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Runti Compl Inner Rewri 22807 pair #381904093
details
property
value
status
complete
benchmark
#4.22.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n053.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rci
runtime (wallclock)
1.86773395538 seconds
cpu usage
12.317107135
max memory
2.16936448E8
stage attributes
key
value
output-size
10603
starexec-result
WORST_CASE(Omega(n^1),O(n^1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /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: quot(x,0(),s(z)) -> s(quot(x,s(z),s(z))) quot(0(),s(y),s(z)) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) - Signature: {quot/3} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {quot} 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: quot(x,0(),s(z)) -> s(quot(x,s(z),s(z))) quot(0(),s(y),s(z)) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) - Signature: {quot/3} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {quot} and constructors {0,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: quot(x,y,z){x -> s(x),y -> s(y)} = quot(s(x),s(y),z) ->^+ quot(x,y,z) = C[quot(x,y,z) = quot(x,y,z){}] ** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: quot(x,0(),s(z)) -> s(quot(x,s(z),s(z))) quot(0(),s(y),s(z)) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) - Signature: {quot/3} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {quot} and constructors {0,s} + Applied Processor: DependencyPairs {dpKind_ = WIDP} + Details: We add the following weak innermost dependency pairs: Strict DPs quot#(x,0(),s(z)) -> c_1(quot#(x,s(z),s(z))) quot#(0(),s(y),s(z)) -> c_2() quot#(s(x),s(y),z) -> c_3(quot#(x,y,z)) Weak DPs and mark the set of starting terms. ** Step 1.b:2: UsableRules WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: quot#(x,0(),s(z)) -> c_1(quot#(x,s(z),s(z))) quot#(0(),s(y),s(z)) -> c_2() quot#(s(x),s(y),z) -> c_3(quot#(x,y,z)) - Strict TRS: quot(x,0(),s(z)) -> s(quot(x,s(z),s(z))) quot(0(),s(y),s(z)) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) - Signature: {quot/3,quot#/3} / {0/0,s/1,c_1/1,c_2/0,c_3/1} - Obligation: innermost runtime complexity wrt. defined symbols {quot#} and constructors {0,s} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: quot#(x,0(),s(z)) -> c_1(quot#(x,s(z),s(z))) quot#(0(),s(y),s(z)) -> c_2() quot#(s(x),s(y),z) -> c_3(quot#(x,y,z)) ** Step 1.b:3: PredecessorEstimation WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: quot#(x,0(),s(z)) -> c_1(quot#(x,s(z),s(z))) quot#(0(),s(y),s(z)) -> c_2() quot#(s(x),s(y),z) -> c_3(quot#(x,y,z)) - Signature: {quot/3,quot#/3} / {0/0,s/1,c_1/1,c_2/0,c_3/1} - Obligation: innermost runtime complexity wrt. defined symbols {quot#} and constructors {0,s} + Applied Processor: PredecessorEstimation {onSelection = all simple predecessor estimation selector} + Details: We estimate the number of application of {2} by application of Pre({2}) = {1,3}.
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