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Runti Compl Full Rewri 10127 pair #381902539
details
property
value
status
complete
benchmark
24.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n045.star.cs.uiowa.edu
space
Various_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
6.32166099548 seconds
cpu usage
24.096337643
max memory
1.95465216E8
stage attributes
key
value
output-size
22326
starexec-result
WORST_CASE(Omega(n^1),O(n^2))
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^2)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^2)) + Considered Problem: - Strict TRS: max(L(x)) -> x max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z))))) max(N(L(0()),L(y))) -> y max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y)))) - Signature: {max/1} / {0/0,L/1,N/2,s/1} - Obligation: runtime complexity wrt. defined symbols {max} and constructors {0,L,N,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: max(L(x)) -> x max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z))))) max(N(L(0()),L(y))) -> y max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y)))) - Signature: {max/1} / {0/0,L/1,N/2,s/1} - Obligation: runtime complexity wrt. defined symbols {max} and constructors {0,L,N,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: max(N(L(x),L(y))){x -> s(x),y -> s(y)} = max(N(L(s(x)),L(s(y)))) ->^+ s(max(N(L(x),L(y)))) = C[max(N(L(x),L(y))) = max(N(L(x),L(y))){}] ** Step 1.b:1: ToInnermost WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: max(L(x)) -> x max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z))))) max(N(L(0()),L(y))) -> y max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y)))) - Signature: {max/1} / {0/0,L/1,N/2,s/1} - Obligation: runtime complexity wrt. defined symbols {max} and constructors {0,L,N,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^2)) + Considered Problem: - Strict TRS: max(L(x)) -> x max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z))))) max(N(L(0()),L(y))) -> y max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y)))) - Signature: {max/1} / {0/0,L/1,N/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {max} and constructors {0,L,N,s} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs max#(L(x)) -> c_1() max#(N(L(x),N(y,z))) -> c_2(max#(N(L(x),L(max(N(y,z))))),max#(N(y,z))) max#(N(L(0()),L(y))) -> c_3() max#(N(L(s(x)),L(s(y)))) -> c_4(max#(N(L(x),L(y)))) Weak DPs and mark the set of starting terms. ** Step 1.b:3: UsableRules WORST_CASE(?,O(n^2)) + Considered Problem: - Strict DPs: max#(L(x)) -> c_1() max#(N(L(x),N(y,z))) -> c_2(max#(N(L(x),L(max(N(y,z))))),max#(N(y,z))) max#(N(L(0()),L(y))) -> c_3() max#(N(L(s(x)),L(s(y)))) -> c_4(max#(N(L(x),L(y)))) - Weak TRS: max(L(x)) -> x max(N(L(x),N(y,z))) -> max(N(L(x),L(max(N(y,z))))) max(N(L(0()),L(y))) -> y max(N(L(s(x)),L(s(y)))) -> s(max(N(L(x),L(y)))) - Signature: {max/1,max#/1} / {0/0,L/1,N/2,s/1,c_1/0,c_2/2,c_3/0,c_4/1} - Obligation: innermost runtime complexity wrt. defined symbols {max#} and constructors {0,L,N,s} + Applied Processor: UsableRules + Details:
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