MAYBE 0.16/0.24 MAYBE 0.16/0.24 0.16/0.24 Problem: 0.16/0.24 active(pairNs()) -> mark(cons(0(),incr(oddNs()))) 0.16/0.24 active(oddNs()) -> mark(incr(pairNs())) 0.16/0.24 active(incr(cons(X,XS))) -> mark(cons(s(X),incr(XS))) 0.16/0.24 active(take(0(),XS)) -> mark(nil()) 0.16/0.24 active(take(s(N),cons(X,XS))) -> mark(cons(X,take(N,XS))) 0.16/0.24 active(zip(nil(),XS)) -> mark(nil()) 0.16/0.24 active(zip(X,nil())) -> mark(nil()) 0.16/0.24 active(zip(cons(X,XS),cons(Y,YS))) -> mark(cons(pair(X,Y),zip(XS,YS))) 0.16/0.24 active(tail(cons(X,XS))) -> mark(XS) 0.16/0.24 active(repItems(nil())) -> mark(nil()) 0.16/0.24 active(repItems(cons(X,XS))) -> mark(cons(X,cons(X,repItems(XS)))) 0.16/0.24 active(cons(X1,X2)) -> cons(active(X1),X2) 0.16/0.24 active(incr(X)) -> incr(active(X)) 0.16/0.24 active(s(X)) -> s(active(X)) 0.16/0.24 active(take(X1,X2)) -> take(active(X1),X2) 0.16/0.24 active(take(X1,X2)) -> take(X1,active(X2)) 0.16/0.24 active(zip(X1,X2)) -> zip(active(X1),X2) 0.16/0.24 active(zip(X1,X2)) -> zip(X1,active(X2)) 0.16/0.24 active(pair(X1,X2)) -> pair(active(X1),X2) 0.16/0.24 active(pair(X1,X2)) -> pair(X1,active(X2)) 0.16/0.24 active(tail(X)) -> tail(active(X)) 0.16/0.24 active(repItems(X)) -> repItems(active(X)) 0.16/0.24 cons(mark(X1),X2) -> mark(cons(X1,X2)) 0.16/0.24 incr(mark(X)) -> mark(incr(X)) 0.16/0.24 s(mark(X)) -> mark(s(X)) 0.16/0.24 take(mark(X1),X2) -> mark(take(X1,X2)) 0.16/0.24 take(X1,mark(X2)) -> mark(take(X1,X2)) 0.16/0.24 zip(mark(X1),X2) -> mark(zip(X1,X2)) 0.16/0.24 zip(X1,mark(X2)) -> mark(zip(X1,X2)) 0.16/0.24 pair(mark(X1),X2) -> mark(pair(X1,X2)) 0.16/0.24 pair(X1,mark(X2)) -> mark(pair(X1,X2)) 0.16/0.24 tail(mark(X)) -> mark(tail(X)) 0.16/0.24 repItems(mark(X)) -> mark(repItems(X)) 0.16/0.24 proper(pairNs()) -> ok(pairNs()) 0.16/0.24 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2)) 0.16/0.24 proper(0()) -> ok(0()) 0.16/0.24 proper(incr(X)) -> incr(proper(X)) 0.16/0.24 proper(oddNs()) -> ok(oddNs()) 0.16/0.24 proper(s(X)) -> s(proper(X)) 0.16/0.24 proper(take(X1,X2)) -> take(proper(X1),proper(X2)) 0.16/0.24 proper(nil()) -> ok(nil()) 0.16/0.24 proper(zip(X1,X2)) -> zip(proper(X1),proper(X2)) 0.16/0.24 proper(pair(X1,X2)) -> pair(proper(X1),proper(X2)) 0.16/0.24 proper(tail(X)) -> tail(proper(X)) 0.16/0.24 proper(repItems(X)) -> repItems(proper(X)) 0.16/0.24 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2)) 0.16/0.24 incr(ok(X)) -> ok(incr(X)) 0.16/0.24 s(ok(X)) -> ok(s(X)) 0.16/0.24 take(ok(X1),ok(X2)) -> ok(take(X1,X2)) 0.16/0.24 zip(ok(X1),ok(X2)) -> ok(zip(X1,X2)) 0.16/0.24 pair(ok(X1),ok(X2)) -> ok(pair(X1,X2)) 0.16/0.24 tail(ok(X)) -> ok(tail(X)) 0.16/0.24 repItems(ok(X)) -> ok(repItems(X)) 0.16/0.24 top(mark(X)) -> top(proper(X)) 0.16/0.24 top(ok(X)) -> top(active(X)) 0.16/0.24 0.16/0.24 Proof: 0.16/0.24 Open 0.16/0.24 EOF