*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        f(s(X)) -> f(X)
        g(cons(0(),Y)) -> g(Y)
        g(cons(s(X),Y)) -> s(X)
        h(cons(X,Y)) -> h(g(cons(X,Y)))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {f/1,g/1,h/1} / {0/0,cons/2,s/1}
      Obligation:
        Full
        basic terms: {f,g,h}/{0,cons,s}
    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:
        f(s(X)) -> f(X)
        g(cons(0(),Y)) -> g(Y)
        g(cons(s(X),Y)) -> s(X)
        h(cons(X,Y)) -> h(g(cons(X,Y)))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {f/1,g/1,h/1} / {0/0,cons/2,s/1}
      Obligation:
        Innermost
        basic terms: {f,g,h}/{0,cons,s}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 1.
      The enriched problem is compatible with follwoing automaton.
        0_0() -> 2
        cons_0(2,2) -> 2
        cons_1(2,2) -> 4
        f_0(2) -> 1
        f_1(2) -> 1
        g_0(2) -> 1
        g_1(2) -> 1
        g_1(2) -> 3
        g_1(4) -> 3
        h_0(2) -> 1
        h_1(3) -> 1
        s_0(2) -> 2
        s_1(2) -> 1
        s_1(2) -> 3
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        f(s(X)) -> f(X)
        g(cons(0(),Y)) -> g(Y)
        g(cons(s(X),Y)) -> s(X)
        h(cons(X,Y)) -> h(g(cons(X,Y)))
      Signature:
        {f/1,g/1,h/1} / {0/0,cons/2,s/1}
      Obligation:
        Innermost
        basic terms: {f,g,h}/{0,cons,s}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).