/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),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
            del(x,nil()) -> nil()
            min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
            min(x,nil()) -> x
            msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
            msort(nil()) -> nil()
        - Signature:
            {del/2,min/2,msort/1} / {./2,<=/2,=/2,if/3,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {del,min,msort} and constructors {.,<=,=,if,nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
            del(x,nil()) -> nil()
            min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
            min(x,nil()) -> x
            msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
            msort(nil()) -> nil()
        - Signature:
            {del/2,min/2,msort/1} / {./2,<=/2,=/2,if/3,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {del,min,msort} and constructors {.,<=,=,if,nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z)))
            del(x,nil()) -> nil()
            min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z))
            min(x,nil()) -> x
            msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y))))
            msort(nil()) -> nil()
        - Signature:
            {del/2,min/2,msort/1} / {./2,<=/2,=/2,if/3,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {del,min,msort} and constructors {.,<=,=,if,nil}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          del(x,z){z -> .(y,z)} =
            del(x,.(y,z)) ->^+ if(=(x,y),z,.(y,del(x,z)))
              = C[del(x,z) = del(x,z){}]

WORST_CASE(Omega(n^1),?)