Referenced by [7], [9].

[7] baaaaaaaaa=baa

Overlap of [1] aab=ba with [6] aba=baaaaa:

a ab aba

Critical pair: abaaaaa=baa.

Reduce LHS:

[6](aba)aaaa
baaaaaaaaa

Referenced by [8].

[8] aaaaaaaaa=aa

Overlap of [2] bbba=a with [7] baaaaaaaaa=baa:

bb ba baaaaaaaaa

Critical pair: bbbaa=aaaaaaaaa.

Reduce LHS:

[2](bbba)a
aa

Flip LHS and RHS.

Referenced by [9].

[9] baaaaaaaa=ba

Overlap of [8] aaaaaaaaa=aa with [1] aab=ba:

aaaaaaa aa aab

Critical pair: aaaaaaaba=aab.

Reduce LHS:

[1]aaaaa(aab)a
[1]aaa(aab)aa
[1]a(aab)aaa
[6](aba)aaa
baaaaaaaa

Reduce RHS:

[1](aab)
ba

Referenced by [10].

[10] aaaaaaaa=a

Overlap of [2] bbba=a with [9] baaaaaaaa=ba:

bb ba baaaaaaaa

Critical pair: bbba=aaaaaaaa.

Reduce LHS:

[2](bbba)
a

Flip LHS and RHS.

Defines rule #1.

Referenced by [11].

[11] ab=baaaa

Overlap of [10] aaaaaaaa=a with [1] aab=ba:

aaaaaa aa aab

Critical pair: aaaaaaba=ab.

Reduce LHS:

[1]aaaa(aab)a
[1]aa(aab)aa
[1](aab)aaa
baaaa

Flip LHS and RHS.

Defines rule #2.