Morphocompletion for #1 ⟨a, b, c, d | dcbadab=aa, ac=1, ca=1, bd=1, db=1⟩

Solved by morph:3/0,2/0,3/0. (See Morphocompletion.)

Step 1

Checking up to 20 rules for overlaps.

• Reduction order:
  • Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1; deg(d) = 2

Rewriting system is not complete: roundsLimit

Collecting factors up to length 4, frequency 1:

Considering [length 3 / frequency 0] dcb=e.

Step 2

Checking up to 20 rules for overlaps.

• Reduction order:
  • Left-to-right recursive path with deg(e) = deg(a) = deg(c) = 0, e < a < c; deg(b) = 1; deg(d) = 2
• Auxiliary generators:
  1. dcb=e

Rewriting system is not complete: roundsLimit

Collecting factors up to length 3, frequency 1:

Considering [length 2 / frequency 0] ce=f.

Step 3

Checking up to 20 rules for overlaps.

• Reduction order:
  • Left-to-right recursive path with deg(e) = deg(f) = deg(a) = deg(c) = 0, e < f < a < c; deg(b) = 1; deg(d) = 2
• Auxiliary generators:
  1. dcb=e
  2. ce=f

Rewriting system is not complete: roundsLimit

Collecting factors up to length 4, frequency 1:

Considering [length 3 / frequency 0] dab=g.

Step 4

• Reduction order:
  • Left-to-right recursive path with deg(e) = deg(f) = deg(a) = deg(c) = 0, e < f < a < c; deg(g) = 1; deg(b) = 2; deg(d) = 3
• Auxiliary generators:
  1. dcb=e
  2. ce=f
  3. dab=g

Rewriting system is complete. See ⟨a, b, c, d | dcbadab=aa, ac=1, ca=1, bd=1, db=1⟩.