/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: a__primes() -> a__sieve(a__from(s(s(0())))) 2: a__from(X) -> cons(mark(X),from(s(X))) 3: a__head(cons(X,Y)) -> mark(X) 4: a__tail(cons(X,Y)) -> mark(Y) 5: a__if(true(),X,Y) -> mark(X) 6: a__if(false(),X,Y) -> mark(Y) 7: a__filter(s(s(X)),cons(Y,Z)) -> a__if(divides(s(s(mark(X))),mark(Y)),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))) 8: a__sieve(cons(X,Y)) -> cons(mark(X),filter(X,sieve(Y))) 9: mark(primes()) -> a__primes() 10: mark(sieve(X)) -> a__sieve(mark(X)) 11: mark(from(X)) -> a__from(mark(X)) 12: mark(head(X)) -> a__head(mark(X)) 13: mark(tail(X)) -> a__tail(mark(X)) 14: mark(if(X1,X2,X3)) -> a__if(mark(X1),X2,X3) 15: mark(filter(X1,X2)) -> a__filter(mark(X1),mark(X2)) 16: mark(s(X)) -> s(mark(X)) 17: mark(0()) -> 0() 18: mark(cons(X1,X2)) -> cons(mark(X1),X2) 19: mark(true()) -> true() 20: mark(false()) -> false() 21: mark(divides(X1,X2)) -> divides(mark(X1),mark(X2)) 22: a__primes() -> primes() 23: a__sieve(X) -> sieve(X) 24: a__from(X) -> from(X) 25: a__head(X) -> head(X) 26: a__tail(X) -> tail(X) 27: a__if(X1,X2,X3) -> if(X1,X2,X3) 28: a__filter(X1,X2) -> filter(X1,X2) Number of strict rules: 28 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #a__from(X) -> #mark(X) #2: #a__if(false(),X,Y) -> #mark(Y) #3: #mark(tail(X)) -> #a__tail(mark(X)) #4: #mark(tail(X)) -> #mark(X) #5: #mark(primes()) -> #a__primes() #6: #mark(from(X)) -> #a__from(mark(X)) #7: #mark(from(X)) -> #mark(X) #8: #mark(head(X)) -> #a__head(mark(X)) #9: #mark(head(X)) -> #mark(X) #10: #mark(if(X1,X2,X3)) -> #a__if(mark(X1),X2,X3) #11: #mark(if(X1,X2,X3)) -> #mark(X1) #12: #a__filter(s(s(X)),cons(Y,Z)) -> #a__if(divides(s(s(mark(X))),mark(Y)),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))) #13: #a__filter(s(s(X)),cons(Y,Z)) -> #mark(X) #14: #a__filter(s(s(X)),cons(Y,Z)) -> #mark(Y) #15: #mark(sieve(X)) -> #a__sieve(mark(X)) #16: #mark(sieve(X)) -> #mark(X) #17: #a__if(true(),X,Y) -> #mark(X) #18: #mark(divides(X1,X2)) -> #mark(X1) #19: #mark(divides(X1,X2)) -> #mark(X2) #20: #mark(s(X)) -> #mark(X) #21: #a__head(cons(X,Y)) -> #mark(X) #22: #a__primes() -> #a__sieve(a__from(s(s(0())))) #23: #a__primes() -> #a__from(s(s(0()))) #24: #a__sieve(cons(X,Y)) -> #mark(X) #25: #mark(filter(X1,X2)) -> #a__filter(mark(X1),mark(X2)) #26: #mark(filter(X1,X2)) -> #mark(X1) #27: #mark(filter(X1,X2)) -> #mark(X2) #28: #a__tail(cons(X,Y)) -> #mark(Y) #29: #mark(cons(X1,X2)) -> #mark(X1) Number of SCCs: 1, DPs: 28 SCC { #1..11 #13..29 } POLO(Sum)... POLO(max)... succeeded. s w: x1 #a__head w: x1 + 3 #a__from w: x1 + 3 a__from w: x1 + 4 false w: 0 #a__filter w: max(x1 + 3, x2 + 1) a__sieve w: x1 + 2 true w: 0 tail w: x1 + 2 #mark w: x1 + 2 0 w: 1 if w: max(x1 + 2, x2, x3) #a__primes w: 9 from w: x1 + 4 mark w: x1 sieve w: x1 + 2 #a__if w: max(x1 + 3, x2 + 2, x3 + 2) head w: x1 + 2 cons w: max(x1 + 4, x2) a__primes w: 8 filter w: max(x1 + 3, x2) primes w: 8 #a__sieve w: x1 + 3 divides w: max(x1 + 1, x2 + 2) a__tail w: x1 + 2 a__filter w: max(x1 + 3, x2) #a__tail w: x1 + 3 a__if w: max(x1 + 2, x2, x3) a__head w: x1 + 2 USABLE RULES: { 1..28 } Removed DPs: #1 #3..9 #11 #13..16 #18 #19 #21..26 #28 #29 Number of SCCs: 1, DPs: 5 SCC { #2 #10 #17 #20 #27 } POLO(Sum)... succeeded. s w: x1 + 1 #a__head w: 1 #a__from w: 1 a__from w: 2 false w: 2 #a__filter w: 0 a__sieve w: 3 true w: 2 tail w: 3 #mark w: x1 + 1 0 w: 2 if w: x1 + x2 + x3 + 2 #a__primes w: 1 from w: 3 mark w: 1 sieve w: x1 + 4 #a__if w: x2 + x3 + 2 head w: 1 cons w: x2 + 2 a__primes w: 2 filter w: x1 + x2 + 2 primes w: 3 #a__sieve w: 1 divides w: x1 + 1 a__tail w: 2 a__filter w: x2 + 1 #a__tail w: 1 a__if w: x3 a__head w: x1 + 1 USABLE RULES: { } Removed DPs: #2 #10 #17 #20 #27 Number of SCCs: 0, DPs: 0