YES(?,O(n^1))
0.17/0.39	YES(?,O(n^1))
0.91/0.40	
0.91/0.40	Problem:
0.91/0.40	 active(and(tt(),X)) -> mark(X)
0.91/0.40	 active(plus(N,0())) -> mark(N)
0.91/0.40	 active(plus(N,s(M))) -> mark(s(plus(N,M)))
0.91/0.40	 active(and(X1,X2)) -> and(active(X1),X2)
0.91/0.40	 active(plus(X1,X2)) -> plus(active(X1),X2)
0.91/0.40	 active(plus(X1,X2)) -> plus(X1,active(X2))
0.91/0.40	 active(s(X)) -> s(active(X))
0.91/0.40	 and(mark(X1),X2) -> mark(and(X1,X2))
0.91/0.40	 plus(mark(X1),X2) -> mark(plus(X1,X2))
0.91/0.40	 plus(X1,mark(X2)) -> mark(plus(X1,X2))
0.91/0.40	 s(mark(X)) -> mark(s(X))
0.91/0.40	 proper(and(X1,X2)) -> and(proper(X1),proper(X2))
0.91/0.40	 proper(tt()) -> ok(tt())
0.91/0.40	 proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
0.91/0.40	 proper(0()) -> ok(0())
0.91/0.40	 proper(s(X)) -> s(proper(X))
0.91/0.40	 and(ok(X1),ok(X2)) -> ok(and(X1,X2))
0.91/0.40	 plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
0.91/0.40	 s(ok(X)) -> ok(s(X))
0.91/0.40	 top(mark(X)) -> top(proper(X))
0.91/0.40	 top(ok(X)) -> top(active(X))
0.91/0.40	
0.91/0.40	Proof:
0.91/0.40	 Bounds Processor:
0.91/0.40	  bound: 2
0.91/0.40	  enrichment: match
0.91/0.40	  automaton:
0.91/0.40	   final states: {10,9,8,7,6,5}
0.91/0.40	   transitions:
0.91/0.40	    top1(20) -> 10*
0.91/0.40	    active1(2) -> 20*
0.91/0.40	    active1(4) -> 20*
0.91/0.40	    active1(1) -> 20*
0.91/0.40	    active1(3) -> 20*
0.91/0.40	    proper1(2) -> 20*
0.91/0.40	    proper1(4) -> 20*
0.91/0.40	    proper1(1) -> 20*
0.91/0.40	    proper1(3) -> 20*
0.91/0.40	    ok1(15) -> 15,8
0.91/0.40	    ok1(17) -> 20,9
0.91/0.40	    ok1(11) -> 11,6
0.91/0.40	    ok1(13) -> 13,7
0.91/0.40	    s1(2) -> 15*
0.91/0.40	    s1(4) -> 15*
0.91/0.40	    s1(1) -> 15*
0.91/0.40	    s1(3) -> 15*
0.91/0.40	    plus1(3,1) -> 13*
0.91/0.40	    plus1(3,3) -> 13*
0.91/0.40	    plus1(4,2) -> 13*
0.91/0.40	    plus1(4,4) -> 13*
0.91/0.40	    plus1(1,2) -> 13*
0.91/0.40	    plus1(1,4) -> 13*
0.91/0.40	    plus1(2,1) -> 13*
0.91/0.40	    plus1(2,3) -> 13*
0.91/0.40	    plus1(3,2) -> 13*
0.91/0.40	    plus1(3,4) -> 13*
0.91/0.40	    plus1(4,1) -> 13*
0.91/0.40	    plus1(4,3) -> 13*
0.91/0.40	    plus1(1,1) -> 13*
0.91/0.40	    plus1(1,3) -> 13*
0.91/0.40	    plus1(2,2) -> 13*
0.91/0.40	    plus1(2,4) -> 13*
0.91/0.40	    and1(3,1) -> 11*
0.91/0.40	    and1(3,3) -> 11*
0.91/0.40	    and1(4,2) -> 11*
0.91/0.40	    and1(4,4) -> 11*
0.91/0.40	    and1(1,2) -> 11*
0.91/0.40	    and1(1,4) -> 11*
0.91/0.40	    and1(2,1) -> 11*
0.91/0.40	    and1(2,3) -> 11*
0.91/0.40	    and1(3,2) -> 11*
0.91/0.40	    and1(3,4) -> 11*
0.91/0.40	    and1(4,1) -> 11*
0.91/0.40	    and1(4,3) -> 11*
0.91/0.40	    and1(1,1) -> 11*
0.91/0.40	    and1(1,3) -> 11*
0.91/0.40	    and1(2,2) -> 11*
0.91/0.40	    and1(2,4) -> 11*
0.91/0.40	    01() -> 17*
0.91/0.40	    tt1() -> 17*
0.91/0.40	    mark1(15) -> 15,8
0.91/0.40	    mark1(11) -> 11,6
0.91/0.40	    mark1(13) -> 13,7
0.91/0.40	    top2(21) -> 10*
0.91/0.40	    active0(2) -> 5*
0.91/0.40	    active0(4) -> 5*
0.91/0.40	    active0(1) -> 5*
0.91/0.40	    active0(3) -> 5*
0.91/0.40	    active2(17) -> 21*
0.91/0.40	    and0(3,1) -> 6*
0.91/0.40	    and0(3,3) -> 6*
0.91/0.40	    and0(4,2) -> 6*
0.91/0.40	    and0(4,4) -> 6*
0.91/0.40	    and0(1,2) -> 6*
0.91/0.40	    and0(1,4) -> 6*
0.91/0.40	    and0(2,1) -> 6*
0.91/0.40	    and0(2,3) -> 6*
0.91/0.40	    and0(3,2) -> 6*
0.91/0.40	    and0(3,4) -> 6*
0.91/0.40	    and0(4,1) -> 6*
0.91/0.40	    and0(4,3) -> 6*
0.91/0.40	    and0(1,1) -> 6*
0.91/0.40	    and0(1,3) -> 6*
0.91/0.40	    and0(2,2) -> 6*
0.91/0.40	    and0(2,4) -> 6*
0.91/0.40	    tt0() -> 1*
0.91/0.40	    mark0(2) -> 2*
0.91/0.40	    mark0(4) -> 2*
0.91/0.40	    mark0(1) -> 2*
0.91/0.40	    mark0(3) -> 2*
0.91/0.40	    plus0(3,1) -> 7*
0.91/0.40	    plus0(3,3) -> 7*
0.91/0.40	    plus0(4,2) -> 7*
0.91/0.40	    plus0(4,4) -> 7*
0.91/0.40	    plus0(1,2) -> 7*
0.91/0.40	    plus0(1,4) -> 7*
0.91/0.40	    plus0(2,1) -> 7*
0.91/0.40	    plus0(2,3) -> 7*
0.91/0.40	    plus0(3,2) -> 7*
0.91/0.40	    plus0(3,4) -> 7*
0.91/0.40	    plus0(4,1) -> 7*
0.91/0.40	    plus0(4,3) -> 7*
0.91/0.40	    plus0(1,1) -> 7*
0.91/0.40	    plus0(1,3) -> 7*
0.91/0.40	    plus0(2,2) -> 7*
0.91/0.40	    plus0(2,4) -> 7*
0.91/0.40	    00() -> 3*
0.91/0.40	    s0(2) -> 8*
0.91/0.40	    s0(4) -> 8*
0.91/0.40	    s0(1) -> 8*
0.91/0.40	    s0(3) -> 8*
0.91/0.40	    proper0(2) -> 9*
0.91/0.40	    proper0(4) -> 9*
0.91/0.40	    proper0(1) -> 9*
0.91/0.40	    proper0(3) -> 9*
0.91/0.40	    ok0(2) -> 4*
0.91/0.40	    ok0(4) -> 4*
0.91/0.40	    ok0(1) -> 4*
0.91/0.40	    ok0(3) -> 4*
0.91/0.40	    top0(2) -> 10*
0.91/0.40	    top0(4) -> 10*
0.91/0.40	    top0(1) -> 10*
0.91/0.40	    top0(3) -> 10*
0.91/0.40	  problem:
0.91/0.40	   
0.91/0.40	  Qed
0.91/0.40	EOF