52.29/14.31 MAYBE 52.29/14.31 52.29/14.32 Problem: 52.29/14.32 lt(x, 0()) -> false() 52.29/14.32 lt(0(), s(y)) -> true() 52.29/14.32 lt(s(x), s(y)) -> lt(x, y) 52.29/14.32 cons(x, cons(y, ys)) -> cons(y, cons(x, ys)) <= lt(x, y) = true() 52.29/14.32 52.29/14.32 Proof: 52.29/14.32 ConCon could not decide confluence of the system. 52.29/14.32 \cite{ALS94}, Theorem 4.1 does not apply. 52.29/14.32 ConCon could not decide whether all 1 critical pairs are joinable or not. 52.29/14.32 CP: cons(x, cons(y, cons(y', z'))) = cons(y', cons(x, cons(y, z'))) <= lt(x, y') = true(), lt(y', y) = true(): 52.29/14.32 ConCon could not decide infeasibility of this critical pair. 52.29/14.32 ConCon could not decide if this system is quasi-decreasing. 52.29/14.32 \cite{O02}, p. 214, Proposition 7.2.50 does not apply. 52.29/14.32 System R transformed to optimized U(R). 52.29/14.32 The external tool could not decide termination of the system. 52.29/14.32 Call external tool: 52.29/14.32 ./ttt2.sh 52.29/14.32 Input: 52.29/14.32 lt(x, 0()) -> false() 52.29/14.32 lt(0(), s(y)) -> true() 52.29/14.32 lt(s(x), s(y)) -> lt(x, y) 52.29/14.32 ?1(true(), x, y, ys) -> cons(y, cons(x, ys)) 52.29/14.32 cons(x, cons(y, ys)) -> ?1(lt(x, y), x, y, ys) 52.29/14.32 52.29/14.32 52.29/14.33 EOF