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Runti Compl Full Rewri 10127 pair #381903043
details
property
value
status
complete
benchmark
kabasci03.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n045.star.cs.uiowa.edu
space
AProVE_07
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
0.235393047333 seconds
cpu usage
0.880899863
max memory
4.804608E7
stage attributes
key
value
output-size
7697
starexec-result
WORST_CASE(?,O(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(1)) * Step 1: Sum WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: h(x,c(y,z),t(w)) -> h(c(s(y),x),z,t(c(t(w),w))) h(c(x,y),c(s(z),z),t(w)) -> h(z,c(y,x),t(t(c(x,c(y,t(w)))))) h(c(s(x),c(s(0()),y)),z,t(x)) -> h(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) t(x) -> x t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x))))) t(t(x)) -> t(c(t(x),x)) - Signature: {h/3,t/1} / {0/0,c/2,s/1} - Obligation: runtime complexity wrt. defined symbols {h,t} and constructors {0,c,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DependencyPairs WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: h(x,c(y,z),t(w)) -> h(c(s(y),x),z,t(c(t(w),w))) h(c(x,y),c(s(z),z),t(w)) -> h(z,c(y,x),t(t(c(x,c(y,t(w)))))) h(c(s(x),c(s(0()),y)),z,t(x)) -> h(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) t(x) -> x t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x))))) t(t(x)) -> t(c(t(x),x)) - Signature: {h/3,t/1} / {0/0,c/2,s/1} - Obligation: runtime complexity wrt. defined symbols {h,t} and constructors {0,c,s} + Applied Processor: DependencyPairs {dpKind_ = WIDP} + Details: We add the following weak dependency pairs: Strict DPs h#(x,c(y,z),t(w)) -> c_1(h#(c(s(y),x),z,t(c(t(w),w)))) h#(c(x,y),c(s(z),z),t(w)) -> c_2(h#(z,c(y,x),t(t(c(x,c(y,t(w))))))) h#(c(s(x),c(s(0()),y)),z,t(x)) -> c_3(h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x)))))) t#(x) -> c_4(x) t#(x) -> c_5(x) t#(t(x)) -> c_6(t#(c(t(x),x))) Weak DPs and mark the set of starting terms. * Step 3: UsableRules WORST_CASE(?,O(1)) + Considered Problem: - Strict DPs: h#(x,c(y,z),t(w)) -> c_1(h#(c(s(y),x),z,t(c(t(w),w)))) h#(c(x,y),c(s(z),z),t(w)) -> c_2(h#(z,c(y,x),t(t(c(x,c(y,t(w))))))) h#(c(s(x),c(s(0()),y)),z,t(x)) -> c_3(h#(y,c(s(0()),c(x,z)),t(t(c(x,s(x)))))) t#(x) -> c_4(x) t#(x) -> c_5(x) t#(t(x)) -> c_6(t#(c(t(x),x))) - Strict TRS: h(x,c(y,z),t(w)) -> h(c(s(y),x),z,t(c(t(w),w))) h(c(x,y),c(s(z),z),t(w)) -> h(z,c(y,x),t(t(c(x,c(y,t(w)))))) h(c(s(x),c(s(0()),y)),z,t(x)) -> h(y,c(s(0()),c(x,z)),t(t(c(x,s(x))))) t(x) -> x t(x) -> c(0(),c(0(),c(0(),c(0(),c(0(),x))))) t(t(x)) -> t(c(t(x),x)) - Signature: {h/3,t/1,h#/3,t#/1} / {0/0,c/2,s/1,c_1/1,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1} - Obligation: runtime complexity wrt. defined symbols {h#,t#} and constructors {0,c,s} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: t#(x) -> c_4(x) t#(x) -> c_5(x) * Step 4: PredecessorEstimationCP WORST_CASE(?,O(1)) + Considered Problem: - Strict DPs: t#(x) -> c_4(x) t#(x) -> c_5(x) - Signature: {h/3,t/1,h#/3,t#/1} / {0/0,c/2,s/1,c_1/1,c_2/1,c_3/1,c_4/1,c_5/1,c_6/1} - Obligation: runtime complexity wrt. defined symbols {h#,t#} and constructors {0,c,s} + Applied Processor: PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}} + Details: We first use the processor NaturalMI {miDimension = 1, miDegree = 0, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly: 1: t#(x) -> c_4(x) 2: t#(x) -> c_5(x) The strictly oriented rules are moved into the weak component. ** Step 4.a:1: NaturalMI WORST_CASE(?,O(1)) + Considered Problem: - Strict DPs: t#(x) -> c_4(x)
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