Certificate for #13004 ⟨a, b | abb=aab, abaa=b

Completion settings:

[1] aab=abb

Axiom: abb=aab.

Flip LHS and RHS.

Referenced by [4], [5], [6], [13].

[2] abaa=b

Axiom: abaa=b.

Referenced by [3], [4], [5], [6], [7], [12].

[3] abab=bbaa

Overlap of [2] abaa=b with [2] abaa=b:

aba a abaa

Critical pair: abab=bbaa.

Referenced by [5], [11].

[4] abbaa=ab

Overlap of [1] aab=abb with [2] abaa=b:

a ab abaa

Critical pair: ab=abbaa.

Flip LHS and RHS.

Referenced by [10].

[5] bbabb=bb

Overlap of [2] abaa=b with [1] aab=abb:

ab aa aab

Critical pair: ababb=bb.

Reduce LHS:

[3](abab)b
[1]bb(aab)
bbabb

Referenced by [8].

[6] bab=bbb

Overlap of [2] abaa=b with [1] aab=abb:

aba a aab

Critical pair: abaabb=bab.

Reduce LHS:

[2](abaa)bb
bbb

Flip LHS and RHS.

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

[7] bbbaa=bb

Overlap of [6] bab=bbb with [2] abaa=b:

b ab abaa

Critical pair: bb=bbbaa.

Flip LHS and RHS.

Referenced by [9], [12], [14].

[8] bbbbb=bb

Simplify [5] bbabb=bb.

Reduce LHS:

[6]b(bab)b
bbbbb

Referenced by [9].

[9] bbaa=bbbb

Overlap of [8] bbbbb=bb with [7] bbbaa=bb:

bb bbb bbbaa

Critical pair: bbbb=bbaa.

Flip LHS and RHS.

Referenced by [10], [11].

[10] abbbb=ab

Simplify [4] abbaa=ab.

Reduce LHS:

[9]a(bbaa)
abbbb

Referenced by [11], [12], [15].

[11] abbb=bbbb

Overlap of [10] abbbb=ab with [6] bab=bbb:

abbb b bab

Critical pair: abbbbbb=abab.

Reduce LHS:

[10](abbbb)bb
abbb

Reduce RHS:

[3](abab)
[9](bbaa)
bbbb

Referenced by [12], [13].

[12] bbbb=b

Overlap of [10] abbbb=ab with [7] bbbaa=bb:

ab bbb bbbaa

Critical pair: abbb=abaa.

Reduce LHS:

[11](abbb)
bbbb

Reduce RHS:

[2](abaa)
b

Defines rule #3.

Referenced by [13], [14], [15].

[13] abb=bbb

Overlap of [1] aab=abb with [12] bbbb=b:

aa b bbbb

Critical pair: aab=abbbbb.

Reduce LHS:

[1](aab)
abb

Reduce RHS:

[11](abbb)bb
[12](bbbb)bb
bbb

Referenced by [15].

[14] baa=bbb

Overlap of [12] bbbb=b with [7] bbbaa=bb:

b bbb bbbaa

Critical pair: bbb=baa.

Flip LHS and RHS.

Defines rule #2.

[15] ab=bb

Overlap of [10] abbbb=ab with [13] abb=bbb:

abbbb abb

Critical pair: bbbbb=ab.

Reduce LHS:

[12](bbbb)b
bb

Flip LHS and RHS.

Defines rule #1.