Problem:
active(zeros()) -> mark(cons(0(),zeros()))
active(and(tt(),X)) -> mark(X)
active(length(nil())) -> mark(0())
active(length(cons(N,L))) -> mark(s(length(L)))
active(cons(X1,X2)) -> cons(active(X1),X2)
active(and(X1,X2)) -> and(active(X1),X2)
active(length(X)) -> length(active(X))
active(s(X)) -> s(active(X))
cons(mark(X1),X2) -> mark(cons(X1,X2))
and(mark(X1),X2) -> mark(and(X1,X2))
length(mark(X)) -> mark(length(X))
s(mark(X)) -> mark(s(X))
proper(zeros()) -> ok(zeros())
proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
proper(0()) -> ok(0())
proper(and(X1,X2)) -> and(proper(X1),proper(X2))
proper(tt()) -> ok(tt())
proper(length(X)) -> length(proper(X))
proper(nil()) -> ok(nil())
proper(s(X)) -> s(proper(X))
cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
and(ok(X1),ok(X2)) -> ok(and(X1,X2))
length(ok(X)) -> ok(length(X))
s(ok(X)) -> ok(s(X))
top(mark(X)) -> top(proper(X))
top(ok(X)) -> top(active(X))
Proof:
Bounds Processor:
bound: 5
enrichment: match
automaton:
final states: {13,12,11,10,9,8,7}
transitions:
cons3(36,35) -> 49*
cons3(45,44) -> 43*
top1(29) -> 13*
active3(49) -> 43*
active1(5) -> 29*
active1(2) -> 29*
active1(4) -> 29*
active1(6) -> 29*
active1(1) -> 29*
active1(3) -> 29*
nil3() -> 50*
proper1(5) -> 29*
proper1(2) -> 29*
proper1(4) -> 29*
proper1(6) -> 29*
proper1(1) -> 29*
proper1(3) -> 29*
tt3() -> 50*
ok1(25) -> 25,10
ok1(15) -> 29,12
ok1(27) -> 27,11
ok1(14) -> 29,12
ok1(21) -> 21,8
ok1(23) -> 23,9
03() -> 53*
s1(5) -> 27*
s1(2) -> 27*
s1(4) -> 27*
s1(6) -> 27*
s1(1) -> 27*
s1(3) -> 27*
zeros3() -> 50*
length1(5) -> 25*
length1(2) -> 25*
length1(4) -> 25*
length1(6) -> 25*
length1(1) -> 25*
length1(3) -> 25*
ok4(56) -> 43*
and1(3,1) -> 23*
and1(3,3) -> 23*
and1(3,5) -> 23*
and1(4,2) -> 23*
and1(4,4) -> 23*
and1(4,6) -> 23*
and1(5,1) -> 23*
and1(5,3) -> 23*
and1(5,5) -> 23*
and1(6,2) -> 23*
and1(1,2) -> 23*
and1(6,4) -> 23*
and1(1,4) -> 23*
and1(6,6) -> 23*
and1(1,6) -> 23*
and1(2,1) -> 23*
and1(2,3) -> 23*
and1(2,5) -> 23*
and1(3,2) -> 23*
and1(3,4) -> 23*
and1(3,6) -> 23*
and1(4,1) -> 23*
and1(4,3) -> 23*
and1(4,5) -> 23*
and1(5,2) -> 23*
and1(5,4) -> 23*
and1(5,6) -> 23*
and1(6,1) -> 23*
and1(1,1) -> 23*
and1(6,3) -> 23*
and1(1,3) -> 23*
and1(6,5) -> 23*
and1(1,5) -> 23*
and1(2,2) -> 23*
and1(2,4) -> 23*
and1(2,6) -> 23*
cons4(55,35) -> 43*
cons4(53,50) -> 56*
cons1(3,1) -> 21*
cons1(3,3) -> 21*
cons1(3,5) -> 21*
cons1(4,2) -> 21*
cons1(4,4) -> 21*
cons1(4,6) -> 21*
cons1(5,1) -> 21*
cons1(5,3) -> 21*
cons1(5,5) -> 21*
cons1(6,2) -> 21*
cons1(1,2) -> 21*
cons1(6,4) -> 21*
cons1(1,4) -> 21*
cons1(6,6) -> 21*
cons1(1,6) -> 21*
cons1(2,1) -> 21*
cons1(2,3) -> 21*
cons1(2,5) -> 21*
cons1(3,2) -> 21*
cons1(3,4) -> 21*
cons1(3,6) -> 21*
cons1(4,1) -> 21*
cons1(4,3) -> 21*
cons1(4,5) -> 21*
cons1(5,2) -> 21*
cons1(5,4) -> 21*
cons1(5,6) -> 21*
cons1(15,14) -> 16*
cons1(6,1) -> 21*
cons1(1,1) -> 21*
cons1(6,3) -> 21*
cons1(1,3) -> 21*
cons1(6,5) -> 21*
cons1(1,5) -> 21*
cons1(2,2) -> 21*
cons1(2,4) -> 21*
cons1(2,6) -> 21*
active4(56) -> 59*
active4(36) -> 55*
nil1() -> 14*
top4(59) -> 13*
tt1() -> 14*
cons5(60,50) -> 59*
01() -> 15*
active5(53) -> 60*
zeros1() -> 14*
mark1(25) -> 25,10
mark1(27) -> 27,11
mark1(21) -> 21,8
mark1(16) -> 29,7
mark1(23) -> 23,9
top2(30) -> 13*
active0(5) -> 7*
active0(2) -> 7*
active0(4) -> 7*
active0(6) -> 7*
active0(1) -> 7*
active0(3) -> 7*
active2(15) -> 30*
active2(14) -> 30*
zeros0() -> 1*
proper2(15) -> 39*
proper2(14) -> 38*
proper2(16) -> 30*
mark0(5) -> 2*
mark0(2) -> 2*
mark0(4) -> 2*
mark0(6) -> 2*
mark0(1) -> 2*
mark0(3) -> 2*
cons2(36,35) -> 37*
cons2(39,38) -> 30*
cons0(3,1) -> 8*
cons0(3,3) -> 8*
cons0(3,5) -> 8*
cons0(4,2) -> 8*
cons0(4,4) -> 8*
cons0(4,6) -> 8*
cons0(5,1) -> 8*
cons0(5,3) -> 8*
cons0(5,5) -> 8*
cons0(6,2) -> 8*
cons0(1,2) -> 8*
cons0(6,4) -> 8*
cons0(1,4) -> 8*
cons0(6,6) -> 8*
cons0(1,6) -> 8*
cons0(2,1) -> 8*
cons0(2,3) -> 8*
cons0(2,5) -> 8*
cons0(3,2) -> 8*
cons0(3,4) -> 8*
cons0(3,6) -> 8*
cons0(4,1) -> 8*
cons0(4,3) -> 8*
cons0(4,5) -> 8*
cons0(5,2) -> 8*
cons0(5,4) -> 8*
cons0(5,6) -> 8*
cons0(6,1) -> 8*
cons0(1,1) -> 8*
cons0(6,3) -> 8*
cons0(1,3) -> 8*
cons0(6,5) -> 8*
cons0(1,5) -> 8*
cons0(2,2) -> 8*
cons0(2,4) -> 8*
cons0(2,6) -> 8*
mark2(37) -> 30*
00() -> 3*
02() -> 36*
and0(3,1) -> 9*
and0(3,3) -> 9*
and0(3,5) -> 9*
and0(4,2) -> 9*
and0(4,4) -> 9*
and0(4,6) -> 9*
and0(5,1) -> 9*
and0(5,3) -> 9*
and0(5,5) -> 9*
and0(6,2) -> 9*
and0(1,2) -> 9*
and0(6,4) -> 9*
and0(1,4) -> 9*
and0(6,6) -> 9*
and0(1,6) -> 9*
and0(2,1) -> 9*
and0(2,3) -> 9*
and0(2,5) -> 9*
and0(3,2) -> 9*
and0(3,4) -> 9*
and0(3,6) -> 9*
and0(4,1) -> 9*
and0(4,3) -> 9*
and0(4,5) -> 9*
and0(5,2) -> 9*
and0(5,4) -> 9*
and0(5,6) -> 9*
and0(6,1) -> 9*
and0(1,1) -> 9*
and0(6,3) -> 9*
and0(1,3) -> 9*
and0(6,5) -> 9*
and0(1,5) -> 9*
and0(2,2) -> 9*
and0(2,4) -> 9*
and0(2,6) -> 9*
zeros2() -> 35*
tt0() -> 4*
top3(43) -> 13*
length0(5) -> 10*
length0(2) -> 10*
length0(4) -> 10*
length0(6) -> 10*
length0(1) -> 10*
length0(3) -> 10*
proper3(35) -> 44*
proper3(37) -> 43*
proper3(36) -> 45*
nil0() -> 5*
ok2(35) -> 38*
ok2(36) -> 39*
s0(5) -> 11*
s0(2) -> 11*
s0(4) -> 11*
s0(6) -> 11*
s0(1) -> 11*
s0(3) -> 11*
nil2() -> 35*
proper0(5) -> 12*
proper0(2) -> 12*
proper0(4) -> 12*
proper0(6) -> 12*
proper0(1) -> 12*
proper0(3) -> 12*
tt2() -> 35*
ok0(5) -> 6*
ok0(2) -> 6*
ok0(4) -> 6*
ok0(6) -> 6*
ok0(1) -> 6*
ok0(3) -> 6*
ok3(50) -> 44*
ok3(49) -> 30*
ok3(53) -> 45*
top0(5) -> 13*
top0(2) -> 13*
top0(4) -> 13*
top0(6) -> 13*
top0(1) -> 13*
top0(3) -> 13*
problem:
Qed