Certificate for #12615 ⟨a, b | baab=aa, babb=b

Completion settings:

[1] baab=aa

Axiom: baab=aa.

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

[2] babb=b

Axiom: babb=b.

Defines rule #5.

Referenced by [3], [4].

[3] aaabb=aa

Overlap of [1] baab=aa with [2] babb=b:

baa b babb

Critical pair: baab=aaabb.

Reduce LHS:

[1](baab)
aa

Flip LHS and RHS.

Referenced by [5], [8], [10], [11].

[4] babaa=aa

Overlap of [2] babb=b with [1] baab=aa:

bab b baab

Critical pair: babaa=baab.

Reduce RHS:

[1](baab)
aa

Referenced by [6], [9].

[5] aaabaa=aaaab

Overlap of [3] aaabb=aa with [1] baab=aa:

aaab b baab

Critical pair: aaabaa=aaaab.

Referenced by [8].

[6] baaa=aab

Overlap of [4] babaa=aa with [1] baab=aa:

ba baa baab

Critical pair: baaa=aab.

Referenced by [7], [8], [9], [10], [11], [13].

[7] aabab=aaaaa

Overlap of [1] baab=aa with [6] baaa=aab:

baa b baaa

Critical pair: baaaab=aaaaa.

Reduce LHS:

[6](baaa)ab
aabab

Referenced by [11].

[8] aaaaa=aaa

Overlap of [3] aaabb=aa with [6] baaa=aab:

aaab b baaa

Critical pair: aaabaab=aaaaa.

Reduce LHS:

[5](aaabaa)b
[3]a(aaabb)
aaa

Flip LHS and RHS.

Referenced by [11].

[9] aabb=aaa

Overlap of [4] babaa=aa with [6] baaa=aab:

ba baa baaa

Critical pair: baaab=aaa.

Reduce LHS:

[6](baaa)b
aabb

Referenced by [10], [12], [14].

[10] aaab=baa

Overlap of [6] baaa=aab with [3] aaabb=aa:

b aaa aaabb

Critical pair: baa=aabbb.

Reduce RHS:

[9](aabb)b
aaab

Flip LHS and RHS.

Referenced by [11].

[11] baa=aab

Overlap of [6] baaa=aab with [3] aaabb=aa:

ba aa aaabb

Critical pair: baaa=aababb.

Reduce LHS:

[6](baaa)
aab

Reduce RHS:

[7](aabab)b
[8](aaaaa)b
[10](aaab)
baa

Flip LHS and RHS.

Defines rule #2.

Referenced by [12], [13].

[12] aaa=aa

Overlap of [1] baab=aa with [11] baa=aab:

baab baa

Critical pair: aabb=aa.

Reduce LHS:

[9](aabb)
aaa

Defines rule #1.

Referenced by [14].

[13] aaba=aab

Overlap of [6] baaa=aab with [11] baa=aab:

baaa baa

Critical pair: aaba=aab.

Defines rule #3.

[14] aabb=aa

Simplify [9] aabb=aaa.

Reduce RHS:

[12](aaa)
aa

Defines rule #4.