*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        f(x,g(y,z)) -> g(f(x,y),z)
        f(x,nil()) -> g(nil(),x)
        norm(g(x,y)) -> s(norm(x))
        norm(nil()) -> 0()
        rem(g(x,y),0()) -> g(x,y)
        rem(g(x,y),s(z)) -> rem(x,z)
        rem(nil(),y) -> nil()
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {f/2,norm/1,rem/2} / {0/0,g/2,nil/0,s/1}
      Obligation:
        Full
        basic terms: {f,norm,rem}/{0,g,nil,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:
        f(x,g(y,z)) -> g(f(x,y),z)
        f(x,nil()) -> g(nil(),x)
        norm(g(x,y)) -> s(norm(x))
        norm(nil()) -> 0()
        rem(g(x,y),0()) -> g(x,y)
        rem(g(x,y),s(z)) -> rem(x,z)
        rem(nil(),y) -> nil()
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {f/2,norm/1,rem/2} / {0/0,g/2,nil/0,s/1}
      Obligation:
        Innermost
        basic terms: {f,norm,rem}/{0,g,nil,s}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 1.
      The enriched problem is compatible with follwoing automaton.
        0_0() -> 2
        0_1() -> 1
        0_1() -> 4
        f_0(2,2) -> 1
        f_1(2,2) -> 3
        g_0(2,2) -> 2
        g_1(2,2) -> 1
        g_1(3,2) -> 1
        g_1(3,2) -> 3
        nil_0() -> 2
        nil_1() -> 1
        nil_1() -> 3
        norm_0(2) -> 1
        norm_1(2) -> 4
        rem_0(2,2) -> 1
        rem_1(2,2) -> 1
        s_0(2) -> 2
        s_1(4) -> 1
        s_1(4) -> 4
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        f(x,g(y,z)) -> g(f(x,y),z)
        f(x,nil()) -> g(nil(),x)
        norm(g(x,y)) -> s(norm(x))
        norm(nil()) -> 0()
        rem(g(x,y),0()) -> g(x,y)
        rem(g(x,y),s(z)) -> rem(x,z)
        rem(nil(),y) -> nil()
      Signature:
        {f/2,norm/1,rem/2} / {0/0,g/2,nil/0,s/1}
      Obligation:
        Innermost
        basic terms: {f,norm,rem}/{0,g,nil,s}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).