MAYBE 0.18/0.20 MAYBE 0.18/0.20 0.18/0.20 Problem: 0.18/0.20 active(minus(0(),Y)) -> mark(0()) 0.18/0.20 active(minus(s(X),s(Y))) -> mark(minus(X,Y)) 0.18/0.20 active(geq(X,0())) -> mark(true()) 0.18/0.20 active(geq(0(),s(Y))) -> mark(false()) 0.18/0.20 active(geq(s(X),s(Y))) -> mark(geq(X,Y)) 0.18/0.20 active(div(0(),s(Y))) -> mark(0()) 0.18/0.20 active(div(s(X),s(Y))) -> mark(if(geq(X,Y),s(div(minus(X,Y),s(Y))),0())) 0.18/0.20 active(if(true(),X,Y)) -> mark(X) 0.18/0.20 active(if(false(),X,Y)) -> mark(Y) 0.18/0.20 active(s(X)) -> s(active(X)) 0.18/0.20 active(div(X1,X2)) -> div(active(X1),X2) 0.18/0.20 active(if(X1,X2,X3)) -> if(active(X1),X2,X3) 0.18/0.20 s(mark(X)) -> mark(s(X)) 0.18/0.20 div(mark(X1),X2) -> mark(div(X1,X2)) 0.18/0.20 if(mark(X1),X2,X3) -> mark(if(X1,X2,X3)) 0.18/0.20 proper(minus(X1,X2)) -> minus(proper(X1),proper(X2)) 0.18/0.20 proper(0()) -> ok(0()) 0.18/0.20 proper(s(X)) -> s(proper(X)) 0.18/0.20 proper(geq(X1,X2)) -> geq(proper(X1),proper(X2)) 0.18/0.20 proper(true()) -> ok(true()) 0.18/0.20 proper(false()) -> ok(false()) 0.18/0.20 proper(div(X1,X2)) -> div(proper(X1),proper(X2)) 0.18/0.20 proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3)) 0.18/0.20 minus(ok(X1),ok(X2)) -> ok(minus(X1,X2)) 0.18/0.20 s(ok(X)) -> ok(s(X)) 0.18/0.20 geq(ok(X1),ok(X2)) -> ok(geq(X1,X2)) 0.18/0.20 div(ok(X1),ok(X2)) -> ok(div(X1,X2)) 0.18/0.20 if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3)) 0.18/0.20 top(mark(X)) -> top(proper(X)) 0.18/0.20 top(ok(X)) -> top(active(X)) 0.18/0.20 0.18/0.20 Proof: 0.18/0.20 Open 0.18/0.21 EOF