/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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

WORST_CASE(Omega(n^1),?)