Certificate for #1963 ⟨a, b | aba=b, aaabb=1⟩

Completion settings:

• Reduction order:
  • Left-to-right recursive path with deg(a) = 0; deg(b) = 1

Axiom: aba=b.

Referenced by [3], [5], [6], [7], [10], [12], [13].

Axiom: aaabb=1.

Referenced by [4].

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

Critical pair: abb=bba.

Referenced by [4], [6], [7], [8], [9], [10], [11].

Simplify [2] aaabb=1.

Reduce LHS:

Referenced by [5], [6], [10], [15].

Overlap of [4] bbaaa=1 with [1] aba=b:

Critical pair: bbaab=ba.

Referenced by [8].

Overlap of [3] abb=bba with [4] bbaaa=1:

Critical pair: ab=bbabaaa.

Reduce RHS:

Flip LHS and RHS.

Referenced by [7], [8].

Overlap of [3] abb=bba with [6] bbbaa=ab:

Critical pair: aab=bbabaa.

Reduce RHS:

Flip LHS and RHS.

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

Overlap of [6] bbbaa=ab with [3] abb=bba:

Critical pair: bbbabba=abbb.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Referenced by [9], [11].

Overlap of [3] abb=bba with [7] bbba=aab:

Critical pair: aaab=bbaba.

Reduce RHS:

Referenced by [14].

Overlap of [7] bbba=aab with [1] aba=b:

Critical pair: bbbb=aabba.

Reduce RHS:

Referenced by [11], [14].

Overlap of [3] abb=bba with [10] bbbb=1:

Critical pair: a=bbabb.

Reduce RHS:

Flip LHS and RHS.

Referenced by [12].

Overlap of [1] aba=b with [11] baab=a:

Critical pair: aa=bab.

Flip LHS and RHS.

Referenced by [13], [14].

Overlap of [1] aba=b with [12] bab=aa:

Critical pair: aaa=bb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [14], [15].

Overlap of [10] bbbb=1 with [12] bab=aa:

Critical pair: bbbaa=ab.

Reduce LHS:

Flip LHS and RHS.

Defines rule #2.

Overlap of [4] bbaaa=1 with [13] bb=aaa:

Critical pair: aaaaaa=1.

Defines rule #1.