MAYBE
0.18/0.22	MAYBE
0.18/0.22	
0.18/0.22	Problem:
0.18/0.22	 active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
0.18/0.22	 active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
0.18/0.22	 active(U21(tt(),M,N)) -> mark(U22(tt(),M,N))
0.18/0.22	 active(U22(tt(),M,N)) -> mark(plus(x(N,M),N))
0.18/0.22	 active(plus(N,0())) -> mark(N)
0.18/0.22	 active(plus(N,s(M))) -> mark(U11(tt(),M,N))
0.18/0.22	 active(x(N,0())) -> mark(0())
0.18/0.22	 active(x(N,s(M))) -> mark(U21(tt(),M,N))
0.18/0.22	 active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
0.18/0.22	 active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
0.18/0.22	 active(s(X)) -> s(active(X))
0.18/0.22	 active(plus(X1,X2)) -> plus(active(X1),X2)
0.18/0.22	 active(plus(X1,X2)) -> plus(X1,active(X2))
0.18/0.22	 active(U21(X1,X2,X3)) -> U21(active(X1),X2,X3)
0.18/0.22	 active(U22(X1,X2,X3)) -> U22(active(X1),X2,X3)
0.18/0.22	 active(x(X1,X2)) -> x(active(X1),X2)
0.18/0.22	 active(x(X1,X2)) -> x(X1,active(X2))
0.18/0.22	 U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
0.18/0.22	 U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
0.18/0.22	 s(mark(X)) -> mark(s(X))
0.18/0.22	 plus(mark(X1),X2) -> mark(plus(X1,X2))
0.18/0.22	 plus(X1,mark(X2)) -> mark(plus(X1,X2))
0.18/0.22	 U21(mark(X1),X2,X3) -> mark(U21(X1,X2,X3))
0.18/0.22	 U22(mark(X1),X2,X3) -> mark(U22(X1,X2,X3))
0.18/0.22	 x(mark(X1),X2) -> mark(x(X1,X2))
0.18/0.22	 x(X1,mark(X2)) -> mark(x(X1,X2))
0.18/0.22	 proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
0.18/0.22	 proper(tt()) -> ok(tt())
0.18/0.22	 proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
0.18/0.22	 proper(s(X)) -> s(proper(X))
0.18/0.22	 proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
0.18/0.22	 proper(U21(X1,X2,X3)) -> U21(proper(X1),proper(X2),proper(X3))
0.18/0.22	 proper(U22(X1,X2,X3)) -> U22(proper(X1),proper(X2),proper(X3))
0.18/0.22	 proper(x(X1,X2)) -> x(proper(X1),proper(X2))
0.18/0.22	 proper(0()) -> ok(0())
0.18/0.22	 U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
0.18/0.22	 U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
0.18/0.22	 s(ok(X)) -> ok(s(X))
0.18/0.22	 plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
0.18/0.22	 U21(ok(X1),ok(X2),ok(X3)) -> ok(U21(X1,X2,X3))
0.18/0.22	 U22(ok(X1),ok(X2),ok(X3)) -> ok(U22(X1,X2,X3))
0.18/0.22	 x(ok(X1),ok(X2)) -> ok(x(X1,X2))
0.18/0.22	 top(mark(X)) -> top(proper(X))
0.18/0.22	 top(ok(X)) -> top(active(X))
0.18/0.22	
0.18/0.22	Proof:
0.18/0.22	 Open
0.18/0.22	EOF