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


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


tct-trs: Prelude.head: empty list
tct-trs: Prelude.head: empty list
tct-trs: Prelude.head: empty list
tct-trs: Prelude.head: empty list
WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            addList(x,y) -> if(le(0(),min(len(x),len(y))),0(),x,y,nil())
            if(false(),c,x,y,z) -> z
            if(true(),c,xs,ys,z) -> if(le(s(c),min(len(xs),len(ys))),s(c),xs,ys,cons(sum(take(c,xs),take(c,ys)),z))
            le(0(),x) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            len(cons(x,xs)) -> s(len(xs))
            len(nil()) -> 0()
            min(0(),y) -> 0()
            min(s(x),0()) -> 0()
            min(s(x),s(y)) -> min(x,y)
            sum(x,0()) -> x
            sum(x,s(y)) -> s(sum(x,y))
            take(0(),cons(y,ys)) -> y
            take(s(x),cons(y,ys)) -> take(x,ys)
        - Signature:
            {addList/2,if/5,le/2,len/1,min/2,sum/2,take/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {addList,if,le,len,min,sum,take} 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:
            addList(x,y) -> if(le(0(),min(len(x),len(y))),0(),x,y,nil())
            if(false(),c,x,y,z) -> z
            if(true(),c,xs,ys,z) -> if(le(s(c),min(len(xs),len(ys))),s(c),xs,ys,cons(sum(take(c,xs),take(c,ys)),z))
            le(0(),x) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            len(cons(x,xs)) -> s(len(xs))
            len(nil()) -> 0()
            min(0(),y) -> 0()
            min(s(x),0()) -> 0()
            min(s(x),s(y)) -> min(x,y)
            sum(x,0()) -> x
            sum(x,s(y)) -> s(sum(x,y))
            take(0(),cons(y,ys)) -> y
            take(s(x),cons(y,ys)) -> take(x,ys)
        - Signature:
            {addList/2,if/5,le/2,len/1,min/2,sum/2,take/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {addList,if,le,len,min,sum,take} 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:
            addList(x,y) -> if(le(0(),min(len(x),len(y))),0(),x,y,nil())
            if(false(),c,x,y,z) -> z
            if(true(),c,xs,ys,z) -> if(le(s(c),min(len(xs),len(ys))),s(c),xs,ys,cons(sum(take(c,xs),take(c,ys)),z))
            le(0(),x) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            len(cons(x,xs)) -> s(len(xs))
            len(nil()) -> 0()
            min(0(),y) -> 0()
            min(s(x),0()) -> 0()
            min(s(x),s(y)) -> min(x,y)
            sum(x,0()) -> x
            sum(x,s(y)) -> s(sum(x,y))
            take(0(),cons(y,ys)) -> y
            take(s(x),cons(y,ys)) -> take(x,ys)
        - Signature:
            {addList/2,if/5,le/2,len/1,min/2,sum/2,take/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {addList,if,le,len,min,sum,take} and constructors {0,cons
            ,false,nil,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          le(x,y){x -> s(x),y -> s(y)} =
            le(s(x),s(y)) ->^+ le(x,y)
              = C[le(x,y) = le(x,y){}]

WORST_CASE(Omega(n^1),?)