/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: plus(x,0()) -> x 2: plus(0(),y) -> y 3: plus(s(x),y) -> s(plus(x,y)) 4: times(0(),y) -> 0() 5: times(s(0()),y) -> y 6: times(s(x),y) -> plus(y,times(x,y)) 7: div(0(),y) -> 0() 8: div(x,y) -> quot(x,y,y) 9: quot(0(),s(y),z) -> 0() 10: quot(s(x),s(y),z) -> quot(x,y,z) 11: quot(x,0(),s(z)) -> s(div(x,s(z))) 12: div(div(x,y),z) -> div(x,times(y,z)) 13: eq(0(),0()) -> true() 14: eq(s(x),0()) -> false() 15: eq(0(),s(y)) -> false() 16: eq(s(x),s(y)) -> eq(x,y) 17: divides(y,x) -> eq(x,times(div(x,y),y)) 18: prime(s(s(x))) -> pr(s(s(x)),s(x)) 19: pr(x,s(0())) -> true() 20: pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y)) 21: if(true(),x,y) -> false() 22: if(false(),x,y) -> pr(x,y) Number of strict rules: 22 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #times(s(x),y) -> #plus(y,times(x,y)) #2: #times(s(x),y) -> #times(x,y) #3: #quot(x,0(),s(z)) -> #div(x,s(z)) #4: #div(div(x,y),z) -> #div(x,times(y,z)) #5: #div(div(x,y),z) -> #times(y,z) #6: #pr(x,s(s(y))) -> #if(divides(s(s(y)),x),x,s(y)) #7: #pr(x,s(s(y))) -> #divides(s(s(y)),x) #8: #quot(s(x),s(y),z) -> #quot(x,y,z) #9: #if(false(),x,y) -> #pr(x,y) #10: #divides(y,x) -> #eq(x,times(div(x,y),y)) #11: #divides(y,x) -> #times(div(x,y),y) #12: #divides(y,x) -> #div(x,y) #13: #eq(s(x),s(y)) -> #eq(x,y) #14: #plus(s(x),y) -> #plus(x,y) #15: #div(x,y) -> #quot(x,y,y) #16: #prime(s(s(x))) -> #pr(s(s(x)),s(x)) Number of SCCs: 5, DPs: 9 SCC { #2 } POLO(Sum)... succeeded. #div w: 0 s w: x1 + 1 prime w: 0 #plus w: 0 #pr w: 0 eq w: 0 false w: 0 div w: 0 true w: 0 #eq w: 0 #prime w: 0 #times w: x1 0 w: 0 if w: 0 quot w: 0 times w: 0 pr w: 0 #divides w: 0 plus w: 0 #if w: 0 #quot w: 0 divides w: 0 USABLE RULES: { } Removed DPs: #2 Number of SCCs: 4, DPs: 8 SCC { #14 } POLO(Sum)... succeeded. #div w: 0 s w: x1 + 1 prime w: 0 #plus w: x1 #pr w: 0 eq w: 0 false w: 0 div w: 0 true w: 0 #eq w: 0 #prime w: 0 #times w: 0 0 w: 0 if w: 0 quot w: 0 times w: 0 pr w: 0 #divides w: 0 plus w: 0 #if w: 0 #quot w: 0 divides w: 0 USABLE RULES: { } Removed DPs: #14 Number of SCCs: 3, DPs: 7 SCC { #13 } POLO(Sum)... succeeded. #div w: 0 s w: x1 + 1 prime w: 0 #plus w: 0 #pr w: 0 eq w: 0 false w: 0 div w: 0 true w: 0 #eq w: x2 #prime w: 0 #times w: 0 0 w: 0 if w: 0 quot w: 0 times w: 0 pr w: 0 #divides w: 0 plus w: 0 #if w: 0 #quot w: 0 divides w: 0 USABLE RULES: { } Removed DPs: #13 Number of SCCs: 2, DPs: 6 SCC { #6 #9 } POLO(Sum)... succeeded. #div w: 0 s w: x1 + 2 prime w: 0 #plus w: 0 #pr w: x1 + x2 + 1 eq w: x1 + x2 false w: 2 div w: x1 + 4 true w: 7 #eq w: 0 #prime w: 0 #times w: 0 0 w: 3 if w: 0 quot w: x2 + x3 times w: x1 + x2 + 1 pr w: 0 #divides w: 0 plus w: x1 + x2 + 3 #if w: x2 + x3 + 2 #quot w: 0 divides w: x2 + 5 USABLE RULES: { 1..5 } Removed DPs: #6 #9 Number of SCCs: 1, DPs: 4 SCC { #3 #4 #8 #15 } POLO(Sum)... succeeded. #div w: x1 s w: x1 + 2 prime w: 0 #plus w: 0 #pr w: 1 eq w: x1 + x2 false w: 2 div w: x1 + x2 + 4 true w: 7 #eq w: 0 #prime w: 0 #times w: 0 0 w: 3 if w: 0 quot w: x2 + x3 times w: x1 + 1 pr w: 0 #divides w: 0 plus w: x1 + 4 #if w: 2 #quot w: x1 divides w: x2 + 5 USABLE RULES: { } Removed DPs: #4 #8 Number of SCCs: 1, DPs: 2 SCC { #3 #15 } POLO(Sum)... POLO(max)... succeeded. #div w: max(x2) s w: 1 prime w: 0 #plus w: 0 #pr w: 0 eq w: 0 false w: 0 div w: 0 true w: 0 #eq w: 0 #prime w: 0 #times w: 0 0 w: 2 if w: 0 quot w: 0 times w: 0 pr w: 0 #divides w: 0 plus w: 0 #if w: 0 #quot w: max(x2, x3) divides w: 0 USABLE RULES: { } Removed DPs: #3 Number of SCCs: 0, DPs: 0