Problem:
 active(f(x)) -> mark(f(f(x)))
 chk(no(f(x))) -> f(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
 mat(f(x),f(y())) -> f(mat(x,y()))
 chk(no(c())) -> active(c())
 mat(f(x),c()) -> no(c())
 f(active(x)) -> active(f(x))
 f(no(x)) -> no(f(x))
 f(mark(x)) -> mark(f(x))
 tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))

Proof:
 Bounds Processor:
  bound: 2
  enrichment: match
  automaton:
   final states: {10,9,8,7,6}
   transitions:
    tp1(27) -> 10*
    chk1(26) -> 27*
    mat1(25,1) -> 26*
    mat1(25,3) -> 26*
    mat1(25,5) -> 26*
    mat1(25,2) -> 26*
    mat1(25,4) -> 26*
    f1(20) -> 21*
    f1(15) -> 16*
    f1(5) -> 13*
    f1(22) -> 23*
    f1(17) -> 18*
    f1(2) -> 13*
    f1(24) -> 25*
    f1(19) -> 20*
    f1(4) -> 13*
    f1(21) -> 22*
    f1(16) -> 17*
    f1(1) -> 13*
    f1(23) -> 24*
    f1(18) -> 19*
    f1(3) -> 13*
    X1() -> 15*
    mark1(13) -> 13,9
    no1(12) -> 26*
    no1(13) -> 13,9
    active1(12) -> 7*
    c1() -> 12*
    active2(41) -> 27*
    c2() -> 41*
    active0(5) -> 6*
    active0(2) -> 6*
    active0(4) -> 6*
    active0(1) -> 6*
    active0(3) -> 6*
    f0(5) -> 9*
    f0(2) -> 9*
    f0(4) -> 9*
    f0(1) -> 9*
    f0(3) -> 9*
    mark0(5) -> 1*
    mark0(2) -> 1*
    mark0(4) -> 1*
    mark0(1) -> 1*
    mark0(3) -> 1*
    chk0(5) -> 7*
    chk0(2) -> 7*
    chk0(4) -> 7*
    chk0(1) -> 7*
    chk0(3) -> 7*
    no0(5) -> 2*
    no0(2) -> 2*
    no0(4) -> 2*
    no0(1) -> 2*
    no0(3) -> 2*
    mat0(3,1) -> 8*
    mat0(3,3) -> 8*
    mat0(3,5) -> 8*
    mat0(4,2) -> 8*
    mat0(4,4) -> 8*
    mat0(5,1) -> 8*
    mat0(5,3) -> 8*
    mat0(5,5) -> 8*
    mat0(1,2) -> 8*
    mat0(1,4) -> 8*
    mat0(2,1) -> 8*
    mat0(2,3) -> 8*
    mat0(2,5) -> 8*
    mat0(3,2) -> 8*
    mat0(3,4) -> 8*
    mat0(4,1) -> 8*
    mat0(4,3) -> 8*
    mat0(4,5) -> 8*
    mat0(5,2) -> 8*
    mat0(5,4) -> 8*
    mat0(1,1) -> 8*
    mat0(1,3) -> 8*
    mat0(1,5) -> 8*
    mat0(2,2) -> 8*
    mat0(2,4) -> 8*
    X0() -> 3*
    y0() -> 4*
    c0() -> 5*
    tp0(5) -> 10*
    tp0(2) -> 10*
    tp0(4) -> 10*
    tp0(1) -> 10*
    tp0(3) -> 10*
  problem:
   
  Qed