MAYBE 0.19/0.20 MAYBE 0.19/0.20 0.19/0.20 Problem: 0.19/0.20 active(and(true(),X)) -> mark(X) 0.19/0.20 active(and(false(),Y)) -> mark(false()) 0.19/0.20 active(if(true(),X,Y)) -> mark(X) 0.19/0.20 active(if(false(),X,Y)) -> mark(Y) 0.19/0.20 active(add(0(),X)) -> mark(X) 0.19/0.20 active(add(s(X),Y)) -> mark(s(add(X,Y))) 0.19/0.20 active(first(0(),X)) -> mark(nil()) 0.19/0.20 active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z))) 0.19/0.20 active(from(X)) -> mark(cons(X,from(s(X)))) 0.19/0.20 active(and(X1,X2)) -> and(active(X1),X2) 0.19/0.20 active(if(X1,X2,X3)) -> if(active(X1),X2,X3) 0.19/0.20 active(add(X1,X2)) -> add(active(X1),X2) 0.19/0.20 active(first(X1,X2)) -> first(active(X1),X2) 0.19/0.20 active(first(X1,X2)) -> first(X1,active(X2)) 0.19/0.20 and(mark(X1),X2) -> mark(and(X1,X2)) 0.19/0.20 if(mark(X1),X2,X3) -> mark(if(X1,X2,X3)) 0.19/0.20 add(mark(X1),X2) -> mark(add(X1,X2)) 0.19/0.20 first(mark(X1),X2) -> mark(first(X1,X2)) 0.19/0.20 first(X1,mark(X2)) -> mark(first(X1,X2)) 0.19/0.20 proper(and(X1,X2)) -> and(proper(X1),proper(X2)) 0.19/0.20 proper(true()) -> ok(true()) 0.19/0.20 proper(false()) -> ok(false()) 0.19/0.20 proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3)) 0.19/0.20 proper(add(X1,X2)) -> add(proper(X1),proper(X2)) 0.19/0.20 proper(0()) -> ok(0()) 0.19/0.20 proper(s(X)) -> s(proper(X)) 0.19/0.20 proper(first(X1,X2)) -> first(proper(X1),proper(X2)) 0.19/0.20 proper(nil()) -> ok(nil()) 0.19/0.20 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) 0.19/0.20 proper(from(X)) -> from(proper(X)) 0.19/0.20 and(ok(X1),ok(X2)) -> ok(and(X1,X2)) 0.19/0.20 if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3)) 0.19/0.20 add(ok(X1),ok(X2)) -> ok(add(X1,X2)) 0.19/0.20 s(ok(X)) -> ok(s(X)) 0.19/0.20 first(ok(X1),ok(X2)) -> ok(first(X1,X2)) 0.19/0.20 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) 0.19/0.20 from(ok(X)) -> ok(from(X)) 0.19/0.20 top(mark(X)) -> top(proper(X)) 0.19/0.20 top(ok(X)) -> top(active(X)) 0.19/0.20 0.19/0.20 Proof: 0.19/0.20 Open 0.19/0.20 EOF