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Runti Compl Full Rewri 10127 pair #381902625
details
property
value
status
complete
benchmark
#4.16.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n073.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
0.117639064789 seconds
cpu usage
0.478589075
max memory
2.932736E7
stage attributes
key
value
output-size
6458
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(s(0()),g(x)) -> f(x,g(x)) g(s(x)) -> g(x) - Signature: {f/2,g/1} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {f,g} 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(s(0()),g(x)) -> f(x,g(x)) g(s(x)) -> g(x) - Signature: {f/2,g/1} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {f,g} and constructors {0,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: g(x){x -> s(x)} = g(s(x)) ->^+ g(x) = C[g(x) = g(x){}] ** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(s(0()),g(x)) -> f(x,g(x)) g(s(x)) -> g(x) - Signature: {f/2,g/1} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {f,g} and constructors {0,s} + Applied Processor: DependencyPairs {dpKind_ = WIDP} + Details: We add the following weak dependency pairs: Strict DPs f#(s(0()),g(x)) -> c_1(f#(x,g(x))) g#(s(x)) -> c_2(g#(x)) Weak DPs and mark the set of starting terms. ** Step 1.b:2: UsableRules WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: f#(s(0()),g(x)) -> c_1(f#(x,g(x))) g#(s(x)) -> c_2(g#(x)) - Strict TRS: f(s(0()),g(x)) -> f(x,g(x)) g(s(x)) -> g(x) - Signature: {f/2,g/1,f#/2,g#/1} / {0/0,s/1,c_1/1,c_2/1} - Obligation: runtime complexity wrt. defined symbols {f#,g#} and constructors {0,s} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: g#(s(x)) -> c_2(g#(x)) ** Step 1.b:3: PredecessorEstimationCP WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: g#(s(x)) -> c_2(g#(x)) - Signature: {f/2,g/1,f#/2,g#/1} / {0/0,s/1,c_1/1,c_2/1} - Obligation: runtime complexity wrt. defined symbols {f#,g#} and constructors {0,s} + Applied Processor: PredecessorEstimationCP {onSelectionCP = any intersect of rules of CDG leaf and strict-rules, withComplexityPair = NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}} + Details: We first use the processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing} to orient following rules strictly: 1: g#(s(x)) -> c_2(g#(x)) The strictly oriented rules are moved into the weak component. *** Step 1.b:3.a:1: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: g#(s(x)) -> c_2(g#(x)) - Signature: {f/2,g/1,f#/2,g#/1} / {0/0,s/1,c_1/1,c_2/1} - Obligation: runtime complexity wrt. defined symbols {f#,g#} and constructors {0,s} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just first alternative for predecessorEstimation on any intersect of rules of CDG leaf and strict-rules}
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