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Runti Compl Full Rewri 10127 pair #381903035
details
property
value
status
complete
benchmark
#3.6a.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n047.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
2.16531395912 seconds
cpu usage
7.52268897
max memory
6.0706816E7
stage attributes
key
value
output-size
20788
starexec-result
WORST_CASE(Omega(n^1),O(n^2))
output
/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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: gcd(0(),y) -> y gcd(s(x),0()) -> s(x) gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y)) if_gcd(false(),s(x),s(y)) -> gcd(minus(y,x),s(x)) if_gcd(true(),s(x),s(y)) -> gcd(minus(x,y),s(y)) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) - Signature: {gcd/2,if_gcd/3,le/2,minus/2} / {0/0,false/0,s/1,true/0} - Obligation: runtime complexity wrt. defined symbols {gcd,if_gcd,le,minus} and constructors {0,false,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: gcd(0(),y) -> y gcd(s(x),0()) -> s(x) gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y)) if_gcd(false(),s(x),s(y)) -> gcd(minus(y,x),s(x)) if_gcd(true(),s(x),s(y)) -> gcd(minus(x,y),s(y)) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) - Signature: {gcd/2,if_gcd/3,le/2,minus/2} / {0/0,false/0,s/1,true/0} - Obligation: runtime complexity wrt. defined symbols {gcd,if_gcd,le,minus} and constructors {0,false,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: le(x,y){x -> s(x),y -> s(y)} = le(s(x),s(y)) ->^+ le(x,y) = C[le(x,y) = le(x,y){}] ** Step 1.b:1: NaturalMI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: gcd(0(),y) -> y gcd(s(x),0()) -> s(x) gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y)) if_gcd(false(),s(x),s(y)) -> gcd(minus(y,x),s(x)) if_gcd(true(),s(x),s(y)) -> gcd(minus(x,y),s(y)) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) - Signature: {gcd/2,if_gcd/3,le/2,minus/2} / {0/0,false/0,s/1,true/0} - Obligation: runtime complexity wrt. defined symbols {gcd,if_gcd,le,minus} and constructors {0,false,s,true} + 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(gcd) = {1}, uargs(if_gcd) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [0] p(false) = [1] p(gcd) = [1] x1 + [1] x2 + [12] p(if_gcd) = [8] x1 + [1] x2 + [1] x3 + [2] p(le) = [1] p(minus) = [1] x1 + [0] p(s) = [1] x1 + [2] p(true) = [1] Following rules are strictly oriented: gcd(0(),y) = [1] y + [12] > [1] y + [0] = y gcd(s(x),0()) = [1] x + [14] > [1] x + [2] = s(x) gcd(s(x),s(y)) = [1] x + [1] y + [16]
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