*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        f(x) -> x
        f(c(s(x),y)) -> f(c(x,s(y)))
        f(f(x)) -> f(d(f(x)))
        g(c(x,s(y))) -> g(c(s(x),y))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {f/1,g/1} / {c/2,d/1,s/1}
      Obligation:
        Innermost
        basic terms: {f,g}/{c,d,s}
    Applied Processor:
      InnermostRuleRemoval
    Proof:
      Arguments of following rules are not normal-forms.
        f(f(x)) -> f(d(f(x)))
      All above mentioned rules can be savely removed.
*** 1.1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        f(x) -> x
        f(c(s(x),y)) -> f(c(x,s(y)))
        g(c(x,s(y))) -> g(c(s(x),y))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {f/1,g/1} / {c/2,d/1,s/1}
      Obligation:
        Innermost
        basic terms: {f,g}/{c,d,s}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 1.
      The enriched problem is compatible with follwoing automaton.
        c_0(2,2) -> 1
        c_0(2,2) -> 2
        c_1(2,4) -> 1
        c_1(2,4) -> 3
        c_1(4,2) -> 5
        d_0(2) -> 1
        d_0(2) -> 2
        f_0(2) -> 1
        f_1(3) -> 1
        g_0(2) -> 1
        g_1(5) -> 1
        s_0(2) -> 1
        s_0(2) -> 2
        s_1(2) -> 4
        s_1(4) -> 4
        2 -> 1
        3 -> 1
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        f(x) -> x
        f(c(s(x),y)) -> f(c(x,s(y)))
        g(c(x,s(y))) -> g(c(s(x),y))
      Signature:
        {f/1,g/1} / {c/2,d/1,s/1}
      Obligation:
        Innermost
        basic terms: {f,g}/{c,d,s}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).