details

property	value
status	complete
benchmark	11.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n035.star.cs.uiowa.edu
space	Der95

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rc
runtime (wallclock)	2.65784692764 seconds
cpu usage	12.982503269
max memory	2.52444672E8

stage attributes

key	value
output-size	19124
starexec-result	WORST_CASE(Omega(n^1),O(n^2))

output

/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1),O(n^2)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^2)) + Considered Problem: - Strict TRS: D(*(x,y)) -> +(*(y,D(x)),*(x,D(y))) D(+(x,y)) -> +(D(x),D(y)) D(-(x,y)) -> -(D(x),D(y)) D(constant()) -> 0() D(div(x,y)) -> -(div(D(x),y),div(*(x,D(y)),pow(y,2()))) D(ln(x)) -> div(D(x),x) D(minus(x)) -> minus(D(x)) D(pow(x,y)) -> +(*(*(y,pow(x,-(y,1()))),D(x)),*(*(pow(x,y),ln(x)),D(y))) D(t()) -> 1() - Signature: {D/1} / {*/2,+/2,-/2,0/0,1/0,2/0,constant/0,div/2,ln/1,minus/1,pow/2,t/0} - Obligation: runtime complexity wrt. defined symbols {D} and constructors {*,+,-,0,1,2,constant,div,ln,minus,pow,t} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: D(*(x,y)) -> +(*(y,D(x)),*(x,D(y))) D(+(x,y)) -> +(D(x),D(y)) D(-(x,y)) -> -(D(x),D(y)) D(constant()) -> 0() D(div(x,y)) -> -(div(D(x),y),div(*(x,D(y)),pow(y,2()))) D(ln(x)) -> div(D(x),x) D(minus(x)) -> minus(D(x)) D(pow(x,y)) -> +(*(*(y,pow(x,-(y,1()))),D(x)),*(*(pow(x,y),ln(x)),D(y))) D(t()) -> 1() - Signature: {D/1} / {*/2,+/2,-/2,0/0,1/0,2/0,constant/0,div/2,ln/1,minus/1,pow/2,t/0} - Obligation: runtime complexity wrt. defined symbols {D} and constructors {*,+,-,0,1,2,constant,div,ln,minus,pow,t} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: D(x){x -> *(x,y)} = D(*(x,y)) ->^+ +(*(y,D(x)),*(x,D(y))) = C[D(x) = D(x){}] ** Step 1.b:1: NaturalPI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: D(*(x,y)) -> +(*(y,D(x)),*(x,D(y))) D(+(x,y)) -> +(D(x),D(y)) D(-(x,y)) -> -(D(x),D(y)) D(constant()) -> 0() D(div(x,y)) -> -(div(D(x),y),div(*(x,D(y)),pow(y,2()))) D(ln(x)) -> div(D(x),x) D(minus(x)) -> minus(D(x)) D(pow(x,y)) -> +(*(*(y,pow(x,-(y,1()))),D(x)),*(*(pow(x,y),ln(x)),D(y))) D(t()) -> 1() - Signature: {D/1} / {*/2,+/2,-/2,0/0,1/0,2/0,constant/0,div/2,ln/1,minus/1,pow/2,t/0} - Obligation: runtime complexity wrt. defined symbols {D} and constructors {*,+,-,0,1,2,constant,div,ln,minus,pow,t} + Applied Processor: NaturalPI {shape = Mixed 2, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(mixed(2)): The following argument positions are considered usable: uargs(*) = {2}, uargs(+) = {1,2}, uargs(-) = {1,2}, uargs(div) = {1}, uargs(minus) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(*) = 1 + x1 + x2 p(+) = x1 + x2 p(-) = x1 + x2 p(0) = 0 p(1) = 2 p(2) = 5 p(D) = 4*x1 + x1^2 p(constant) = 1 p(div) = 2 + x1 + x2 p(ln) = 2 + x1 p(minus) = 2 + x1 p(pow) = 2 + x1 + x2 p(t) = 2 Following rules are strictly oriented: D(*(x,y)) = 5 + 6*x + 2*x*y + x^2 + 6*y + y^2 > 2 + 5*x + x^2 + 5*y + y^2 = +(*(y,D(x)),*(x,D(y))) popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to Runti Compl Full Rewri 10127