Certificate for #394 ⟨a, b | abaaaab=b

Completion settings:

[1] abaaaab=b

Axiom: abaaaab=b.

Referenced by [2], [3], [4], [5], [6].

[2] baaaab=abaaab

Overlap of [1] abaaaab=b with [1] abaaaab=b:

abaaa ab abaaaab

Critical pair: abaaab=baaaab.

Flip LHS and RHS.

Referenced by [3], [6], [7].

[3] baaab=abaab

Overlap of [2] baaaab=abaaab with [1] abaaaab=b:

baaa ab abaaaab

Critical pair: baaab=abaaabaaaab.

Reduce RHS:

[1]abaa(abaaaab)
abaab

Referenced by [4], [6], [7], [8].

[4] baab=abab

Overlap of [3] baaab=abaab with [1] abaaaab=b:

baa ab abaaaab

Critical pair: baab=abaabaaaab.

Reduce RHS:

[1]aba(abaaaab)
abab

Referenced by [5], [6], [7], [8], [9].

[5] bab=abb

Overlap of [4] baab=abab with [1] abaaaab=b:

ba ab abaaaab

Critical pair: bab=ababaaaab.

Reduce RHS:

[1]ab(abaaaab)
abb

Defines rule #1.

Referenced by [6], [7], [8], [9].

[6] aaaaabb=b

Overlap of [1] abaaaab=b with [2] baaaab=abaaab:

a baaaab baaaab

Critical pair: aabaaab=b.

Reduce LHS:

[3]aa(baaab)
[4]aaa(baab)
[5]aaaa(bab)
aaaaabb

Defines rule #5.

[7] baaaab=aaaabb

Simplify [2] baaaab=abaaab.

Reduce RHS:

[3]a(baaab)
[4]aa(baab)
[5]aaa(bab)
aaaabb

Defines rule #4.

[8] baaab=aaabb

Simplify [3] baaab=abaab.

Reduce RHS:

[4]a(baab)
[5]aa(bab)
aaabb

Defines rule #3.

[9] baab=aabb

Simplify [4] baab=abab.

Reduce RHS:

[5]a(bab)
aabb

Defines rule #2.