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Runti Compl Inner Rewri 22807 pair #381904127
details
property
value
status
complete
benchmark
#3.6.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n027.star.cs.uiowa.edu
space
AG01
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rci
runtime (wallclock)
6.61896085739 seconds
cpu usage
21.388626099
max memory
1.18181888E8
stage attributes
key
value
output-size
43839
starexec-result
WORST_CASE(Omega(n^1),O(n^2))
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^2)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^2)) + Considered Problem: - Strict TRS: gcd(0(),y) -> y gcd(s(x),0()) -> s(x) gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y)) if_gcd(false(),s(x),s(y)) -> gcd(minus(y,x),s(x)) if_gcd(true(),s(x),s(y)) -> gcd(minus(x,y),s(y)) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) minus(x,0()) -> x minus(x,s(y)) -> pred(minus(x,y)) pred(s(x)) -> x - Signature: {gcd/2,if_gcd/3,le/2,minus/2,pred/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {gcd,if_gcd,le,minus,pred} and constructors {0,false,s ,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: gcd(0(),y) -> y gcd(s(x),0()) -> s(x) gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y)) if_gcd(false(),s(x),s(y)) -> gcd(minus(y,x),s(x)) if_gcd(true(),s(x),s(y)) -> gcd(minus(x,y),s(y)) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) minus(x,0()) -> x minus(x,s(y)) -> pred(minus(x,y)) pred(s(x)) -> x - Signature: {gcd/2,if_gcd/3,le/2,minus/2,pred/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {gcd,if_gcd,le,minus,pred} and constructors {0,false,s ,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: le(x,y){x -> s(x),y -> s(y)} = le(s(x),s(y)) ->^+ le(x,y) = C[le(x,y) = le(x,y){}] ** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: gcd(0(),y) -> y gcd(s(x),0()) -> s(x) gcd(s(x),s(y)) -> if_gcd(le(y,x),s(x),s(y)) if_gcd(false(),s(x),s(y)) -> gcd(minus(y,x),s(x)) if_gcd(true(),s(x),s(y)) -> gcd(minus(x,y),s(y)) le(0(),y) -> true() le(s(x),0()) -> false() le(s(x),s(y)) -> le(x,y) minus(x,0()) -> x minus(x,s(y)) -> pred(minus(x,y)) pred(s(x)) -> x - Signature: {gcd/2,if_gcd/3,le/2,minus/2,pred/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {gcd,if_gcd,le,minus,pred} and constructors {0,false,s ,true} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs gcd#(0(),y) -> c_1() gcd#(s(x),0()) -> c_2() gcd#(s(x),s(y)) -> c_3(if_gcd#(le(y,x),s(x),s(y)),le#(y,x)) if_gcd#(false(),s(x),s(y)) -> c_4(gcd#(minus(y,x),s(x)),minus#(y,x)) if_gcd#(true(),s(x),s(y)) -> c_5(gcd#(minus(x,y),s(y)),minus#(x,y)) le#(0(),y) -> c_6() le#(s(x),0()) -> c_7() le#(s(x),s(y)) -> c_8(le#(x,y)) minus#(x,0()) -> c_9() minus#(x,s(y)) -> c_10(pred#(minus(x,y)),minus#(x,y)) pred#(s(x)) -> c_11() Weak DPs and mark the set of starting terms. ** Step 1.b:2: PredecessorEstimation WORST_CASE(?,O(n^2)) + Considered Problem: - Strict DPs:
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