Runti Compl Inner Rewri 22807 pair #381904630

details

property	value
status	complete
benchmark	2.12.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n027.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rci
runtime (wallclock)	13.9346978664 seconds
cpu usage	53.384561435
max memory	2.60214784E8

stage attributes

key	value
output-size	53173
starexec-result	WORST_CASE(Omega(n^1),O(n^3))

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

** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict TRS:
            *(0(),y) -> 0()
            *(p(x),y) -> +(*(x,y),minus(y))
            *(s(x),y) -> +(*(x,y),y)
            +(0(),y) -> y
            +(p(x),y) -> p(+(x,y))
            +(s(x),y) -> s(+(x,y))
            minus(0()) -> 0()
            minus(p(x)) -> s(minus(x))
            minus(s(x)) -> p(minus(x))
        - Signature:
            {*/2,+/2,minus/1} / {0/0,p/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*,+,minus} and constructors {0,p,s}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          *#(0(),y) -> c_1()
          *#(p(x),y) -> c_2(+#(*(x,y),minus(y)),*#(x,y),minus#(y))
          *#(s(x),y) -> c_3(+#(*(x,y),y),*#(x,y))
          +#(0(),y) -> c_4()
          +#(p(x),y) -> c_5(+#(x,y))
          +#(s(x),y) -> c_6(+#(x,y))
          minus#(0()) -> c_7()
          minus#(p(x)) -> c_8(minus#(x))
          minus#(s(x)) -> c_9(minus#(x))
        Weak DPs
          
        
        and mark the set of starting terms.
** Step 1.b:2: PredecessorEstimation WORST_CASE(?,O(n^3))
    + Considered Problem:
        - Strict DPs:
            *#(0(),y) -> c_1()
            *#(p(x),y) -> c_2(+#(*(x,y),minus(y)),*#(x,y),minus#(y))
            *#(s(x),y) -> c_3(+#(*(x,y),y),*#(x,y))
            +#(0(),y) -> c_4()
            +#(p(x),y) -> c_5(+#(x,y))
            +#(s(x),y) -> c_6(+#(x,y))
            minus#(0()) -> c_7()
            minus#(p(x)) -> c_8(minus#(x))
            minus#(s(x)) -> c_9(minus#(x))
        - Weak TRS:
            *(0(),y) -> 0()

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