/export/starexec/sandbox/solver/bin/starexec_run_Default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: p(s(x)) -> x 2: plus(x,0()) -> x 3: plus(0(),y) -> y 4: plus(s(x),y) -> s(plus(x,y)) 5: plus(s(x),y) -> s(plus(p(s(x)),y)) 6: plus(x,s(y)) -> s(plus(x,p(s(y)))) 7: times(0(),y) -> 0() 8: times(s(0()),y) -> y 9: times(s(x),y) -> plus(y,times(x,y)) 10: div(0(),y) -> 0() 11: div(x,y) -> quot(x,y,y) 12: quot(0(),s(y),z) -> 0() 13: quot(s(x),s(y),z) -> quot(x,y,z) 14: quot(x,0(),s(z)) -> s(div(x,s(z))) 15: div(div(x,y),z) -> div(x,times(y,z)) 16: eq(0(),0()) -> true() 17: eq(s(x),0()) -> false() 18: eq(0(),s(y)) -> false() 19: eq(s(x),s(y)) -> eq(x,y) 20: divides(y,x) -> eq(x,times(div(x,y),y)) 21: prime(s(s(x))) -> pr(s(s(x)),s(x)) 22: pr(x,s(0())) -> true() 23: pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y)) 24: if(true(),x,y) -> false() 25: if(false(),x,y) -> pr(x,y) Number of strict rules: 25 Direct POLO(bPol) ... failed. Uncurrying p 1: p^1_s(x) -> x 2: plus(x,0()) -> x 3: plus(0(),y) -> y 4: plus(s(x),y) -> s(plus(x,y)) 5: plus(s(x),y) -> s(plus(p^1_s(x),y)) 6: plus(x,s(y)) -> s(plus(x,p^1_s(y))) 7: times(0(),y) -> 0() 8: times(s(0()),y) -> y 9: times(s(x),y) -> plus(y,times(x,y)) 10: div(0(),y) -> 0() 11: div(x,y) -> quot(x,y,y) 12: quot(0(),s(y),z) -> 0() 13: quot(s(x),s(y),z) -> quot(x,y,z) 14: quot(x,0(),s(z)) -> s(div(x,s(z))) 15: div(div(x,y),z) -> div(x,times(y,z)) 16: eq(0(),0()) -> true() 17: eq(s(x),0()) -> false() 18: eq(0(),s(y)) -> false() 19: eq(s(x),s(y)) -> eq(x,y) 20: divides(y,x) -> eq(x,times(div(x,y),y)) 21: prime(s(s(x))) -> pr(s(s(x)),s(x)) 22: pr(x,s(0())) -> true() 23: pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y)) 24: if(true(),x,y) -> false() 25: if(false(),x,y) -> pr(x,y) 26: p(s(_1)) ->= p^1_s(_1) Number of strict rules: 25 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #plus(x,s(y)) -> #plus(x,p^1_s(y)) #2: #plus(x,s(y)) -> #p^1_s(y) #3: #quot(s(x),s(y),z) -> #quot(x,y,z) #4: #times(s(x),y) -> #plus(y,times(x,y)) #5: #times(s(x),y) -> #times(x,y) #6: #div(x,y) -> #quot(x,y,y) #7: #pr(x,s(s(y))) -> #if(divides(s(s(y)),x),x,s(y)) #8: #pr(x,s(s(y))) -> #divides(s(s(y)),x) #9: #quot(x,0(),s(z)) -> #div(x,s(z)) #10: #if(false(),x,y) -> #pr(x,y) #11: #divides(y,x) -> #eq(x,times(div(x,y),y)) #12: #divides(y,x) -> #times(div(x,y),y) #13: #divides(y,x) -> #div(x,y) #14: #plus(s(x),y) -> #plus(p^1_s(x),y) #15: #plus(s(x),y) -> #p^1_s(x) #16: #eq(s(x),s(y)) -> #eq(x,y) #17: #p(s(_1)) ->? #p^1_s(_1) #18: #prime(s(s(x))) -> #pr(s(s(x)),s(x)) #19: #div(div(x,y),z) -> #div(x,times(y,z)) #20: #div(div(x,y),z) -> #times(y,z) #21: #plus(s(x),y) -> #plus(x,y) Number of SCCs: 5, DPs: 11 SCC { #5 } POLO(Sum)... succeeded. #div w: 0 s w: x1 + 1 #p^1_s w: 0 prime w: 0 #plus w: 0 #pr w: 0 eq w: 0 false w: 0 div w: 0 p^1_s w: 0 #p w: 0 true w: 0 #eq w: 0 #prime w: 0 p 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: #5 Number of SCCs: 4, DPs: 10 SCC { #16 } POLO(Sum)... succeeded. #div w: 0 s w: x1 + 1 #p^1_s w: 0 prime w: 0 #plus w: 0 #pr w: 0 eq w: 0 false w: 0 div w: 0 p^1_s w: 0 #p w: 0 true w: 0 #eq w: x2 #prime w: 0 p 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: #16 Number of SCCs: 3, DPs: 9 SCC { #7 #10 } POLO(Sum)... succeeded. #div w: 0 s w: x1 + 2 #p^1_s w: 0 prime w: 0 #plus w: 0 #pr w: x1 + x2 eq w: x2 false w: 3 div w: x1 + 1 p^1_s w: 1 #p w: 0 true w: 2 #eq w: 0 #prime w: 0 p w: 0 #times w: 0 0 w: 1 if w: 0 quot w: 0 times w: x1 + 1 pr w: 0 #divides w: 0 plus w: x1 + x2 + 3 #if w: x2 + x3 + 1 #quot w: 0 divides w: x1 + x2 + 2 USABLE RULES: { } Removed DPs: #7 #10 Number of SCCs: 2, DPs: 7 SCC { #1 #14 #21 } POLO(Sum)... succeeded. #div w: 0 s w: x1 + 2 #p^1_s w: 0 prime w: 0 #plus w: x1 #pr w: 0 eq w: x2 false w: 3 div w: x1 + 1 p^1_s w: x1 + 1 #p w: 0 true w: 2 #eq w: 0 #prime w: 0 p w: 0 #times w: 0 0 w: 1 if w: 0 quot w: 0 times w: x1 + 1 pr w: 0 #divides w: 0 plus w: x1 + x2 + 3 #if w: 1 #quot w: 0 divides w: x1 + x2 + 2 USABLE RULES: { 1 } Removed DPs: #14 #21 Number of SCCs: 2, DPs: 5 SCC { #1 } POLO(Sum)... succeeded. #div w: 0 s w: x1 + 2 #p^1_s w: 0 prime w: 0 #plus w: x1 + x2 #pr w: 0 eq w: x2 false w: 3 div w: x1 + 1 p^1_s w: x1 + 1 #p w: 0 true w: 2 #eq w: 0 #prime w: 0 p w: 0 #times w: 0 0 w: 1 if w: 0 quot w: 0 times w: x1 + 1 pr w: 0 #divides w: 0 plus w: x1 + x2 + 3 #if w: 1 #quot w: 0 divides w: x1 + x2 + 2 USABLE RULES: { 1 } Removed DPs: #1 Number of SCCs: 1, DPs: 4 SCC { #3 #6 #9 #19 } POLO(Sum)... succeeded. #div w: x1 s w: x1 + 2 #p^1_s w: 0 prime w: 0 #plus w: x1 + x2 #pr w: 0 eq w: x2 false w: 3 div w: x1 + x2 + 1 p^1_s w: x1 + 1 #p w: 0 true w: 2 #eq w: 0 #prime w: 0 p w: 0 #times w: 0 0 w: 1 if w: 0 quot w: 0 times w: x1 + 1 pr w: 0 #divides w: 0 plus w: x1 + x2 + 3 #if w: 1 #quot w: x1 divides w: x1 + x2 + 2 USABLE RULES: { 1 } Removed DPs: #3 #19 Number of SCCs: 1, DPs: 2 SCC { #6 #9 } POLO(Sum)... POLO(max)... succeeded. #div w: max(x2 + 2) s w: 0 #p^1_s w: 0 prime w: 0 #plus w: 0 #pr w: 0 eq w: 0 false w: 0 div w: 0 p^1_s w: 0 #p w: 0 true w: 0 #eq w: 0 #prime w: 0 p 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 + 1) divides w: 0 USABLE RULES: { } Removed DPs: #6 #9 Number of SCCs: 0, DPs: 0