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Runti Compl Full Rewri 10127 pair #381902694
details
property
value
status
complete
benchmark
elimdupl.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
Rubio_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rc
runtime (wallclock)
9.19191098213 seconds
cpu usage
31.696834343
max memory
1.38616832E8
stage attributes
key
value
output-size
53639
starexec-result
WORST_CASE(Omega(n^1),O(n^3))
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^3)) * Step 1: Sum WORST_CASE(Omega(n^1),O(n^3)) + Considered Problem: - Strict TRS: eq(0(),0()) -> true() eq(0(),s(X)) -> false() eq(s(X),0()) -> false() eq(s(X),s(Y)) -> eq(X,Y) ifrm(false(),N,add(M,X)) -> add(M,rm(N,X)) ifrm(true(),N,add(M,X)) -> rm(N,X) purge(add(N,X)) -> add(N,purge(rm(N,X))) purge(nil()) -> nil() rm(N,add(M,X)) -> ifrm(eq(N,M),N,add(M,X)) rm(N,nil()) -> nil() - Signature: {eq/2,ifrm/3,purge/1,rm/2} / {0/0,add/2,false/0,nil/0,s/1,true/0} - Obligation: runtime complexity wrt. defined symbols {eq,ifrm,purge,rm} and constructors {0,add,false,nil,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: eq(0(),0()) -> true() eq(0(),s(X)) -> false() eq(s(X),0()) -> false() eq(s(X),s(Y)) -> eq(X,Y) ifrm(false(),N,add(M,X)) -> add(M,rm(N,X)) ifrm(true(),N,add(M,X)) -> rm(N,X) purge(add(N,X)) -> add(N,purge(rm(N,X))) purge(nil()) -> nil() rm(N,add(M,X)) -> ifrm(eq(N,M),N,add(M,X)) rm(N,nil()) -> nil() - Signature: {eq/2,ifrm/3,purge/1,rm/2} / {0/0,add/2,false/0,nil/0,s/1,true/0} - Obligation: runtime complexity wrt. defined symbols {eq,ifrm,purge,rm} and constructors {0,add,false,nil,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: eq(x,y){x -> s(x),y -> s(y)} = eq(s(x),s(y)) ->^+ eq(x,y) = C[eq(x,y) = eq(x,y){}] ** Step 1.b:1: NaturalMI WORST_CASE(?,O(n^3)) + Considered Problem: - Strict TRS: eq(0(),0()) -> true() eq(0(),s(X)) -> false() eq(s(X),0()) -> false() eq(s(X),s(Y)) -> eq(X,Y) ifrm(false(),N,add(M,X)) -> add(M,rm(N,X)) ifrm(true(),N,add(M,X)) -> rm(N,X) purge(add(N,X)) -> add(N,purge(rm(N,X))) purge(nil()) -> nil() rm(N,add(M,X)) -> ifrm(eq(N,M),N,add(M,X)) rm(N,nil()) -> nil() - Signature: {eq/2,ifrm/3,purge/1,rm/2} / {0/0,add/2,false/0,nil/0,s/1,true/0} - Obligation: runtime complexity wrt. defined symbols {eq,ifrm,purge,rm} and constructors {0,add,false,nil,s,true} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: uargs(add) = {2}, uargs(ifrm) = {1,3}, uargs(purge) = {1}, uargs(rm) = {2} Following symbols are considered usable: all TcT has computed the following interpretation: p(0) = [2] p(add) = [1] x2 + [0] p(eq) = [0] p(false) = [0] p(ifrm) = [4] x1 + [1] x3 + [0] p(nil) = [1] p(purge) = [8] x1 + [2] p(rm) = [1] x2 + [0] p(s) = [1] x1 + [1] p(true) = [0] Following rules are strictly oriented: purge(nil()) = [10] > [1] = nil()
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