Certificate for #13179 ⟨a, b | abb=aaa, baa=ab

Completion settings:

[1] abb=aaa

Axiom: abb=aaa.

Referenced by [3].

[2] ab=baa

Axiom: baa=ab.

Flip LHS and RHS.

Defines rule #2.

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

[3] bbaaaa=aaa

Overlap of [1] abb=aaa with [2] ab=baa:

abb ab

Critical pair: baab=aaa.

Reduce LHS:

[2]ba(ab)
[2]b(ab)aa
bbaaaa

Referenced by [4], [5], [6], [7], [10].

[4] aaaaaaa=aaaa

Overlap of [2] ab=baa with [3] bbaaaa=aaa:

a b bbaaaa

Critical pair: aaaa=baabaaaa.

Reduce RHS:

[2]ba(ab)aaaa
[2]b(ab)aaaaaa
[3](bbaaaa)aaaa
aaaaaaa

Flip LHS and RHS.

Referenced by [5], [6].

[5] baaaaaa=baaaa

Overlap of [3] bbaaaa=aaa with [2] ab=baa:

bbaaa a ab

Critical pair: bbaaabaa=aaab.

Reduce LHS:

[2]bbaa(ab)aa
[2]bba(ab)aaaa
[2]bb(ab)aaaaaa
[3]b(bbaaaa)aaaa
[4]b(aaaaaaa)
baaaa

Reduce RHS:

[2]aa(ab)
[2]a(ab)aa
[2](ab)aaaa
baaaaaa

Flip LHS and RHS.

Referenced by [8].

[6] aaaaaa=aaa

Overlap of [3] bbaaaa=aaa with [4] aaaaaaa=aaaa:

bb aaaa aaaaaaa

Critical pair: bbaaaa=aaaaaa.

Reduce LHS:

[3](bbaaaa)
aaa

Flip LHS and RHS.

Referenced by [7], [8], [9].

[7] bbaaa=aaaaa

Overlap of [3] bbaaaa=aaa with [6] aaaaaa=aaa:

bb aaaa aaaaaa

Critical pair: bbaaa=aaaaa.

Referenced by [9], [10], [11].

[8] baaaa=baaa

Simplify [5] baaaaaa=baaaa.

Reduce LHS:

[6]b(aaaaaa)
baaa

Flip LHS and RHS.

Referenced by [9].

[9] aaaaa=aaa

Overlap of [7] bbaaa=aaaaa with [8] baaaa=baaa:

b baaa baaaa

Critical pair: bbaaa=aaaaaa.

Reduce LHS:

[7](bbaaa)
aaaaa

Reduce RHS:

[6](aaaaaa)
aaa

Referenced by [10].

[10] aaaa=aaa

Overlap of [3] bbaaaa=aaa with [9] aaaaa=aaa:

bb aaaa aaaaa

Critical pair: bbaaa=aaaa.

Reduce LHS:

[7](bbaaa)
[9](aaaaa)
aaa

Flip LHS and RHS.

Defines rule #1.

Referenced by [11].

[11] bbaaa=aaa

Simplify [7] bbaaa=aaaaa.

Reduce RHS:

[10](aaaa)a
[10](aaaa)
aaa

Defines rule #3.