58.18/16.84 MAYBE 58.18/16.84 58.18/16.84 Problem: 58.18/16.84 App(App(App(S(), a), b), c) -> App(App(a, c), App(b, c)) <= a = I(), b = I(), c = I() 58.18/16.84 App(App(K(), a), b) -> a <= a = I(), b = I() 58.18/16.84 App(I(), a) -> a <= a = I() 58.18/16.84 58.18/16.84 Proof: 58.18/16.85 ConCon could not decide confluence of the system. 58.18/16.85 \cite{ALS94}, Theorem 4.1 does not apply. 58.18/16.85 ConCon could not decide if this system is quasi-decreasing. 58.18/16.85 \cite{O02}, p. 214, Proposition 7.2.50 does not apply. 58.18/16.85 System R transformed to U(R). 58.18/16.85 The external tool could not decide termination of the system. 58.18/16.85 Call external tool: 58.18/16.85 ./ttt2.sh 58.18/16.85 Input: 58.18/16.85 ?3(I(), a, b, c) -> App(App(a, c), App(b, c)) 58.18/16.85 ?2(I(), a, b, c) -> ?3(c, a, b, c) 58.18/16.85 ?1(I(), a, b, c) -> ?2(b, a, b, c) 58.18/16.85 App(App(App(S(), a), b), c) -> ?1(a, a, b, c) 58.18/16.85 ?5(I(), a, b) -> a 58.18/16.85 ?4(I(), a, b) -> ?5(b, a, b) 58.18/16.85 App(App(K(), a), b) -> ?4(a, a, b) 58.18/16.85 ?6(I(), a) -> a 58.18/16.85 App(I(), a) -> ?6(a, a) 58.18/16.85 58.18/16.85 58.18/16.85 EOF