YES(?,O(n^1))
3.26/1.07	YES(?,O(n^1))
3.26/1.09	
3.26/1.09	Problem:
3.26/1.09	 active(zeros()) -> mark(cons(0(),zeros()))
3.26/1.09	 active(and(tt(),X)) -> mark(X)
3.26/1.09	 active(length(nil())) -> mark(0())
3.26/1.09	 active(length(cons(N,L))) -> mark(s(length(L)))
3.26/1.09	 active(take(0(),IL)) -> mark(nil())
3.26/1.09	 active(take(s(M),cons(N,IL))) -> mark(cons(N,take(M,IL)))
3.26/1.09	 active(cons(X1,X2)) -> cons(active(X1),X2)
3.26/1.09	 active(and(X1,X2)) -> and(active(X1),X2)
3.26/1.09	 active(length(X)) -> length(active(X))
3.26/1.09	 active(s(X)) -> s(active(X))
3.26/1.09	 active(take(X1,X2)) -> take(active(X1),X2)
3.26/1.09	 active(take(X1,X2)) -> take(X1,active(X2))
3.26/1.09	 cons(mark(X1),X2) -> mark(cons(X1,X2))
3.26/1.09	 and(mark(X1),X2) -> mark(and(X1,X2))
3.26/1.09	 length(mark(X)) -> mark(length(X))
3.26/1.09	 s(mark(X)) -> mark(s(X))
3.26/1.09	 take(mark(X1),X2) -> mark(take(X1,X2))
3.26/1.09	 take(X1,mark(X2)) -> mark(take(X1,X2))
3.26/1.09	 proper(zeros()) -> ok(zeros())
3.26/1.09	 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
3.26/1.09	 proper(0()) -> ok(0())
3.26/1.09	 proper(and(X1,X2)) -> and(proper(X1),proper(X2))
3.26/1.09	 proper(tt()) -> ok(tt())
3.26/1.09	 proper(length(X)) -> length(proper(X))
3.26/1.09	 proper(nil()) -> ok(nil())
3.26/1.09	 proper(s(X)) -> s(proper(X))
3.26/1.09	 proper(take(X1,X2)) -> take(proper(X1),proper(X2))
3.26/1.09	 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
3.26/1.09	 and(ok(X1),ok(X2)) -> ok(and(X1,X2))
3.26/1.09	 length(ok(X)) -> ok(length(X))
3.26/1.09	 s(ok(X)) -> ok(s(X))
3.26/1.09	 take(ok(X1),ok(X2)) -> ok(take(X1,X2))
3.26/1.09	 top(mark(X)) -> top(proper(X))
3.26/1.09	 top(ok(X)) -> top(active(X))
3.26/1.09	
3.26/1.09	Proof:
3.26/1.09	 Bounds Processor:
3.26/1.09	  bound: 5
3.26/1.09	  enrichment: match
3.26/1.09	  automaton:
3.26/1.09	   final states: {14,13,12,11,10,9,8,7}
3.26/1.09	   transitions:
3.26/1.09	    active3(52) -> 46*
3.26/1.09	    top1(32) -> 14*
3.26/1.09	    nil3() -> 53*
3.26/1.09	    active1(5) -> 32*
3.26/1.09	    active1(2) -> 32*
3.26/1.09	    active1(4) -> 32*
3.26/1.09	    active1(6) -> 32*
3.26/1.09	    active1(1) -> 32*
3.26/1.09	    active1(3) -> 32*
3.26/1.09	    tt3() -> 53*
3.26/1.09	    proper1(5) -> 32*
3.26/1.09	    proper1(2) -> 32*
3.26/1.09	    proper1(4) -> 32*
3.26/1.09	    proper1(6) -> 32*
3.26/1.09	    proper1(1) -> 32*
3.26/1.09	    proper1(3) -> 32*
3.26/1.09	    03() -> 56*
3.26/1.09	    ok1(25) -> 25,10
3.26/1.09	    ok1(27) -> 27,11
3.26/1.09	    ok1(29) -> 29,12
3.26/1.09	    ok1(19) -> 32,13
3.26/1.09	    ok1(21) -> 21,8
3.26/1.09	    ok1(23) -> 23,9
3.26/1.09	    ok1(18) -> 32,13
3.26/1.09	    zeros3() -> 53*
3.26/1.09	    take1(3,1) -> 29*
3.26/1.09	    take1(3,3) -> 29*
3.26/1.09	    take1(3,5) -> 29*
3.26/1.09	    take1(4,2) -> 29*
3.26/1.09	    take1(4,4) -> 29*
3.26/1.09	    take1(4,6) -> 29*
3.26/1.09	    take1(5,1) -> 29*
3.26/1.09	    take1(5,3) -> 29*
3.26/1.09	    take1(5,5) -> 29*
3.26/1.09	    take1(6,2) -> 29*
3.26/1.09	    take1(1,2) -> 29*
3.26/1.09	    take1(6,4) -> 29*
3.26/1.09	    take1(1,4) -> 29*
3.26/1.09	    take1(6,6) -> 29*
3.26/1.09	    take1(1,6) -> 29*
3.26/1.09	    take1(2,1) -> 29*
3.26/1.09	    take1(2,3) -> 29*
3.26/1.09	    take1(2,5) -> 29*
3.26/1.09	    take1(3,2) -> 29*
3.26/1.09	    take1(3,4) -> 29*
3.26/1.09	    take1(3,6) -> 29*
3.26/1.09	    take1(4,1) -> 29*
3.26/1.09	    take1(4,3) -> 29*
3.26/1.09	    take1(4,5) -> 29*
3.26/1.09	    take1(5,2) -> 29*
3.26/1.09	    take1(5,4) -> 29*
3.26/1.09	    take1(5,6) -> 29*
3.26/1.09	    take1(6,1) -> 29*
3.26/1.09	    take1(1,1) -> 29*
3.26/1.09	    take1(6,3) -> 29*
3.26/1.09	    take1(1,3) -> 29*
3.26/1.09	    take1(6,5) -> 29*
3.26/1.09	    take1(1,5) -> 29*
3.26/1.09	    take1(2,2) -> 29*
3.26/1.09	    take1(2,4) -> 29*
3.26/1.09	    take1(2,6) -> 29*
3.26/1.09	    ok4(59) -> 46*
3.26/1.09	    s1(5) -> 27*
3.26/1.09	    s1(2) -> 27*
3.26/1.09	    s1(4) -> 27*
3.26/1.09	    s1(6) -> 27*
3.26/1.09	    s1(1) -> 27*
3.26/1.09	    s1(3) -> 27*
3.26/1.09	    cons4(56,53) -> 59*
3.26/1.09	    cons4(58,38) -> 46*
3.26/1.09	    length1(5) -> 25*
3.26/1.09	    length1(2) -> 25*
3.26/1.09	    length1(4) -> 25*
3.26/1.09	    length1(6) -> 25*
3.26/1.09	    length1(1) -> 25*
3.26/1.09	    length1(3) -> 25*
3.26/1.09	    active4(59) -> 62*
3.26/1.09	    active4(39) -> 58*
3.26/1.09	    and1(2,6) -> 23*
3.26/1.09	    and1(3,1) -> 23*
3.26/1.09	    and1(3,3) -> 23*
3.26/1.09	    and1(3,5) -> 23*
3.26/1.09	    and1(4,2) -> 23*
3.26/1.09	    and1(4,4) -> 23*
3.26/1.09	    and1(4,6) -> 23*
3.26/1.09	    and1(5,1) -> 23*
3.26/1.09	    and1(5,3) -> 23*
3.26/1.09	    and1(5,5) -> 23*
3.26/1.09	    and1(6,2) -> 23*
3.26/1.09	    and1(1,2) -> 23*
3.26/1.09	    and1(6,4) -> 23*
3.26/1.09	    and1(1,4) -> 23*
3.26/1.09	    and1(6,6) -> 23*
3.26/1.09	    and1(1,6) -> 23*
3.26/1.09	    and1(2,1) -> 23*
3.26/1.09	    and1(2,3) -> 23*
3.26/1.09	    and1(2,5) -> 23*
3.26/1.09	    and1(3,2) -> 23*
3.26/1.09	    and1(3,4) -> 23*
3.26/1.09	    and1(3,6) -> 23*
3.26/1.09	    and1(4,1) -> 23*
3.26/1.09	    and1(4,3) -> 23*
3.26/1.09	    and1(4,5) -> 23*
3.26/1.09	    and1(5,2) -> 23*
3.26/1.09	    and1(5,4) -> 23*
3.26/1.09	    and1(5,6) -> 23*
3.26/1.09	    and1(6,1) -> 23*
3.26/1.09	    and1(1,1) -> 23*
3.26/1.09	    and1(6,3) -> 23*
3.26/1.09	    and1(1,3) -> 23*
3.26/1.09	    and1(6,5) -> 23*
3.26/1.09	    and1(1,5) -> 23*
3.26/1.09	    and1(2,2) -> 23*
3.26/1.09	    and1(2,4) -> 23*
3.26/1.09	    top4(62) -> 14*
3.26/1.09	    cons1(2,6) -> 21*
3.26/1.09	    cons1(3,1) -> 21*
3.26/1.09	    cons1(3,3) -> 21*
3.26/1.09	    cons1(3,5) -> 21*
3.26/1.09	    cons1(4,2) -> 21*
3.26/1.09	    cons1(4,4) -> 21*
3.26/1.09	    cons1(4,6) -> 21*
3.26/1.09	    cons1(19,18) -> 20*
3.26/1.09	    cons1(5,1) -> 21*
3.26/1.09	    cons1(5,3) -> 21*
3.26/1.09	    cons1(5,5) -> 21*
3.26/1.09	    cons1(6,2) -> 21*
3.26/1.09	    cons1(1,2) -> 21*
3.26/1.09	    cons1(6,4) -> 21*
3.26/1.09	    cons1(1,4) -> 21*
3.26/1.09	    cons1(6,6) -> 21*
3.26/1.09	    cons1(1,6) -> 21*
3.26/1.09	    cons1(2,1) -> 21*
3.26/1.09	    cons1(2,3) -> 21*
3.26/1.09	    cons1(2,5) -> 21*
3.26/1.09	    cons1(3,2) -> 21*
3.26/1.09	    cons1(3,4) -> 21*
3.26/1.09	    cons1(3,6) -> 21*
3.26/1.09	    cons1(4,1) -> 21*
3.26/1.09	    cons1(4,3) -> 21*
3.26/1.09	    cons1(4,5) -> 21*
3.26/1.09	    cons1(5,2) -> 21*
3.26/1.09	    cons1(5,4) -> 21*
3.26/1.09	    cons1(5,6) -> 21*
3.26/1.09	    cons1(6,1) -> 21*
3.26/1.09	    cons1(1,1) -> 21*
3.26/1.09	    cons1(6,3) -> 21*
3.26/1.09	    cons1(1,3) -> 21*
3.26/1.09	    cons1(6,5) -> 21*
3.26/1.09	    cons1(1,5) -> 21*
3.26/1.09	    cons1(2,2) -> 21*
3.26/1.09	    cons1(2,4) -> 21*
3.26/1.09	    cons5(63,53) -> 62*
3.26/1.09	    nil1() -> 18*
3.26/1.09	    active5(56) -> 63*
3.26/1.09	    tt1() -> 18*
3.26/1.09	    01() -> 19*
3.26/1.09	    zeros1() -> 18*
3.26/1.09	    mark1(25) -> 25,10
3.26/1.09	    mark1(20) -> 32,7
3.26/1.09	    mark1(27) -> 27,11
3.26/1.09	    mark1(29) -> 29,12
3.26/1.09	    mark1(21) -> 21,8
3.26/1.09	    mark1(23) -> 23,9
3.26/1.09	    top2(33) -> 14*
3.26/1.09	    active0(5) -> 7*
3.26/1.09	    active0(2) -> 7*
3.26/1.09	    active0(4) -> 7*
3.26/1.09	    active0(6) -> 7*
3.26/1.09	    active0(1) -> 7*
3.26/1.09	    active0(3) -> 7*
3.26/1.09	    active2(19) -> 33*
3.26/1.09	    active2(18) -> 33*
3.26/1.09	    zeros0() -> 1*
3.26/1.09	    proper2(20) -> 33*
3.26/1.09	    proper2(19) -> 42*
3.26/1.09	    proper2(18) -> 41*
3.26/1.09	    mark0(5) -> 2*
3.26/1.09	    mark0(2) -> 2*
3.26/1.09	    mark0(4) -> 2*
3.26/1.09	    mark0(6) -> 2*
3.26/1.09	    mark0(1) -> 2*
3.26/1.09	    mark0(3) -> 2*
3.26/1.09	    cons2(39,38) -> 40*
3.26/1.09	    cons2(42,41) -> 33*
3.26/1.09	    cons0(3,1) -> 8*
3.26/1.09	    cons0(3,3) -> 8*
3.26/1.09	    cons0(3,5) -> 8*
3.26/1.09	    cons0(4,2) -> 8*
3.26/1.09	    cons0(4,4) -> 8*
3.26/1.09	    cons0(4,6) -> 8*
3.26/1.09	    cons0(5,1) -> 8*
3.26/1.09	    cons0(5,3) -> 8*
3.26/1.09	    cons0(5,5) -> 8*
3.26/1.09	    cons0(6,2) -> 8*
3.26/1.09	    cons0(1,2) -> 8*
3.26/1.09	    cons0(6,4) -> 8*
3.26/1.09	    cons0(1,4) -> 8*
3.26/1.09	    cons0(6,6) -> 8*
3.26/1.09	    cons0(1,6) -> 8*
3.26/1.09	    cons0(2,1) -> 8*
3.26/1.09	    cons0(2,3) -> 8*
3.26/1.09	    cons0(2,5) -> 8*
3.26/1.09	    cons0(3,2) -> 8*
3.26/1.09	    cons0(3,4) -> 8*
3.26/1.09	    cons0(3,6) -> 8*
3.26/1.09	    cons0(4,1) -> 8*
3.26/1.09	    cons0(4,3) -> 8*
3.26/1.09	    cons0(4,5) -> 8*
3.26/1.09	    cons0(5,2) -> 8*
3.26/1.09	    cons0(5,4) -> 8*
3.26/1.09	    cons0(5,6) -> 8*
3.26/1.09	    cons0(6,1) -> 8*
3.26/1.09	    cons0(1,1) -> 8*
3.26/1.09	    cons0(6,3) -> 8*
3.26/1.09	    cons0(1,3) -> 8*
3.26/1.09	    cons0(6,5) -> 8*
3.26/1.09	    cons0(1,5) -> 8*
3.26/1.09	    cons0(2,2) -> 8*
3.26/1.09	    cons0(2,4) -> 8*
3.26/1.09	    cons0(2,6) -> 8*
3.26/1.09	    mark2(40) -> 33*
3.26/1.09	    00() -> 3*
3.26/1.09	    02() -> 39*
3.26/1.09	    and0(3,1) -> 9*
3.26/1.09	    and0(3,3) -> 9*
3.26/1.09	    and0(3,5) -> 9*
3.26/1.09	    and0(4,2) -> 9*
3.26/1.09	    and0(4,4) -> 9*
3.26/1.09	    and0(4,6) -> 9*
3.26/1.09	    and0(5,1) -> 9*
3.26/1.09	    and0(5,3) -> 9*
3.26/1.09	    and0(5,5) -> 9*
3.26/1.09	    and0(6,2) -> 9*
3.26/1.09	    and0(1,2) -> 9*
3.26/1.09	    and0(6,4) -> 9*
3.26/1.09	    and0(1,4) -> 9*
3.26/1.09	    and0(6,6) -> 9*
3.26/1.09	    and0(1,6) -> 9*
3.26/1.09	    and0(2,1) -> 9*
3.26/1.09	    and0(2,3) -> 9*
3.26/1.09	    and0(2,5) -> 9*
3.26/1.09	    and0(3,2) -> 9*
3.26/1.09	    and0(3,4) -> 9*
3.26/1.09	    and0(3,6) -> 9*
3.26/1.09	    and0(4,1) -> 9*
3.26/1.09	    and0(4,3) -> 9*
3.26/1.09	    and0(4,5) -> 9*
3.26/1.09	    and0(5,2) -> 9*
3.26/1.09	    and0(5,4) -> 9*
3.26/1.09	    and0(5,6) -> 9*
3.26/1.09	    and0(6,1) -> 9*
3.26/1.09	    and0(1,1) -> 9*
3.26/1.09	    and0(6,3) -> 9*
3.26/1.09	    and0(1,3) -> 9*
3.26/1.09	    and0(6,5) -> 9*
3.26/1.09	    and0(1,5) -> 9*
3.26/1.09	    and0(2,2) -> 9*
3.26/1.09	    and0(2,4) -> 9*
3.26/1.09	    and0(2,6) -> 9*
3.26/1.09	    zeros2() -> 38*
3.26/1.09	    tt0() -> 4*
3.26/1.09	    top3(46) -> 14*
3.26/1.09	    length0(5) -> 10*
3.26/1.09	    length0(2) -> 10*
3.26/1.09	    length0(4) -> 10*
3.26/1.09	    length0(6) -> 10*
3.26/1.09	    length0(1) -> 10*
3.26/1.09	    length0(3) -> 10*
3.26/1.09	    proper3(40) -> 46*
3.26/1.09	    proper3(39) -> 48*
3.26/1.09	    proper3(38) -> 47*
3.26/1.09	    nil0() -> 5*
3.26/1.09	    ok2(39) -> 42*
3.26/1.09	    ok2(38) -> 41*
3.26/1.09	    s0(5) -> 11*
3.26/1.09	    s0(2) -> 11*
3.26/1.09	    s0(4) -> 11*
3.26/1.09	    s0(6) -> 11*
3.26/1.09	    s0(1) -> 11*
3.26/1.09	    s0(3) -> 11*
3.26/1.09	    nil2() -> 38*
3.26/1.09	    take0(3,1) -> 12*
3.26/1.09	    take0(3,3) -> 12*
3.26/1.09	    take0(3,5) -> 12*
3.26/1.09	    take0(4,2) -> 12*
3.26/1.09	    take0(4,4) -> 12*
3.26/1.09	    take0(4,6) -> 12*
3.26/1.09	    take0(5,1) -> 12*
3.26/1.09	    take0(5,3) -> 12*
3.26/1.09	    take0(5,5) -> 12*
3.26/1.09	    take0(6,2) -> 12*
3.26/1.09	    take0(1,2) -> 12*
3.26/1.09	    take0(6,4) -> 12*
3.26/1.09	    take0(1,4) -> 12*
3.26/1.09	    take0(6,6) -> 12*
3.26/1.09	    take0(1,6) -> 12*
3.26/1.09	    take0(2,1) -> 12*
3.26/1.09	    take0(2,3) -> 12*
3.26/1.09	    take0(2,5) -> 12*
3.26/1.09	    take0(3,2) -> 12*
3.26/1.09	    take0(3,4) -> 12*
3.26/1.09	    take0(3,6) -> 12*
3.26/1.09	    take0(4,1) -> 12*
3.26/1.09	    take0(4,3) -> 12*
3.26/1.09	    take0(4,5) -> 12*
3.26/1.09	    take0(5,2) -> 12*
3.26/1.09	    take0(5,4) -> 12*
3.26/1.09	    take0(5,6) -> 12*
3.26/1.09	    take0(6,1) -> 12*
3.26/1.09	    take0(1,1) -> 12*
3.26/1.09	    take0(6,3) -> 12*
3.26/1.09	    take0(1,3) -> 12*
3.26/1.09	    take0(6,5) -> 12*
3.26/1.09	    take0(1,5) -> 12*
3.26/1.09	    take0(2,2) -> 12*
3.26/1.09	    take0(2,4) -> 12*
3.26/1.09	    take0(2,6) -> 12*
3.26/1.09	    tt2() -> 38*
3.26/1.09	    proper0(5) -> 13*
3.26/1.09	    proper0(2) -> 13*
3.26/1.09	    proper0(4) -> 13*
3.26/1.09	    proper0(6) -> 13*
3.26/1.09	    proper0(1) -> 13*
3.26/1.09	    proper0(3) -> 13*
3.26/1.09	    ok3(52) -> 33*
3.26/1.09	    ok3(56) -> 48*
3.26/1.09	    ok3(53) -> 47*
3.26/1.09	    ok0(5) -> 6*
3.26/1.09	    ok0(2) -> 6*
3.26/1.09	    ok0(4) -> 6*
3.26/1.09	    ok0(6) -> 6*
3.26/1.09	    ok0(1) -> 6*
3.26/1.09	    ok0(3) -> 6*
3.26/1.09	    cons3(48,47) -> 46*
3.26/1.09	    cons3(39,38) -> 52*
3.26/1.09	    top0(5) -> 14*
3.26/1.09	    top0(2) -> 14*
3.26/1.09	    top0(4) -> 14*
3.26/1.09	    top0(6) -> 14*
3.26/1.09	    top0(1) -> 14*
3.26/1.09	    top0(3) -> 14*
3.26/1.09	  problem:
3.26/1.09	   
3.26/1.09	  Qed
3.26/1.09	EOF