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Runti Compl Full Rewri 10127 pair #381902525
details
property
value
status
complete
benchmark
jones2.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n036.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
0.240136146545 seconds
cpu usage
0.889263739
max memory
3.4557952E7
stage attributes
key
value
output-size
8561
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(cons(x,k),l) -> g(k,l,cons(x,k)) f(empty(),l) -> l g(a,b,c) -> f(a,cons(b,c)) - Signature: {f/2,g/3} / {cons/2,empty/0} - Obligation: runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(cons(x,k),l) -> g(k,l,cons(x,k)) f(empty(),l) -> l g(a,b,c) -> f(a,cons(b,c)) - Signature: {f/2,g/3} / {cons/2,empty/0} - Obligation: runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(x,z){x -> cons(y,x)} = f(cons(y,x),z) ->^+ f(x,cons(z,cons(y,x))) = C[f(x,cons(z,cons(y,x))) = f(x,z){z -> cons(z,cons(y,x))}] ** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(cons(x,k),l) -> g(k,l,cons(x,k)) f(empty(),l) -> l g(a,b,c) -> f(a,cons(b,c)) - Signature: {f/2,g/3} / {cons/2,empty/0} - Obligation: runtime complexity wrt. defined symbols {f,g} and constructors {cons,empty} + Applied Processor: DependencyPairs {dpKind_ = WIDP} + Details: We add the following weak dependency pairs: Strict DPs f#(cons(x,k),l) -> c_1(g#(k,l,cons(x,k))) f#(empty(),l) -> c_2(l) g#(a,b,c) -> c_3(f#(a,cons(b,c))) Weak DPs and mark the set of starting terms. ** Step 1.b:2: UsableRules WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: f#(cons(x,k),l) -> c_1(g#(k,l,cons(x,k))) f#(empty(),l) -> c_2(l) g#(a,b,c) -> c_3(f#(a,cons(b,c))) - Strict TRS: f(cons(x,k),l) -> g(k,l,cons(x,k)) f(empty(),l) -> l g(a,b,c) -> f(a,cons(b,c)) - Signature: {f/2,g/3,f#/2,g#/3} / {cons/2,empty/0,c_1/1,c_2/1,c_3/1} - Obligation: runtime complexity wrt. defined symbols {f#,g#} and constructors {cons,empty} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: f#(cons(x,k),l) -> c_1(g#(k,l,cons(x,k))) f#(empty(),l) -> c_2(l) g#(a,b,c) -> c_3(f#(a,cons(b,c))) ** Step 1.b:3: PredecessorEstimationCP WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: f#(cons(x,k),l) -> c_1(g#(k,l,cons(x,k))) f#(empty(),l) -> c_2(l) g#(a,b,c) -> c_3(f#(a,cons(b,c))) - Signature: {f/2,g/3,f#/2,g#/3} / {cons/2,empty/0,c_1/1,c_2/1,c_3/1} - Obligation: runtime complexity wrt. defined symbols {f#,g#} and constructors {cons,empty} + 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: f#(cons(x,k),l) -> c_1(g#(k,l,cons(x,k))) 2: f#(empty(),l) -> c_2(l) 3: g#(a,b,c) -> c_3(f#(a,cons(b,c)))
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