Consider the TRS R consisting of the rewrite rules 1: p(m,n,s(r)) -> p(m,r,n) 2: p(m,s(n),0) -> p(0,n,m) 3: p(m,0,0) -> m There are 2 dependency pairs: 4: P(m,n,s(r)) -> P(m,r,n) 5: P(m,s(n),0) -> P(0,n,m) The approximated dependency graph contains one SCC: {4,5}. - Consider the SCC {4,5}. There are no usable rules. By taking the polynomial interpretation [0] = 1, [s](x) = x + 1 and [P](x,y,z) = x + y + z + 1, the rules in {4,5} are strictly decreasing. Hence the TRS is terminating.