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Runti Compl Full Rewri 10127 pair #381902869
details
property
value
status
complete
benchmark
#4.34.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
Strategy_removed_AG01
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
1.53282499313 seconds
cpu usage
5.493369579
max memory
6.9984256E7
stage attributes
key
value
output-size
15577
starexec-result
WORST_CASE(Omega(n^1),O(n^3))
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^3)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^3)) + Considered Problem: - Strict TRS: f(0()) -> true() f(1()) -> false() f(s(x)) -> f(x) g(x,c(y)) -> g(x,g(s(c(y)),y)) g(s(x),s(y)) -> if(f(x),s(x),s(y)) if(false(),x,y) -> y if(true(),x,y) -> x - Signature: {f/1,g/2,if/3} / {0/0,1/0,c/1,false/0,s/1,true/0} - Obligation: runtime complexity wrt. defined symbols {f,g,if} and constructors {0,1,c,false,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(0()) -> true() f(1()) -> false() f(s(x)) -> f(x) g(x,c(y)) -> g(x,g(s(c(y)),y)) g(s(x),s(y)) -> if(f(x),s(x),s(y)) if(false(),x,y) -> y if(true(),x,y) -> x - Signature: {f/1,g/2,if/3} / {0/0,1/0,c/1,false/0,s/1,true/0} - Obligation: runtime complexity wrt. defined symbols {f,g,if} and constructors {0,1,c,false,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(x){x -> s(x)} = f(s(x)) ->^+ f(x) = C[f(x) = f(x){}] ** Step 1.b:1: NaturalPI WORST_CASE(?,O(n^3)) + Considered Problem: - Strict TRS: f(0()) -> true() f(1()) -> false() f(s(x)) -> f(x) g(x,c(y)) -> g(x,g(s(c(y)),y)) g(s(x),s(y)) -> if(f(x),s(x),s(y)) if(false(),x,y) -> y if(true(),x,y) -> x - Signature: {f/1,g/2,if/3} / {0/0,1/0,c/1,false/0,s/1,true/0} - Obligation: runtime complexity wrt. defined symbols {f,g,if} and constructors {0,1,c,false,s,true} + 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(g) = {2}, uargs(if) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = 2 p(1) = 0 p(c) = 15 + x1 p(f) = 0 p(false) = 0 p(g) = 5 + x2 p(if) = 2 + x1 + 4*x2 + x3 p(s) = 0 p(true) = 0 Following rules are strictly oriented: g(x,c(y)) = 20 + y > 10 + y = g(x,g(s(c(y)),y)) g(s(x),s(y)) = 5 > 2 = if(f(x),s(x),s(y)) if(false(),x,y) = 2 + 4*x + y > y = y if(true(),x,y) = 2 + 4*x + y > x = x
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