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Runti Compl Full Rewri 10127 pair #381902842
details
property
value
status
complete
benchmark
#3.23.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n051.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
0.0774600505829 seconds
cpu usage
0.239745744
max memory
2.0758528E7
stage attributes
key
value
output-size
5358
starexec-result
WORST_CASE(Omega(n^1),O(n^1))
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^1)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: f(0(),y) -> 0() f(s(x),y) -> f(f(x,y),y) - Signature: {f/2} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {f} 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: f(0(),y) -> 0() f(s(x),y) -> f(f(x,y),y) - Signature: {f/2} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {f} and constructors {0,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(x,y){x -> s(x)} = f(s(x),y) ->^+ f(f(x,y),y) = C[f(x,y) = f(x,y){}] ** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(0(),y) -> 0() f(s(x),y) -> f(f(x,y),y) - Signature: {f/2} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {f} and constructors {0,s} + Applied Processor: DependencyPairs {dpKind_ = WIDP} + Details: We add the following weak dependency pairs: Strict DPs f#(0(),y) -> c_1() f#(s(x),y) -> c_2(f#(f(x,y),y)) Weak DPs and mark the set of starting terms. ** Step 1.b:2: WeightGap WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: f#(0(),y) -> c_1() f#(s(x),y) -> c_2(f#(f(x,y),y)) - Strict TRS: f(0(),y) -> 0() f(s(x),y) -> f(f(x,y),y) - Signature: {f/2,f#/2} / {0/0,s/1,c_1/0,c_2/1} - Obligation: runtime complexity wrt. defined symbols {f#} and constructors {0,s} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnTrs} + Details: The weightgap principle applies using the following constant growth matrix-interpretation: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(f) = {1}, uargs(f#) = {1}, uargs(c_2) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [2] p(f) = [1] x1 + [2] p(s) = [1] x1 + [3] p(f#) = [1] x1 + [0] p(c_1) = [0] p(c_2) = [1] x1 + [0] Following rules are strictly oriented: f#(0(),y) = [2] > [0] = c_1() f#(s(x),y) = [1] x + [3] > [1] x + [2] = c_2(f#(f(x,y),y)) f(0(),y) = [4]
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