Runti Compl Inner Rewri 22807 pair #381904313

details

property	value
status	complete
benchmark	#4.33.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n038.star.cs.uiowa.edu
space	Strategy_removed_AG01

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rci
runtime (wallclock)	8.15144920349 seconds
cpu usage	39.275103734
max memory	1.9822592E8

stage attributes

key	value
output-size	22267
starexec-result	WORST_CASE(Omega(n^1),O(n^3))

output

/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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

** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict TRS:
            sum(cons(0(),x),y) -> sum(x,y)
            sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y))
            sum(nil(),y) -> y
            weight(cons(n,cons(m,x))) -> weight(sum(cons(n,cons(m,x)),cons(0(),x)))
            weight(cons(n,nil())) -> n
        - Signature:
            {sum/2,weight/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {sum,weight} and constructors {0,cons,nil,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          sum#(cons(0(),x),y) -> c_1(sum#(x,y))
          sum#(cons(s(n),x),cons(m,y)) -> c_2(sum#(cons(n,x),cons(s(m),y)))
          sum#(nil(),y) -> c_3()
          weight#(cons(n,cons(m,x))) -> c_4(weight#(sum(cons(n,cons(m,x)),cons(0(),x)))
                                           ,sum#(cons(n,cons(m,x)),cons(0(),x)))
          weight#(cons(n,nil())) -> c_5()
        Weak DPs
          
        
        and mark the set of starting terms.
** Step 1.b:2: PredecessorEstimation WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict DPs:
            sum#(cons(0(),x),y) -> c_1(sum#(x,y))
            sum#(cons(s(n),x),cons(m,y)) -> c_2(sum#(cons(n,x),cons(s(m),y)))
            sum#(nil(),y) -> c_3()
            weight#(cons(n,cons(m,x))) -> c_4(weight#(sum(cons(n,cons(m,x)),cons(0(),x)))
                                             ,sum#(cons(n,cons(m,x)),cons(0(),x)))
            weight#(cons(n,nil())) -> c_5()
        - Weak TRS:
            sum(cons(0(),x),y) -> sum(x,y)
            sum(cons(s(n),x),cons(m,y)) -> sum(cons(n,x),cons(s(m),y))
            sum(nil(),y) -> y
            weight(cons(n,cons(m,x))) -> weight(sum(cons(n,cons(m,x)),cons(0(),x)))
            weight(cons(n,nil())) -> n
        - Signature:
            {sum/2,weight/1,sum#/2,weight#/1} / {0/0,cons/2,nil/0,s/1,c_1/1,c_2/1,c_3/0,c_4/2,c_5/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {sum#,weight#} and constructors {0,cons,nil,s}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {3,5}
        by application of
          Pre({3,5}) = {1,4}.
        Here rules are labelled as follows:
          1: sum#(cons(0(),x),y) -> c_1(sum#(x,y))
          2: sum#(cons(s(n),x),cons(m,y)) -> c_2(sum#(cons(n,x),cons(s(m),y)))

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