Certificate for #24172 ⟨a, b | aa=a, babbbab=a

Completion settings:

[1] aa=a

Axiom: aa=a.

Defines rule #1.

Referenced by [4], [5], [7], [8], [9], [10], [11].

[2] babbbab=a

Axiom: babbbab=a.

Referenced by [3], [4], [6], [8], [9], [10].

[3] babba=abbab

Overlap of [2] babbbab=a with [2] babbbab=a:

babb bab babbbab

Critical pair: babba=abbab.

Referenced by [5], [6], [7], [9].

[4] babbba=abbbab

Overlap of [2] babbbab=a with [2] babbbab=a:

babbba b babbbab

Critical pair: babbbaa=aabbbab.

Reduce LHS:

[1]babbb(aa)
babbba

Reduce RHS:

[1](aa)bbbab
abbbab

Referenced by [7], [9].

[5] abbaba=abbab

Overlap of [3] babba=abbab with [1] aa=a:

babb a aa

Critical pair: babba=abbaba.

Reduce LHS:

[3](babba)
abbab

Flip LHS and RHS.

Referenced by [8].

[6] abbabbbbab=baba

Overlap of [3] babba=abbab with [2] babbbab=a:

bab ba babbbab

Critical pair: baba=abbabbbbab.

Flip LHS and RHS.

Referenced by [8].

[7] abbbabb=abbabbb

Overlap of [3] babba=abbab with [3] babba=abbab:

bab ba babba

Critical pair: bababbab=abbabbba.

Reduce LHS:

[3]ba(babba)b
[1]b(aa)bbabb
[3](babba)bb
abbabbb

Reduce RHS:

[4]ab(babbba)
[4]a(babbba)b
[1](aa)bbbabb
abbbabb

Flip LHS and RHS.

Referenced by [9].

[8] baba=abba

Overlap of [5] abbaba=abbab with [2] babbbab=a:

abba ba babbbab

Critical pair: abbaa=abbabbbbab.

Reduce LHS:

[1]abb(aa)
abba

Reduce RHS:

[6](abbabbbbab)
baba

Flip LHS and RHS.

Referenced by [9], [10].

[9] abbabbb=a

Overlap of [2] babbbab=a with [8] baba=abba:

babb bab baba

Critical pair: babbabba=aa.

Reduce LHS:

[3](babba)bba
[4]ab(babbba)
[4]a(babbba)b
[1](aa)bbbabb
[7](abbbabb)
abbabbb

Reduce RHS:

[1](aa)
a

Referenced by [10], [11].

[10] ba=ab

Overlap of [8] baba=abba with [2] babbbab=a:

ba ba babbbab

Critical pair: baa=abbabbbab.

Reduce LHS:

[1]b(aa)
ba

Reduce RHS:

[9](abbabbb)ab
[1](aa)b
ab

Defines rule #2.

Referenced by [11].

[11] abbbbb=a

Simplify [9] abbabbb=a.

Reduce LHS:

[10]ab(ba)bbb
[10]a(ba)bbbb
[1](aa)bbbbb
abbbbb

Defines rule #3.