*** 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:
        Full
        basic terms: {g}/{0,f,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:
        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 = 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() -> 4
        0_2() -> 9
        0_2() -> 10
        f_0(2,2) -> 1
        f_0(2,2) -> 2
        f_1(2,2) -> 3
        f_1(2,4) -> 1
        f_1(2,4) -> 2
        f_1(2,9) -> 11
        f_1(2,10) -> 12
        f_1(5,6) -> 1
        f_1(6,6) -> 5
        f_1(6,6) -> 6
        f_1(6,6) -> 7
        f_1(6,6) -> 8
        f_2(7,8) -> 1
        f_2(8,13) -> 5
        f_2(8,13) -> 6
        f_2(8,13) -> 7
        f_2(8,13) -> 8
        g_0(2,2) -> 1
        g_1(2,4) -> 5
        g_1(2,4) -> 6
        g_1(3,4) -> 1
        g_1(4,4) -> 6
        g_1(11,4) -> 7
        g_1(12,4) -> 8
        g_2(2,9) -> 7
        g_2(2,10) -> 8
        g_2(4,10) -> 13
        g_2(9,10) -> 13
        g_2(10,10) -> 13
        s_0(2) -> 1
        s_0(2) -> 2
        2 -> 1
*** 1.1.1 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).