*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        e(g(X)) -> e(X)
        f(a()) -> f(c(a()))
        f(a()) -> f(d(a()))
        f(c(X)) -> X
        f(c(a())) -> f(d(b()))
        f(c(b())) -> f(d(a()))
        f(d(X)) -> X
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {e/1,f/1} / {a/0,b/0,c/1,d/1,g/1}
      Obligation:
        Full
        basic terms: {e,f}/{a,b,c,d,g}
    Applied Processor:
      ToInnermost
    Proof:
      switch to innermost, as the system is overlay and right linear and does not contain weak rules
*** 1.1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        e(g(X)) -> e(X)
        f(a()) -> f(c(a()))
        f(a()) -> f(d(a()))
        f(c(X)) -> X
        f(c(a())) -> f(d(b()))
        f(c(b())) -> f(d(a()))
        f(d(X)) -> X
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {e/1,f/1} / {a/0,b/0,c/1,d/1,g/1}
      Obligation:
        Innermost
        basic terms: {e,f}/{a,b,c,d,g}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 2.
      The enriched problem is compatible with follwoing automaton.
        a_0() -> 1
        a_0() -> 2
        a_1() -> 1
        a_1() -> 4
        a_2() -> 1
        a_2() -> 6
        b_0() -> 1
        b_0() -> 2
        b_1() -> 1
        b_1() -> 4
        b_2() -> 1
        b_2() -> 6
        c_0(2) -> 1
        c_0(2) -> 2
        c_1(4) -> 3
        d_0(2) -> 1
        d_0(2) -> 2
        d_1(4) -> 3
        d_2(6) -> 5
        e_0(2) -> 1
        e_1(2) -> 1
        f_0(2) -> 1
        f_1(3) -> 1
        f_2(5) -> 1
        g_0(2) -> 1
        g_0(2) -> 2
        2 -> 1
        4 -> 1
        6 -> 1
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        e(g(X)) -> e(X)
        f(a()) -> f(c(a()))
        f(a()) -> f(d(a()))
        f(c(X)) -> X
        f(c(a())) -> f(d(b()))
        f(c(b())) -> f(d(a()))
        f(d(X)) -> X
      Signature:
        {e/1,f/1} / {a/0,b/0,c/1,d/1,g/1}
      Obligation:
        Innermost
        basic terms: {e,f}/{a,b,c,d,g}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).