/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: p(0()) -> 0() 2: p(s(x)) -> x 3: plus(x,0()) -> x 4: plus(0(),y) -> y 5: plus(s(x),y) -> s(plus(x,y)) 6: plus(s(x),y) -> s(plus(p(s(x)),y)) 7: plus(x,s(y)) -> s(plus(x,p(s(y)))) 8: times(0(),y) -> 0() 9: times(s(0()),y) -> y 10: times(s(x),y) -> plus(y,times(x,y)) 11: div(0(),y) -> 0() 12: div(x,y) -> quot(x,y,y) 13: quot(zero(y),s(y),z) -> 0() 14: quot(s(x),s(y),z) -> quot(x,y,z) 15: quot(x,0(),s(z)) -> s(div(x,s(z))) 16: div(div(x,y),z) -> div(x,times(zero(y),z)) 17: eq(0(),0()) -> true() 18: eq(s(x),0()) -> false() 19: eq(0(),s(y)) -> false() 20: eq(s(x),s(y)) -> eq(x,y) 21: divides(y,x) -> eq(x,times(div(x,y),y)) 22: prime(s(s(x))) -> pr(s(s(x)),s(x)) 23: pr(x,s(0())) -> true() 24: pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y)) 25: if(true(),x,y) -> false() 26: if(false(),x,y) -> pr(x,y) 27: zero(div(x,x)) -> x 28: zero(divides(x,x)) -> x 29: zero(times(x,x)) -> x 30: zero(quot(x,x,x)) -> x 31: zero(s(x)) -> if(eq(x,s(0())),plus(zero(0()),0()),s(plus(0(),zero(0())))) Number of strict rules: 31 Direct POLO(bPol) ... failed. Uncurrying p 1: p^1_0() -> 0() 2: p^1_s(x) -> x 3: plus(x,0()) -> x 4: plus(0(),y) -> y 5: plus(s(x),y) -> s(plus(x,y)) 6: plus(s(x),y) -> s(plus(p^1_s(x),y)) 7: plus(x,s(y)) -> s(plus(x,p^1_s(y))) 8: times(0(),y) -> 0() 9: times(s(0()),y) -> y 10: times(s(x),y) -> plus(y,times(x,y)) 11: div(0(),y) -> 0() 12: div(x,y) -> quot(x,y,y) 13: quot(zero(y),s(y),z) -> 0() 14: quot(s(x),s(y),z) -> quot(x,y,z) 15: quot(x,0(),s(z)) -> s(div(x,s(z))) 16: div(div(x,y),z) -> div(x,times(zero(y),z)) 17: eq(0(),0()) -> true() 18: eq(s(x),0()) -> false() 19: eq(0(),s(y)) -> false() 20: eq(s(x),s(y)) -> eq(x,y) 21: divides(y,x) -> eq(x,times(div(x,y),y)) 22: prime(s(s(x))) -> pr(s(s(x)),s(x)) 23: pr(x,s(0())) -> true() 24: pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y)) 25: if(true(),x,y) -> false() 26: if(false(),x,y) -> pr(x,y) 27: zero(div(x,x)) -> x 28: zero(divides(x,x)) -> x 29: zero(times(x,x)) -> x 30: zero(quot(x,x,x)) -> x 31: zero(s(x)) -> if(eq(x,s(0())),plus(zero(0()),0()),s(plus(0(),zero(0())))) 32: p(0()) ->= p^1_0() 33: p(s(_1)) ->= p^1_s(_1) Number of strict rules: 31 Direct POLO(bPol) ... failed. Dependency Pairs: #1: #plus(s(x),y) -> #plus(p^1_s(x),y) #2: #plus(s(x),y) -> #p^1_s(x) #3: #pr(x,s(s(y))) -> #if(divides(s(s(y)),x),x,s(y)) #4: #pr(x,s(s(y))) -> #divides(s(s(y)),x) #5: #div(x,y) -> #quot(x,y,y) #6: #zero(s(x)) -> #if(eq(x,s(0())),plus(zero(0()),0()),s(plus(0(),zero(0())))) #7: #zero(s(x)) -> #eq(x,s(0())) #8: #zero(s(x)) -> #plus(zero(0()),0()) #9: #zero(s(x)) -> #zero(0()) #10: #zero(s(x)) -> #plus(0(),zero(0())) #11: #zero(s(x)) -> #zero(0()) #12: #quot(s(x),s(y),z) -> #quot(x,y,z) #13: #eq(s(x),s(y)) -> #eq(x,y) #14: #plus(x,s(y)) -> #plus(x,p^1_s(y)) #15: #plus(x,s(y)) -> #p^1_s(y) #16: #times(s(x),y) -> #plus(y,times(x,y)) #17: #times(s(x),y) -> #times(x,y) #18: #p(s(_1)) ->? #p^1_s(_1) #19: #plus(s(x),y) -> #plus(x,y) #20: #prime(s(s(x))) -> #pr(s(s(x)),s(x)) #21: #p(0()) ->? #p^1_0() #22: #if(false(),x,y) -> #pr(x,y) #23: #divides(y,x) -> #eq(x,times(div(x,y),y)) #24: #divides(y,x) -> #times(div(x,y),y) #25: #divides(y,x) -> #div(x,y) #26: #div(div(x,y),z) -> #div(x,times(zero(y),z)) #27: #div(div(x,y),z) -> #times(zero(y),z) #28: #div(div(x,y),z) -> #zero(y) #29: #quot(x,0(),s(z)) -> #div(x,s(z)) Number of SCCs: 4, DPs: 15 SCC { #17 } POLO(Sum)... succeeded. zero w: 0 #div w: 0 s w: x1 + 1 #p^1_0 w: 0 #p^1_s w: 0 prime w: 0 p^1_0 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 #zero w: 0 divides w: 0 USABLE RULES: { } Removed DPs: #17 Number of SCCs: 3, DPs: 14 SCC { #13 } POLO(Sum)... succeeded. zero w: 0 #div w: 0 s w: x1 + 1 #p^1_0 w: 0 #p^1_s w: 0 prime w: 0 p^1_0 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 #zero w: 0 divides w: 0 USABLE RULES: { } Removed DPs: #13 Number of SCCs: 2, DPs: 13 SCC { #1 #14 #19 } POLO(Sum)... succeeded. zero w: 0 #div w: 0 s w: x1 + 2 #p^1_0 w: 0 #p^1_s w: 0 prime w: 0 p^1_0 w: 0 #plus w: x1 + x2 #pr w: 0 eq w: 0 false w: 0 div w: 0 p^1_s w: x1 + 1 #p w: 0 true w: 0 #eq w: 0 #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 #zero w: 0 divides w: 0 USABLE RULES: { 2 } Removed DPs: #1 #14 #19 Number of SCCs: 1, DPs: 10 SCC { #3..6 #12 #22 #25 #26 #28 #29 } POLO(Sum)... succeeded. zero w: 1 #div w: x1 + 25 s w: x1 + 3 #p^1_0 w: 0 #p^1_s w: 0 prime w: 0 p^1_0 w: 0 #plus w: x1 + x2 #pr w: x1 + 27 eq w: x1 + 6 false w: 10 div w: x1 + 10 p^1_s w: x1 #p w: 0 true w: 8 #eq w: 0 #prime w: 0 p w: 0 #times w: 0 0 w: 1 if w: x2 + x3 quot w: x2 + 11 times w: x1 + 1 pr w: 1 #divides w: x2 + 26 plus w: x1 + x2 + 4 #if w: x2 + 27 #quot w: x1 + 25 #zero w: 34 divides w: x1 + 5 USABLE RULES: { 2..7 } Removed DPs: #4 #6 #12 #25 #26 #28 Number of SCCs: 2, DPs: 4 SCC { #5 #29 } POLO(Sum)... POLO(max)... succeeded. zero w: 0 #div w: max(x2 + 2) s w: 0 #p^1_0 w: 0 #p^1_s w: 0 prime w: 0 p^1_0 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) #zero w: 0 divides w: 0 USABLE RULES: { } Removed DPs: #5 #29 Number of SCCs: 1, DPs: 2 SCC { #3 #22 } POLO(Sum)... succeeded. zero w: 1 #div w: 25 s w: x1 + 3 #p^1_0 w: 0 #p^1_s w: 0 prime w: 0 p^1_0 w: 0 #plus w: x1 + x2 #pr w: x1 + x2 + 26 eq w: x1 + 6 false w: 10 div w: x1 + 10 p^1_s w: x1 #p w: 0 true w: 8 #eq w: 0 #prime w: 0 p w: 0 #times w: 0 0 w: 1 if w: x2 + x3 quot w: x2 + 11 times w: x1 + 1 pr w: 1 #divides w: 26 plus w: x1 + x2 + 4 #if w: x2 + x3 + 27 #quot w: 25 #zero w: 34 divides w: x1 + 5 USABLE RULES: { 2..7 } Removed DPs: #3 #22 Number of SCCs: 0, DPs: 0