/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:
            fac(x) -> loop(x,s(0()),s(0()))
            if(false(),x,c,y) -> loop(x,s(c),times(y,s(c)))
            if(true(),x,c,y) -> y
            loop(x,c,y) -> if(lt(x,c),x,c,y)
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(x,y))
        - Signature:
            {fac/1,if/4,loop/3,lt/2,plus/2,times/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {fac,if,loop,lt,plus,times} 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:
            fac(x) -> loop(x,s(0()),s(0()))
            if(false(),x,c,y) -> loop(x,s(c),times(y,s(c)))
            if(true(),x,c,y) -> y
            loop(x,c,y) -> if(lt(x,c),x,c,y)
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(x,y))
        - Signature:
            {fac/1,if/4,loop/3,lt/2,plus/2,times/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {fac,if,loop,lt,plus,times} 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:
            fac(x) -> loop(x,s(0()),s(0()))
            if(false(),x,c,y) -> loop(x,s(c),times(y,s(c)))
            if(true(),x,c,y) -> y
            loop(x,c,y) -> if(lt(x,c),x,c,y)
            lt(x,0()) -> false()
            lt(0(),s(x)) -> true()
            lt(s(x),s(y)) -> lt(x,y)
            plus(0(),y) -> y
            plus(s(x),y) -> s(plus(x,y))
            times(0(),y) -> 0()
            times(s(x),y) -> plus(y,times(x,y))
        - Signature:
            {fac/1,if/4,loop/3,lt/2,plus/2,times/2} / {0/0,false/0,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {fac,if,loop,lt,plus,times} 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),?)