Certificate for #19001 ⟨a, b | aab=b, ababaa=b

Completion settings:

[1] aab=b

Axiom: aab=b.

Defines rule #2.

Referenced by [3], [4], [5], [7], [12].

[2] ababaa=b

Axiom: ababaa=b.

Referenced by [3], [4], [9].

[3] babaa=ab

Overlap of [1] aab=b with [2] ababaa=b:

a ab ababaa

Critical pair: ab=babaa.

Flip LHS and RHS.

Referenced by [7], [8], [10], [11].

[4] ababb=bb

Overlap of [2] ababaa=b with [1] aab=b:

abab aa aab

Critical pair: ababb=bb.

Referenced by [5], [6].

[5] babb=abb

Overlap of [1] aab=b with [4] ababb=bb:

a ab ababb

Critical pair: abb=babb.

Flip LHS and RHS.

Referenced by [6].

[6] bbb=bb

Overlap of [5] babb=abb with [5] babb=abb:

bab b babb

Critical pair: bababb=abbabb.

Reduce LHS:

[4]b(ababb)
bbb

Reduce RHS:

[5]ab(babb)
[4](ababb)
bb

Referenced by [8], [9].

[7] babab=abab

Overlap of [3] babaa=ab with [1] aab=b:

baba a aab

Critical pair: babab=abab.

Referenced by [9].

[8] bbab=bab

Overlap of [6] bbb=bb with [3] babaa=ab:

bb b babaa

Critical pair: bbab=bbabaa.

Reduce RHS:

[3]b(babaa)
bab

Referenced by [9], [10].

[9] bb=b

Overlap of [8] bbab=bab with [2] ababaa=b:

bb ab ababaa

Critical pair: bbb=bababaa.

Reduce LHS:

[6](bbb)
bb

Reduce RHS:

[7](babab)aa
[2](ababaa)
b

Defines rule #1.

Referenced by [11].

[10] bab=ab

Overlap of [8] bbab=bab with [3] babaa=ab:

b bab babaa

Critical pair: bab=babaa.

Reduce RHS:

[3](babaa)
ab

Defines rule #4.

Referenced by [11].

[11] abaa=ab

Overlap of [9] bb=b with [3] babaa=ab:

b b babaa

Critical pair: bab=babaa.

Reduce LHS:

[10](bab)
ab

Reduce RHS:

[10](bab)aa
abaa

Flip LHS and RHS.

Referenced by [12].

[12] baa=b

Overlap of [1] aab=b with [11] abaa=ab:

a ab abaa

Critical pair: aab=baa.

Reduce LHS:

[1](aab)
b

Flip LHS and RHS.

Defines rule #3.