Certificate for #18619 ⟨a, b | aba=b, aaaaabb=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], [8], [9], [10], [11], [12], [13], [15].

Axiom: aaaaabb=1.

Referenced by [4].

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

Critical pair: abb=bba.

Referenced by [4], [5], [6], [7], [8], [9], [10].

Simplify [2] aaaaabb=1.

Reduce LHS:

Referenced by [5], [10], [14].

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

Critical pair: ab=bbabaaaaa.

Reduce RHS:

Flip LHS and RHS.

Referenced by [6].

Overlap of [3] abb=bba with [5] bbbaaaa=ab:

Critical pair: aab=bbabaaaa.

Reduce RHS:

Flip LHS and RHS.

Referenced by [7].

Overlap of [3] abb=bba with [6] bbbaaa=aab:

Critical pair: aaab=bbabaaa.

Reduce RHS:

Flip LHS and RHS.

Referenced by [8].

Overlap of [3] abb=bba with [7] bbbaa=aaab:

Critical pair: aaaab=bbabaa.

Reduce RHS:

Flip LHS and RHS.

Referenced by [9], [10].

Overlap of [3] abb=bba with [8] bbba=aaaab:

Critical pair: aaaaab=bbaba.

Reduce RHS:

Flip LHS and RHS.

Referenced by [10].

Overlap of [3] abb=bba with [8] bbba=aaaab:

Critical pair: abaaaab=bbabba.

Reduce LHS:

Reduce RHS:

Referenced by [11].

Overlap of [1] aba=b with [10] baaab=aa:

Critical pair: aaa=baab.

Flip LHS and RHS.

Referenced by [12].

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

Critical pair: aaaa=bab.

Flip LHS and RHS.

Referenced by [13].

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

Critical pair: aaaaa=bb.

Flip LHS and RHS.

Defines rule #3.

Referenced by [14].

Overlap of [4] bbaaaaa=1 with [13] bb=aaaaa:

Critical pair: aaaaaaaaaa=1.

Defines rule #1.

Referenced by [15].

Overlap of [1] aba=b with [14] aaaaaaaaaa=1:

Critical pair: ab=baaaaaaaaa.

Defines rule #2.