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Runti Compl Full Rewri 10127 pair #381902955
details
property
value
status
complete
benchmark
#3.41.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n047.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
1.44572615623 seconds
cpu usage
5.666490278
max memory
9.12384E7
stage attributes
key
value
output-size
7636
starexec-result
WORST_CASE(Omega(n^1),O(n^2))
output
/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1),O(n^2)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^2)) + Considered Problem: - Strict TRS: fac(0()) -> s(0()) fac(s(x)) -> times(s(x),fac(p(s(x)))) p(s(x)) -> x - Signature: {fac/1,p/1} / {0/0,s/1,times/2} - Obligation: runtime complexity wrt. defined symbols {fac,p} and constructors {0,s,times} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: fac(0()) -> s(0()) fac(s(x)) -> times(s(x),fac(p(s(x)))) p(s(x)) -> x - Signature: {fac/1,p/1} / {0/0,s/1,times/2} - Obligation: runtime complexity wrt. defined symbols {fac,p} and constructors {0,s,times} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: fac(x){x -> s(x)} = fac(s(x)) ->^+ times(s(x),fac(x)) = C[fac(x) = fac(x){}] ** Step 1.b:1: NaturalPI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: fac(0()) -> s(0()) fac(s(x)) -> times(s(x),fac(p(s(x)))) p(s(x)) -> x - Signature: {fac/1,p/1} / {0/0,s/1,times/2} - Obligation: runtime complexity wrt. defined symbols {fac,p} and constructors {0,s,times} + 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(fac) = {1}, uargs(times) = {2} Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = 2 p(fac) = 8 + 8*x1 p(p) = x1 p(s) = x1 p(times) = x2 Following rules are strictly oriented: fac(0()) = 24 > 2 = s(0()) Following rules are (at-least) weakly oriented: fac(s(x)) = 8 + 8*x >= 8 + 8*x = times(s(x),fac(p(s(x)))) p(s(x)) = x >= x = x ** Step 1.b:2: NaturalPI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: fac(s(x)) -> times(s(x),fac(p(s(x)))) p(s(x)) -> x - Weak TRS: fac(0()) -> s(0()) - Signature: {fac/1,p/1} / {0/0,s/1,times/2} - Obligation: runtime complexity wrt. defined symbols {fac,p} and constructors {0,s,times} + 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(fac) = {1}, uargs(times) = {2}
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