Termination Proof Script

• Consider the SCC {13,17,19-22}. The usable rules are {1-3,6-12}. By taking the AF π with π(activate) = π(ACTIVATE) = π(from) = π(n__from) = π(n__s) = π(s) = 1 and π(cons) = π(FIRST) = 2 together with the lexicographic path order with precedence 0 ≻ nil and n__first ≈ first, the rules in {1,3,6-13,17,19} are weakly decreasing and the rules in {2,20-22} are strictly decreasing. There is one new SCC.
  • Consider the SCC {17,19}. There are no usable rules. By taking the AF π with π(ACTIVATE) = π(n__from) = 1 together with the lexicographic path order with empty precedence, rule 17 is weakly decreasing and rule 19 is strictly decreasing. There is one new SCC.
    • Consider the SCC {17}. By taking the AF π with π(ACTIVATE) = 1 together with the lexicographic path order with empty precedence, rule 17 is strictly decreasing.


• Consider the SCC {14}. The usable rules are {1-3,6-12}. By taking the AF π with π(activate) = π(first) = π(n__first) = π(SEL) = 1, π(cons) = 2 and π(from) = π(n__from) = [ ] together with the lexicographic path order with precedence 0 ≻ nil, n__from ≈ from and n__s ≈ s, the rules in {1,6-12} are weakly decreasing and the rules in {2,3,14} are strictly decreasing.