/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:
            eq(0(),0()) -> true()
            eq(0(),s(m)) -> false()
            eq(s(n),0()) -> false()
            eq(s(n),s(m)) -> eq(n,m)
            if_min(false(),cons(n,cons(m,x))) -> min(cons(m,x))
            if_min(true(),cons(n,cons(m,x))) -> min(cons(n,x))
            if_replace(false(),n,m,cons(k,x)) -> cons(k,replace(n,m,x))
            if_replace(true(),n,m,cons(k,x)) -> cons(m,x)
            le(0(),m) -> true()
            le(s(n),0()) -> false()
            le(s(n),s(m)) -> le(n,m)
            min(cons(n,cons(m,x))) -> if_min(le(n,m),cons(n,cons(m,x)))
            min(cons(0(),nil())) -> 0()
            min(cons(s(n),nil())) -> s(n)
            replace(n,m,cons(k,x)) -> if_replace(eq(n,k),n,m,cons(k,x))
            replace(n,m,nil()) -> nil()
            sort(cons(n,x)) -> cons(min(cons(n,x)),sort(replace(min(cons(n,x)),n,x)))
            sort(nil()) -> nil()
        - Signature:
            {eq/2,if_min/2,if_replace/4,le/2,min/1,replace/3,sort/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {eq,if_min,if_replace,le,min,replace,sort} and constructors {0,cons
            ,false,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            eq(0(),0()) -> true()
            eq(0(),s(m)) -> false()
            eq(s(n),0()) -> false()
            eq(s(n),s(m)) -> eq(n,m)
            if_min(false(),cons(n,cons(m,x))) -> min(cons(m,x))
            if_min(true(),cons(n,cons(m,x))) -> min(cons(n,x))
            if_replace(false(),n,m,cons(k,x)) -> cons(k,replace(n,m,x))
            if_replace(true(),n,m,cons(k,x)) -> cons(m,x)
            le(0(),m) -> true()
            le(s(n),0()) -> false()
            le(s(n),s(m)) -> le(n,m)
            min(cons(n,cons(m,x))) -> if_min(le(n,m),cons(n,cons(m,x)))
            min(cons(0(),nil())) -> 0()
            min(cons(s(n),nil())) -> s(n)
            replace(n,m,cons(k,x)) -> if_replace(eq(n,k),n,m,cons(k,x))
            replace(n,m,nil()) -> nil()
            sort(cons(n,x)) -> cons(min(cons(n,x)),sort(replace(min(cons(n,x)),n,x)))
            sort(nil()) -> nil()
        - Signature:
            {eq/2,if_min/2,if_replace/4,le/2,min/1,replace/3,sort/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {eq,if_min,if_replace,le,min,replace,sort} and constructors {0,cons
            ,false,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            eq(0(),0()) -> true()
            eq(0(),s(m)) -> false()
            eq(s(n),0()) -> false()
            eq(s(n),s(m)) -> eq(n,m)
            if_min(false(),cons(n,cons(m,x))) -> min(cons(m,x))
            if_min(true(),cons(n,cons(m,x))) -> min(cons(n,x))
            if_replace(false(),n,m,cons(k,x)) -> cons(k,replace(n,m,x))
            if_replace(true(),n,m,cons(k,x)) -> cons(m,x)
            le(0(),m) -> true()
            le(s(n),0()) -> false()
            le(s(n),s(m)) -> le(n,m)
            min(cons(n,cons(m,x))) -> if_min(le(n,m),cons(n,cons(m,x)))
            min(cons(0(),nil())) -> 0()
            min(cons(s(n),nil())) -> s(n)
            replace(n,m,cons(k,x)) -> if_replace(eq(n,k),n,m,cons(k,x))
            replace(n,m,nil()) -> nil()
            sort(cons(n,x)) -> cons(min(cons(n,x)),sort(replace(min(cons(n,x)),n,x)))
            sort(nil()) -> nil()
        - Signature:
            {eq/2,if_min/2,if_replace/4,le/2,min/1,replace/3,sort/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {eq,if_min,if_replace,le,min,replace,sort} and constructors {0,cons
            ,false,nil,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          eq(x,y){x -> s(x),y -> s(y)} =
            eq(s(x),s(y)) ->^+ eq(x,y)
              = C[eq(x,y) = eq(x,y){}]

WORST_CASE(Omega(n^1),?)