/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(NON_POLY,?)
* Step 1: Sum.  WORST_CASE(NON_POLY,?)
    + Considered Problem:
        - Strict TRS:
            fib(0()) -> s(0())
            fib(s(0())) -> s(0())
            fib(s(s(x))) -> if(true(),0(),s(s(x)),0(),0())
            fibo(0()) -> fib(0())
            fibo(s(0())) -> fib(s(0()))
            fibo(s(s(x))) -> sum(fibo(s(x)),fibo(x))
            if(false(),c,s(s(x)),a,b) -> sum(fibo(a),fibo(b))
            if(true(),c,s(s(x)),a,b) -> if(lt(s(c),s(s(x))),s(c),s(s(x)),b,c)
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
            sum(x,0()) -> x
            sum(x,s(y)) -> s(sum(x,y))
        - Signature:
            {fib/1,fibo/1,if/5,lt/2,sum/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {fib,fibo,if,lt,sum} and constructors {0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(NON_POLY,?)
    + Considered Problem:
        - Strict TRS:
            fib(0()) -> s(0())
            fib(s(0())) -> s(0())
            fib(s(s(x))) -> if(true(),0(),s(s(x)),0(),0())
            fibo(0()) -> fib(0())
            fibo(s(0())) -> fib(s(0()))
            fibo(s(s(x))) -> sum(fibo(s(x)),fibo(x))
            if(false(),c,s(s(x)),a,b) -> sum(fibo(a),fibo(b))
            if(true(),c,s(s(x)),a,b) -> if(lt(s(c),s(s(x))),s(c),s(s(x)),b,c)
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
            sum(x,0()) -> x
            sum(x,s(y)) -> s(sum(x,y))
        - Signature:
            {fib/1,fibo/1,if/5,lt/2,sum/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {fib,fibo,if,lt,sum} and constructors {0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(NON_POLY,?)
    + Considered Problem:
        - Strict TRS:
            fib(0()) -> s(0())
            fib(s(0())) -> s(0())
            fib(s(s(x))) -> if(true(),0(),s(s(x)),0(),0())
            fibo(0()) -> fib(0())
            fibo(s(0())) -> fib(s(0()))
            fibo(s(s(x))) -> sum(fibo(s(x)),fibo(x))
            if(false(),c,s(s(x)),a,b) -> sum(fibo(a),fibo(b))
            if(true(),c,s(s(x)),a,b) -> if(lt(s(c),s(s(x))),s(c),s(s(x)),b,c)
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
            sum(x,0()) -> x
            sum(x,s(y)) -> s(sum(x,y))
        - Signature:
            {fib/1,fibo/1,if/5,lt/2,sum/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {fib,fibo,if,lt,sum} and constructors {0,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          fibo(s(x)){x -> s(x)} =
            fibo(s(s(x))) ->^+ sum(fibo(s(x)),fibo(x))
              = C[fibo(s(x)) = fibo(s(x)){}]
          fibo(x){x -> s(s(x))} =
            fibo(s(s(x))) ->^+ sum(fibo(s(x)),fibo(x))
              = C[fibo(x) = fibo(x){}]

WORST_CASE(NON_POLY,?)