/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:
            +(x,#()) -> x
            +(x,+(y,z)) -> +(+(x,y),z)
            +(#(),x) -> x
            +(0(x),0(y)) -> 0(+(x,y))
            +(0(x),1(y)) -> 1(+(x,y))
            +(1(x),0(y)) -> 1(+(x,y))
            +(1(x),1(y)) -> 0(+(+(x,y),1(#())))
            -(x,#()) -> x
            -(#(),x) -> #()
            -(0(x),0(y)) -> 0(-(x,y))
            -(0(x),1(y)) -> 1(-(-(x,y),1(#())))
            -(1(x),0(y)) -> 1(-(x,y))
            -(1(x),1(y)) -> 0(-(x,y))
            0(#()) -> #()
            and(x,false()) -> false()
            and(x,true()) -> x
            bs(l(x)) -> true()
            bs(n(x,y,z)) -> and(and(ge(x,max(y)),ge(min(z),x)),and(bs(y),bs(z)))
            ge(x,#()) -> true()
            ge(#(),0(x)) -> ge(#(),x)
            ge(#(),1(x)) -> false()
            ge(0(x),0(y)) -> ge(x,y)
            ge(0(x),1(y)) -> not(ge(y,x))
            ge(1(x),0(y)) -> ge(x,y)
            ge(1(x),1(y)) -> ge(x,y)
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            max(l(x)) -> x
            max(n(x,y,z)) -> max(z)
            min(l(x)) -> x
            min(n(x,y,z)) -> min(y)
            not(false()) -> true()
            not(true()) -> false()
            size(l(x)) -> 1(#())
            size(n(x,y,z)) -> +(+(size(x),size(y)),1(#()))
            val(l(x)) -> x
            val(n(x,y,z)) -> x
            wb(l(x)) -> true()
            wb(n(x,y,z)) -> and(if(ge(size(y),size(z)),ge(1(#()),-(size(y),size(z))),ge(1(#()),-(size(z),size(y))))
                               ,and(wb(y),wb(z)))
        - Signature:
            {+/2,-/2,0/1,and/2,bs/1,ge/2,if/3,max/1,min/1,not/1,size/1,val/1,wb/1} / {#/0,1/1,false/0,l/1,n/3,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {+,-,0,and,bs,ge,if,max,min,not,size,val,wb} and constructors {#,1
            ,false,l,n,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            +(x,#()) -> x
            +(x,+(y,z)) -> +(+(x,y),z)
            +(#(),x) -> x
            +(0(x),0(y)) -> 0(+(x,y))
            +(0(x),1(y)) -> 1(+(x,y))
            +(1(x),0(y)) -> 1(+(x,y))
            +(1(x),1(y)) -> 0(+(+(x,y),1(#())))
            -(x,#()) -> x
            -(#(),x) -> #()
            -(0(x),0(y)) -> 0(-(x,y))
            -(0(x),1(y)) -> 1(-(-(x,y),1(#())))
            -(1(x),0(y)) -> 1(-(x,y))
            -(1(x),1(y)) -> 0(-(x,y))
            0(#()) -> #()
            and(x,false()) -> false()
            and(x,true()) -> x
            bs(l(x)) -> true()
            bs(n(x,y,z)) -> and(and(ge(x,max(y)),ge(min(z),x)),and(bs(y),bs(z)))
            ge(x,#()) -> true()
            ge(#(),0(x)) -> ge(#(),x)
            ge(#(),1(x)) -> false()
            ge(0(x),0(y)) -> ge(x,y)
            ge(0(x),1(y)) -> not(ge(y,x))
            ge(1(x),0(y)) -> ge(x,y)
            ge(1(x),1(y)) -> ge(x,y)
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            max(l(x)) -> x
            max(n(x,y,z)) -> max(z)
            min(l(x)) -> x
            min(n(x,y,z)) -> min(y)
            not(false()) -> true()
            not(true()) -> false()
            size(l(x)) -> 1(#())
            size(n(x,y,z)) -> +(+(size(x),size(y)),1(#()))
            val(l(x)) -> x
            val(n(x,y,z)) -> x
            wb(l(x)) -> true()
            wb(n(x,y,z)) -> and(if(ge(size(y),size(z)),ge(1(#()),-(size(y),size(z))),ge(1(#()),-(size(z),size(y))))
                               ,and(wb(y),wb(z)))
        - Signature:
            {+/2,-/2,0/1,and/2,bs/1,ge/2,if/3,max/1,min/1,not/1,size/1,val/1,wb/1} / {#/0,1/1,false/0,l/1,n/3,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {+,-,0,and,bs,ge,if,max,min,not,size,val,wb} and constructors {#,1
            ,false,l,n,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            +(x,#()) -> x
            +(x,+(y,z)) -> +(+(x,y),z)
            +(#(),x) -> x
            +(0(x),0(y)) -> 0(+(x,y))
            +(0(x),1(y)) -> 1(+(x,y))
            +(1(x),0(y)) -> 1(+(x,y))
            +(1(x),1(y)) -> 0(+(+(x,y),1(#())))
            -(x,#()) -> x
            -(#(),x) -> #()
            -(0(x),0(y)) -> 0(-(x,y))
            -(0(x),1(y)) -> 1(-(-(x,y),1(#())))
            -(1(x),0(y)) -> 1(-(x,y))
            -(1(x),1(y)) -> 0(-(x,y))
            0(#()) -> #()
            and(x,false()) -> false()
            and(x,true()) -> x
            bs(l(x)) -> true()
            bs(n(x,y,z)) -> and(and(ge(x,max(y)),ge(min(z),x)),and(bs(y),bs(z)))
            ge(x,#()) -> true()
            ge(#(),0(x)) -> ge(#(),x)
            ge(#(),1(x)) -> false()
            ge(0(x),0(y)) -> ge(x,y)
            ge(0(x),1(y)) -> not(ge(y,x))
            ge(1(x),0(y)) -> ge(x,y)
            ge(1(x),1(y)) -> ge(x,y)
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            max(l(x)) -> x
            max(n(x,y,z)) -> max(z)
            min(l(x)) -> x
            min(n(x,y,z)) -> min(y)
            not(false()) -> true()
            not(true()) -> false()
            size(l(x)) -> 1(#())
            size(n(x,y,z)) -> +(+(size(x),size(y)),1(#()))
            val(l(x)) -> x
            val(n(x,y,z)) -> x
            wb(l(x)) -> true()
            wb(n(x,y,z)) -> and(if(ge(size(y),size(z)),ge(1(#()),-(size(y),size(z))),ge(1(#()),-(size(z),size(y))))
                               ,and(wb(y),wb(z)))
        - Signature:
            {+/2,-/2,0/1,and/2,bs/1,ge/2,if/3,max/1,min/1,not/1,size/1,val/1,wb/1} / {#/0,1/1,false/0,l/1,n/3,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {+,-,0,and,bs,ge,if,max,min,not,size,val,wb} and constructors {#,1
            ,false,l,n,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          +(x,y){x -> 1(x),y -> 1(y)} =
            +(1(x),1(y)) ->^+ 0(+(+(x,y),1(#())))
              = C[+(x,y) = +(x,y){}]

WORST_CASE(Omega(n^1),?)