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Runti Compl Inner Rewri 22807 pair #381904036
details
property
value
status
complete
benchmark
4.12.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n074.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rci
runtime (wallclock)
3.52890896797 seconds
cpu usage
5.493223915
max memory
3.4136064E7
stage attributes
key
value
output-size
4098
starexec-result
WORST_CASE(?,O(n^1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(?,O(n^1)) * Step 1: Sum WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: +(0(),y) -> y +(s(x),0()) -> s(x) +(s(x),s(y)) -> s(+(s(x),+(y,0()))) - Signature: {+/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} and constructors {0,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: +(0(),y) -> y +(s(x),0()) -> s(x) +(s(x),s(y)) -> s(+(s(x),+(y,0()))) - Signature: {+/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} and constructors {0,s} + Applied Processor: NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(+) = {2}, uargs(s) = {1} Following symbols are considered usable: {+} TcT has computed the following interpretation: p(+) = x1 + 8*x2 p(0) = 0 p(s) = 3 + x1 Following rules are strictly oriented: +(s(x),s(y)) = 27 + x + 8*y > 6 + x + 8*y = s(+(s(x),+(y,0()))) Following rules are (at-least) weakly oriented: +(0(),y) = 8*y >= y = y +(s(x),0()) = 3 + x >= 3 + x = s(x) * Step 3: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: +(0(),y) -> y +(s(x),0()) -> s(x) - Weak TRS: +(s(x),s(y)) -> s(+(s(x),+(y,0()))) - Signature: {+/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+} and constructors {0,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(+) = {2}, uargs(s) = {1} Following symbols are considered usable: {+} TcT has computed the following interpretation: p(+) = [1] x1 + [8] x2 + [2] p(0) = [0] p(s) = [1] x1 + [3] Following rules are strictly oriented: +(0(),y) = [8] y + [2] > [1] y + [0] = y +(s(x),0()) = [1] x + [5] > [1] x + [3] = s(x) Following rules are (at-least) weakly oriented: +(s(x),s(y)) = [1] x + [8] y + [29] >= [1] x + [8] y + [24]
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