*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        a__c(X) -> c(X)
        a__c(X) -> d(X)
        a__f(X) -> f(X)
        a__f(f(X)) -> a__c(f(g(f(X))))
        a__h(X) -> a__c(d(X))
        a__h(X) -> h(X)
        mark(c(X)) -> a__c(X)
        mark(d(X)) -> d(X)
        mark(f(X)) -> a__f(mark(X))
        mark(g(X)) -> g(X)
        mark(h(X)) -> a__h(mark(X))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {a__c/1,a__f/1,a__h/1,mark/1} / {c/1,d/1,f/1,g/1,h/1}
      Obligation:
        Full
        basic terms: {a__c,a__f,a__h,mark}/{c,d,f,g,h}
    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:
        a__c(X) -> c(X)
        a__c(X) -> d(X)
        a__f(X) -> f(X)
        a__f(f(X)) -> a__c(f(g(f(X))))
        a__h(X) -> a__c(d(X))
        a__h(X) -> h(X)
        mark(c(X)) -> a__c(X)
        mark(d(X)) -> d(X)
        mark(f(X)) -> a__f(mark(X))
        mark(g(X)) -> g(X)
        mark(h(X)) -> a__h(mark(X))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {a__c/1,a__f/1,a__h/1,mark/1} / {c/1,d/1,f/1,g/1,h/1}
      Obligation:
        Innermost
        basic terms: {a__c,a__f,a__h,mark}/{c,d,f,g,h}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 3.
      The enriched problem is compatible with follwoing automaton.
        a__c_0(2) -> 1
        a__c_1(1) -> 1
        a__c_1(2) -> 1
        a__c_1(2) -> 5
        a__c_1(3) -> 1
        a__c_2(6) -> 1
        a__c_2(6) -> 5
        a__f_0(2) -> 1
        a__f_1(5) -> 1
        a__f_1(5) -> 5
        a__h_0(2) -> 1
        a__h_1(5) -> 1
        a__h_1(5) -> 5
        c_0(2) -> 2
        c_1(2) -> 1
        c_2(1) -> 1
        c_2(2) -> 1
        c_2(2) -> 5
        c_2(3) -> 1
        c_3(6) -> 1
        c_3(6) -> 5
        d_0(2) -> 2
        d_1(2) -> 1
        d_1(2) -> 5
        d_2(1) -> 1
        d_2(2) -> 1
        d_2(2) -> 5
        d_2(3) -> 1
        d_2(5) -> 6
        d_3(6) -> 1
        d_3(6) -> 5
        f_0(2) -> 2
        f_1(2) -> 1
        f_1(4) -> 3
        f_2(5) -> 1
        f_2(5) -> 5
        f_2(7) -> 6
        g_0(2) -> 2
        g_1(1) -> 4
        g_1(2) -> 1
        g_1(2) -> 5
        g_2(5) -> 7
        h_0(2) -> 2
        h_1(2) -> 1
        h_2(5) -> 1
        h_2(5) -> 5
        mark_0(2) -> 1
        mark_1(2) -> 5
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        a__c(X) -> c(X)
        a__c(X) -> d(X)
        a__f(X) -> f(X)
        a__f(f(X)) -> a__c(f(g(f(X))))
        a__h(X) -> a__c(d(X))
        a__h(X) -> h(X)
        mark(c(X)) -> a__c(X)
        mark(d(X)) -> d(X)
        mark(f(X)) -> a__f(mark(X))
        mark(g(X)) -> g(X)
        mark(h(X)) -> a__h(mark(X))
      Signature:
        {a__c/1,a__f/1,a__h/1,mark/1} / {c/1,d/1,f/1,g/1,h/1}
      Obligation:
        Innermost
        basic terms: {a__c,a__f,a__h,mark}/{c,d,f,g,h}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).