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


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WORST_CASE(?,O(n^1))
* Step 1: Sum.  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:
             runtime complexity wrt. defined symbols {f,g,h2,i,k} and constructors {0,h,h1,j,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: 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:
             runtime complexity wrt. defined symbols {f,g,h2,i,k} and constructors {0,h,h1,j,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() -> 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
* Step 3: 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:
             runtime complexity wrt. defined symbols {f,g,h2,i,k} and constructors {0,h,h1,j,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))