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Runti Compl Full Rewri 10127 pair #381902863
details
property
value
status
complete
benchmark
#3.15.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n058.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
0.229703187943 seconds
cpu usage
0.866108973
max memory
2.9085696E7
stage attributes
key
value
output-size
12439
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: average(x,s(s(s(y)))) -> s(average(s(x),y)) average(0(),0()) -> 0() average(0(),s(0())) -> 0() average(0(),s(s(0()))) -> s(0()) average(s(x),y) -> average(x,s(y)) - Signature: {average/2} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {average} 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: average(x,s(s(s(y)))) -> s(average(s(x),y)) average(0(),0()) -> 0() average(0(),s(0())) -> 0() average(0(),s(s(0()))) -> s(0()) average(s(x),y) -> average(x,s(y)) - Signature: {average/2} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {average} and constructors {0,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: average(x,y){y -> s(s(s(y)))} = average(x,s(s(s(y)))) ->^+ s(average(s(x),y)) = C[average(s(x),y) = average(x,y){x -> s(x)}] ** Step 1.b:1: ToInnermost WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: average(x,s(s(s(y)))) -> s(average(s(x),y)) average(0(),0()) -> 0() average(0(),s(0())) -> 0() average(0(),s(s(0()))) -> s(0()) average(s(x),y) -> average(x,s(y)) - Signature: {average/2} / {0/0,s/1} - Obligation: runtime complexity wrt. defined symbols {average} and constructors {0,s} + Applied Processor: ToInnermost + Details: switch to innermost, as the system is overlay and right linear and does not contain weak rules ** Step 1.b:2: DependencyPairs WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: average(x,s(s(s(y)))) -> s(average(s(x),y)) average(0(),0()) -> 0() average(0(),s(0())) -> 0() average(0(),s(s(0()))) -> s(0()) average(s(x),y) -> average(x,s(y)) - Signature: {average/2} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {average} and constructors {0,s} + Applied Processor: DependencyPairs {dpKind_ = WIDP} + Details: We add the following weak innermost dependency pairs: Strict DPs average#(x,s(s(s(y)))) -> c_1(average#(s(x),y)) average#(0(),0()) -> c_2() average#(0(),s(0())) -> c_3() average#(0(),s(s(0()))) -> c_4() average#(s(x),y) -> c_5(average#(x,s(y))) Weak DPs and mark the set of starting terms. ** Step 1.b:3: UsableRules WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: average#(x,s(s(s(y)))) -> c_1(average#(s(x),y)) average#(0(),0()) -> c_2() average#(0(),s(0())) -> c_3() average#(0(),s(s(0()))) -> c_4() average#(s(x),y) -> c_5(average#(x,s(y))) - Strict TRS: average(x,s(s(s(y)))) -> s(average(s(x),y)) average(0(),0()) -> 0() average(0(),s(0())) -> 0() average(0(),s(s(0()))) -> s(0()) average(s(x),y) -> average(x,s(y))
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