Exercise 1.20

Read Exercise 1.20 ~ Solution

Normal order

(gcd 206 40)
01: zero? 40 
(gcd 40 (remainder 206 40))
02: zero? (remainder 206 40)                                                  
(gcd (remainder 206 40) (remainder 40 (remainder 206 40)))
03: zero? (remainder 40 (remainder 206 40))                                   
04: zero? (remainder 40 6)
zero? 4                                                                   
(gcd (remainder 40 (remainder 206 40)) (remainder (remainder 206 40) (remainder 40 (remainder 206 40))))
05: zero? (remainder (remainder 206 40) (remainder 40 (remainder 206 40)))    
06: zero? (remainder 6 (remainder 40 (remainder 206 40)))                     
07: zero? (remainder 6 (remainder 40 6))                                      
08: zero? (remainder 6 4)                                                     
zero? 2
(gcd (remainder (remainder 206 40) (remainder 40 (remainder 206 40))) (remainder (remainder 40 (remainder 206 40)) (remainder (remainder 206 40) (remainder 40 (remainder 206 40)))))
09: zero? (remainder (remainder 40 (remainder 206 40)) (remainder (remainder 206 40) (remainder 40 (remainder 206 40))))
10: zero? (remainder (remainder 40 6) (remainder (remainder 206 40) (remainder 40 (remainder 206 40))))  
11: zero? (remainder 4 (remainder (remainder 206 40) (remainder 40 (remainder 206 40))))                 
12: zero? (remainder 4 (remainder (remainder 206 40) (remainder 40 6)))                                  
13: zero? (remainder 4 (remainder (remainder 206 40) 4))                                                 
14: zero? (remainder 4 (remainder 6 4))                                                                  
15: zero? (remainder 4 2)                                                                                
zero? 2                                                                                              
(gcd (remainder (remainder 40 (remainder 206 40)) (remainder (remainder 206 40) (remainder 40 (remainder 206 40)))) 
     (remainder (remainder (remainder 206 40) (remainder 40 (remainder 206 40))) (remainder (remainder 40 (remainder 206 40)) (remainder (remainder 206 40) (remainder 40 (remainder 206 40))))))
16: zero? (remainder (remainder (remainder 206 40) (remainder 40 (remainder 206 40))) (remainder (remainder 40 (remainder 206 40)) (remainder (remainder 206 40) (remainder 40 (remainder 206 40))))))
17: zero? (remainder (remainder 6 (remainder 40 (remainder 206 40))) (remainder (remainder 40 (remainder 206 40)) (remainder (remainder 206 40) (remainder 40 (remainder 206 40))))))
18: zero? (remainder (remainder 6 (remainder 40 6)) (remainder (remainder 40 (remainder 206 40)) (remainder (remainder 206 40) (remainder 40 (remainder 206 40))))))
19: zero? (remainder (remainder 6 4) (remainder (remainder 40 (remainder 206 40)) (remainder (remainder 206 40) (remainder 40 (remainder 206 40))))))
20: zero? (remainder 2 (remainder (remainder 40 (remainder 206 40)) (remainder (remainder 206 40) (remainder 40 (remainder 206 40))))))
21: zero? (remainder 2 (remainder (remainder 40 6) (remainder (remainder 206 40) (remainder 40 (remainder 206 40))))))
22: zero? (remainder 2 (remainder 4 (remainder (remainder 206 40) (remainder 40 (remainder 206 40))))))
23: zero? (remainder 2 (remainder 4 (remainder 6 (remainder 40 (remainder 206 40)))))
24: zero? (remainder 2 (remainder 4 (remainder 6 (remainder 40 6))))
25: zero? (remainder 2 (remainder 4 (remainder 6 4)))
26: zero? (remainder 2 (remainder 4 2))
27: zero? (remainder 2 2)
zero? 0
-> (remainder (remainder 40 (remainder 206 40)) (remainder (remainder 206 40) (remainder 40 (remainder 206 40))))
28: -> (remainder (remainder 40 6) (remainder (remainder 206 40) (remainder 40 (remainder 206 40))))
29: -> (remainder 4 (remainder (remainder 206 40) (remainder 40 (remainder 206 40))))
30: -> (remainder 4 (remainder 6 (remainder 40 (remainder 206 40))))
31: -> (remainder 4 (remainder 6 (remainder 40 6)))
32: -> (remainder 4 (remainder 6 4))
32: -> (remainder 4 2)
33: -> (remainder 4 2)
-> 2

Applicative order

(gcd 206 40)
zero? 40
(gcd (40 (remainder 206 40)))
rc 01:: (gcd 40 6)
zero? 6
(gcd 6 (remainder 40 6))
rc 02:: (gcd 6 4)
(gcd 6 4)
zero? 4
(gcd 4 (remainder 6 4))
rc 03:: (gcd 4 2)
zero? 2
(gcd 2 (remainder 4 2))
rc 04:: (gcd 2 2)
zero? 2
(gcd (2 (remainder 2 2)))
rc 05:: (gcd (2 0))
zero? 0
-> 2

As centfunjiii pointed out these calculations are wrong and added an extra step.
Corrected version:

(gcd 206 40)
zero? 40
(gcd (40 (remainder 206 40)))
rc 01:: (gcd 40 6)
zero? 6
(gcd 6 (remainder 40 6))
rc 02:: (gcd 6 4)
(gcd 6 4)
zero? 4
(gcd 4 (remainder 6 4))
rc 03:: (gcd 4 2)
zero? 2
(gcd 2 (remainder 4 2))
rc 04:: (gcd 2 0)
zero? 0
-> 2