/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:
            choice(cons(x,xs)) -> x
            choice(cons(x,xs)) -> choice(xs)
            eq(0(x),1(y)) -> false()
            eq(1(x),0(y)) -> false()
            eq(1(x),1(y)) -> eq(x,y)
            eq(O(x),0(y)) -> eq(x,y)
            eq(nil(),nil()) -> true()
            guess(cons(clause,cnf)) -> cons(choice(clause),guess(cnf))
            guess(nil()) -> nil()
            if(false(),t,e) -> e
            if(true(),t,e) -> t
            member(x,cons(y,ys)) -> if(eq(x,y),true(),member(x,ys))
            member(x,nil()) -> false()
            negate(0(x)) -> 1(x)
            negate(1(x)) -> 0(x)
            sat(cnf) -> satck(cnf,guess(cnf))
            satck(cnf,assign) -> if(verify(assign),assign,unsat())
            verify(cons(l,ls)) -> if(member(negate(l),ls),false(),verify(ls))
            verify(nil()) -> true()
        - Signature:
            {choice/1,eq/2,guess/1,if/3,member/2,negate/1,sat/1,satck/2,verify/1} / {0/1,1/1,O/1,cons/2,false/0,nil/0
            ,true/0,unsat/0}
        - Obligation:
             runtime complexity wrt. defined symbols {choice,eq,guess,if,member,negate,sat,satck
            ,verify} and constructors {0,1,O,cons,false,nil,true,unsat}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            choice(cons(x,xs)) -> x
            choice(cons(x,xs)) -> choice(xs)
            eq(0(x),1(y)) -> false()
            eq(1(x),0(y)) -> false()
            eq(1(x),1(y)) -> eq(x,y)
            eq(O(x),0(y)) -> eq(x,y)
            eq(nil(),nil()) -> true()
            guess(cons(clause,cnf)) -> cons(choice(clause),guess(cnf))
            guess(nil()) -> nil()
            if(false(),t,e) -> e
            if(true(),t,e) -> t
            member(x,cons(y,ys)) -> if(eq(x,y),true(),member(x,ys))
            member(x,nil()) -> false()
            negate(0(x)) -> 1(x)
            negate(1(x)) -> 0(x)
            sat(cnf) -> satck(cnf,guess(cnf))
            satck(cnf,assign) -> if(verify(assign),assign,unsat())
            verify(cons(l,ls)) -> if(member(negate(l),ls),false(),verify(ls))
            verify(nil()) -> true()
        - Signature:
            {choice/1,eq/2,guess/1,if/3,member/2,negate/1,sat/1,satck/2,verify/1} / {0/1,1/1,O/1,cons/2,false/0,nil/0
            ,true/0,unsat/0}
        - Obligation:
             runtime complexity wrt. defined symbols {choice,eq,guess,if,member,negate,sat,satck
            ,verify} and constructors {0,1,O,cons,false,nil,true,unsat}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            choice(cons(x,xs)) -> x
            choice(cons(x,xs)) -> choice(xs)
            eq(0(x),1(y)) -> false()
            eq(1(x),0(y)) -> false()
            eq(1(x),1(y)) -> eq(x,y)
            eq(O(x),0(y)) -> eq(x,y)
            eq(nil(),nil()) -> true()
            guess(cons(clause,cnf)) -> cons(choice(clause),guess(cnf))
            guess(nil()) -> nil()
            if(false(),t,e) -> e
            if(true(),t,e) -> t
            member(x,cons(y,ys)) -> if(eq(x,y),true(),member(x,ys))
            member(x,nil()) -> false()
            negate(0(x)) -> 1(x)
            negate(1(x)) -> 0(x)
            sat(cnf) -> satck(cnf,guess(cnf))
            satck(cnf,assign) -> if(verify(assign),assign,unsat())
            verify(cons(l,ls)) -> if(member(negate(l),ls),false(),verify(ls))
            verify(nil()) -> true()
        - Signature:
            {choice/1,eq/2,guess/1,if/3,member/2,negate/1,sat/1,satck/2,verify/1} / {0/1,1/1,O/1,cons/2,false/0,nil/0
            ,true/0,unsat/0}
        - Obligation:
             runtime complexity wrt. defined symbols {choice,eq,guess,if,member,negate,sat,satck
            ,verify} and constructors {0,1,O,cons,false,nil,true,unsat}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          choice(y){y -> cons(x,y)} =
            choice(cons(x,y)) ->^+ choice(y)
              = C[choice(y) = choice(y){}]

WORST_CASE(Omega(n^1),?)