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Runti Compl Inner Rewri 22807 pair #381904012
details
property
value
status
complete
benchmark
IJCAR_1.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n073.star.cs.uiowa.edu
space
AProVE_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rci
runtime (wallclock)
2.81427907944 seconds
cpu usage
18.293189372
max memory
9.1742208E7
stage attributes
key
value
output-size
12357
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: div(x,y) -> quot(x,y,y) div(0(),y) -> 0() quot(x,0(),s(z)) -> s(div(x,s(z))) quot(0(),s(y),z) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) - Signature: {div/2,quot/3} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {div,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: div(x,y) -> quot(x,y,y) div(0(),y) -> 0() quot(x,0(),s(z)) -> s(div(x,s(z))) quot(0(),s(y),z) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) - Signature: {div/2,quot/3} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {div,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: div(x,y) -> quot(x,y,y) div(0(),y) -> 0() quot(x,0(),s(z)) -> s(div(x,s(z))) quot(0(),s(y),z) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) - Signature: {div/2,quot/3} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {div,quot} and constructors {0,s} + Applied Processor: DependencyPairs {dpKind_ = WIDP} + Details: We add the following weak innermost dependency pairs: Strict DPs div#(x,y) -> c_1(quot#(x,y,y)) div#(0(),y) -> c_2() quot#(x,0(),s(z)) -> c_3(div#(x,s(z))) quot#(0(),s(y),z) -> c_4() quot#(s(x),s(y),z) -> c_5(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: div#(x,y) -> c_1(quot#(x,y,y)) div#(0(),y) -> c_2() quot#(x,0(),s(z)) -> c_3(div#(x,s(z))) quot#(0(),s(y),z) -> c_4() quot#(s(x),s(y),z) -> c_5(quot#(x,y,z)) - Strict TRS: div(x,y) -> quot(x,y,y) div(0(),y) -> 0() quot(x,0(),s(z)) -> s(div(x,s(z))) quot(0(),s(y),z) -> 0() quot(s(x),s(y),z) -> quot(x,y,z) - Signature: {div/2,quot/3,div#/2,quot#/3} / {0/0,s/1,c_1/1,c_2/0,c_3/1,c_4/0,c_5/1} - Obligation: innermost runtime complexity wrt. defined symbols {div#,quot#} and constructors {0,s} + Applied Processor: UsableRules + Details: We replace rewrite rules by usable rules: div#(x,y) -> c_1(quot#(x,y,y)) div#(0(),y) -> c_2() quot#(x,0(),s(z)) -> c_3(div#(x,s(z))) quot#(0(),s(y),z) -> c_4() quot#(s(x),s(y),z) -> c_5(quot#(x,y,z)) ** Step 1.b:3: PredecessorEstimation WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs:
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