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Runti Compl Full Rewri 10127 pair #381902307
details
property
value
status
complete
benchmark
2.40.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n057.star.cs.uiowa.edu
space
SK90
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
0.161005973816 seconds
cpu usage
0.642386986
max memory
4.4826624E7
stage attributes
key
value
output-size
10871
starexec-result
WORST_CASE(Omega(n^1),O(n^1))
output
/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /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: mem(x,nil()) -> false() mem(x,set(y)) -> =(x,y) mem(x,union(y,z)) -> or(mem(x,y),mem(x,z)) or(x,true()) -> true() or(false(),false()) -> false() or(true(),y) -> true() - Signature: {mem/2,or/2} / {=/2,false/0,nil/0,set/1,true/0,union/2} - Obligation: runtime complexity wrt. defined symbols {mem,or} and constructors {=,false,nil,set,true,union} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: mem(x,nil()) -> false() mem(x,set(y)) -> =(x,y) mem(x,union(y,z)) -> or(mem(x,y),mem(x,z)) or(x,true()) -> true() or(false(),false()) -> false() or(true(),y) -> true() - Signature: {mem/2,or/2} / {=/2,false/0,nil/0,set/1,true/0,union/2} - Obligation: runtime complexity wrt. defined symbols {mem,or} and constructors {=,false,nil,set,true,union} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: mem(x,y){y -> union(y,z)} = mem(x,union(y,z)) ->^+ or(mem(x,y),mem(x,z)) = C[mem(x,y) = mem(x,y){}] ** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: mem(x,nil()) -> false() mem(x,set(y)) -> =(x,y) mem(x,union(y,z)) -> or(mem(x,y),mem(x,z)) or(x,true()) -> true() or(false(),false()) -> false() or(true(),y) -> true() - Signature: {mem/2,or/2} / {=/2,false/0,nil/0,set/1,true/0,union/2} - Obligation: runtime complexity wrt. defined symbols {mem,or} and constructors {=,false,nil,set,true,union} + Applied Processor: DependencyPairs {dpKind_ = WIDP} + Details: We add the following weak dependency pairs: Strict DPs mem#(x,nil()) -> c_1() mem#(x,set(y)) -> c_2(x,y) mem#(x,union(y,z)) -> c_3(or#(mem(x,y),mem(x,z))) or#(x,true()) -> c_4() or#(false(),false()) -> c_5() or#(true(),y) -> c_6() Weak DPs and mark the set of starting terms. ** Step 1.b:2: WeightGap WORST_CASE(?,O(n^1)) + Considered Problem: - Strict DPs: mem#(x,nil()) -> c_1() mem#(x,set(y)) -> c_2(x,y) mem#(x,union(y,z)) -> c_3(or#(mem(x,y),mem(x,z))) or#(x,true()) -> c_4() or#(false(),false()) -> c_5() or#(true(),y) -> c_6() - Strict TRS: mem(x,nil()) -> false() mem(x,set(y)) -> =(x,y) mem(x,union(y,z)) -> or(mem(x,y),mem(x,z)) or(x,true()) -> true() or(false(),false()) -> false() or(true(),y) -> true() - Signature: {mem/2,or/2,mem#/2,or#/2} / {=/2,false/0,nil/0,set/1,true/0,union/2,c_1/0,c_2/2,c_3/1,c_4/0,c_5/0,c_6/0} - Obligation: runtime complexity wrt. defined symbols {mem#,or#} and constructors {=,false,nil,set,true,union} + Applied Processor: WeightGap {wgDimension = 1, wgDegree = 1, wgKind = Algebraic, wgUArgs = UArgs, wgOn = WgOnTrs} + Details: The weightgap principle applies using the following constant growth matrix-interpretation: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable:
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