/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:
            sub(0(),0()) -> 0()
            sub(0(),s(x)) -> 0()
            sub(s(x),0()) -> s(x)
            sub(s(x),s(y)) -> sub(x,y)
            zero(cons(x,xs)) -> zero2(sub(x,x),cons(x,xs))
            zero(nil()) -> zero2(0(),nil())
            zero2(0(),cons(x,xs)) -> cons(sub(x,x),zero(xs))
            zero2(0(),nil()) -> nil()
            zero2(s(y),cons(x,xs)) -> zero(cons(x,xs))
            zero2(s(y),nil()) -> zero(nil())
        - Signature:
            {sub/2,zero/1,zero2/2} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {sub,zero,zero2} and constructors {0,cons,nil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            sub(0(),0()) -> 0()
            sub(0(),s(x)) -> 0()
            sub(s(x),0()) -> s(x)
            sub(s(x),s(y)) -> sub(x,y)
            zero(cons(x,xs)) -> zero2(sub(x,x),cons(x,xs))
            zero(nil()) -> zero2(0(),nil())
            zero2(0(),cons(x,xs)) -> cons(sub(x,x),zero(xs))
            zero2(0(),nil()) -> nil()
            zero2(s(y),cons(x,xs)) -> zero(cons(x,xs))
            zero2(s(y),nil()) -> zero(nil())
        - Signature:
            {sub/2,zero/1,zero2/2} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {sub,zero,zero2} and constructors {0,cons,nil,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            sub(0(),0()) -> 0()
            sub(0(),s(x)) -> 0()
            sub(s(x),0()) -> s(x)
            sub(s(x),s(y)) -> sub(x,y)
            zero(cons(x,xs)) -> zero2(sub(x,x),cons(x,xs))
            zero(nil()) -> zero2(0(),nil())
            zero2(0(),cons(x,xs)) -> cons(sub(x,x),zero(xs))
            zero2(0(),nil()) -> nil()
            zero2(s(y),cons(x,xs)) -> zero(cons(x,xs))
            zero2(s(y),nil()) -> zero(nil())
        - Signature:
            {sub/2,zero/1,zero2/2} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {sub,zero,zero2} and constructors {0,cons,nil,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          sub(x,y){x -> s(x),y -> s(y)} =
            sub(s(x),s(y)) ->^+ sub(x,y)
              = C[sub(x,y) = sub(x,y){}]

WORST_CASE(Omega(n^1),?)