/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


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

** Step 1.b:1: Ara WORST_CASE(?,O(n^2))
    + Considered Problem:
        - Strict TRS:
            -(x,0()) -> x
            -(0(),s(y)) -> 0()
            -(s(x),s(y)) -> -(x,y)
            div(x,0()) -> 0()
            div(0(),y) -> 0()
            div(s(x),s(y)) -> if(lt(x,y),0(),s(div(-(x,y),s(y))))
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
        - Signature:
            {-/2,div/2,if/3,lt/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {-,div,if,lt} and constructors {0,false,s,true}
    + Applied Processor:
        Ara {araHeuristics = Heuristics, minDegree = 1, maxDegree = 2, araTimeout = 3, araRuleShifting = Nothing}
    + Details:
        Signatures used:
        ----------------
          - :: ["A"(4, 1) x "A"(0, 0)] -(1)-> "A"(4, 1)
          0 :: [] -(0)-> "A"(0, 0)
          0 :: [] -(0)-> "A"(4, 1)
          0 :: [] -(0)-> "A"(1, 0)
          div :: ["A"(4, 1) x "A"(0, 0)] -(1)-> "A"(0, 0)
          false :: [] -(0)-> "A"(0, 0)
          if :: ["A"(0, 0) x "A"(0, 0) x "A"(0, 0)] -(1)-> "A"(0, 0)
          lt :: ["A"(1, 0) x "A"(0, 0)] -(1)-> "A"(0, 0)
          s :: ["A"(0, 0)] -(0)-> "A"(0, 0)
          s :: ["A"(5, 1)] -(4)-> "A"(4, 1)
          s :: ["A"(1, 0)] -(1)-> "A"(1, 0)
          true :: [] -(0)-> "A"(0, 0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
          "0_A" :: [] -(0)-> "A"(0)
          "false_A" :: [] -(0)-> "A"(0)
          "s_A" :: ["A"(0)] -(0)-> "A"(0)
          "true_A" :: [] -(0)-> "A"(0)
        

WORST_CASE(Omega(n^1),O(n^2))