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


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WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            eq(0(),0()) -> true()
            eq(0(),s(y)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            if1(false(),x,y,xs) -> min(cons(y,xs))
            if1(true(),x,y,xs) -> min(cons(x,xs))
            if2(false(),x,y,xs) -> cons(y,rm(x,xs))
            if2(true(),x,y,xs) -> rm(x,xs)
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            min(cons(x,cons(y,xs))) -> if1(le(x,y),x,y,xs)
            min(cons(x,nil())) -> x
            min(nil()) -> 0()
            minsort(cons(x,xs)) -> cons(min(cons(x,xs)),minsort(rm(min(cons(x,xs)),cons(x,xs))))
            minsort(nil()) -> nil()
            rm(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
            rm(x,nil()) -> nil()
        - Signature:
            {eq/2,if1/4,if2/4,le/2,min/1,minsort/1,rm/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {eq,if1,if2,le,min,minsort,rm} 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(y)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            if1(false(),x,y,xs) -> min(cons(y,xs))
            if1(true(),x,y,xs) -> min(cons(x,xs))
            if2(false(),x,y,xs) -> cons(y,rm(x,xs))
            if2(true(),x,y,xs) -> rm(x,xs)
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            min(cons(x,cons(y,xs))) -> if1(le(x,y),x,y,xs)
            min(cons(x,nil())) -> x
            min(nil()) -> 0()
            minsort(cons(x,xs)) -> cons(min(cons(x,xs)),minsort(rm(min(cons(x,xs)),cons(x,xs))))
            minsort(nil()) -> nil()
            rm(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
            rm(x,nil()) -> nil()
        - Signature:
            {eq/2,if1/4,if2/4,le/2,min/1,minsort/1,rm/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {eq,if1,if2,le,min,minsort,rm} 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(y)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            if1(false(),x,y,xs) -> min(cons(y,xs))
            if1(true(),x,y,xs) -> min(cons(x,xs))
            if2(false(),x,y,xs) -> cons(y,rm(x,xs))
            if2(true(),x,y,xs) -> rm(x,xs)
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            min(cons(x,cons(y,xs))) -> if1(le(x,y),x,y,xs)
            min(cons(x,nil())) -> x
            min(nil()) -> 0()
            minsort(cons(x,xs)) -> cons(min(cons(x,xs)),minsort(rm(min(cons(x,xs)),cons(x,xs))))
            minsort(nil()) -> nil()
            rm(x,cons(y,xs)) -> if2(eq(x,y),x,y,xs)
            rm(x,nil()) -> nil()
        - Signature:
            {eq/2,if1/4,if2/4,le/2,min/1,minsort/1,rm/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {eq,if1,if2,le,min,minsort,rm} 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),?)