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Runti Compl Full Rewri 10127 pair #381902753
details
property
value
status
complete
benchmark
polo2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n072.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
3.9862639904 seconds
cpu usage
18.35662057
max memory
6.259712E8
stage attributes
key
value
output-size
23908
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: dx(X) -> one() dx(a()) -> zero() dx(div(ALPHA,BETA)) -> minus(div(dx(ALPHA),BETA),times(ALPHA,div(dx(BETA),exp(BETA,two())))) dx(exp(ALPHA,BETA)) -> plus(times(BETA,times(exp(ALPHA,minus(BETA,one())),dx(ALPHA))) ,times(exp(ALPHA,BETA),times(ln(ALPHA),dx(BETA)))) dx(ln(ALPHA)) -> div(dx(ALPHA),ALPHA) dx(minus(ALPHA,BETA)) -> minus(dx(ALPHA),dx(BETA)) dx(neg(ALPHA)) -> neg(dx(ALPHA)) dx(plus(ALPHA,BETA)) -> plus(dx(ALPHA),dx(BETA)) dx(times(ALPHA,BETA)) -> plus(times(BETA,dx(ALPHA)),times(ALPHA,dx(BETA))) - Signature: {dx/1} / {a/0,div/2,exp/2,ln/1,minus/2,neg/1,one/0,plus/2,times/2,two/0,zero/0} - Obligation: runtime complexity wrt. defined symbols {dx} and constructors {a,div,exp,ln,minus,neg,one,plus,times,two ,zero} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: dx(X) -> one() dx(a()) -> zero() dx(div(ALPHA,BETA)) -> minus(div(dx(ALPHA),BETA),times(ALPHA,div(dx(BETA),exp(BETA,two())))) dx(exp(ALPHA,BETA)) -> plus(times(BETA,times(exp(ALPHA,minus(BETA,one())),dx(ALPHA))) ,times(exp(ALPHA,BETA),times(ln(ALPHA),dx(BETA)))) dx(ln(ALPHA)) -> div(dx(ALPHA),ALPHA) dx(minus(ALPHA,BETA)) -> minus(dx(ALPHA),dx(BETA)) dx(neg(ALPHA)) -> neg(dx(ALPHA)) dx(plus(ALPHA,BETA)) -> plus(dx(ALPHA),dx(BETA)) dx(times(ALPHA,BETA)) -> plus(times(BETA,dx(ALPHA)),times(ALPHA,dx(BETA))) - Signature: {dx/1} / {a/0,div/2,exp/2,ln/1,minus/2,neg/1,one/0,plus/2,times/2,two/0,zero/0} - Obligation: runtime complexity wrt. defined symbols {dx} and constructors {a,div,exp,ln,minus,neg,one,plus,times,two ,zero} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: dx(x){x -> div(x,y)} = dx(div(x,y)) ->^+ minus(div(dx(x),y),times(x,div(dx(y),exp(y,two())))) = C[dx(x) = dx(x){}] ** Step 1.b:1: NaturalPI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: dx(X) -> one() dx(a()) -> zero() dx(div(ALPHA,BETA)) -> minus(div(dx(ALPHA),BETA),times(ALPHA,div(dx(BETA),exp(BETA,two())))) dx(exp(ALPHA,BETA)) -> plus(times(BETA,times(exp(ALPHA,minus(BETA,one())),dx(ALPHA))) ,times(exp(ALPHA,BETA),times(ln(ALPHA),dx(BETA)))) dx(ln(ALPHA)) -> div(dx(ALPHA),ALPHA) dx(minus(ALPHA,BETA)) -> minus(dx(ALPHA),dx(BETA)) dx(neg(ALPHA)) -> neg(dx(ALPHA)) dx(plus(ALPHA,BETA)) -> plus(dx(ALPHA),dx(BETA)) dx(times(ALPHA,BETA)) -> plus(times(BETA,dx(ALPHA)),times(ALPHA,dx(BETA))) - Signature: {dx/1} / {a/0,div/2,exp/2,ln/1,minus/2,neg/1,one/0,plus/2,times/2,two/0,zero/0} - Obligation: runtime complexity wrt. defined symbols {dx} and constructors {a,div,exp,ln,minus,neg,one,plus,times,two ,zero} + 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(div) = {1}, uargs(minus) = {1,2}, uargs(neg) = {1}, uargs(plus) = {1,2}, uargs(times) = {2} Following symbols are considered usable: all TcT has computed the following interpretation: p(a) = 0 p(div) = 2 + x1 + x2 p(dx) = 1 + 5*x1 + x1^2 p(exp) = 2 + x1 + x2 p(ln) = 2 + x1 p(minus) = 2 + x1 + x2 p(neg) = x1 p(one) = 0 p(plus) = 1 + x1 + x2 p(times) = 1 + x1 + x2 p(two) = 2 p(zero) = 1
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