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TRS Standard pair #516967553
details
property
value
status
complete
benchmark
quicksort.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n076.star.cs.uiowa.edu
space
AProVE_06
run statistics
property
value
solver
NaTT 2.1
configuration
default
runtime (wallclock)
0.301346063614 seconds
cpu usage
0.291549963
max memory
2.041856E7
stage attributes
key
value
output-size
6202
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: le(0(),y) -> true() 2: le(s(x),0()) -> false() 3: le(s(x),s(y)) -> le(x,y) 4: app(nil(),y) -> y 5: app(add(n,x),y) -> add(n,app(x,y)) 6: low(n,nil()) -> nil() 7: low(n,add(m,x)) -> if_low(le(m,n),n,add(m,x)) 8: if_low(true(),n,add(m,x)) -> add(m,low(n,x)) 9: if_low(false(),n,add(m,x)) -> low(n,x) 10: high(n,nil()) -> nil() 11: high(n,add(m,x)) -> if_high(le(m,n),n,add(m,x)) 12: if_high(true(),n,add(m,x)) -> high(n,x) 13: if_high(false(),n,add(m,x)) -> add(m,high(n,x)) 14: head(add(n,x)) -> n 15: tail(add(n,x)) -> x 16: isempty(nil()) -> true() 17: isempty(add(n,x)) -> false() 18: quicksort(x) -> if_qs(isempty(x),low(head(x),tail(x)),head(x),high(head(x),tail(x))) 19: if_qs(true(),x,n,y) -> nil() 20: if_qs(false(),x,n,y) -> app(quicksort(x),add(n,quicksort(y))) Number of strict rules: 20 Direct poly ... failed. Freezing ... failed. Dependency Pairs: #1: #if_high(false(),n,add(m,x)) -> #high(n,x) #2: #if_low(false(),n,add(m,x)) -> #low(n,x) #3: #high(n,add(m,x)) -> #if_high(le(m,n),n,add(m,x)) #4: #high(n,add(m,x)) -> #le(m,n) #5: #if_high(true(),n,add(m,x)) -> #high(n,x) #6: #if_qs(false(),x,n,y) -> #app(quicksort(x),add(n,quicksort(y))) #7: #if_qs(false(),x,n,y) -> #quicksort(x) #8: #if_qs(false(),x,n,y) -> #quicksort(y) #9: #low(n,add(m,x)) -> #if_low(le(m,n),n,add(m,x)) #10: #low(n,add(m,x)) -> #le(m,n) #11: #app(add(n,x),y) -> #app(x,y) #12: #le(s(x),s(y)) -> #le(x,y) #13: #if_low(true(),n,add(m,x)) -> #low(n,x) #14: #quicksort(x) -> #if_qs(isempty(x),low(head(x),tail(x)),head(x),high(head(x),tail(x))) #15: #quicksort(x) -> #isempty(x) #16: #quicksort(x) -> #low(head(x),tail(x)) #17: #quicksort(x) -> #head(x) #18: #quicksort(x) -> #tail(x) #19: #quicksort(x) -> #head(x) #20: #quicksort(x) -> #high(head(x),tail(x)) #21: #quicksort(x) -> #head(x) #22: #quicksort(x) -> #tail(x) Number of SCCs: 5, DPs: 11 SCC { #11 } Sum... succeeded. isempty(x1) w: (0) le(x1,x2) w: (0) s(x1) w: (0) #le(x1,x2) w: (0) if_high(x1,x2,x3) w: (0) #if_qs(x1,x2,x3,x4) w: (0) if_qs(x1,x2,x3,x4) w: (0) #isempty(x1) w: (0) #quicksort(x1) w: (0) #high(x1,x2) w: (0) false() w: (0) #head(x1) w: (0) #if_high(x1,x2,x3) w: (0) quicksort(x1) w: (0) true() w: (0) tail(x1) w: (0) 0() w: (0) high(x1,x2) w: (0) nil() w: (0) #tail(x1) w: (0) #app(x1,x2) w: (x1) low(x1,x2) w: (0) head(x1) w: (0) add(x1,x2) w: (1 + x2) if_low(x1,x2,x3) w: (0) #if_low(x1,x2,x3) w: (0) #low(x1,x2) w: (0) app(x1,x2) w: (0) USABLE RULES: { } Removed DPs: #11 Number of SCCs: 4, DPs: 10 SCC { #12 } Sum... succeeded. isempty(x1) w: (0) le(x1,x2) w: (0) s(x1) w: (1 + x1) #le(x1,x2) w: (x2) if_high(x1,x2,x3) w: (0) #if_qs(x1,x2,x3,x4) w: (0) if_qs(x1,x2,x3,x4) w: (0) #isempty(x1) w: (0) #quicksort(x1) w: (0) #high(x1,x2) w: (0)
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