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

WORST_CASE(Omega(n^1),?)