/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: minus(x,0()) -> x 2: minus(s(x),s(y)) -> minus(x,y) 3: quot(0(),s(y)) -> 0() 4: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) 5: le(0(),y) -> true() 6: le(s(x),0()) -> false() 7: le(s(x),s(y)) -> le(x,y) 8: app(nil(),y) -> y 9: app(add(n,x),y) -> add(n,app(x,y)) 10: low(n,nil()) -> nil() 11: low(n,add(m,x)) -> if_low(le(m,n),n,add(m,x)) 12: if_low(true(),n,add(m,x)) -> add(m,low(n,x)) 13: if_low(false(),n,add(m,x)) -> low(n,x) 14: high(n,nil()) -> nil() 15: high(n,add(m,x)) -> if_high(le(m,n),n,add(m,x)) 16: if_high(true(),n,add(m,x)) -> high(n,x) 17: if_high(false(),n,add(m,x)) -> add(m,high(n,x)) 18: quicksort(nil()) -> nil() 19: quicksort(add(n,x)) -> app(quicksort(low(n,x)),add(n,quicksort(high(n,x)))) 20: rand(x) ->= x 21: rand(x) ->= rand(s(x)) Number of strict rules: 19 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #minus(s(x),s(y)) -> #minus(x,y) #2: #if_low(false(),n,add(m,x)) -> #low(n,x) #3: #app(add(n,x),y) -> #app(x,y) #4: #low(n,add(m,x)) -> #if_low(le(m,n),n,add(m,x)) #5: #low(n,add(m,x)) -> #le(m,n) #6: #if_low(true(),n,add(m,x)) -> #low(n,x) #7: #le(s(x),s(y)) -> #le(x,y) #8: #if_high(false(),n,add(m,x)) -> #high(n,x) #9: #quicksort(add(n,x)) -> #app(quicksort(low(n,x)),add(n,quicksort(high(n,x)))) #10: #quicksort(add(n,x)) -> #quicksort(low(n,x)) #11: #quicksort(add(n,x)) -> #low(n,x) #12: #quicksort(add(n,x)) -> #quicksort(high(n,x)) #13: #quicksort(add(n,x)) -> #high(n,x) #14: #if_high(true(),n,add(m,x)) -> #high(n,x) #15: #high(n,add(m,x)) -> #if_high(le(m,n),n,add(m,x)) #16: #high(n,add(m,x)) -> #le(m,n) #17: #quot(s(x),s(y)) -> #quot(minus(x,y),s(y)) #18: #quot(s(x),s(y)) -> #minus(x,y) Number of SCCs: 7, DPs: 12 SCC { #1 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. le s: [] p: 4 w: max(x1 + 5, x2 + 6) s s: [1] p: 1 w: x1 #le s: [] p: 0 w: max(x1) minus s: 1 if_high s: [] p: 2 w: max(x2 + 2, x3) #quicksort s: [] p: 0 w: 1 #high s: [2] p: 0 w: max(x2) false s: [] p: 1 w: 4 #if_high s: [3,2] p: 0 w: max(x2, x3) quicksort s: [1] p: 2 w: x1 true s: [] p: 1 w: 0 rand s: [] p: 0 w: x1 + 1 0 s: [] p: 0 w: 4 quot s: 1 high s: [] p: 2 w: max(x1 + 2, x2) nil s: [] p: 1 w: 1 #app s: [] p: 0 w: max(x2) #minus s: [2] p: 2 w: max(x2) low s: [] p: 3 w: max(x1 + 2, x2) add s: [] p: 2 w: max(x1 + 3, x2) #quot s: [] p: 0 w: max(x1 + 1) if_low s: [] p: 3 w: max(x2 + 2, x3) #if_low s: [1,2,3] p: 0 w: max(x1, x2 + 1, x3) #low s: [] p: 0 w: max(x2) app s: [2] p: 2 w: max(x1, x2) Removed DPs: #1 Number of SCCs: 6, DPs: 11 SCC { #3 } POLO(Sum)... POLO(max)... QLPOS... succeeded. le s: [] p: 5 s s: 1 #le s: [1] p: 0 minus s: [1,2] p: 3 if_high s: 3 #quicksort s: [] p: 0 #high s: [] p: 0 false s: [] p: 2 #if_high s: [1,2] p: 0 quicksort s: [1] p: 7 true s: [] p: 0 rand s: [1] p: 0 0 s: [] p: 2 quot s: [] p: 2 high s: 2 nil s: [] p: 7 #app s: 1 #minus s: [] p: 0 low s: 2 add s: [1,2] p: 5 #quot s: [] p: 0 if_low s: 3 #if_low s: [] p: 0 #low s: [] p: 0 app s: [2,1] p: 6 Removed DPs: #3 Number of SCCs: 5, DPs: 10 SCC { #7 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. le s: [] p: 4 w: max(x1 + 5, x2 + 6) s s: [1] p: 1 w: x1 #le s: [1,2] p: 2 w: max(x1, x2 + 1) minus s: 1 if_high s: [] p: 2 w: max(x2 + 2, x3) #quicksort s: [] p: 0 w: 1 #high s: [2] p: 0 w: max(x2) false s: [] p: 1 w: 4 #if_high s: [3,2] p: 0 w: max(x2, x3) quicksort s: [1] p: 2 w: x1 true s: [] p: 1 w: 0 rand s: [] p: 0 w: x1 + 1 0 s: [] p: 0 w: 4 quot s: 1 high s: [] p: 2 w: max(x1 + 2, x2) nil s: [] p: 1 w: 1 #app s: [] p: 0 w: max(x2) #minus s: [2] p: 2 w: max(x2) low s: [] p: 3 w: max(x1 + 2, x2) add s: [] p: 2 w: max(x1 + 3, x2) #quot s: [] p: 0 w: max(x1 + 1) if_low s: [] p: 3 w: max(x2 + 2, x3) #if_low s: [1,2,3] p: 0 w: max(x1, x2 + 1, x3) #low s: [] p: 0 w: max(x2) app s: [2] p: 2 w: max(x1, x2) Removed DPs: #7 Number of SCCs: 4, DPs: 9 SCC { #17 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. le s: [] p: 4 w: max(x1 + 5, x2 + 6) s s: [1] p: 1 w: x1 #le s: [1,2] p: 2 w: max(x1, x2 + 1) minus s: 1 if_high s: [] p: 2 w: max(x2 + 2, x3) #quicksort s: [] p: 0 w: 1 #high s: [2] p: 0 w: max(x2) false s: [] p: 1 w: 4 #if_high s: [3,2] p: 0 w: max(x2, x3) quicksort s: [1] p: 2 w: x1 true s: [] p: 1 w: 0 rand s: [] p: 0 w: x1 + 1 0 s: [] p: 0 w: 4 quot s: 1 high s: [] p: 2 w: max(x1 + 2, x2) nil s: [] p: 1 w: 1 #app s: [] p: 0 w: max(x2) #minus s: [2] p: 2 w: max(x2) low s: [] p: 3 w: max(x1 + 2, x2) add s: [] p: 2 w: max(x1 + 3, x2) #quot s: [2,1] p: 1 w: max(x1 + 1, x2) if_low s: [] p: 3 w: max(x2 + 2, x3) #if_low s: [1,2,3] p: 0 w: max(x1, x2 + 1, x3) #low s: [] p: 0 w: max(x2) app s: [2] p: 2 w: max(x1, x2) Removed DPs: #17 Number of SCCs: 3, DPs: 8 SCC { #10 #12 } POLO(Sum)... POLO(max)... QLPOS... succeeded. le s: [] p: 5 s s: 1 #le s: [2] p: 0 minus s: 1 if_high s: 3 #quicksort s: [1] p: 0 #high s: [] p: 0 false s: [] p: 2 #if_high s: [1,2] p: 0 quicksort s: [1] p: 7 true s: [] p: 0 rand s: [1] p: 0 0 s: [] p: 2 quot s: [] p: 2 high s: 2 nil s: [] p: 7 #app s: 1 #minus s: [] p: 0 low s: 2 add s: [1,2] p: 5 #quot s: [] p: 1 if_low s: 3 #if_low s: [] p: 0 #low s: [] p: 0 app s: [2,1] p: 6 Removed DPs: #10 #12 Number of SCCs: 2, DPs: 6 SCC { #8 #14 #15 } POLO(Sum)... POLO(max)... QLPOS... succeeded. le s: [] p: 5 s s: 1 #le s: [2] p: 0 minus s: 1 if_high s: 3 #quicksort s: [1] p: 0 #high s: [2] p: 2 false s: [] p: 1 #if_high s: [1,3] p: 2 quicksort s: [1] p: 7 true s: [] p: 3 rand s: [1] p: 0 0 s: [] p: 4 quot s: [] p: 4 high s: 2 nil s: [] p: 7 #app s: 1 #minus s: [] p: 0 low s: 2 add s: [1,2] p: 5 #quot s: [] p: 1 if_low s: 3 #if_low s: [] p: 0 #low s: [] p: 0 app s: [2,1] p: 6 Removed DPs: #8 #14 #15 Number of SCCs: 1, DPs: 3 SCC { #2 #4 #6 } POLO(Sum)... POLO(max)... QLPOS... succeeded. le s: [] p: 5 s s: 1 #le s: [2] p: 0 minus s: 1 if_high s: 3 #quicksort s: [1] p: 0 #high s: [2] p: 2 false s: [] p: 1 #if_high s: [1,3] p: 2 quicksort s: [1] p: 7 true s: [] p: 3 rand s: [1] p: 0 0 s: [] p: 4 quot s: [] p: 4 high s: 2 nil s: [] p: 7 #app s: 1 #minus s: [] p: 0 low s: 2 add s: [1,2] p: 5 #quot s: [] p: 1 if_low s: 3 #if_low s: [3] p: 6 #low s: [2] p: 6 app s: [2,1] p: 6 Removed DPs: #6 Number of SCCs: 1, DPs: 2 SCC { #2 #4 } POLO(Sum)... POLO(max)... QLPOS... succeeded. le s: [] p: 5 s s: 1 #le s: [2] p: 0 minus s: 1 if_high s: 3 #quicksort s: [1] p: 0 #high s: [2] p: 2 false s: [] p: 1 #if_high s: [1,3] p: 2 quicksort s: [1] p: 7 true s: [] p: 3 rand s: [1] p: 0 0 s: [] p: 4 quot s: [] p: 4 high s: 2 nil s: [] p: 7 #app s: 1 #minus s: [] p: 0 low s: 2 add s: [1,2] p: 5 #quot s: [] p: 1 if_low s: 3 #if_low s: [3] p: 5 #low s: [2] p: 5 app s: [2,1] p: 6 Removed DPs: #2 Number of SCCs: 0, DPs: 0