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Runti Compl Full Rewri 10127 pair #381903134
details
property
value
status
complete
benchmark
4.18.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n029.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
0.199283123016 seconds
cpu usage
0.920224844
max memory
3.4893824E7
stage attributes
key
value
output-size
6406
starexec-result
WORST_CASE(?,O(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(?,O(1)) * Step 1: Sum WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: gcd(x,0()) -> x gcd(0(),y) -> y gcd(s(x),s(y)) -> if(<(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y))) - Signature: {gcd/2} / {-/2,0/0,</2,if/3,s/1} - Obligation: runtime complexity wrt. defined symbols {gcd} and constructors {-,0,<,if,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DependencyPairs WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: gcd(x,0()) -> x gcd(0(),y) -> y gcd(s(x),s(y)) -> if(<(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y))) - Signature: {gcd/2} / {-/2,0/0,</2,if/3,s/1} - Obligation: runtime complexity wrt. defined symbols {gcd} and constructors {-,0,<,if,s} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following weak dependency pairs: Strict DPs gcd#(x,0()) -> c_1(x) gcd#(0(),y) -> c_2(y) gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y))) Weak DPs and mark the set of starting terms. * Step 3: UsableRules WORST_CASE(?,O(1)) + Considered Problem: - Strict DPs: gcd#(x,0()) -> c_1(x) gcd#(0(),y) -> c_2(y) gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y))) - Strict TRS: gcd(x,0()) -> x gcd(0(),y) -> y gcd(s(x),s(y)) -> if(<(x,y),gcd(s(x),-(y,x)),gcd(-(x,y),s(y))) - Signature: {gcd/2,gcd#/2} / {-/2,0/0,</2,if/3,s/1,c_1/1,c_2/1,c_3/4} - Obligation: runtime complexity wrt. defined symbols {gcd#} and constructors {-,0,<,if,s} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: gcd#(x,0()) -> c_1(x) gcd#(0(),y) -> c_2(y) gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y))) * Step 4: SimplifyRHS WORST_CASE(?,O(1)) + Considered Problem: - Strict DPs: gcd#(x,0()) -> c_1(x) gcd#(0(),y) -> c_2(y) gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y))) - Signature: {gcd/2,gcd#/2} / {-/2,0/0,</2,if/3,s/1,c_1/1,c_2/1,c_3/4} - Obligation: runtime complexity wrt. defined symbols {gcd#} and constructors {-,0,<,if,s} + Applied Processor: SimplifyRHS + Details: Consider the dependency graph 1:S:gcd#(x,0()) -> c_1(x) -->_1 gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y))):3 -->_1 gcd#(0(),y) -> c_2(y):2 -->_1 gcd#(x,0()) -> c_1(x):1 2:S:gcd#(0(),y) -> c_2(y) -->_1 gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y))):3 -->_1 gcd#(0(),y) -> c_2(y):2 -->_1 gcd#(x,0()) -> c_1(x):1 3:S:gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y))) -->_2 gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y))):3 -->_1 gcd#(s(x),s(y)) -> c_3(x,y,gcd#(s(x),-(y,x)),gcd#(-(x,y),s(y))):3 -->_2 gcd#(0(),y) -> c_2(y):2 -->_1 gcd#(0(),y) -> c_2(y):2 -->_2 gcd#(x,0()) -> c_1(x):1 -->_1 gcd#(x,0()) -> c_1(x):1 Due to missing edges in the depndency graph, the right-hand sides of following rules could be simplified: gcd#(s(x),s(y)) -> c_3(x,y) * Step 5: WeightGap WORST_CASE(?,O(1))
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