53.25/14.43 MAYBE 53.25/14.43 53.25/14.43 Problem: 53.25/14.43 lt(x, 0()) -> false() 53.25/14.43 lt(0(), s(y)) -> true() 53.25/14.43 lt(s(x), s(y)) -> lt(x, y) 53.25/14.43 cons(x, cons(y, ys)) -> cons(y, cons(x, ys)) <= lt(x, y) = true() 53.25/14.43 53.25/14.43 Proof: 53.25/14.43 ConCon could not decide confluence of the system. 53.25/14.43 \cite{ALS94}, Theorem 4.1 does not apply. 53.25/14.43 ConCon could not decide whether all 1 critical pairs are joinable or not. 53.25/14.43 CP: cons(x, cons(y, cons(y', z'))) = cons(y', cons(x, cons(y, z'))) <= lt(x, y') = true(), lt(y', y) = true(): 53.25/14.43 ConCon could not decide infeasibility of this critical pair. 53.25/14.43 ConCon could not decide if this system is quasi-decreasing. 53.25/14.43 \cite{O02}, p. 214, Proposition 7.2.50 does not apply. 53.25/14.43 System R transformed to optimized U(R). 53.25/14.43 The external tool could not decide termination of the system. 53.25/14.43 Call external tool: 53.25/14.43 ./ttt2.sh 53.25/14.43 Input: 53.25/14.43 lt(x, 0()) -> false() 53.25/14.43 lt(0(), s(y)) -> true() 53.25/14.43 lt(s(x), s(y)) -> lt(x, y) 53.25/14.43 ?1(true(), x, y, ys) -> cons(y, cons(x, ys)) 53.25/14.43 cons(x, cons(y, ys)) -> ?1(lt(x, y), x, y, ys) 53.25/14.43 53.25/14.43 53.25/14.45 EOF