*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        f(.(.(x,y),z)) -> f(.(x,.(y,z)))
        f(.(nil(),y)) -> .(nil(),f(y))
        f(nil()) -> nil()
        g(.(x,.(y,z))) -> g(.(.(x,y),z))
        g(.(x,nil())) -> .(g(x),nil())
        g(nil()) -> nil()
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {f/1,g/1} / {./2,nil/0}
      Obligation:
        Full
        basic terms: {f,g}/{.,nil}
    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(.(.(x,y),z)) -> f(.(x,.(y,z)))
        f(.(nil(),y)) -> .(nil(),f(y))
        f(nil()) -> nil()
        g(.(x,.(y,z))) -> g(.(.(x,y),z))
        g(.(x,nil())) -> .(g(x),nil())
        g(nil()) -> nil()
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {f/1,g/1} / {./2,nil/0}
      Obligation:
        Innermost
        basic terms: {f,g}/{.,nil}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 1.
      The enriched problem is compatible with follwoing automaton.
        ._0(2,2) -> 2
        ._1(2,2) -> 4
        ._1(2,3) -> 3
        ._1(2,4) -> 3
        ._1(4,2) -> 7
        ._1(5,6) -> 1
        ._1(5,6) -> 5
        ._1(6,6) -> 6
        ._1(7,2) -> 7
        f_0(2) -> 1
        f_1(2) -> 6
        f_1(3) -> 1
        f_1(3) -> 6
        f_1(4) -> 6
        g_0(2) -> 1
        g_1(2) -> 5
        g_1(4) -> 5
        g_1(7) -> 1
        g_1(7) -> 5
        nil_0() -> 2
        nil_1() -> 1
        nil_1() -> 5
        nil_1() -> 6
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        f(.(.(x,y),z)) -> f(.(x,.(y,z)))
        f(.(nil(),y)) -> .(nil(),f(y))
        f(nil()) -> nil()
        g(.(x,.(y,z))) -> g(.(.(x,y),z))
        g(.(x,nil())) -> .(g(x),nil())
        g(nil()) -> nil()
      Signature:
        {f/1,g/1} / {./2,nil/0}
      Obligation:
        Innermost
        basic terms: {f,g}/{.,nil}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).