Runti Compl Full Rewri 10127 pair #381902798

details

property	value
status	complete
benchmark	#3.12.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n069.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rc
runtime (wallclock)	16.4058439732 seconds
cpu usage	42.10361654
max memory	1.20614912E8

stage attributes

key	value
output-size	51373
starexec-result	WORST_CASE(Omega(n^1),O(n^3))

output

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

** Step 1.b:1: ToInnermost WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict TRS:
            app(add(n,x),y) -> add(n,app(x,y))
            app(nil(),y) -> y
            reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
            reverse(nil()) -> nil()
            shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
            shuffle(nil()) -> nil()
        - Signature:
            {app/2,reverse/1,shuffle/1} / {add/2,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {app,reverse,shuffle} and constructors {add,nil}
    + Applied Processor:
        ToInnermost
    + Details:
        switch to innermost, as the system is overlay and right linear and does not contain weak rules
** Step 1.b:2: DependencyPairs WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict TRS:
            app(add(n,x),y) -> add(n,app(x,y))
            app(nil(),y) -> y
            reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
            reverse(nil()) -> nil()
            shuffle(add(n,x)) -> add(n,shuffle(reverse(x)))
            shuffle(nil()) -> nil()
        - Signature:
            {app/2,reverse/1,shuffle/1} / {add/2,nil/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {app,reverse,shuffle} and constructors {add,nil}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          app#(add(n,x),y) -> c_1(app#(x,y))
          app#(nil(),y) -> c_2()
          reverse#(add(n,x)) -> c_3(app#(reverse(x),add(n,nil())),reverse#(x))
          reverse#(nil()) -> c_4()
          shuffle#(add(n,x)) -> c_5(shuffle#(reverse(x)),reverse#(x))
          shuffle#(nil()) -> c_6()
        Weak DPs
          
        
        and mark the set of starting terms.
** Step 1.b:3: UsableRules WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict DPs:
            app#(add(n,x),y) -> c_1(app#(x,y))
            app#(nil(),y) -> c_2()
            reverse#(add(n,x)) -> c_3(app#(reverse(x),add(n,nil())),reverse#(x))
            reverse#(nil()) -> c_4()
            shuffle#(add(n,x)) -> c_5(shuffle#(reverse(x)),reverse#(x))
            shuffle#(nil()) -> c_6()

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