/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:
            fib(x) -> fibiter(x,0(),0(),s(0()))
            fibiter(b,c,x,y) -> if(lt(c,b),b,c,x,y)
            if(false(),b,c,x,y) -> x
            if(true(),b,c,x,y) -> fibiter(b,s(c),y,plus(x,y))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
        - Signature:
            {fib/1,fibiter/4,if/5,lt/2,plus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {fib,fibiter,if,lt,plus} and constructors {0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            fib(x) -> fibiter(x,0(),0(),s(0()))
            fibiter(b,c,x,y) -> if(lt(c,b),b,c,x,y)
            if(false(),b,c,x,y) -> x
            if(true(),b,c,x,y) -> fibiter(b,s(c),y,plus(x,y))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
        - Signature:
            {fib/1,fibiter/4,if/5,lt/2,plus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {fib,fibiter,if,lt,plus} and constructors {0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            fib(x) -> fibiter(x,0(),0(),s(0()))
            fibiter(b,c,x,y) -> if(lt(c,b),b,c,x,y)
            if(false(),b,c,x,y) -> x
            if(true(),b,c,x,y) -> fibiter(b,s(c),y,plus(x,y))
            lt(x,0()) -> false()
            lt(0(),s(y)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
        - Signature:
            {fib/1,fibiter/4,if/5,lt/2,plus/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {fib,fibiter,if,lt,plus} and constructors {0,false,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          lt(x,y){x -> s(x),y -> s(y)} =
            lt(s(x),s(y)) ->^+ lt(x,y)
              = C[lt(x,y) = lt(x,y){}]

WORST_CASE(Omega(n^1),?)