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Runti Compl Full Rewri 10127 pair #381902750
details
property
value
status
complete
benchmark
#3.53b.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n070.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
1.25828289986 seconds
cpu usage
5.239418666
max memory
9.5051776E7
stage attributes
key
value
output-size
18674
starexec-result
WORST_CASE(Omega(n^1),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(Omega(n^1),O(n^1)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: f(x,y,s(z)) -> s(f(0(),1(),z)) f(0(),1(),x) -> f(s(x),x,x) g(x,y) -> x g(x,y) -> y - Signature: {f/3,g/2} / {0/0,1/0,s/1} - Obligation: runtime complexity wrt. defined symbols {f,g} and constructors {0,1,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,y,s(z)) -> s(f(0(),1(),z)) f(0(),1(),x) -> f(s(x),x,x) g(x,y) -> x g(x,y) -> y - Signature: {f/3,g/2} / {0/0,1/0,s/1} - Obligation: runtime complexity wrt. defined symbols {f,g} and constructors {0,1,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(x,y,z){z -> s(z)} = f(x,y,s(z)) ->^+ s(f(0(),1(),z)) = C[f(0(),1(),z) = f(x,y,z){x -> 0(),y -> 1()}] ** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(x,y,s(z)) -> s(f(0(),1(),z)) f(0(),1(),x) -> f(s(x),x,x) g(x,y) -> x g(x,y) -> y - Signature: {f/3,g/2} / {0/0,1/0,s/1} - Obligation: runtime complexity wrt. defined symbols {f,g} and constructors {0,1,s} + Applied Processor: DependencyPairs {dpKind_ = WIDP} + Details: We add the following weak dependency pairs: Strict DPs f#(x,y,s(z)) -> c_1(f#(0(),1(),z)) f#(0(),1(),x) -> c_2(f#(s(x),x,x)) g#(x,y) -> c_3(x) g#(x,y) -> c_4(y) Weak DPs and mark the set of starting terms. ** Step 1.b:2: UsableRules WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: f#(x,y,s(z)) -> c_1(f#(0(),1(),z)) f#(0(),1(),x) -> c_2(f#(s(x),x,x)) g#(x,y) -> c_3(x) g#(x,y) -> c_4(y) - Strict TRS: f(x,y,s(z)) -> s(f(0(),1(),z)) f(0(),1(),x) -> f(s(x),x,x) g(x,y) -> x g(x,y) -> y - Signature: {f/3,g/2,f#/3,g#/2} / {0/0,1/0,s/1,c_1/1,c_2/1,c_3/1,c_4/1} - Obligation: runtime complexity wrt. defined symbols {f#,g#} and constructors {0,1,s} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: f#(x,y,s(z)) -> c_1(f#(0(),1(),z)) f#(0(),1(),x) -> c_2(f#(s(x),x,x)) g#(x,y) -> c_3(x) g#(x,y) -> c_4(y) ** Step 1.b:3: PredecessorEstimationCP WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: f#(x,y,s(z)) -> c_1(f#(0(),1(),z)) f#(0(),1(),x) -> c_2(f#(s(x),x,x)) g#(x,y) -> c_3(x) g#(x,y) -> c_4(y) - Signature: {f/3,g/2,f#/3,g#/2} / {0/0,1/0,s/1,c_1/1,c_2/1,c_3/1,c_4/1} - Obligation:
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