/export/starexec/sandbox/solver/bin/starexec_run_tct_dc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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WORST_CASE(?,O(n^1))
* Step 1: Bounds WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            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:
             derivational complexity wrt. signature {0,f,g,h,h1,h2,i,j,k,s}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          0_0() -> 1
          0_1() -> 2
          0_2() -> 7
          f_0(1,1) -> 1
          f_1(1,5) -> 4
          g_0(1) -> 1
          g_1(4) -> 1
          g_1(4) -> 4
          h_0(1) -> 1
          h1_0(1,1) -> 1
          h1_1(1,1) -> 3
          h1_1(2,1) -> 1
          h1_1(2,1) -> 3
          h1_1(2,1) -> 5
          h1_1(6,1) -> 3
          h1_2(2,1) -> 8
          h1_2(6,1) -> 5
          h2_0(1,1,1) -> 1
          h2_1(2,1,3) -> 1
          h2_1(2,1,5) -> 4
          h2_1(10,1,5) -> 4
          h2_2(6,1,5) -> 1
          h2_2(6,1,5) -> 4
          h2_2(6,1,8) -> 1
          h2_2(6,1,8) -> 4
          h2_2(7,1,5) -> 4
          h2_2(7,1,8) -> 4
          h2_2(9,1,5) -> 1
          h2_2(9,1,5) -> 4
          h2_2(9,1,8) -> 1
          h2_2(9,1,8) -> 4
          i_0(1) -> 1
          j_0(1,1) -> 1
          k_0(1) -> 1
          k_1(1) -> 5
          s_0(1) -> 1
          s_1(1) -> 2
          s_1(2) -> 2
          s_1(6) -> 2
          s_1(7) -> 10
          s_1(9) -> 2
          s_1(10) -> 2
          s_2(2) -> 6
          s_2(6) -> 6
          s_2(7) -> 9
          s_2(9) -> 6
          s_2(10) -> 6
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            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:
             derivational complexity wrt. signature {0,f,g,h,h1,h2,i,j,k,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))