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Runti Compl Full Rewri 10127 pair #381902726
details
property
value
status
complete
benchmark
koen.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n056.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
0.40297794342 seconds
cpu usage
2.000724798
max memory
4.012032E7
stage attributes
key
value
output-size
6648
starexec-result
WORST_CASE(?,O(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(?,O(1)) * Step 1: Sum WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: f(X,X) -> c(X) f(X,c(X)) -> f(s(X),X) f(s(X),X) -> f(X,a(X)) - Signature: {f/2} / {a/1,c/1,s/1} - Obligation: runtime complexity wrt. defined symbols {f} and constructors {a,c,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DependencyPairs WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: f(X,X) -> c(X) f(X,c(X)) -> f(s(X),X) f(s(X),X) -> f(X,a(X)) - Signature: {f/2} / {a/1,c/1,s/1} - Obligation: runtime complexity wrt. defined symbols {f} and constructors {a,c,s} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following weak dependency pairs: Strict DPs f#(X,X) -> c_1(X) f#(X,c(X)) -> c_2(f#(s(X),X)) f#(s(X),X) -> c_3(f#(X,a(X))) Weak DPs and mark the set of starting terms. * Step 3: UsableRules WORST_CASE(?,O(1)) + Considered Problem: - Strict DPs: f#(X,X) -> c_1(X) f#(X,c(X)) -> c_2(f#(s(X),X)) f#(s(X),X) -> c_3(f#(X,a(X))) - Strict TRS: f(X,X) -> c(X) f(X,c(X)) -> f(s(X),X) f(s(X),X) -> f(X,a(X)) - Signature: {f/2,f#/2} / {a/1,c/1,s/1,c_1/1,c_2/1,c_3/1} - Obligation: runtime complexity wrt. defined symbols {f#} and constructors {a,c,s} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: f#(X,X) -> c_1(X) f#(X,c(X)) -> c_2(f#(s(X),X)) f#(s(X),X) -> c_3(f#(X,a(X))) * Step 4: WeightGap WORST_CASE(?,O(1)) + Considered Problem: - Strict DPs: f#(X,X) -> c_1(X) f#(X,c(X)) -> c_2(f#(s(X),X)) f#(s(X),X) -> c_3(f#(X,a(X))) - Signature: {f/2,f#/2} / {a/1,c/1,s/1,c_1/1,c_2/1,c_3/1} - Obligation: runtime complexity wrt. defined symbols {f#} and constructors {a,c,s} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 0, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnAny} + Details: The weightgap principle applies using the following constant growth matrix-interpretation: We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 0 non-zero interpretation-entries in the diagonal of the component-wise maxima): The following argument positions are considered usable: uargs(c_2) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(a) = [2] p(c) = [1] p(f) = [1] x2 + [1] p(s) = [1] p(f#) = [4] p(c_1) = [1] p(c_2) = [1] x1 + [3] p(c_3) = [0] Following rules are strictly oriented: f#(X,X) = [4] > [1] = c_1(X)
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