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Runti Compl Full Rewri 10127 pair #381902725
details
property
value
status
complete
benchmark
cime4.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n037.star.cs.uiowa.edu
space
Secret_05_TRS
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
0.404834032059 seconds
cpu usage
1.725354
max memory
3.9677952E7
stage attributes
key
value
output-size
15878
starexec-result
WORST_CASE(?,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(?,O(n^1)) * Step 1: Sum WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(k(a()),k(b()),X) -> f(X,X,X) g(X) -> u(h(X),h(X),X) h(d()) -> c(a()) h(d()) -> c(b()) u(d(),c(Y),X) -> k(Y) - Signature: {f/3,g/1,h/1,u/3} / {a/0,b/0,c/1,d/0,k/1} - Obligation: runtime complexity wrt. defined symbols {f,g,h,u} and constructors {a,b,c,d,k} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DependencyPairs WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(k(a()),k(b()),X) -> f(X,X,X) g(X) -> u(h(X),h(X),X) h(d()) -> c(a()) h(d()) -> c(b()) u(d(),c(Y),X) -> k(Y) - Signature: {f/3,g/1,h/1,u/3} / {a/0,b/0,c/1,d/0,k/1} - Obligation: runtime complexity wrt. defined symbols {f,g,h,u} and constructors {a,b,c,d,k} + Applied Processor: DependencyPairs {dpKind_ = WIDP} + Details: We add the following weak dependency pairs: Strict DPs f#(k(a()),k(b()),X) -> c_1(f#(X,X,X)) g#(X) -> c_2(u#(h(X),h(X),X)) h#(d()) -> c_3() h#(d()) -> c_4() u#(d(),c(Y),X) -> c_5(Y) Weak DPs and mark the set of starting terms. * Step 3: UsableRules WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: f#(k(a()),k(b()),X) -> c_1(f#(X,X,X)) g#(X) -> c_2(u#(h(X),h(X),X)) h#(d()) -> c_3() h#(d()) -> c_4() u#(d(),c(Y),X) -> c_5(Y) - Strict TRS: f(k(a()),k(b()),X) -> f(X,X,X) g(X) -> u(h(X),h(X),X) h(d()) -> c(a()) h(d()) -> c(b()) u(d(),c(Y),X) -> k(Y) - Signature: {f/3,g/1,h/1,u/3,f#/3,g#/1,h#/1,u#/3} / {a/0,b/0,c/1,d/0,k/1,c_1/1,c_2/1,c_3/0,c_4/0,c_5/1} - Obligation: runtime complexity wrt. defined symbols {f#,g#,h#,u#} and constructors {a,b,c,d,k} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: h(d()) -> c(a()) h(d()) -> c(b()) f#(k(a()),k(b()),X) -> c_1(f#(X,X,X)) g#(X) -> c_2(u#(h(X),h(X),X)) h#(d()) -> c_3() h#(d()) -> c_4() u#(d(),c(Y),X) -> c_5(Y) * Step 4: WeightGap WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: f#(k(a()),k(b()),X) -> c_1(f#(X,X,X)) g#(X) -> c_2(u#(h(X),h(X),X)) h#(d()) -> c_3() h#(d()) -> c_4() u#(d(),c(Y),X) -> c_5(Y) - Strict TRS: h(d()) -> c(a()) h(d()) -> c(b()) - Signature: {f/3,g/1,h/1,u/3,f#/3,g#/1,h#/1,u#/3} / {a/0,b/0,c/1,d/0,k/1,c_1/1,c_2/1,c_3/0,c_4/0,c_5/1} - Obligation: runtime complexity wrt. defined symbols {f#,g#,h#,u#} and constructors {a,b,c,d,k} + 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:
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