*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        active(f(x)) -> mark(f(f(x)))
        chk(no(c())) -> active(c())
        chk(no(f(x))) -> f(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
        f(active(x)) -> active(f(x))
        f(mark(x)) -> mark(f(x))
        f(no(x)) -> no(f(x))
        mat(f(x),c()) -> no(c())
        mat(f(x),f(y())) -> f(mat(x,y()))
        tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {active/1,chk/1,f/1,mat/2,tp/1} / {X/0,c/0,mark/1,no/1,y/0}
      Obligation:
        Full
        basic terms: {active,chk,f,mat,tp}/{X,c,mark,no,y}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 2.
      The enriched problem is compatible with follwoing automaton.
        X_0() -> 2
        X_1() -> 17
        active_0(2) -> 1
        active_1(3) -> 1
        active_2(18) -> 5
        c_0() -> 2
        c_1() -> 3
        c_2() -> 18
        chk_0(2) -> 1
        chk_1(6) -> 5
        f_0(2) -> 1
        f_1(2) -> 4
        f_1(8) -> 7
        f_1(9) -> 8
        f_1(10) -> 9
        f_1(11) -> 10
        f_1(12) -> 11
        f_1(13) -> 12
        f_1(14) -> 13
        f_1(15) -> 14
        f_1(16) -> 15
        f_1(17) -> 16
        mark_0(2) -> 2
        mark_1(4) -> 1
        mark_1(4) -> 4
        mat_0(2,2) -> 1
        mat_1(7,2) -> 6
        no_0(2) -> 2
        no_1(3) -> 6
        no_1(4) -> 1
        no_1(4) -> 4
        tp_0(2) -> 1
        tp_1(5) -> 1
        y_0() -> 2
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        active(f(x)) -> mark(f(f(x)))
        chk(no(c())) -> active(c())
        chk(no(f(x))) -> f(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
        f(active(x)) -> active(f(x))
        f(mark(x)) -> mark(f(x))
        f(no(x)) -> no(f(x))
        mat(f(x),c()) -> no(c())
        mat(f(x),f(y())) -> f(mat(x,y()))
        tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
      Signature:
        {active/1,chk/1,f/1,mat/2,tp/1} / {X/0,c/0,mark/1,no/1,y/0}
      Obligation:
        Full
        basic terms: {active,chk,f,mat,tp}/{X,c,mark,no,y}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).