Certificate for #1748 ⟨a, b | abaaaaaab=b⟩

Completion settings:

[1] abaaaaaab=b

Axiom: abaaaaaab=b.

Referenced by [2], [3], [4], [5], [6], [7], [8].

[2] baaaaaab=abaaaaab

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

abaaaaa ab abaaaaaab

Critical pair: abaaaaab=baaaaaab.

Flip LHS and RHS.

Referenced by [3], [8], [9].

[3] baaaaab=abaaaab

Overlap of [2] baaaaaab=abaaaaab with [1] abaaaaaab=b:

baaaaa ab abaaaaaab

Critical pair: baaaaab=abaaaaabaaaaaab.

Reduce RHS:

[1]abaaaa(abaaaaaab)
⇒ abaaaab

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

[4] baaaab=abaaab

Overlap of [3] baaaaab=abaaaab with [1] abaaaaaab=b:

baaaa ab abaaaaaab

Critical pair: baaaab=abaaaabaaaaaab.

Reduce RHS:

[1]abaaa(abaaaaaab)
⇒ abaaab

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

[5] baaab=abaab

Overlap of [4] baaaab=abaaab with [1] abaaaaaab=b:

baaa ab abaaaaaab

Critical pair: baaab=abaaabaaaaaab.

Reduce RHS:

[1]abaa(abaaaaaab)
⇒ abaab

Referenced by [6], [8], [9], [10], [11], [12].

[6] baab=abab

Overlap of [5] baaab=abaab with [1] abaaaaaab=b:

baa ab abaaaaaab

Critical pair: baab=abaabaaaaaab.

Reduce RHS:

[1]aba(abaaaaaab)
⇒ abab

Referenced by [7], [8], [9], [10], [11], [12], [13].

[7] bab=abb

Overlap of [6] baab=abab with [1] abaaaaaab=b:

ba ab abaaaaaab

Critical pair: bab=ababaaaaaab.

Reduce RHS:

[1]ab(abaaaaaab)
⇒ abb

Defines rule #1.

Referenced by [8], [9], [10], [11], [12], [13].

[8] aaaaaaabb=b

Overlap of [1] abaaaaaab=b with [2] baaaaaab=abaaaaab:

a baaaaaab baaaaaab

Critical pair: aabaaaaab=b.

Reduce LHS:

[3]aa(baaaaab)
[4]⇒ aaa(baaaab)
[5]⇒ aaaa(baaab)
[6]⇒ aaaaa(baab)
[7]⇒ aaaaaa(bab)
⇒ aaaaaaabb

Defines rule #7.

[9] baaaaaab=aaaaaabb

Simplify [2] baaaaaab=abaaaaab.

Reduce RHS:

[3]a(baaaaab)
[4]⇒ aa(baaaab)
[5]⇒ aaa(baaab)
[6]⇒ aaaa(baab)
[7]⇒ aaaaa(bab)
⇒ aaaaaabb

Defines rule #6.

[10] baaaaab=aaaaabb

Simplify [3] baaaaab=abaaaab.

Reduce RHS:

[4]a(baaaab)
[5]⇒ aa(baaab)
[6]⇒ aaa(baab)
[7]⇒ aaaa(bab)
⇒ aaaaabb

Defines rule #5.

[11] baaaab=aaaabb

Simplify [4] baaaab=abaaab.

Reduce RHS:

[5]a(baaab)
[6]⇒ aa(baab)
[7]⇒ aaa(bab)
⇒ aaaabb

Defines rule #4.

[12] baaab=aaabb

Simplify [5] baaab=abaab.

Reduce RHS:

[6]a(baab)
[7]⇒ aa(bab)
⇒ aaabb

Defines rule #3.

[13] baab=aabb

Simplify [6] baab=abab.

Reduce RHS:

[7]a(bab)
⇒ aabb

Defines rule #2.