/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:
            empty(cons(n,x)) -> false()
            empty(nil()) -> true()
            head(cons(n,x)) -> n
            if(false(),b,x) -> if2(b,x)
            if(true(),b,x) -> weight_undefined_error()
            if2(false(),x) -> weight(sum(x,cons(0(),tail(tail(x)))))
            if2(true(),x) -> head(x)
            sum(cons(0(),x),y) -> sum(x,y)
            sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y))
            sum(nil(),y) -> y
            tail(cons(n,x)) -> x
            tail(nil()) -> nil()
            weight(x) -> if(empty(x),empty(tail(x)),x)
        - Signature:
            {empty/1,head/1,if/3,if2/2,sum/2,tail/1,weight/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0
            ,weight_undefined_error/0}
        - Obligation:
             runtime complexity wrt. defined symbols {empty,head,if,if2,sum,tail,weight} and constructors {0,cons,false
            ,nil,s,true,weight_undefined_error}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            empty(cons(n,x)) -> false()
            empty(nil()) -> true()
            head(cons(n,x)) -> n
            if(false(),b,x) -> if2(b,x)
            if(true(),b,x) -> weight_undefined_error()
            if2(false(),x) -> weight(sum(x,cons(0(),tail(tail(x)))))
            if2(true(),x) -> head(x)
            sum(cons(0(),x),y) -> sum(x,y)
            sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y))
            sum(nil(),y) -> y
            tail(cons(n,x)) -> x
            tail(nil()) -> nil()
            weight(x) -> if(empty(x),empty(tail(x)),x)
        - Signature:
            {empty/1,head/1,if/3,if2/2,sum/2,tail/1,weight/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0
            ,weight_undefined_error/0}
        - Obligation:
             runtime complexity wrt. defined symbols {empty,head,if,if2,sum,tail,weight} and constructors {0,cons,false
            ,nil,s,true,weight_undefined_error}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            empty(cons(n,x)) -> false()
            empty(nil()) -> true()
            head(cons(n,x)) -> n
            if(false(),b,x) -> if2(b,x)
            if(true(),b,x) -> weight_undefined_error()
            if2(false(),x) -> weight(sum(x,cons(0(),tail(tail(x)))))
            if2(true(),x) -> head(x)
            sum(cons(0(),x),y) -> sum(x,y)
            sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y))
            sum(nil(),y) -> y
            tail(cons(n,x)) -> x
            tail(nil()) -> nil()
            weight(x) -> if(empty(x),empty(tail(x)),x)
        - Signature:
            {empty/1,head/1,if/3,if2/2,sum/2,tail/1,weight/1} / {0/0,cons/2,false/0,nil/0,s/1,true/0
            ,weight_undefined_error/0}
        - Obligation:
             runtime complexity wrt. defined symbols {empty,head,if,if2,sum,tail,weight} and constructors {0,cons,false
            ,nil,s,true,weight_undefined_error}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          sum(x,y){x -> cons(0(),x)} =
            sum(cons(0(),x),y) ->^+ sum(x,y)
              = C[sum(x,y) = sum(x,y){}]

WORST_CASE(Omega(n^1),?)