*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        f(x1,0()) -> g(x1,0())
        f(y,S(x)) -> f(S(y),x)
        g(0(),x2) -> x2
        g(S(x),y) -> g(x,S(y))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {f/2,g/2} / {0/0,S/1}
      Obligation:
        Innermost
        basic terms: {f,g}/{0,S}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 2.
      The enriched problem is compatible with follwoing automaton.
        0_0() -> 1
        0_0() -> 2
        0_1() -> 1
        0_1() -> 3
        S_0(2) -> 1
        S_0(2) -> 2
        S_1(2) -> 1
        S_1(2) -> 4
        S_1(3) -> 1
        S_1(3) -> 3
        S_1(4) -> 1
        S_1(4) -> 4
        S_1(5) -> 1
        S_1(5) -> 3
        S_2(3) -> 1
        S_2(3) -> 5
        S_2(5) -> 1
        S_2(5) -> 5
        f_0(2,2) -> 1
        f_1(4,2) -> 1
        g_0(2,2) -> 1
        g_1(2,3) -> 1
        g_1(2,4) -> 1
        g_1(4,3) -> 1
        g_2(2,5) -> 1
        g_2(4,5) -> 1
        2 -> 1
        3 -> 1
        4 -> 1
        5 -> 1
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        f(x1,0()) -> g(x1,0())
        f(y,S(x)) -> f(S(y),x)
        g(0(),x2) -> x2
        g(S(x),y) -> g(x,S(y))
      Signature:
        {f/2,g/2} / {0/0,S/1}
      Obligation:
        Innermost
        basic terms: {f,g}/{0,S}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).