Certificate for #5141 ⟨a, b | aabaaba=baaa⟩

Completion settings:

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

Axiom: aabaaba=baaa.

Referenced by [4].

Axiom: aabaab=c.

Referenced by [5], [6].

Axiom: baa=d.

Defines rule #8.

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

Simplify [1] aabaaba=baaa.

Reduce RHS:

Referenced by [5].

Overlap of [4] aabaaba=da with [2] aabaab=c:

Critical pair: ca=da.

Flip LHS and RHS.

Defines rule #1.

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

Overlap of [2] aabaab=c with [3] baa=d:

Critical pair: aadb=c.

Defines rule #6.

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

Overlap of [3] baa=d with [6] aadb=c:

Critical pair: bc=ddb.

Defines rule #7.

Overlap of [3] baa=d with [6] aadb=c:

Critical pair: bac=dadb.

Reduce RHS:

Defines rule #9.

Overlap of [5] da=ca with [6] aadb=c:

Critical pair: dc=caadb.

Reduce RHS:

Defines rule #2.

Referenced by [11], [12].

Overlap of [6] aadb=c with [3] baa=d:

Critical pair: aadd=caa.

Defines rule #3.

Referenced by [11], [12].

Overlap of [10] aadd=caa with [5] da=ca:

Critical pair: aadca=caaa.

Reduce LHS:

Defines rule #4.

Overlap of [10] aadd=caa with [9] dc=cc:

Critical pair: aadcc=caac.

Reduce LHS:

Defines rule #5.