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Runti Compl Full Rewri 10127 pair #381902666
details
property
value
status
complete
benchmark
#4.14.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n049.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
0.0720779895782 seconds
cpu usage
0.297723752
max memory
2.8868608E7
stage attributes
key
value
output-size
8283
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(g(x),s(0())) -> f(g(x),g(x)) g(0()) -> 0() g(s(x)) -> s(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(g(x),s(0())) -> f(g(x),g(x)) g(0()) -> 0() g(s(x)) -> s(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)) ->^+ s(g(x)) = C[g(x) = g(x){}] ** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(g(x),s(0())) -> f(g(x),g(x)) g(0()) -> 0() g(s(x)) -> s(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#(g(x),s(0())) -> c_1(f#(g(x),g(x))) g#(0()) -> c_2() g#(s(x)) -> c_3(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#(g(x),s(0())) -> c_1(f#(g(x),g(x))) g#(0()) -> c_2() g#(s(x)) -> c_3(g#(x)) - Strict TRS: f(g(x),s(0())) -> f(g(x),g(x)) g(0()) -> 0() g(s(x)) -> s(g(x)) - Signature: {f/2,g/1,f#/2,g#/1} / {0/0,s/1,c_1/1,c_2/0,c_3/1} - Obligation: runtime complexity wrt. defined symbols {f#,g#} and constructors {0,s} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: g#(0()) -> c_2() g#(s(x)) -> c_3(g#(x)) ** Step 1.b:3: PredecessorEstimation WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: g#(0()) -> c_2() g#(s(x)) -> c_3(g#(x)) - Signature: {f/2,g/1,f#/2,g#/1} / {0/0,s/1,c_1/1,c_2/0,c_3/1} - Obligation: runtime complexity wrt. defined symbols {f#,g#} and constructors {0,s} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {1} by application of Pre({1}) = {2}. Here rules are labelled as follows: 1: g#(0()) -> c_2()
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