details

property	value
status	complete
benchmark	#3.52.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n056.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	tct 2018-07-13
configuration	tct_rci
runtime (wallclock)	0.720929145813 seconds
cpu usage	3.261170275
max memory	5.0245632E7

stage attributes

key	value
output-size	7846
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,y,s(z)) -> s(f(0(),1(),z)) f(0(),1(),x) -> f(s(x),x,x) - Signature: {f/3} / {0/0,1/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} 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) - Signature: {f/3} / {0/0,1/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} 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) - Signature: {f/3} / {0/0,1/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {0,1,s} + Applied Processor: DependencyPairs {dpKind_ = WIDP} + Details: We add the following weak innermost 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)) 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)) - Strict TRS: f(x,y,s(z)) -> s(f(0(),1(),z)) f(0(),1(),x) -> f(s(x),x,x) - Signature: {f/3,f#/3} / {0/0,1/0,s/1,c_1/1,c_2/1} - Obligation: innermost runtime complexity wrt. defined symbols {f#} 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)) ** 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)) - Signature: {f/3,f#/3} / {0/0,1/0,s/1,c_1/1,c_2/1} - Obligation: innermost runtime complexity wrt. defined symbols {f#} and constructors {0,1,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: f#(x,y,s(z)) -> c_1(f#(0(),1(),z)) Consider the set of all dependency pairs 1: f#(x,y,s(z)) -> c_1(f#(0(),1(),z)) 2: f#(0(),1(),x) -> c_2(f#(s(x),x,x)) Processor NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Nothing}induces the complexity certificateTIME (?,O(n^1)) SPACE(?,?)on application of the dependency pairs {1} These cover all (indirect) predecessors of dependency pairs {1,2} their number of applications is equally bounded. popout

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job log

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actions

all output return to Runti Compl Inner Rewri 22807