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Runti Compl Full Rewri 10127 pair #381902196
details
property
value
status
complete
benchmark
gm.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
Rubio_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
0.49694609642 seconds
cpu usage
2.308932534
max memory
4.6886912E7
stage attributes
key
value
output-size
16594
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: div(0(),s(Y)) -> 0() div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y))) minus(X,0()) -> X minus(s(X),s(Y)) -> p(minus(X,Y)) p(s(X)) -> X - Signature: {div/2,minus/2,p/1} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {div,minus,p} and constructors {0,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: div(0(),s(Y)) -> 0() div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y))) minus(X,0()) -> X minus(s(X),s(Y)) -> p(minus(X,Y)) p(s(X)) -> X - Signature: {div/2,minus/2,p/1} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {div,minus,p} and constructors {0,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: minus(x,y){x -> s(x),y -> s(y)} = minus(s(x),s(y)) ->^+ p(minus(x,y)) = C[minus(x,y) = minus(x,y){}] ** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: div(0(),s(Y)) -> 0() div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y))) minus(X,0()) -> X minus(s(X),s(Y)) -> p(minus(X,Y)) p(s(X)) -> X - Signature: {div/2,minus/2,p/1} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {div,minus,p} and constructors {0,s} + Applied Processor: DependencyPairs {dpKind_ = WIDP} + Details: We add the following weak dependency pairs: Strict DPs div#(0(),s(Y)) -> c_1() div#(s(X),s(Y)) -> c_2(div#(minus(X,Y),s(Y))) minus#(X,0()) -> c_3(X) minus#(s(X),s(Y)) -> c_4(p#(minus(X,Y))) p#(s(X)) -> c_5(X) Weak DPs and mark the set of starting terms. ** Step 1.b:2: UsableRules WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: div#(0(),s(Y)) -> c_1() div#(s(X),s(Y)) -> c_2(div#(minus(X,Y),s(Y))) minus#(X,0()) -> c_3(X) minus#(s(X),s(Y)) -> c_4(p#(minus(X,Y))) p#(s(X)) -> c_5(X) - Strict TRS: div(0(),s(Y)) -> 0() div(s(X),s(Y)) -> s(div(minus(X,Y),s(Y))) minus(X,0()) -> X minus(s(X),s(Y)) -> p(minus(X,Y)) p(s(X)) -> X - Signature: {div/2,minus/2,p/1,div#/2,minus#/2,p#/1} / {0/0,s/1,c_1/0,c_2/1,c_3/1,c_4/1,c_5/1} - Obligation: runtime complexity wrt. defined symbols {div#,minus#,p#} and constructors {0,s} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: minus(X,0()) -> X minus(s(X),s(Y)) -> p(minus(X,Y)) p(s(X)) -> X div#(0(),s(Y)) -> c_1() div#(s(X),s(Y)) -> c_2(div#(minus(X,Y),s(Y))) minus#(X,0()) -> c_3(X) minus#(s(X),s(Y)) -> c_4(p#(minus(X,Y))) p#(s(X)) -> c_5(X)
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