/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,y)) -> *(f(x),f(y))
            f(+(x,s(0()))) -> +(s(s(0())),f(x))
            f(0()) -> s(0())
            f(s(0())) -> *(s(s(0())),f(0()))
            f(s(0())) -> s(s(0()))
        - Signature:
            {f/1} / {*/2,+/2,0/0,s/1}
        - Obligation:
             derivational complexity wrt. signature {*,+,0,f,s}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 3.
        The enriched problem is compatible with follwoing automaton.
          *_0(1,1) -> 1
          *_1(2,3) -> 1
          *_1(3,3) -> 2
          *_1(3,3) -> 3
          *_1(4,7) -> 1
          *_1(4,7) -> 2
          *_1(4,7) -> 3
          *_2(8,9) -> 2
          *_2(8,9) -> 3
          *_2(8,9) -> 9
          *_3(14,15) -> 9
          +_0(1,1) -> 1
          +_1(4,2) -> 1
          +_1(4,3) -> 1
          +_1(4,3) -> 2
          +_1(4,3) -> 3
          +_2(8,8) -> 2
          +_2(8,8) -> 3
          +_2(8,8) -> 9
          0_0() -> 1
          0_1() -> 6
          0_2() -> 10
          0_2() -> 12
          0_3() -> 13
          f_0(1) -> 1
          f_1(1) -> 2
          f_1(1) -> 3
          f_1(2) -> 3
          f_1(3) -> 3
          f_1(4) -> 2
          f_1(6) -> 7
          f_2(2) -> 9
          f_2(3) -> 9
          f_2(4) -> 8
          f_2(8) -> 8
          f_2(8) -> 9
          f_2(10) -> 9
          f_3(8) -> 14
          f_3(8) -> 15
          s_0(1) -> 1
          s_1(5) -> 1
          s_1(5) -> 2
          s_1(5) -> 3
          s_1(5) -> 4
          s_1(6) -> 1
          s_1(6) -> 2
          s_1(6) -> 3
          s_1(6) -> 5
          s_2(11) -> 2
          s_2(11) -> 3
          s_2(11) -> 8
          s_2(11) -> 9
          s_2(12) -> 7
          s_2(12) -> 11
          s_3(13) -> 9
* Step 2: EmptyProcessor WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(+(x,y)) -> *(f(x),f(y))
            f(+(x,s(0()))) -> +(s(s(0())),f(x))
            f(0()) -> s(0())
            f(s(0())) -> *(s(s(0())),f(0()))
            f(s(0())) -> s(s(0()))
        - Signature:
            {f/1} / {*/2,+/2,0/0,s/1}
        - Obligation:
             derivational complexity wrt. signature {*,+,0,f,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))