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Runti Compl Full Rewri 10127 pair #381902390
details
property
value
status
complete
benchmark
prov.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
Rubio_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
0.326184034348 seconds
cpu usage
1.232270358
max memory
5.2445184E7
stage attributes
key
value
output-size
4943
starexec-result
WORST_CASE(Omega(n^1),O(n^1))
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^1)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X) u21(ackout(X),Y) -> u22(ackin(Y,X)) - Signature: {ackin/2,u21/2} / {ackout/1,s/1,u22/1} - Obligation: runtime complexity wrt. defined symbols {ackin,u21} and constructors {ackout,s,u22} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X) u21(ackout(X),Y) -> u22(ackin(Y,X)) - Signature: {ackin/2,u21/2} / {ackout/1,s/1,u22/1} - Obligation: runtime complexity wrt. defined symbols {ackin,u21} and constructors {ackout,s,u22} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: ackin(s(x),y){y -> s(y)} = ackin(s(x),s(y)) ->^+ u21(ackin(s(x),y),x) = C[ackin(s(x),y) = ackin(s(x),y){}] ** Step 1.b:1: NaturalPI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X) u21(ackout(X),Y) -> u22(ackin(Y,X)) - Signature: {ackin/2,u21/2} / {ackout/1,s/1,u22/1} - Obligation: runtime complexity wrt. defined symbols {ackin,u21} and constructors {ackout,s,u22} + 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(u21) = {1}, uargs(u22) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(ackin) = 0 p(ackout) = 2 p(s) = 0 p(u21) = 2*x1 p(u22) = 3 + x1 Following rules are strictly oriented: u21(ackout(X),Y) = 4 > 3 = u22(ackin(Y,X)) Following rules are (at-least) weakly oriented: ackin(s(X),s(Y)) = 0 >= 0 = u21(ackin(s(X),Y),X) ** Step 1.b:2: NaturalMI WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: ackin(s(X),s(Y)) -> u21(ackin(s(X),Y),X) - Weak TRS: u21(ackout(X),Y) -> u22(ackin(Y,X)) - Signature: {ackin/2,u21/2} / {ackout/1,s/1,u22/1} - Obligation: runtime complexity wrt. defined symbols {ackin,u21} and constructors {ackout,s,u22} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(u21) = {1}, uargs(u22) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(ackin) = [1] x2 + [8] p(ackout) = [1] x1 + [9] p(s) = [1] x1 + [8] p(u21) = [1] x1 + [0] p(u22) = [1] x1 + [1]
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