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Runti Compl Inner Rewri 22807 pair #381904253
details
property
value
status
complete
benchmark
enno.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n042.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
tct 2018-07-13
configuration
tct_rci
runtime (wallclock)
7.41680693626 seconds
cpu usage
30.44003327
max memory
1.33914624E8
stage attributes
key
value
output-size
83847
starexec-result
WORST_CASE(Omega(n^1),O(n^3))
output
/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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: append(add(N,X),Y) -> add(N,append(X,Y)) append(nil(),Y) -> Y f_1(pair(X,Z),N,M,Y) -> f_2(lt(N,M),N,M,Y,X,Z) f_2(false(),N,M,Y,X,Z) -> pair(add(M,X),Z) f_2(true(),N,M,Y,X,Z) -> pair(X,add(M,Z)) f_3(pair(Y,Z),N,X) -> append(qsort(Y),add(X,qsort(Z))) lt(0(),s(X)) -> true() lt(s(X),0()) -> false() lt(s(X),s(Y)) -> lt(X,Y) qsort(add(N,X)) -> f_3(split(N,X),N,X) qsort(nil()) -> nil() split(N,add(M,Y)) -> f_1(split(N,Y),N,M,Y) split(N,nil()) -> pair(nil(),nil()) - Signature: {append/2,f_1/4,f_2/6,f_3/3,lt/2,qsort/1,split/2} / {0/0,add/2,false/0,nil/0,pair/2,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {append,f_1,f_2,f_3,lt,qsort,split} and constructors {0 ,add,false,nil,pair,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: append(add(N,X),Y) -> add(N,append(X,Y)) append(nil(),Y) -> Y f_1(pair(X,Z),N,M,Y) -> f_2(lt(N,M),N,M,Y,X,Z) f_2(false(),N,M,Y,X,Z) -> pair(add(M,X),Z) f_2(true(),N,M,Y,X,Z) -> pair(X,add(M,Z)) f_3(pair(Y,Z),N,X) -> append(qsort(Y),add(X,qsort(Z))) lt(0(),s(X)) -> true() lt(s(X),0()) -> false() lt(s(X),s(Y)) -> lt(X,Y) qsort(add(N,X)) -> f_3(split(N,X),N,X) qsort(nil()) -> nil() split(N,add(M,Y)) -> f_1(split(N,Y),N,M,Y) split(N,nil()) -> pair(nil(),nil()) - Signature: {append/2,f_1/4,f_2/6,f_3/3,lt/2,qsort/1,split/2} / {0/0,add/2,false/0,nil/0,pair/2,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {append,f_1,f_2,f_3,lt,qsort,split} and constructors {0 ,add,false,nil,pair,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: append(y,z){y -> add(x,y)} = append(add(x,y),z) ->^+ add(x,append(y,z)) = C[append(y,z) = append(y,z){}] ** Step 1.b:1: DependencyPairs WORST_CASE(?,O(n^3)) + Considered Problem: - Strict TRS: append(add(N,X),Y) -> add(N,append(X,Y)) append(nil(),Y) -> Y f_1(pair(X,Z),N,M,Y) -> f_2(lt(N,M),N,M,Y,X,Z) f_2(false(),N,M,Y,X,Z) -> pair(add(M,X),Z) f_2(true(),N,M,Y,X,Z) -> pair(X,add(M,Z)) f_3(pair(Y,Z),N,X) -> append(qsort(Y),add(X,qsort(Z))) lt(0(),s(X)) -> true() lt(s(X),0()) -> false() lt(s(X),s(Y)) -> lt(X,Y) qsort(add(N,X)) -> f_3(split(N,X),N,X) qsort(nil()) -> nil() split(N,add(M,Y)) -> f_1(split(N,Y),N,M,Y) split(N,nil()) -> pair(nil(),nil()) - Signature: {append/2,f_1/4,f_2/6,f_3/3,lt/2,qsort/1,split/2} / {0/0,add/2,false/0,nil/0,pair/2,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {append,f_1,f_2,f_3,lt,qsort,split} and constructors {0 ,add,false,nil,pair,s,true} + Applied Processor: DependencyPairs {dpKind_ = DT} + Details: We add the following dependency tuples: Strict DPs append#(add(N,X),Y) -> c_1(append#(X,Y)) append#(nil(),Y) -> c_2() f_1#(pair(X,Z),N,M,Y) -> c_3(f_2#(lt(N,M),N,M,Y,X,Z),lt#(N,M)) f_2#(false(),N,M,Y,X,Z) -> c_4() f_2#(true(),N,M,Y,X,Z) -> c_5() f_3#(pair(Y,Z),N,X) -> c_6(append#(qsort(Y),add(X,qsort(Z))),qsort#(Y),qsort#(Z)) lt#(0(),s(X)) -> c_7() lt#(s(X),0()) -> c_8() lt#(s(X),s(Y)) -> c_9(lt#(X,Y)) qsort#(add(N,X)) -> c_10(f_3#(split(N,X),N,X),split#(N,X)) qsort#(nil()) -> c_11() split#(N,add(M,Y)) -> c_12(f_1#(split(N,Y),N,M,Y),split#(N,Y))
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