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


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WORST_CASE(Omega(n^1),O(n^1))
* Step 1: Sum.  WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            eq0(0(),0()) -> S(0())
            eq0(0(),S(x)) -> 0()
            eq0(S(x),0()) -> 0()
            eq0(S(x'),S(x)) -> eq0(x',x)
        - Signature:
            {eq0/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {eq0} and constructors {0,S}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            eq0(0(),0()) -> S(0())
            eq0(0(),S(x)) -> 0()
            eq0(S(x),0()) -> 0()
            eq0(S(x'),S(x)) -> eq0(x',x)
        - Signature:
            {eq0/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {eq0} and constructors {0,S}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:2: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            eq0(0(),0()) -> S(0())
            eq0(0(),S(x)) -> 0()
            eq0(S(x),0()) -> 0()
            eq0(S(x'),S(x)) -> eq0(x',x)
        - Signature:
            {eq0/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {eq0} and constructors {0,S}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          eq0(x,y){x -> S(x),y -> S(y)} =
            eq0(S(x),S(y)) ->^+ eq0(x,y)
              = C[eq0(x,y) = eq0(x,y){}]

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            eq0(0(),0()) -> S(0())
            eq0(0(),S(x)) -> 0()
            eq0(S(x),0()) -> 0()
            eq0(S(x'),S(x)) -> eq0(x',x)
        - Signature:
            {eq0/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {eq0} and constructors {0,S}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 1.
        The enriched problem is compatible with follwoing automaton.
          0_0() -> 2
          0_1() -> 1
          0_1() -> 3
          S_0(2) -> 2
          S_1(3) -> 1
          eq0_0(2,2) -> 1
          eq0_1(2,2) -> 1
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            eq0(0(),0()) -> S(0())
            eq0(0(),S(x)) -> 0()
            eq0(S(x),0()) -> 0()
            eq0(S(x'),S(x)) -> eq0(x',x)
        - Signature:
            {eq0/2} / {0/0,S/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {eq0} and constructors {0,S}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(Omega(n^1),O(n^1))