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Runti Compl Inner Rewri 22807 pair #381905134
details
property
value
status
complete
benchmark
Ex4_4_Luc96b_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n037.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rci
runtime (wallclock)
13.6081590652 seconds
cpu usage
98.617878702
max memory
2.74046976E8
stage attributes
key
value
output-size
10055
starexec-result
WORST_CASE(Omega(n^1),O(n^3))
output
/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1),O(n^3)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^3)) + Considered Problem: - Strict TRS: a__f(X1,X2) -> f(X1,X2) a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y)) mark(f(X1,X2)) -> a__f(mark(X1),X2) mark(g(X)) -> g(mark(X)) - Signature: {a__f/2,mark/1} / {f/2,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {f,g} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a__f(X1,X2) -> f(X1,X2) a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y)) mark(f(X1,X2)) -> a__f(mark(X1),X2) mark(g(X)) -> g(mark(X)) - Signature: {a__f/2,mark/1} / {f/2,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {f,g} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: mark(x){x -> f(x,y)} = mark(f(x,y)) ->^+ a__f(mark(x),y) = C[mark(x) = mark(x){}] ** Step 1.b:1: NaturalPI WORST_CASE(?,O(n^3)) + Considered Problem: - Strict TRS: a__f(X1,X2) -> f(X1,X2) a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y)) mark(f(X1,X2)) -> a__f(mark(X1),X2) mark(g(X)) -> g(mark(X)) - Signature: {a__f/2,mark/1} / {f/2,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {f,g} + Applied Processor: NaturalPI {shape = Linear, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(linear): The following argument positions are considered usable: uargs(a__f) = {1}, uargs(g) = {1} Following symbols are considered usable: {a__f,mark} TcT has computed the following interpretation: p(a__f) = x1 p(f) = x1 p(g) = 2 + x1 p(mark) = x1 Following rules are strictly oriented: a__f(g(X),Y) = 2 + X > X = a__f(mark(X),f(g(X),Y)) Following rules are (at-least) weakly oriented: a__f(X1,X2) = X1 >= X1 = f(X1,X2) mark(f(X1,X2)) = X1 >= X1 = a__f(mark(X1),X2) mark(g(X)) = 2 + X >= 2 + X = g(mark(X)) ** Step 1.b:2: NaturalMI WORST_CASE(?,O(n^3)) + Considered Problem: - Strict TRS: a__f(X1,X2) -> f(X1,X2) mark(f(X1,X2)) -> a__f(mark(X1),X2) mark(g(X)) -> g(mark(X)) - Weak TRS: a__f(g(X),Y) -> a__f(mark(X),f(g(X),Y)) - Signature: {a__f/2,mark/1} / {f/2,g/1} - Obligation: innermost runtime complexity wrt. defined symbols {a__f,mark} and constructors {f,g} + Applied Processor:
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