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Runti Compl Inner Rewri 22807 pair #381904183
details
property
value
status
complete
benchmark
22.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n050.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rci
runtime (wallclock)
0.823123931885 seconds
cpu usage
3.131500586
max memory
5.5394304E7
stage attributes
key
value
output-size
11633
starexec-result
WORST_CASE(Omega(n^1),O(n^1))
output
/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /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(x,0()) -> s(0()) f(s(x),s(y)) -> s(f(x,y)) g(0(),x) -> g(f(x,x),x) - Signature: {f/2,g/2} / {0/0,s/1} - Obligation: innermost 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(x,0()) -> s(0()) f(s(x),s(y)) -> s(f(x,y)) g(0(),x) -> g(f(x,x),x) - Signature: {f/2,g/2} / {0/0,s/1} - Obligation: innermost 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: f(x,y){x -> s(x),y -> s(y)} = f(s(x),s(y)) ->^+ s(f(x,y)) = C[f(x,y) = f(x,y){}] ** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x,0()) -> s(0()) f(s(x),s(y)) -> s(f(x,y)) g(0(),x) -> g(f(x,x),x) - Signature: {f/2,g/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,s} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs f#(x,0()) -> c_1() f#(s(x),s(y)) -> c_2(f#(x,y)) g#(0(),x) -> c_3(g#(f(x,x),x),f#(x,x)) Weak DPs and mark the set of starting terms. ** Step 1.b:2: PredecessorEstimation WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: f#(x,0()) -> c_1() f#(s(x),s(y)) -> c_2(f#(x,y)) g#(0(),x) -> c_3(g#(f(x,x),x),f#(x,x)) - Weak TRS: f(x,0()) -> s(0()) f(s(x),s(y)) -> s(f(x,y)) g(0(),x) -> g(f(x,x),x) - Signature: {f/2,g/2,f#/2,g#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/2} - Obligation: innermost 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}) = {2,3}. Here rules are labelled as follows: 1: f#(x,0()) -> c_1() 2: f#(s(x),s(y)) -> c_2(f#(x,y)) 3: g#(0(),x) -> c_3(g#(f(x,x),x),f#(x,x)) ** Step 1.b:3: RemoveWeakSuffixes WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: f#(s(x),s(y)) -> c_2(f#(x,y)) g#(0(),x) -> c_3(g#(f(x,x),x),f#(x,x)) - Weak DPs: f#(x,0()) -> c_1() - Weak TRS: f(x,0()) -> s(0()) f(s(x),s(y)) -> s(f(x,y)) g(0(),x) -> g(f(x,x),x) - Signature: {f/2,g/2,f#/2,g#/2} / {0/0,s/1,c_1/0,c_2/1,c_3/2}
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