Runti Compl Inner Rewri 22807 pair #381904394

details

property	value
status	timeout (wallclock)
benchmark	thiemann03.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
space	AProVE_07

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rci
runtime (wallclock)	295.420130014 seconds
cpu usage	1233.3869805
max memory	5.640491008E9

stage attributes

unavailable

output

/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /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:
            app(add(n,x),y) -> add(n,app(x,y))
            app(nil(),y) -> y
            head(add(n,x)) -> n
            if(false(),x,y,z) -> shuff(reverse(tail(x)),z)
            if(true(),x,y,z) -> y
            null(add(n,x)) -> false()
            null(nil()) -> true()
            reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
            reverse(nil()) -> nil()
            shuff(x,y) -> if(null(x),x,y,app(y,add(head(x),nil())))
            shuffle(x) -> shuff(x,nil())
            tail(add(n,x)) -> x
            tail(nil()) -> nil()
        - Signature:
            {app/2,head/1,if/4,null/1,reverse/1,shuff/2,shuffle/1,tail/1} / {add/2,false/0,nil/0,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {app,head,if,null,reverse,shuff,shuffle
            ,tail} and constructors {add,false,nil,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            app(add(n,x),y) -> add(n,app(x,y))
            app(nil(),y) -> y
            head(add(n,x)) -> n
            if(false(),x,y,z) -> shuff(reverse(tail(x)),z)
            if(true(),x,y,z) -> y
            null(add(n,x)) -> false()
            null(nil()) -> true()
            reverse(add(n,x)) -> app(reverse(x),add(n,nil()))
            reverse(nil()) -> nil()
            shuff(x,y) -> if(null(x),x,y,app(y,add(head(x),nil())))
            shuffle(x) -> shuff(x,nil())
            tail(add(n,x)) -> x
            tail(nil()) -> nil()
        - Signature:
            {app/2,head/1,if/4,null/1,reverse/1,shuff/2,shuffle/1,tail/1} / {add/2,false/0,nil/0,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {app,head,if,null,reverse,shuff,shuffle
            ,tail} and constructors {add,false,nil,true}
    + 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){}]

WORST_CASE(Omega(n^1),?)

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