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Deriv Compl Full Rewri 33144 pair #381922066
details
property
value
status
complete
benchmark
bintrees.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n030.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_dc
runtime (wallclock)
30.1020851135 seconds
cpu usage
92.165233736
max memory
4.24845312E8
stage attributes
key
value
output-size
7332
starexec-result
WORST_CASE(?,O(n^2))
output
/export/starexec/sandbox2/solver/bin/starexec_run_tct_dc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^2)) * Step 1: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: concat(cons(U,V),Y) -> cons(U,concat(V,Y)) concat(leaf(),Y) -> Y lessleaves(X,leaf()) -> false() lessleaves(cons(U,V),cons(W,Z)) -> lessleaves(concat(U,V),concat(W,Z)) lessleaves(leaf(),cons(W,Z)) -> true() - Signature: {concat/2,lessleaves/2} / {cons/2,false/0,leaf/0,true/0} - Obligation: derivational complexity wrt. signature {concat,cons,false,leaf,lessleaves,true} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Just any strict-rules} + Details: We apply a matrix interpretation of kind triangular matrix interpretation: Following symbols are considered usable: all TcT has computed the following interpretation: p(concat) = [1] x1 + [1] x2 + [0] p(cons) = [1] x1 + [1] x2 + [8] p(false) = [0] p(leaf) = [8] p(lessleaves) = [1] x1 + [1] x2 + [8] p(true) = [0] Following rules are strictly oriented: concat(leaf(),Y) = [1] Y + [8] > [1] Y + [0] = Y lessleaves(X,leaf()) = [1] X + [16] > [0] = false() lessleaves(cons(U,V),cons(W,Z)) = [1] U + [1] V + [1] W + [1] Z + [24] > [1] U + [1] V + [1] W + [1] Z + [8] = lessleaves(concat(U,V),concat(W,Z)) lessleaves(leaf(),cons(W,Z)) = [1] W + [1] Z + [24] > [0] = true() Following rules are (at-least) weakly oriented: concat(cons(U,V),Y) = [1] U + [1] V + [1] Y + [8] >= [1] U + [1] V + [1] Y + [8] = cons(U,concat(V,Y)) * Step 2: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: concat(cons(U,V),Y) -> cons(U,concat(V,Y)) - Weak TRS: concat(leaf(),Y) -> Y lessleaves(X,leaf()) -> false() lessleaves(cons(U,V),cons(W,Z)) -> lessleaves(concat(U,V),concat(W,Z)) lessleaves(leaf(),cons(W,Z)) -> true() - Signature: {concat/2,lessleaves/2} / {cons/2,false/0,leaf/0,true/0} - Obligation: derivational complexity wrt. signature {concat,cons,false,leaf,lessleaves,true} + Applied Processor: NaturalMI {miDimension = 2, miDegree = 2, miKind = Algebraic, uargs = NoUArgs, urules = NoURules, selector = Just any strict-rules} + Details: We apply a matrix interpretation of kind triangular matrix interpretation: Following symbols are considered usable: all TcT has computed the following interpretation: p(concat) = [1 1] x1 + [1 0] x2 + [0] [0 1] [0 1] [4] p(cons) = [1 1] x1 + [1 0] x2 + [0] [0 0] [0 1] [1] p(false) = [1] [0] p(leaf) = [5] [4] p(lessleaves) = [1 0] x1 + [1 0] x2 + [0] [0 0] [0 0] [1] p(true) = [5] [0] Following rules are strictly oriented: concat(cons(U,V),Y) = [1 1] U + [1 1] V + [1 0] Y + [1] [0 0] [0 1] [0 1] [5] > [1 1] U + [1 1] V + [1 0] Y + [0] [0 0] [0 1] [0 1] [5] = cons(U,concat(V,Y)) Following rules are (at-least) weakly oriented:
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