*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        g(x,s(y)) -> g(f(x,y),0())
        g(0(),f(x,x)) -> x
        g(f(x,y),0()) -> f(g(x,0()),g(y,0()))
        g(s(x),y) -> g(f(x,y),0())
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {g/2} / {0/0,f/2,s/1}
      Obligation:
        Innermost
        basic terms: {g}/{0,f,s}
    Applied Processor:
      Bounds {initialAutomaton = perSymbol, enrichment = match}
    Proof:
      The problem is match-bounded by 2.
      The enriched problem is compatible with follwoing automaton.
        0_0() -> 1
        0_0() -> 3
        0_1() -> 6
        0_2() -> 11
        0_2() -> 12
        f_0(1,1) -> 2
        f_0(1,1) -> 3
        f_0(1,2) -> 2
        f_0(1,2) -> 3
        f_0(1,4) -> 2
        f_0(1,4) -> 3
        f_0(2,1) -> 2
        f_0(2,1) -> 3
        f_0(2,2) -> 2
        f_0(2,2) -> 3
        f_0(2,4) -> 2
        f_0(2,4) -> 3
        f_0(4,1) -> 2
        f_0(4,1) -> 3
        f_0(4,2) -> 2
        f_0(4,2) -> 3
        f_0(4,4) -> 2
        f_0(4,4) -> 3
        f_1(1,1) -> 5
        f_1(1,2) -> 5
        f_1(1,4) -> 5
        f_1(1,6) -> 1
        f_1(1,6) -> 3
        f_1(1,12) -> 13
        f_1(2,1) -> 5
        f_1(2,2) -> 5
        f_1(2,4) -> 5
        f_1(2,6) -> 1
        f_1(2,6) -> 3
        f_1(2,12) -> 13
        f_1(4,1) -> 5
        f_1(4,2) -> 5
        f_1(4,4) -> 5
        f_1(4,6) -> 1
        f_1(4,6) -> 3
        f_1(4,12) -> 13
        f_1(7,8) -> 3
        f_1(8,8) -> 3
        f_1(8,8) -> 8
        f_1(8,8) -> 10
        f_2(9,10) -> 3
        f_2(10,10) -> 3
        f_2(10,14) -> 7
        f_2(10,14) -> 8
        f_2(10,14) -> 9
        f_2(10,14) -> 10
        g_0(1,1) -> 3
        g_0(1,2) -> 3
        g_0(1,4) -> 3
        g_0(2,1) -> 3
        g_0(2,2) -> 3
        g_0(2,4) -> 3
        g_0(4,1) -> 3
        g_0(4,2) -> 3
        g_0(4,4) -> 3
        g_1(1,6) -> 7
        g_1(1,6) -> 8
        g_1(2,6) -> 8
        g_1(4,6) -> 8
        g_1(5,6) -> 3
        g_1(6,6) -> 8
        g_1(13,6) -> 10
        g_2(1,11) -> 9
        g_2(1,12) -> 10
        g_2(2,12) -> 10
        g_2(4,12) -> 10
        g_2(6,12) -> 14
        g_2(12,12) -> 14
        s_0(1) -> 3
        s_0(1) -> 4
        s_0(2) -> 3
        s_0(2) -> 4
        s_0(4) -> 3
        s_0(4) -> 4
        1 -> 3
        2 -> 3
        4 -> 3
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        g(x,s(y)) -> g(f(x,y),0())
        g(0(),f(x,x)) -> x
        g(f(x,y),0()) -> f(g(x,0()),g(y,0()))
        g(s(x),y) -> g(f(x,y),0())
      Signature:
        {g/2} / {0/0,f/2,s/1}
      Obligation:
        Innermost
        basic terms: {g}/{0,f,s}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).