/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(Omega(n^1),O(n^1))
* Step 1: Sum.  WORST_CASE(Omega(n^1),O(n^1))
    + Considered Problem:
        - Strict TRS:
            p(m,n,s(r)) -> p(m,r,n)
            p(m,0(),0()) -> m
            p(m,s(n),0()) -> p(0(),n,m)
        - Signature:
            {p/3} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {p} 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:
            p(m,n,s(r)) -> p(m,r,n)
            p(m,0(),0()) -> m
            p(m,s(n),0()) -> p(0(),n,m)
        - Signature:
            {p/3} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {p} 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:
            p(m,n,s(r)) -> p(m,r,n)
            p(m,0(),0()) -> m
            p(m,s(n),0()) -> p(0(),n,m)
        - Signature:
            {p/3} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {p} and constructors {0,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          p(x,v,z){v -> s(v),z -> s(z)} =
            p(x,s(v),s(z)) ->^+ p(x,v,z)
              = C[p(x,v,z) = p(x,v,z){}]

** Step 1.b:1: ToInnermost.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            p(m,n,s(r)) -> p(m,r,n)
            p(m,0(),0()) -> m
            p(m,s(n),0()) -> p(0(),n,m)
        - Signature:
            {p/3} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {p} and constructors {0,s}
    + Applied Processor:
        ToInnermost
    + Details:
        switch to innermost, as the system is overlay and right linear and does not contain weak rules
** Step 1.b:2: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            p(m,n,s(r)) -> p(m,r,n)
            p(m,0(),0()) -> m
            p(m,s(n),0()) -> p(0(),n,m)
        - Signature:
            {p/3} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {p} 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() -> 1
          0_0() -> 2
          0_1() -> 1
          0_1() -> 2
          p_0(2,2,2) -> 1
          p_1(2,2,2) -> 1
          s_0(2) -> 1
          s_0(2) -> 2
          2 -> 1
** Step 1.b:3: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            p(m,n,s(r)) -> p(m,r,n)
            p(m,0(),0()) -> m
            p(m,s(n),0()) -> p(0(),n,m)
        - Signature:
            {p/3} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {p} 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))