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Runti Compl Full Rewri 10127 pair #381902193
details
property
value
status
complete
benchmark
hydra.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n039.star.cs.uiowa.edu
space
Mixed_TRS
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
0.531501054764 seconds
cpu usage
1.772784614
max memory
4.9291264E7
stage attributes
key
value
output-size
4499
starexec-result
WORST_CASE(Omega(n^1),O(n^2))
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^2)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^2)) + Considered Problem: - Strict TRS: copy(0(),y,z) -> f(z) copy(s(x),y,z) -> copy(x,y,cons(f(y),z)) f(cons(f(cons(nil(),y)),z)) -> copy(n(),y,z) f(cons(nil(),y)) -> y - Signature: {copy/3,f/1} / {0/0,cons/2,n/0,nil/0,s/1} - Obligation: runtime complexity wrt. defined symbols {copy,f} and constructors {0,cons,n,nil,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: copy(0(),y,z) -> f(z) copy(s(x),y,z) -> copy(x,y,cons(f(y),z)) f(cons(f(cons(nil(),y)),z)) -> copy(n(),y,z) f(cons(nil(),y)) -> y - Signature: {copy/3,f/1} / {0/0,cons/2,n/0,nil/0,s/1} - Obligation: runtime complexity wrt. defined symbols {copy,f} and constructors {0,cons,n,nil,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: copy(x,y,z){x -> s(x)} = copy(s(x),y,z) ->^+ copy(x,y,cons(f(y),z)) = C[copy(x,y,cons(f(y),z)) = copy(x,y,z){z -> cons(f(y),z)}] ** Step 1.b:1: NaturalPI WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: copy(0(),y,z) -> f(z) copy(s(x),y,z) -> copy(x,y,cons(f(y),z)) f(cons(f(cons(nil(),y)),z)) -> copy(n(),y,z) f(cons(nil(),y)) -> y - Signature: {copy/3,f/1} / {0/0,cons/2,n/0,nil/0,s/1} - Obligation: runtime complexity wrt. defined symbols {copy,f} and constructors {0,cons,n,nil,s} + Applied Processor: NaturalPI {shape = Mixed 2, restrict = Restrict, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a polynomial interpretation of kind constructor-based(mixed(2)): The following argument positions are considered usable: uargs(cons) = {1,2}, uargs(copy) = {2,3}, uargs(f) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = 0 p(cons) = x1 + x2 p(copy) = 4 + 5*x1 + x1*x2 + x2 + x3 p(f) = 3 + x1 p(n) = 0 p(nil) = 0 p(s) = 2 + x1 Following rules are strictly oriented: copy(0(),y,z) = 4 + y + z > 3 + z = f(z) copy(s(x),y,z) = 14 + 5*x + x*y + 3*y + z > 7 + 5*x + x*y + 2*y + z = copy(x,y,cons(f(y),z)) f(cons(f(cons(nil(),y)),z)) = 6 + y + z > 4 + y + z = copy(n(),y,z) f(cons(nil(),y)) = 3 + y > y = y Following rules are (at-least) weakly oriented: ** Step 1.b:2: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: copy(0(),y,z) -> f(z) copy(s(x),y,z) -> copy(x,y,cons(f(y),z)) f(cons(f(cons(nil(),y)),z)) -> copy(n(),y,z) f(cons(nil(),y)) -> y - Signature:
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