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Runti Compl Full Rewri 10127 pair #381903025
details
property
value
status
complete
benchmark
#3.1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n035.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
0.115225076675 seconds
cpu usage
0.403671439
max memory
3.0826496E7
stage attributes
key
value
output-size
4021
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: minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) - Signature: {minus/2,quot/2} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {minus,quot} and constructors {0,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) - Signature: {minus/2,quot/2} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {minus,quot} and constructors {0,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: minus(x,y){x -> s(x),y -> s(y)} = minus(s(x),s(y)) ->^+ minus(x,y) = C[minus(x,y) = minus(x,y){}] ** Step 1.b:1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) - Signature: {minus/2,quot/2} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {minus,quot} 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(minus) = {1}, uargs(quot) = {1}, uargs(s) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [1] p(minus) = [1] x1 + [1] p(quot) = [4] x1 + [3] p(s) = [1] x1 + [2] Following rules are strictly oriented: minus(x,0()) = [1] x + [1] > [1] x + [0] = x minus(s(x),s(y)) = [1] x + [3] > [1] x + [1] = minus(x,y) quot(0(),s(y)) = [7] > [1] = 0() quot(s(x),s(y)) = [4] x + [11] > [4] x + [9] = s(quot(minus(x,y),s(y))) Following rules are (at-least) weakly oriented: ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: minus(x,0()) -> x minus(s(x),s(y)) -> minus(x,y) quot(0(),s(y)) -> 0() quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) - Signature: {minus/2,quot/2} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {minus,quot} and constructors {0,s}
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