Certificate for #3936 ⟨a, b | aaaabbaba=ab⟩

Completion settings:

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

Axiom: aaaabbaba=ab.

Referenced by [3].

Axiom: ab=c.

Defines rule #1.

Referenced by [3], [4], [5], [8].

Simplify [1] aaaabbaba=ab.

Reduce RHS:

Referenced by [4].

Overlap of [3] aaaabbaba=c with [2] ab=c:

Critical pair: aaacbaba=c.

Reduce LHS:

Defines rule #2.

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

Overlap of [4] aaacbca=c with [2] ab=c:

Critical pair: aaacbcc=cb.

Defines rule #4.

Referenced by [6], [11].

Overlap of [4] aaacbca=c with [4] aaacbca=c:

Critical pair: aaacbcc=caacbca.

Reduce LHS:

Flip LHS and RHS.

Defines rule #3.

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

Overlap of [4] aaacbca=c with [6] caacbca=cb:

Critical pair: aaacbcb=cacbca.

Defines rule #6.

Referenced by [12].

Overlap of [6] caacbca=cb with [2] ab=c:

Critical pair: caacbcc=cbb.

Flip LHS and RHS.

Defines rule #5.

Overlap of [6] caacbca=cb with [4] aaacbca=c:

Critical pair: caacbcc=cbaacbca.

Flip LHS and RHS.

Defines rule #8.

Overlap of [6] caacbca=cb with [6] caacbca=cb:

Critical pair: caacbcb=cbacbca.

Flip LHS and RHS.

Defines rule #7.

Overlap of [6] caacbca=cb with [5] aaacbcc=cb:

Critical pair: caacbccb=cbaacbcc.

Flip LHS and RHS.

Defines rule #9.

Overlap of [6] caacbca=cb with [7] aaacbcb=cacbca:

Critical pair: caacbccacbca=cbaacbcb.

Flip LHS and RHS.

Defines rule #10.