/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:
            count(n,x) -> if(isEmpty(n)
                            ,isEmpty(left(n))
                            ,right(n)
                            ,node(left(left(n)),node(right(left(n)),right(n)))
                            ,x
                            ,inc(x))
            if(false(),false(),n,m,x,y) -> count(m,x)
            if(false(),true(),n,m,x,y) -> count(n,y)
            if(true(),b,n,m,x,y) -> x
            inc(0()) -> s(0())
            inc(s(x)) -> s(inc(x))
            isEmpty(empty()) -> true()
            isEmpty(node(l,r)) -> false()
            left(empty()) -> empty()
            left(node(l,r)) -> l
            nrOfNodes(n) -> count(n,0())
            right(empty()) -> empty()
            right(node(l,r)) -> r
        - Signature:
            {count/2,if/6,inc/1,isEmpty/1,left/1,nrOfNodes/1,right/1} / {0/0,empty/0,false/0,node/2,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {count,if,inc,isEmpty,left,nrOfNodes,right} and constructors {0
            ,empty,false,node,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            count(n,x) -> if(isEmpty(n)
                            ,isEmpty(left(n))
                            ,right(n)
                            ,node(left(left(n)),node(right(left(n)),right(n)))
                            ,x
                            ,inc(x))
            if(false(),false(),n,m,x,y) -> count(m,x)
            if(false(),true(),n,m,x,y) -> count(n,y)
            if(true(),b,n,m,x,y) -> x
            inc(0()) -> s(0())
            inc(s(x)) -> s(inc(x))
            isEmpty(empty()) -> true()
            isEmpty(node(l,r)) -> false()
            left(empty()) -> empty()
            left(node(l,r)) -> l
            nrOfNodes(n) -> count(n,0())
            right(empty()) -> empty()
            right(node(l,r)) -> r
        - Signature:
            {count/2,if/6,inc/1,isEmpty/1,left/1,nrOfNodes/1,right/1} / {0/0,empty/0,false/0,node/2,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {count,if,inc,isEmpty,left,nrOfNodes,right} and constructors {0
            ,empty,false,node,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            count(n,x) -> if(isEmpty(n)
                            ,isEmpty(left(n))
                            ,right(n)
                            ,node(left(left(n)),node(right(left(n)),right(n)))
                            ,x
                            ,inc(x))
            if(false(),false(),n,m,x,y) -> count(m,x)
            if(false(),true(),n,m,x,y) -> count(n,y)
            if(true(),b,n,m,x,y) -> x
            inc(0()) -> s(0())
            inc(s(x)) -> s(inc(x))
            isEmpty(empty()) -> true()
            isEmpty(node(l,r)) -> false()
            left(empty()) -> empty()
            left(node(l,r)) -> l
            nrOfNodes(n) -> count(n,0())
            right(empty()) -> empty()
            right(node(l,r)) -> r
        - Signature:
            {count/2,if/6,inc/1,isEmpty/1,left/1,nrOfNodes/1,right/1} / {0/0,empty/0,false/0,node/2,s/1,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {count,if,inc,isEmpty,left,nrOfNodes,right} and constructors {0
            ,empty,false,node,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          inc(x){x -> s(x)} =
            inc(s(x)) ->^+ s(inc(x))
              = C[inc(x) = inc(x){}]

WORST_CASE(Omega(n^1),?)