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


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


WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__diff(X,Y) -> a__if(a__leq(mark(X),mark(Y)),0(),s(diff(p(X),Y)))
            a__diff(X1,X2) -> diff(X1,X2)
            a__if(X1,X2,X3) -> if(X1,X2,X3)
            a__if(false(),X,Y) -> mark(Y)
            a__if(true(),X,Y) -> mark(X)
            a__leq(X1,X2) -> leq(X1,X2)
            a__leq(0(),Y) -> true()
            a__leq(s(X),0()) -> false()
            a__leq(s(X),s(Y)) -> a__leq(mark(X),mark(Y))
            a__p(X) -> p(X)
            a__p(0()) -> 0()
            a__p(s(X)) -> mark(X)
            mark(0()) -> 0()
            mark(diff(X1,X2)) -> a__diff(mark(X1),mark(X2))
            mark(false()) -> false()
            mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
            mark(leq(X1,X2)) -> a__leq(mark(X1),mark(X2))
            mark(p(X)) -> a__p(mark(X))
            mark(s(X)) -> s(mark(X))
            mark(true()) -> true()
        - Signature:
            {a__diff/2,a__if/3,a__leq/2,a__p/1,mark/1} / {0/0,diff/2,false/0,if/3,leq/2,p/1,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__diff,a__if,a__leq,a__p,mark} and constructors {0,diff,false,if
            ,leq,p,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__diff(X,Y) -> a__if(a__leq(mark(X),mark(Y)),0(),s(diff(p(X),Y)))
            a__diff(X1,X2) -> diff(X1,X2)
            a__if(X1,X2,X3) -> if(X1,X2,X3)
            a__if(false(),X,Y) -> mark(Y)
            a__if(true(),X,Y) -> mark(X)
            a__leq(X1,X2) -> leq(X1,X2)
            a__leq(0(),Y) -> true()
            a__leq(s(X),0()) -> false()
            a__leq(s(X),s(Y)) -> a__leq(mark(X),mark(Y))
            a__p(X) -> p(X)
            a__p(0()) -> 0()
            a__p(s(X)) -> mark(X)
            mark(0()) -> 0()
            mark(diff(X1,X2)) -> a__diff(mark(X1),mark(X2))
            mark(false()) -> false()
            mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
            mark(leq(X1,X2)) -> a__leq(mark(X1),mark(X2))
            mark(p(X)) -> a__p(mark(X))
            mark(s(X)) -> s(mark(X))
            mark(true()) -> true()
        - Signature:
            {a__diff/2,a__if/3,a__leq/2,a__p/1,mark/1} / {0/0,diff/2,false/0,if/3,leq/2,p/1,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__diff,a__if,a__leq,a__p,mark} and constructors {0,diff,false,if
            ,leq,p,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__diff(X,Y) -> a__if(a__leq(mark(X),mark(Y)),0(),s(diff(p(X),Y)))
            a__diff(X1,X2) -> diff(X1,X2)
            a__if(X1,X2,X3) -> if(X1,X2,X3)
            a__if(false(),X,Y) -> mark(Y)
            a__if(true(),X,Y) -> mark(X)
            a__leq(X1,X2) -> leq(X1,X2)
            a__leq(0(),Y) -> true()
            a__leq(s(X),0()) -> false()
            a__leq(s(X),s(Y)) -> a__leq(mark(X),mark(Y))
            a__p(X) -> p(X)
            a__p(0()) -> 0()
            a__p(s(X)) -> mark(X)
            mark(0()) -> 0()
            mark(diff(X1,X2)) -> a__diff(mark(X1),mark(X2))
            mark(false()) -> false()
            mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3)
            mark(leq(X1,X2)) -> a__leq(mark(X1),mark(X2))
            mark(p(X)) -> a__p(mark(X))
            mark(s(X)) -> s(mark(X))
            mark(true()) -> true()
        - Signature:
            {a__diff/2,a__if/3,a__leq/2,a__p/1,mark/1} / {0/0,diff/2,false/0,if/3,leq/2,p/1,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__diff,a__if,a__leq,a__p,mark} and constructors {0,diff,false,if
            ,leq,p,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          mark(x){x -> diff(x,y)} =
            mark(diff(x,y)) ->^+ a__diff(mark(x),mark(y))
              = C[mark(x) = mark(x){}]

WORST_CASE(Omega(n^1),?)