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Runti Compl Full Rewri 10127 pair #381903946
details
property
value
status
complete
benchmark
Ex4_7_56_Bor03_Z.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n070.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
0.331610918045 seconds
cpu usage
1.310707788
max memory
4.2876928E7
stage attributes
key
value
output-size
7453
starexec-result
WORST_CASE(Omega(n^1),O(n^1))
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^1)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__from(X)) -> from(X) after(0(),XS) -> XS after(s(N),cons(X,XS)) -> after(N,activate(XS)) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) - Signature: {activate/1,after/2,from/1} / {0/0,cons/2,n__from/1,s/1} - Obligation: runtime complexity wrt. defined symbols {activate,after,from} and constructors {0,cons,n__from,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__from(X)) -> from(X) after(0(),XS) -> XS after(s(N),cons(X,XS)) -> after(N,activate(XS)) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) - Signature: {activate/1,after/2,from/1} / {0/0,cons/2,n__from/1,s/1} - Obligation: runtime complexity wrt. defined symbols {activate,after,from} and constructors {0,cons,n__from,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: after(y,x){y -> s(y),x -> cons(u,x)} = after(s(y),cons(u,x)) ->^+ after(y,x) = C[after(y,x) = after(y,x){}] ** Step 1.b:1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__from(X)) -> from(X) after(0(),XS) -> XS after(s(N),cons(X,XS)) -> after(N,activate(XS)) from(X) -> cons(X,n__from(s(X))) from(X) -> n__from(X) - Signature: {activate/1,after/2,from/1} / {0/0,cons/2,n__from/1,s/1} - Obligation: runtime complexity wrt. defined symbols {activate,after,from} and constructors {0,cons,n__from,s} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(after) = {2} Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [6] p(activate) = [1] x1 + [1] p(after) = [2] x1 + [8] x2 + [0] p(cons) = [1] x2 + [0] p(from) = [7] p(n__from) = [7] p(s) = [1] x1 + [8] Following rules are strictly oriented: activate(X) = [1] X + [1] > [1] X + [0] = X activate(n__from(X)) = [8] > [7] = from(X) after(0(),XS) = [8] XS + [12] > [1] XS + [0] = XS after(s(N),cons(X,XS)) = [2] N + [8] XS + [16] > [2] N + [8] XS + [8] = after(N,activate(XS)) Following rules are (at-least) weakly oriented: from(X) = [7] >= [7] = cons(X,n__from(s(X))) from(X) = [7]
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