YES(?,O(n^1))
0.18/0.92	YES(?,O(n^1))
0.18/0.93	
0.18/0.93	Problem:
0.18/0.93	 active(U11(tt(),M,N)) -> mark(U12(tt(),M,N))
0.18/0.93	 active(U12(tt(),M,N)) -> mark(s(plus(N,M)))
0.18/0.93	 active(plus(N,0())) -> mark(N)
0.18/0.93	 active(plus(N,s(M))) -> mark(U11(tt(),M,N))
0.18/0.93	 active(U11(X1,X2,X3)) -> U11(active(X1),X2,X3)
0.18/0.93	 active(U12(X1,X2,X3)) -> U12(active(X1),X2,X3)
0.18/0.93	 active(s(X)) -> s(active(X))
0.18/0.93	 active(plus(X1,X2)) -> plus(active(X1),X2)
0.18/0.93	 active(plus(X1,X2)) -> plus(X1,active(X2))
0.18/0.93	 U11(mark(X1),X2,X3) -> mark(U11(X1,X2,X3))
0.18/0.93	 U12(mark(X1),X2,X3) -> mark(U12(X1,X2,X3))
0.18/0.93	 s(mark(X)) -> mark(s(X))
0.18/0.93	 plus(mark(X1),X2) -> mark(plus(X1,X2))
0.18/0.93	 plus(X1,mark(X2)) -> mark(plus(X1,X2))
0.18/0.93	 proper(U11(X1,X2,X3)) -> U11(proper(X1),proper(X2),proper(X3))
0.18/0.93	 proper(tt()) -> ok(tt())
0.18/0.93	 proper(U12(X1,X2,X3)) -> U12(proper(X1),proper(X2),proper(X3))
0.18/0.93	 proper(s(X)) -> s(proper(X))
0.18/0.93	 proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
0.18/0.93	 proper(0()) -> ok(0())
0.18/0.93	 U11(ok(X1),ok(X2),ok(X3)) -> ok(U11(X1,X2,X3))
0.18/0.93	 U12(ok(X1),ok(X2),ok(X3)) -> ok(U12(X1,X2,X3))
0.18/0.93	 s(ok(X)) -> ok(s(X))
0.18/0.93	 plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
0.18/0.93	 top(mark(X)) -> top(proper(X))
0.18/0.93	 top(ok(X)) -> top(active(X))
0.18/0.93	
0.18/0.93	Proof:
0.18/0.93	 Bounds Processor:
0.18/0.93	  bound: 2
0.18/0.93	  enrichment: match
0.18/0.93	  automaton:
0.18/0.93	   final states: {11,10,9,8,7,6,5}
0.18/0.93	   transitions:
0.18/0.93	    top1(23) -> 11*
0.18/0.93	    active1(2) -> 23*
0.18/0.93	    active1(4) -> 23*
0.18/0.93	    active1(1) -> 23*
0.18/0.93	    active1(3) -> 23*
0.18/0.93	    proper1(2) -> 23*
0.18/0.93	    proper1(4) -> 23*
0.18/0.93	    proper1(1) -> 23*
0.18/0.93	    proper1(3) -> 23*
0.18/0.93	    ok1(15) -> 15,7
0.18/0.93	    ok1(17) -> 17,8
0.18/0.93	    ok1(19) -> 19,9
0.18/0.93	    ok1(21) -> 23,10
0.18/0.93	    ok1(13) -> 13,6
0.18/0.93	    plus1(3,1) -> 19*
0.18/0.93	    plus1(3,3) -> 19*
0.18/0.93	    plus1(4,2) -> 19*
0.18/0.93	    plus1(4,4) -> 19*
0.18/0.93	    plus1(1,2) -> 19*
0.18/0.93	    plus1(1,4) -> 19*
0.18/0.93	    plus1(2,1) -> 19*
0.18/0.93	    plus1(2,3) -> 19*
0.18/0.93	    plus1(3,2) -> 19*
0.18/0.93	    plus1(3,4) -> 19*
0.18/0.93	    plus1(4,1) -> 19*
0.18/0.93	    plus1(4,3) -> 19*
0.18/0.93	    plus1(1,1) -> 19*
0.18/0.93	    plus1(1,3) -> 19*
0.18/0.93	    plus1(2,2) -> 19*
0.18/0.93	    plus1(2,4) -> 19*
0.18/0.93	    s1(2) -> 17*
0.18/0.93	    s1(4) -> 17*
0.18/0.93	    s1(1) -> 17*
0.18/0.93	    s1(3) -> 17*
0.18/0.93	    U121(3,2,2) -> 15*
0.18/0.93	    U121(3,4,2) -> 15*
0.18/0.93	    U121(1,1,4) -> 15*
0.18/0.93	    U121(1,3,4) -> 15*
0.18/0.93	    U121(4,1,2) -> 15*
0.18/0.93	    U121(1,1,1) -> 15*
0.18/0.93	    U121(4,3,2) -> 15*
0.18/0.93	    U121(1,3,1) -> 15*
0.18/0.93	    U121(2,2,4) -> 15*
0.18/0.93	    U121(2,4,4) -> 15*
0.18/0.93	    U121(1,2,3) -> 15*
0.18/0.93	    U121(1,4,3) -> 15*
0.18/0.93	    U121(2,2,1) -> 15*
0.18/0.93	    U121(2,4,1) -> 15*
0.18/0.93	    U121(3,1,4) -> 15*
0.18/0.93	    U121(3,3,4) -> 15*
0.18/0.93	    U121(2,1,3) -> 15*
0.18/0.93	    U121(2,3,3) -> 15*
0.18/0.93	    U121(3,1,1) -> 15*
0.18/0.93	    U121(1,1,2) -> 15*
0.18/0.93	    U121(3,3,1) -> 15*
0.18/0.93	    U121(1,3,2) -> 15*
0.18/0.93	    U121(4,2,4) -> 15*
0.18/0.93	    U121(4,4,4) -> 15*
0.18/0.93	    U121(3,2,3) -> 15*
0.18/0.93	    U121(3,4,3) -> 15*
0.18/0.93	    U121(4,2,1) -> 15*
0.18/0.93	    U121(2,2,2) -> 15*
0.18/0.93	    U121(4,4,1) -> 15*
0.18/0.93	    U121(2,4,2) -> 15*
0.18/0.93	    U121(4,1,3) -> 15*
0.18/0.93	    U121(4,3,3) -> 15*
0.18/0.93	    U121(3,1,2) -> 15*
0.18/0.93	    U121(3,3,2) -> 15*
0.18/0.93	    U121(1,2,4) -> 15*
0.18/0.93	    U121(1,4,4) -> 15*
0.18/0.93	    U121(4,2,2) -> 15*
0.18/0.93	    U121(1,2,1) -> 15*
0.18/0.93	    U121(4,4,2) -> 15*
0.18/0.93	    U121(1,4,1) -> 15*
0.18/0.93	    U121(2,1,4) -> 15*
0.18/0.93	    U121(2,3,4) -> 15*
0.18/0.93	    U121(1,1,3) -> 15*
0.18/0.93	    U121(1,3,3) -> 15*
0.18/0.93	    U121(2,1,1) -> 15*
0.18/0.93	    U121(2,3,1) -> 15*
0.18/0.93	    U121(3,2,4) -> 15*
0.18/0.93	    U121(3,4,4) -> 15*
0.18/0.93	    U121(2,2,3) -> 15*
0.18/0.93	    U121(2,4,3) -> 15*
0.18/0.93	    U121(3,2,1) -> 15*
0.18/0.93	    U121(1,2,2) -> 15*
0.18/0.93	    U121(3,4,1) -> 15*
0.18/0.93	    U121(1,4,2) -> 15*
0.18/0.93	    U121(4,1,4) -> 15*
0.18/0.93	    U121(4,3,4) -> 15*
0.18/0.93	    U121(3,1,3) -> 15*
0.18/0.93	    U121(3,3,3) -> 15*
0.18/0.93	    U121(4,1,1) -> 15*
0.18/0.93	    U121(2,1,2) -> 15*
0.18/0.93	    U121(4,3,1) -> 15*
0.18/0.93	    U121(2,3,2) -> 15*
0.18/0.93	    U121(4,2,3) -> 15*
0.18/0.93	    U121(4,4,3) -> 15*
0.18/0.93	    U111(3,2,2) -> 13*
0.18/0.93	    U111(3,4,2) -> 13*
0.18/0.93	    U111(1,1,4) -> 13*
0.18/0.93	    U111(1,3,4) -> 13*
0.18/0.93	    U111(4,1,2) -> 13*
0.18/0.93	    U111(1,1,1) -> 13*
0.18/0.93	    U111(4,3,2) -> 13*
0.18/0.93	    U111(1,3,1) -> 13*
0.18/0.93	    U111(2,2,4) -> 13*
0.18/0.93	    U111(2,4,4) -> 13*
0.18/0.93	    U111(1,2,3) -> 13*
0.18/0.93	    U111(1,4,3) -> 13*
0.18/0.93	    U111(2,2,1) -> 13*
0.18/0.93	    U111(2,4,1) -> 13*
0.18/0.93	    U111(3,1,4) -> 13*
0.18/0.93	    U111(3,3,4) -> 13*
0.18/0.93	    U111(2,1,3) -> 13*
0.18/0.93	    U111(2,3,3) -> 13*
0.18/0.93	    U111(3,1,1) -> 13*
0.18/0.93	    U111(1,1,2) -> 13*
0.18/0.93	    U111(3,3,1) -> 13*
0.18/0.93	    U111(1,3,2) -> 13*
0.18/0.93	    U111(4,2,4) -> 13*
0.18/0.93	    U111(4,4,4) -> 13*
0.18/0.93	    U111(3,2,3) -> 13*
0.18/0.93	    U111(3,4,3) -> 13*
0.18/0.93	    U111(4,2,1) -> 13*
0.18/0.93	    U111(2,2,2) -> 13*
0.18/0.93	    U111(4,4,1) -> 13*
0.18/0.93	    U111(2,4,2) -> 13*
0.18/0.93	    U111(4,1,3) -> 13*
0.18/0.93	    U111(4,3,3) -> 13*
0.18/0.93	    U111(3,1,2) -> 13*
0.18/0.93	    U111(3,3,2) -> 13*
0.18/0.93	    U111(1,2,4) -> 13*
0.18/0.93	    U111(1,4,4) -> 13*
0.18/0.93	    U111(4,2,2) -> 13*
0.18/0.93	    U111(1,2,1) -> 13*
0.18/0.93	    U111(4,4,2) -> 13*
0.18/0.93	    U111(1,4,1) -> 13*
0.18/0.93	    U111(2,1,4) -> 13*
0.18/0.93	    U111(2,3,4) -> 13*
0.18/0.93	    U111(1,1,3) -> 13*
0.18/0.93	    U111(1,3,3) -> 13*
0.18/0.93	    U111(2,1,1) -> 13*
0.18/0.93	    U111(2,3,1) -> 13*
0.18/0.93	    U111(3,2,4) -> 13*
0.18/0.93	    U111(3,4,4) -> 13*
0.18/0.93	    U111(2,2,3) -> 13*
0.18/0.93	    U111(2,4,3) -> 13*
0.18/0.93	    U111(3,2,1) -> 13*
0.18/0.93	    U111(1,2,2) -> 13*
0.18/0.93	    U111(3,4,1) -> 13*
0.18/0.93	    U111(1,4,2) -> 13*
0.18/0.93	    U111(4,1,4) -> 13*
0.18/0.93	    U111(4,3,4) -> 13*
0.18/0.93	    U111(3,1,3) -> 13*
0.18/0.93	    U111(3,3,3) -> 13*
0.18/0.93	    U111(4,1,1) -> 13*
0.18/0.93	    U111(2,1,2) -> 13*
0.18/0.93	    U111(4,3,1) -> 13*
0.18/0.93	    U111(2,3,2) -> 13*
0.18/0.93	    U111(4,2,3) -> 13*
0.18/0.93	    U111(4,4,3) -> 13*
0.18/0.93	    01() -> 21*
0.18/0.93	    tt1() -> 21*
0.18/0.93	    mark1(15) -> 15,7
0.18/0.93	    mark1(17) -> 17,8
0.18/0.93	    mark1(19) -> 19,9
0.18/0.93	    mark1(13) -> 13,6
0.18/0.93	    top2(24) -> 11*
0.18/0.93	    active0(2) -> 5*
0.18/0.93	    active0(4) -> 5*
0.18/0.93	    active0(1) -> 5*
0.18/0.93	    active0(3) -> 5*
0.18/0.93	    active2(21) -> 24*
0.18/0.93	    U110(3,4,2) -> 6*
0.18/0.93	    U110(1,1,4) -> 6*
0.18/0.93	    U110(1,3,4) -> 6*
0.18/0.93	    U110(4,1,2) -> 6*
0.18/0.93	    U110(1,1,1) -> 6*
0.18/0.93	    U110(4,3,2) -> 6*
0.18/0.93	    U110(1,3,1) -> 6*
0.18/0.93	    U110(2,2,4) -> 6*
0.18/0.93	    U110(2,4,4) -> 6*
0.18/0.93	    U110(1,2,3) -> 6*
0.18/0.93	    U110(1,4,3) -> 6*
0.18/0.93	    U110(2,2,1) -> 6*
0.18/0.93	    U110(2,4,1) -> 6*
0.18/0.93	    U110(3,1,4) -> 6*
0.18/0.93	    U110(3,3,4) -> 6*
0.18/0.93	    U110(2,1,3) -> 6*
0.18/0.93	    U110(2,3,3) -> 6*
0.18/0.93	    U110(3,1,1) -> 6*
0.18/0.93	    U110(1,1,2) -> 6*
0.18/0.93	    U110(3,3,1) -> 6*
0.18/0.93	    U110(1,3,2) -> 6*
0.18/0.93	    U110(4,2,4) -> 6*
0.18/0.93	    U110(4,4,4) -> 6*
0.18/0.93	    U110(3,2,3) -> 6*
0.18/0.93	    U110(3,4,3) -> 6*
0.18/0.93	    U110(4,2,1) -> 6*
0.18/0.93	    U110(2,2,2) -> 6*
0.18/0.93	    U110(4,4,1) -> 6*
0.18/0.93	    U110(2,4,2) -> 6*
0.18/0.93	    U110(4,1,3) -> 6*
0.18/0.93	    U110(4,3,3) -> 6*
0.18/0.93	    U110(3,1,2) -> 6*
0.18/0.93	    U110(3,3,2) -> 6*
0.18/0.93	    U110(1,2,4) -> 6*
0.18/0.93	    U110(1,4,4) -> 6*
0.18/0.93	    U110(4,2,2) -> 6*
0.18/0.93	    U110(1,2,1) -> 6*
0.18/0.93	    U110(4,4,2) -> 6*
0.18/0.93	    U110(1,4,1) -> 6*
0.18/0.93	    U110(2,1,4) -> 6*
0.18/0.93	    U110(2,3,4) -> 6*
0.18/0.93	    U110(1,1,3) -> 6*
0.18/0.93	    U110(1,3,3) -> 6*
0.18/0.93	    U110(2,1,1) -> 6*
0.18/0.93	    U110(2,3,1) -> 6*
0.18/0.93	    U110(3,2,4) -> 6*
0.18/0.93	    U110(3,4,4) -> 6*
0.18/0.93	    U110(2,2,3) -> 6*
0.18/0.94	    U110(2,4,3) -> 6*
0.18/0.94	    U110(3,2,1) -> 6*
0.18/0.94	    U110(1,2,2) -> 6*
0.18/0.94	    U110(3,4,1) -> 6*
0.18/0.94	    U110(1,4,2) -> 6*
0.18/0.94	    U110(4,1,4) -> 6*
0.18/0.94	    U110(4,3,4) -> 6*
0.18/0.94	    U110(3,1,3) -> 6*
0.18/0.94	    U110(3,3,3) -> 6*
0.18/0.94	    U110(4,1,1) -> 6*
0.18/0.94	    U110(2,1,2) -> 6*
0.18/0.94	    U110(4,3,1) -> 6*
0.18/0.94	    U110(2,3,2) -> 6*
0.18/0.94	    U110(4,2,3) -> 6*
0.18/0.94	    U110(4,4,3) -> 6*
0.18/0.94	    U110(3,2,2) -> 6*
0.18/0.94	    tt0() -> 1*
0.18/0.94	    mark0(2) -> 2*
0.18/0.94	    mark0(4) -> 2*
0.18/0.94	    mark0(1) -> 2*
0.18/0.94	    mark0(3) -> 2*
0.18/0.94	    U120(3,2,2) -> 7*
0.18/0.94	    U120(3,4,2) -> 7*
0.18/0.94	    U120(1,1,4) -> 7*
0.18/0.94	    U120(1,3,4) -> 7*
0.18/0.94	    U120(4,1,2) -> 7*
0.18/0.94	    U120(1,1,1) -> 7*
0.18/0.94	    U120(4,3,2) -> 7*
0.18/0.94	    U120(1,3,1) -> 7*
0.18/0.94	    U120(2,2,4) -> 7*
0.18/0.94	    U120(2,4,4) -> 7*
0.18/0.94	    U120(1,2,3) -> 7*
0.18/0.94	    U120(1,4,3) -> 7*
0.18/0.94	    U120(2,2,1) -> 7*
0.18/0.94	    U120(2,4,1) -> 7*
0.18/0.94	    U120(3,1,4) -> 7*
0.18/0.94	    U120(3,3,4) -> 7*
0.18/0.94	    U120(2,1,3) -> 7*
0.18/0.94	    U120(2,3,3) -> 7*
0.18/0.94	    U120(3,1,1) -> 7*
0.18/0.94	    U120(1,1,2) -> 7*
0.18/0.94	    U120(3,3,1) -> 7*
0.18/0.94	    U120(1,3,2) -> 7*
0.18/0.94	    U120(4,2,4) -> 7*
0.18/0.94	    U120(4,4,4) -> 7*
0.18/0.94	    U120(3,2,3) -> 7*
0.18/0.94	    U120(3,4,3) -> 7*
0.18/0.94	    U120(4,2,1) -> 7*
0.18/0.94	    U120(2,2,2) -> 7*
0.18/0.94	    U120(4,4,1) -> 7*
0.18/0.94	    U120(2,4,2) -> 7*
0.18/0.94	    U120(4,1,3) -> 7*
0.18/0.94	    U120(4,3,3) -> 7*
0.18/0.94	    U120(3,1,2) -> 7*
0.18/0.94	    U120(3,3,2) -> 7*
0.18/0.94	    U120(1,2,4) -> 7*
0.18/0.94	    U120(1,4,4) -> 7*
0.18/0.94	    U120(4,2,2) -> 7*
0.18/0.94	    U120(1,2,1) -> 7*
0.18/0.94	    U120(4,4,2) -> 7*
0.18/0.94	    U120(1,4,1) -> 7*
0.18/0.94	    U120(2,1,4) -> 7*
0.18/0.94	    U120(2,3,4) -> 7*
0.18/0.94	    U120(1,1,3) -> 7*
0.18/0.94	    U120(1,3,3) -> 7*
0.18/0.94	    U120(2,1,1) -> 7*
0.18/0.94	    U120(2,3,1) -> 7*
0.18/0.94	    U120(3,2,4) -> 7*
0.18/0.94	    U120(3,4,4) -> 7*
0.18/0.94	    U120(2,2,3) -> 7*
0.18/0.94	    U120(2,4,3) -> 7*
0.18/0.94	    U120(3,2,1) -> 7*
0.18/0.94	    U120(1,2,2) -> 7*
0.18/0.94	    U120(3,4,1) -> 7*
0.18/0.94	    U120(1,4,2) -> 7*
0.18/0.94	    U120(4,1,4) -> 7*
0.18/0.94	    U120(4,3,4) -> 7*
0.18/0.94	    U120(3,1,3) -> 7*
0.18/0.94	    U120(3,3,3) -> 7*
0.18/0.94	    U120(4,1,1) -> 7*
0.18/0.94	    U120(2,1,2) -> 7*
0.18/0.94	    U120(4,3,1) -> 7*
0.18/0.94	    U120(2,3,2) -> 7*
0.18/0.94	    U120(4,2,3) -> 7*
0.18/0.94	    U120(4,4,3) -> 7*
0.18/0.94	    s0(2) -> 8*
0.18/0.94	    s0(4) -> 8*
0.18/0.94	    s0(1) -> 8*
0.18/0.94	    s0(3) -> 8*
0.18/0.94	    plus0(3,1) -> 9*
0.18/0.94	    plus0(3,3) -> 9*
0.18/0.94	    plus0(4,2) -> 9*
0.18/0.94	    plus0(4,4) -> 9*
0.18/0.94	    plus0(1,2) -> 9*
0.18/0.94	    plus0(1,4) -> 9*
0.18/0.94	    plus0(2,1) -> 9*
0.18/0.94	    plus0(2,3) -> 9*
0.18/0.94	    plus0(3,2) -> 9*
0.18/0.94	    plus0(3,4) -> 9*
0.18/0.94	    plus0(4,1) -> 9*
0.18/0.94	    plus0(4,3) -> 9*
0.18/0.94	    plus0(1,1) -> 9*
0.18/0.94	    plus0(1,3) -> 9*
0.18/0.94	    plus0(2,2) -> 9*
0.18/0.94	    plus0(2,4) -> 9*
0.18/0.94	    00() -> 3*
0.18/0.94	    proper0(2) -> 10*
0.18/0.94	    proper0(4) -> 10*
0.18/0.94	    proper0(1) -> 10*
0.18/0.94	    proper0(3) -> 10*
0.18/0.94	    ok0(2) -> 4*
0.18/0.94	    ok0(4) -> 4*
0.18/0.94	    ok0(1) -> 4*
0.18/0.94	    ok0(3) -> 4*
0.18/0.94	    top0(2) -> 11*
0.18/0.94	    top0(4) -> 11*
0.18/0.94	    top0(1) -> 11*
0.18/0.94	    top0(3) -> 11*
0.18/0.94	  problem:
0.18/0.94	   
0.18/0.94	  Qed
0.18/0.94	EOF