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Runti Compl Full Rewri 10127 pair #381902844
details
property
value
status
complete
benchmark
bn122.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n055.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
0.285551071167 seconds
cpu usage
1.404427964
max memory
3.7896192E7
stage attributes
key
value
output-size
8309
starexec-result
WORST_CASE(Omega(n^1),O(n^1))
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^1)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: plus(plus(X,Y),Z) -> plus(X,plus(Y,Z)) times(X,s(Y)) -> plus(X,times(Y,X)) - Signature: {plus/2,times/2} / {s/1} - Obligation: runtime complexity wrt. defined symbols {plus,times} and constructors {s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: plus(plus(X,Y),Z) -> plus(X,plus(Y,Z)) times(X,s(Y)) -> plus(X,times(Y,X)) - Signature: {plus/2,times/2} / {s/1} - Obligation: runtime complexity wrt. defined symbols {plus,times} and constructors {s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: times(z,x){z -> s(z),x -> s(x)} = times(s(z),s(x)) ->^+ plus(s(z),plus(x,times(z,x))) = C[times(z,x) = times(z,x){}] ** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: plus(plus(X,Y),Z) -> plus(X,plus(Y,Z)) times(X,s(Y)) -> plus(X,times(Y,X)) - Signature: {plus/2,times/2} / {s/1} - Obligation: runtime complexity wrt. defined symbols {plus,times} and constructors {s} + Applied Processor: DependencyPairs {dpKind_ = WIDP} + Details: We add the following weak dependency pairs: Strict DPs plus#(plus(X,Y),Z) -> c_1(plus#(X,plus(Y,Z))) times#(X,s(Y)) -> c_2(plus#(X,times(Y,X))) Weak DPs and mark the set of starting terms. ** Step 1.b:2: WeightGap WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: plus#(plus(X,Y),Z) -> c_1(plus#(X,plus(Y,Z))) times#(X,s(Y)) -> c_2(plus#(X,times(Y,X))) - Strict TRS: plus(plus(X,Y),Z) -> plus(X,plus(Y,Z)) times(X,s(Y)) -> plus(X,times(Y,X)) - Signature: {plus/2,times/2,plus#/2,times#/2} / {s/1,c_1/1,c_2/1} - Obligation: runtime complexity wrt. defined symbols {plus#,times#} and constructors {s} + Applied Processor: WeightGap {wgDimension = 2, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnTrs} + Details: The weightgap principle applies using the following constant growth matrix-interpretation: We apply a matrix interpretation of kind constructor based matrix interpretation (containing no more than 1 non-zero interpretation-entries in the diagonal of the component-wise maxima): The following argument positions are considered usable: uargs(plus) = {2}, uargs(plus#) = {2}, uargs(c_1) = {1}, uargs(c_2) = {1} Following symbols are considered usable: all TcT has computed the following interpretation: p(plus) = [0 1] x1 + [1 0] x2 + [0] [0 2] [0 1] [2] p(s) = [1 1] x1 + [4] [0 0] [0] p(times) = [1 1] x1 + [1 0] x2 + [5] [2 2] [2 0] [0] p(plus#) = [0 4] x1 + [1 0] x2 + [5] [1 7] [0 1] [0] p(times#) = [1 6] x1 + [2 0] x2 + [0] [0 0] [0 0] [0] p(c_1) = [1 0] x1 + [0] [0 1] [0] p(c_2) = [1 0] x1 + [0] [0 1] [0] Following rules are strictly oriented:
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