*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        f(x,h1(y,z)) -> h2(0(),x,h1(y,z))
        f(j(x,y),y) -> g(f(x,k(y)))
        g(h2(x,y,h1(z,u))) -> h2(s(x),y,h1(z,u))
        h2(x,j(y,h1(z,u)),h1(z,u)) -> h2(s(x),y,h1(s(z),u))
        i(f(x,h(y))) -> y
        i(h2(s(x),y,h1(x,z))) -> z
        k(h(x)) -> h1(0(),x)
        k(h1(x,y)) -> h1(s(x),y)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {f/2,g/1,h2/3,i/1,k/1} / {0/0,h/1,h1/2,j/2,s/1}
      Obligation:
        Innermost
        basic terms: {f,g,h2,i,k}/{0,h,h1,j,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() -> 2
        0_1() -> 3
        0_2() -> 7
        f_0(2,2) -> 1
        f_1(2,6) -> 5
        g_0(2) -> 1
        g_1(5) -> 1
        g_1(5) -> 5
        h_0(2) -> 2
        h1_0(2,2) -> 2
        h1_1(2,2) -> 4
        h1_1(3,2) -> 1
        h1_1(3,2) -> 6
        h1_2(3,2) -> 8
        h2_0(2,2,2) -> 1
        h2_1(3,2,4) -> 1
        h2_1(3,2,6) -> 5
        h2_1(10,2,6) -> 5
        h2_2(7,2,8) -> 5
        h2_2(9,2,8) -> 1
        h2_2(9,2,8) -> 5
        i_0(2) -> 1
        j_0(2,2) -> 2
        k_0(2) -> 1
        k_1(2) -> 6
        s_0(2) -> 2
        s_1(2) -> 2
        s_1(2) -> 3
        s_1(3) -> 3
        s_1(7) -> 10
        s_1(9) -> 3
        s_1(10) -> 3
        s_2(3) -> 9
        s_2(7) -> 9
        s_2(9) -> 9
        s_2(10) -> 9
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        f(x,h1(y,z)) -> h2(0(),x,h1(y,z))
        f(j(x,y),y) -> g(f(x,k(y)))
        g(h2(x,y,h1(z,u))) -> h2(s(x),y,h1(z,u))
        h2(x,j(y,h1(z,u)),h1(z,u)) -> h2(s(x),y,h1(s(z),u))
        i(f(x,h(y))) -> y
        i(h2(s(x),y,h1(x,z))) -> z
        k(h(x)) -> h1(0(),x)
        k(h1(x,y)) -> h1(s(x),y)
      Signature:
        {f/2,g/1,h2/3,i/1,k/1} / {0/0,h/1,h1/2,j/2,s/1}
      Obligation:
        Innermost
        basic terms: {f,g,h2,i,k}/{0,h,h1,j,s}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).