Certificate for #13064 ⟨a, b | baa=abb, aaaa=a

Completion settings:

[1] abb=baa

Axiom: baa=abb.

Flip LHS and RHS.

Defines rule #1.

Referenced by [3], [5], [6], [8], [9], [11].

[2] aaaa=a

Axiom: aaaa=a.

Defines rule #2.

Referenced by [3], [4], [5], [6], [7], [9], [10], [11].

[3] aaabaa=baa

Overlap of [2] aaaa=a with [1] abb=baa:

aaa a abb

Critical pair: aaabaa=abb.

Reduce RHS:

[1](abb)
baa

Referenced by [4], [5].

[4] aaaba=ba

Overlap of [3] aaabaa=baa with [2] aaaa=a:

aaab aa aaaa

Critical pair: aaaba=baaaa.

Reduce RHS:

[2]b(aaaa)
ba

Referenced by [5].

[5] aaba=bbaa

Overlap of [3] aaabaa=baa with [3] aaabaa=baa:

aaab aa aaabaa

Critical pair: aaabbaa=baaabaa.

Reduce LHS:

[1]aa(abb)aa
[2]aab(aaaa)
aaba

Reduce RHS:

[4]b(aaaba)a
bbaa

Defines rule #3.

Referenced by [6], [8], [11].

[6] bbabaa=aba

Overlap of [5] aaba=bbaa with [1] abb=baa:

aab a abb

Critical pair: aabbaa=bbaabb.

Reduce LHS:

[1]a(abb)aa
[2]ab(aaaa)
aba

Reduce RHS:

[1]bba(abb)
bbabaa

Flip LHS and RHS.

Referenced by [7].

[7] bbaba=abaaa

Overlap of [6] bbabaa=aba with [2] aaaa=a:

bbab aa aaaa

Critical pair: bbaba=abaaa.

Defines rule #4.

Referenced by [8].

[8] bbbbbaa=ababaaa

Overlap of [1] abb=baa with [7] bbaba=abaaa:

ab b bbaba

Critical pair: ababaaa=baababa.

Reduce RHS:

[5]b(aaba)ba
[5]bbb(aaba)
bbbbbaa

Flip LHS and RHS.

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

[9] abababaaa=bababa

Overlap of [1] abb=baa with [8] bbbbbaa=ababaaa:

ab b bbbbbaa

Critical pair: abababaaa=baabbbbaa.

Reduce RHS:

[1]ba(abb)bbaa
[1]baba(abb)aa
[2]babab(aaaa)
bababa

Referenced by [11].

[10] bbbbba=ababaa

Overlap of [8] bbbbbaa=ababaaa with [2] aaaa=a:

bbbbb aa aaaa

Critical pair: bbbbba=ababaaaaa.

Reduce RHS:

[2]abab(aaaa)a
ababaa

Defines rule #5.

Referenced by [11].

[11] abababa=bababaa

Overlap of [8] bbbbbaa=ababaaa with [5] aaba=bbaa:

bbbbba a aaba

Critical pair: bbbbbabbaa=ababaaaaba.

Reduce LHS:

[10](bbbbba)bbaa
[1]ababa(abb)aa
[9](abababaaa)a
bababaa

Reduce RHS:

[2]abab(aaaa)ba
abababa

Flip LHS and RHS.

Defines rule #6.