TORPAcyc is applied to the string rewriting system
a a  -> b c 
b b  -> c d 
c c  -> d d d 
d d d  -> a c 
interpretation of a: 9
interpretation of b: 8
interpretation of c: 9
interpretation of d: 6
remove rule 2
continue with:
a a  -> b c 
c c  -> d d d 
d d d  -> a c 
interpretation of a: 4
interpretation of b: 0
interpretation of c: 5
interpretation of d: 3
remove rule 2
continue with:
a a  -> b c 
d d d  -> a c 
interpretation of a: 3
interpretation of b: 0
interpretation of c: 0
interpretation of d: 2
remove rule 2
continue with:
a a  -> b c 
interpretation of a: 2
interpretation of b: 0
interpretation of c: 0
interpretation of d: 10
remove rule 1
termination has been proved