Certificate for #1955 ⟨a, b | aabaabba=ab⟩

Completion settings:

• Auxiliary generators:
  1. c = abb
• Reduction order:
  • Left-to-right recursive path with deg(c) = 0; deg(a) = deg(b) = 1, a < b

Axiom: aabaabba=ab.

Referenced by [3].

Axiom: abb=c.

Defines rule #1.

Referenced by [3], [4], [5], [7], [10].

Overlap of [1] aabaabba=ab with [2] abb=c:

Critical pair: aabaca=ab.

Defines rule #7.

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

Overlap of [3] aabaca=ab with [2] abb=c:

Critical pair: aabacc=abbb.

Reduce RHS:

Defines rule #3.

Referenced by [6], [7], [8], [12].

Overlap of [3] aabaca=ab with [3] aabaca=ab:

Critical pair: aabacab=ababaca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #13.

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

Overlap of [3] aabaca=ab with [4] aabacc=cb:

Critical pair: aabaccb=ababacc.

Reduce LHS:

Flip LHS and RHS.

Defines rule #9.

Referenced by [8], [9], [16].

Overlap of [3] aabaca=ab with [5] ababaca=c:

Critical pair: aabacc=abbabaca.

Reduce LHS:

Reduce RHS:

Flip LHS and RHS.

Defines rule #4.

Referenced by [10], [11], [12], [13], [14], [15].

Overlap of [5] ababaca=c with [4] aabacc=cb:

Critical pair: ababaccb=cabacc.

Reduce LHS:

Defines rule #2.

Referenced by [16].

Overlap of [5] ababaca=c with [5] ababaca=c:

Critical pair: ababacc=cbabaca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #10.

Referenced by [17].

Overlap of [3] aabaca=ab with [7] cabaca=cb:

Critical pair: aabacb=abbaca.

Reduce RHS:

Defines rule #8.

Referenced by [15], [17].

Overlap of [5] ababaca=c with [7] cabaca=cb:

Critical pair: ababacb=cbaca.

Defines rule #14.

Overlap of [7] cabaca=cb with [4] aabacc=cb:

Critical pair: cabaccb=cbabacc.

Flip LHS and RHS.

Defines rule #5.

Referenced by [17].

Overlap of [7] cabaca=cb with [5] ababaca=c:

Critical pair: cabacc=cbbabaca.

Flip LHS and RHS.

Defines rule #15.

Overlap of [7] cabaca=cb with [7] cabaca=cb:

Critical pair: cabacb=cbbaca.

Flip LHS and RHS.

Defines rule #6.

Overlap of [7] cabaca=cb with [10] aabacb=caca:

Critical pair: cabaccaca=cbabacb.

Flip LHS and RHS.

Defines rule #11.

Overlap of [6] ababacc=cbb with [8] cbbb=cabacc:

Critical pair: ababaccabacc=cbbbbb.

Reduce LHS:

Reduce RHS:

Defines rule #12.

Overlap of [9] cbabaca=cbb with [10] aabacb=caca:

Critical pair: cbabaccaca=cbbabacb.

Reduce LHS:

Flip LHS and RHS.

Defines rule #16.