/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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


WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            append(cons(x,y),z) -> cons(x,append(y,z))
            append(nil(),y) -> y
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            help(c,l,cons(x,y),z) -> if(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l)
            if(x,false(),z,c,l) -> help(s(c),l,x,z)
            if(x,true(),z,c,l) -> z
            length(cons(x,y)) -> s(length(y))
            length(nil()) -> 0()
            rev(x) -> if(x,eq(0(),length(x)),nil(),0(),length(x))
        - Signature:
            {append/2,ge/2,help/4,if/5,length/1,rev/1} / {0/0,cons/2,eq/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {append,ge,help,if,length,rev} and constructors {0,cons,eq,false
            ,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            append(cons(x,y),z) -> cons(x,append(y,z))
            append(nil(),y) -> y
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            help(c,l,cons(x,y),z) -> if(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l)
            if(x,false(),z,c,l) -> help(s(c),l,x,z)
            if(x,true(),z,c,l) -> z
            length(cons(x,y)) -> s(length(y))
            length(nil()) -> 0()
            rev(x) -> if(x,eq(0(),length(x)),nil(),0(),length(x))
        - Signature:
            {append/2,ge/2,help/4,if/5,length/1,rev/1} / {0/0,cons/2,eq/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {append,ge,help,if,length,rev} and constructors {0,cons,eq,false
            ,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            append(cons(x,y),z) -> cons(x,append(y,z))
            append(nil(),y) -> y
            ge(x,0()) -> true()
            ge(0(),s(y)) -> false()
            ge(s(x),s(y)) -> ge(x,y)
            help(c,l,cons(x,y),z) -> if(append(y,cons(x,nil())),ge(c,l),cons(x,z),c,l)
            if(x,false(),z,c,l) -> help(s(c),l,x,z)
            if(x,true(),z,c,l) -> z
            length(cons(x,y)) -> s(length(y))
            length(nil()) -> 0()
            rev(x) -> if(x,eq(0(),length(x)),nil(),0(),length(x))
        - Signature:
            {append/2,ge/2,help/4,if/5,length/1,rev/1} / {0/0,cons/2,eq/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {append,ge,help,if,length,rev} and constructors {0,cons,eq,false
            ,nil,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          append(y,z){y -> cons(x,y)} =
            append(cons(x,y),z) ->^+ cons(x,append(y,z))
              = C[append(y,z) = append(y,z){}]

WORST_CASE(Omega(n^1),?)