/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- MAYBE Input TRS: 1: active(primes()) -> mark(sieve(from(s(s(0()))))) 2: active(from(X)) -> mark(cons(X,from(s(X)))) 3: active(head(cons(X,Y))) -> mark(X) 4: active(tail(cons(X,Y))) -> mark(Y) 5: active(if(true(),X,Y)) -> mark(X) 6: active(if(false(),X,Y)) -> mark(Y) 7: active(filter(s(s(X)),cons(Y,Z))) -> mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))) 8: active(sieve(cons(X,Y))) -> mark(cons(X,filter(X,sieve(Y)))) 9: mark(primes()) -> active(primes()) 10: mark(sieve(X)) -> active(sieve(mark(X))) 11: mark(from(X)) -> active(from(mark(X))) 12: mark(s(X)) -> active(s(mark(X))) 13: mark(0()) -> active(0()) 14: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) 15: mark(head(X)) -> active(head(mark(X))) 16: mark(tail(X)) -> active(tail(mark(X))) 17: mark(if(X1,X2,X3)) -> active(if(mark(X1),X2,X3)) 18: mark(true()) -> active(true()) 19: mark(false()) -> active(false()) 20: mark(filter(X1,X2)) -> active(filter(mark(X1),mark(X2))) 21: mark(divides(X1,X2)) -> active(divides(mark(X1),mark(X2))) 22: sieve(mark(X)) -> sieve(X) 23: sieve(active(X)) -> sieve(X) 24: from(mark(X)) -> from(X) 25: from(active(X)) -> from(X) 26: s(mark(X)) -> s(X) 27: s(active(X)) -> s(X) 28: cons(mark(X1),X2) -> cons(X1,X2) 29: cons(X1,mark(X2)) -> cons(X1,X2) 30: cons(active(X1),X2) -> cons(X1,X2) 31: cons(X1,active(X2)) -> cons(X1,X2) 32: head(mark(X)) -> head(X) 33: head(active(X)) -> head(X) 34: tail(mark(X)) -> tail(X) 35: tail(active(X)) -> tail(X) 36: if(mark(X1),X2,X3) -> if(X1,X2,X3) 37: if(X1,mark(X2),X3) -> if(X1,X2,X3) 38: if(X1,X2,mark(X3)) -> if(X1,X2,X3) 39: if(active(X1),X2,X3) -> if(X1,X2,X3) 40: if(X1,active(X2),X3) -> if(X1,X2,X3) 41: if(X1,X2,active(X3)) -> if(X1,X2,X3) 42: filter(mark(X1),X2) -> filter(X1,X2) 43: filter(X1,mark(X2)) -> filter(X1,X2) 44: filter(active(X1),X2) -> filter(X1,X2) 45: filter(X1,active(X2)) -> filter(X1,X2) 46: divides(mark(X1),X2) -> divides(X1,X2) 47: divides(X1,mark(X2)) -> divides(X1,X2) 48: divides(active(X1),X2) -> divides(X1,X2) 49: divides(X1,active(X2)) -> divides(X1,X2) Number of strict rules: 49 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #active(from(X)) -> #mark(cons(X,from(s(X)))) #2: #active(from(X)) -> #cons(X,from(s(X))) #3: #active(from(X)) -> #from(s(X)) #4: #active(from(X)) -> #s(X) #5: #filter(X1,mark(X2)) -> #filter(X1,X2) #6: #cons(X1,mark(X2)) -> #cons(X1,X2) #7: #tail(active(X)) -> #tail(X) #8: #divides(mark(X1),X2) -> #divides(X1,X2) #9: #filter(mark(X1),X2) -> #filter(X1,X2) #10: #if(X1,X2,active(X3)) -> #if(X1,X2,X3) #11: #if(X1,mark(X2),X3) -> #if(X1,X2,X3) #12: #divides(X1,mark(X2)) -> #divides(X1,X2) #13: #divides(active(X1),X2) -> #divides(X1,X2) #14: #if(X1,X2,mark(X3)) -> #if(X1,X2,X3) #15: #active(if(false(),X,Y)) -> #mark(Y) #16: #if(X1,active(X2),X3) -> #if(X1,X2,X3) #17: #mark(0()) -> #active(0()) #18: #mark(primes()) -> #active(primes()) #19: #mark(from(X)) -> #active(from(mark(X))) #20: #mark(from(X)) -> #from(mark(X)) #21: #mark(from(X)) -> #mark(X) #22: #from(mark(X)) -> #from(X) #23: #sieve(active(X)) -> #sieve(X) #24: #filter(X1,active(X2)) -> #filter(X1,X2) #25: #mark(s(X)) -> #active(s(mark(X))) #26: #mark(s(X)) -> #s(mark(X)) #27: #mark(s(X)) -> #mark(X) #28: #cons(X1,active(X2)) -> #cons(X1,X2) #29: #mark(cons(X1,X2)) -> #active(cons(mark(X1),X2)) #30: #mark(cons(X1,X2)) -> #cons(mark(X1),X2) #31: #mark(cons(X1,X2)) -> #mark(X1) #32: #cons(active(X1),X2) -> #cons(X1,X2) #33: #divides(X1,active(X2)) -> #divides(X1,X2) #34: #from(active(X)) -> #from(X) #35: #mark(filter(X1,X2)) -> #active(filter(mark(X1),mark(X2))) #36: #mark(filter(X1,X2)) -> #filter(mark(X1),mark(X2)) #37: #mark(filter(X1,X2)) -> #mark(X1) #38: #mark(filter(X1,X2)) -> #mark(X2) #39: #active(filter(s(s(X)),cons(Y,Z))) -> #mark(if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y))))) #40: #active(filter(s(s(X)),cons(Y,Z))) -> #if(divides(s(s(X)),Y),filter(s(s(X)),Z),cons(Y,filter(X,sieve(Y)))) #41: #active(filter(s(s(X)),cons(Y,Z))) -> #divides(s(s(X)),Y) #42: #active(filter(s(s(X)),cons(Y,Z))) -> #filter(s(s(X)),Z) #43: #active(filter(s(s(X)),cons(Y,Z))) -> #cons(Y,filter(X,sieve(Y))) #44: #active(filter(s(s(X)),cons(Y,Z))) -> #filter(X,sieve(Y)) #45: #active(filter(s(s(X)),cons(Y,Z))) -> #sieve(Y) #46: #if(active(X1),X2,X3) -> #if(X1,X2,X3) #47: #mark(sieve(X)) -> #active(sieve(mark(X))) #48: #mark(sieve(X)) -> #sieve(mark(X)) #49: #mark(sieve(X)) -> #mark(X) #50: #head(active(X)) -> #head(X) #51: #active(if(true(),X,Y)) -> #mark(X) #52: #filter(active(X1),X2) -> #filter(X1,X2) #53: #cons(mark(X1),X2) -> #cons(X1,X2) #54: #sieve(mark(X)) -> #sieve(X) #55: #tail(mark(X)) -> #tail(X) #56: #s(active(X)) -> #s(X) #57: #mark(if(X1,X2,X3)) -> #active(if(mark(X1),X2,X3)) #58: #mark(if(X1,X2,X3)) -> #if(mark(X1),X2,X3) #59: #mark(if(X1,X2,X3)) -> #mark(X1) #60: #head(mark(X)) -> #head(X) #61: #mark(false()) -> #active(false()) #62: #s(mark(X)) -> #s(X) #63: #if(mark(X1),X2,X3) -> #if(X1,X2,X3) #64: #mark(divides(X1,X2)) -> #active(divides(mark(X1),mark(X2))) #65: #mark(divides(X1,X2)) -> #divides(mark(X1),mark(X2)) #66: #mark(divides(X1,X2)) -> #mark(X1) #67: #mark(divides(X1,X2)) -> #mark(X2) #68: #mark(tail(X)) -> #active(tail(mark(X))) #69: #mark(tail(X)) -> #tail(mark(X)) #70: #mark(tail(X)) -> #mark(X) #71: #active(head(cons(X,Y))) -> #mark(X) #72: #active(primes()) -> #mark(sieve(from(s(s(0()))))) #73: #active(primes()) -> #sieve(from(s(s(0())))) #74: #active(primes()) -> #from(s(s(0()))) #75: #active(primes()) -> #s(s(0())) #76: #active(primes()) -> #s(0()) #77: #active(sieve(cons(X,Y))) -> #mark(cons(X,filter(X,sieve(Y)))) #78: #active(sieve(cons(X,Y))) -> #cons(X,filter(X,sieve(Y))) #79: #active(sieve(cons(X,Y))) -> #filter(X,sieve(Y)) #80: #active(sieve(cons(X,Y))) -> #sieve(Y) #81: #mark(head(X)) -> #active(head(mark(X))) #82: #mark(head(X)) -> #head(mark(X)) #83: #mark(head(X)) -> #mark(X) #84: #active(tail(cons(X,Y))) -> #mark(Y) #85: #mark(true()) -> #active(true()) Number of SCCs: 10, DPs: 54 SCC { #56 #62 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #filter w: 0 false w: 0 #head w: 0 true w: 0 tail w: 0 #mark w: 0 0 w: 0 if w: 0 from w: 0 #s w: x1 #tail w: 0 mark w: x1 + 1 sieve w: 0 #divides w: 0 #from w: 0 active w: x1 + 1 head w: 0 cons w: 0 #if w: 0 #active w: 0 filter w: 0 primes w: 0 #sieve w: 0 divides w: 0 USABLE RULES: { } Removed DPs: #56 #62 Number of SCCs: 9, DPs: 52 SCC { #7 #55 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #filter w: 0 false w: 0 #head w: 0 true w: 0 tail w: 0 #mark w: 0 0 w: 0 if w: 0 from w: 0 #s w: 0 #tail w: x1 mark w: x1 + 1 sieve w: 0 #divides w: 0 #from w: 0 active w: x1 + 1 head w: 0 cons w: 0 #if w: 0 #active w: 0 filter w: 0 primes w: 0 #sieve w: 0 divides w: 0 USABLE RULES: { } Removed DPs: #7 #55 Number of SCCs: 8, DPs: 50 SCC { #50 #60 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #filter w: 0 false w: 0 #head w: x1 true w: 0 tail w: 0 #mark w: 0 0 w: 0 if w: 0 from w: 0 #s w: 0 #tail w: 0 mark w: x1 + 1 sieve w: 0 #divides w: 0 #from w: 0 active w: x1 + 1 head w: 0 cons w: 0 #if w: 0 #active w: 0 filter w: 0 primes w: 0 #sieve w: 0 divides w: 0 USABLE RULES: { } Removed DPs: #50 #60 Number of SCCs: 7, DPs: 48 SCC { #23 #54 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #filter w: 0 false w: 0 #head w: 0 true w: 0 tail w: 0 #mark w: 0 0 w: 0 if w: 0 from w: 0 #s w: 0 #tail w: 0 mark w: x1 + 1 sieve w: 0 #divides w: 0 #from w: 0 active w: x1 + 1 head w: 0 cons w: 0 #if w: 0 #active w: 0 filter w: 0 primes w: 0 #sieve w: x1 divides w: 0 USABLE RULES: { } Removed DPs: #23 #54 Number of SCCs: 6, DPs: 46 SCC { #22 #34 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #filter w: 0 false w: 0 #head w: 0 true w: 0 tail w: 0 #mark w: 0 0 w: 0 if w: 0 from w: 0 #s w: 0 #tail w: 0 mark w: x1 + 1 sieve w: 0 #divides w: 0 #from w: x1 active w: x1 + 1 head w: 0 cons w: 0 #if w: 0 #active w: 0 filter w: 0 primes w: 0 #sieve w: 0 divides w: 0 USABLE RULES: { } Removed DPs: #22 #34 Number of SCCs: 5, DPs: 44 SCC { #8 #12 #13 #33 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #filter w: 0 false w: 0 #head w: 0 true w: 0 tail w: 0 #mark w: 0 0 w: 0 if w: 0 from w: 0 #s w: 0 #tail w: 0 mark w: x1 + 1 sieve w: 0 #divides w: x1 #from w: 0 active w: x1 + 1 head w: 0 cons w: 0 #if w: 0 #active w: 0 filter w: 0 primes w: 0 #sieve w: 0 divides w: 0 USABLE RULES: { } Removed DPs: #8 #13 Number of SCCs: 5, DPs: 42 SCC { #12 #33 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #filter w: 0 false w: 0 #head w: 0 true w: 0 tail w: 0 #mark w: 0 0 w: 0 if w: 0 from w: 0 #s w: 0 #tail w: 0 mark w: x1 + 1 sieve w: 0 #divides w: x2 #from w: 0 active w: x1 + 1 head w: 0 cons w: 0 #if w: 0 #active w: 0 filter w: 0 primes w: 0 #sieve w: 0 divides w: 0 USABLE RULES: { } Removed DPs: #12 #33 Number of SCCs: 4, DPs: 40 SCC { #5 #9 #24 #52 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #filter w: x1 false w: 0 #head w: 0 true w: 0 tail w: 0 #mark w: 0 0 w: 0 if w: 0 from w: 0 #s w: 0 #tail w: 0 mark w: x1 + 1 sieve w: 0 #divides w: 0 #from w: 0 active w: x1 + 1 head w: 0 cons w: 0 #if w: 0 #active w: 0 filter w: 0 primes w: 0 #sieve w: 0 divides w: 0 USABLE RULES: { } Removed DPs: #9 #52 Number of SCCs: 4, DPs: 38 SCC { #5 #24 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #filter w: x2 false w: 0 #head w: 0 true w: 0 tail w: 0 #mark w: 0 0 w: 0 if w: 0 from w: 0 #s w: 0 #tail w: 0 mark w: x1 + 1 sieve w: 0 #divides w: 0 #from w: 0 active w: x1 + 1 head w: 0 cons w: 0 #if w: 0 #active w: 0 filter w: 0 primes w: 0 #sieve w: 0 divides w: 0 USABLE RULES: { } Removed DPs: #5 #24 Number of SCCs: 3, DPs: 36 SCC { #6 #28 #32 #53 } POLO(Sum)... succeeded. #cons w: x1 s w: 0 #filter w: 0 false w: 0 #head w: 0 true w: 0 tail w: 0 #mark w: 0 0 w: 0 if w: 0 from w: 0 #s w: 0 #tail w: 0 mark w: x1 + 1 sieve w: 0 #divides w: 0 #from w: 0 active w: x1 + 1 head w: 0 cons w: 0 #if w: 0 #active w: 0 filter w: 0 primes w: 0 #sieve w: 0 divides w: 0 USABLE RULES: { } Removed DPs: #32 #53 Number of SCCs: 3, DPs: 34 SCC { #6 #28 } POLO(Sum)... succeeded. #cons w: x2 s w: 0 #filter w: 0 false w: 0 #head w: 0 true w: 0 tail w: 0 #mark w: 0 0 w: 0 if w: 0 from w: 0 #s w: 0 #tail w: 0 mark w: x1 + 1 sieve w: 0 #divides w: 0 #from w: 0 active w: x1 + 1 head w: 0 cons w: 0 #if w: 0 #active w: 0 filter w: 0 primes w: 0 #sieve w: 0 divides w: 0 USABLE RULES: { } Removed DPs: #6 #28 Number of SCCs: 2, DPs: 32 SCC { #10 #11 #14 #16 #46 #63 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #filter w: 0 false w: 0 #head w: 0 true w: 0 tail w: 0 #mark w: 0 0 w: 0 if w: 0 from w: 0 #s w: 0 #tail w: 0 mark w: x1 + 1 sieve w: 0 #divides w: 0 #from w: 0 active w: x1 + 1 head w: 0 cons w: 0 #if w: x2 + x3 #active w: 0 filter w: 0 primes w: 0 #sieve w: 0 divides w: 0 USABLE RULES: { } Removed DPs: #10 #11 #14 #16 Number of SCCs: 2, DPs: 28 SCC { #46 #63 } POLO(Sum)... succeeded. #cons w: 0 s w: 0 #filter w: 0 false w: 0 #head w: 0 true w: 0 tail w: 0 #mark w: 0 0 w: 0 if w: 0 from w: 0 #s w: 0 #tail w: 0 mark w: x1 + 1 sieve w: 0 #divides w: 0 #from w: 0 active w: x1 + 1 head w: 0 cons w: 0 #if w: x1 #active w: 0 filter w: 0 primes w: 0 #sieve w: 0 divides w: 0 USABLE RULES: { } Removed DPs: #46 #63 Number of SCCs: 1, DPs: 26 SCC { #1 #15 #18 #19 #21 #27 #31 #35 #37..39 #47 #49 #51 #57 #59 #66..68 #70..72 #77 #81 #83 #84 } POLO(Sum)... POLO(max)... succeeded. #cons w: 0 s w: x1 #filter w: 0 false w: 1 #head w: 0 true w: 1 tail w: x1 + 1 #mark w: x1 0 w: 1 if w: max(x1 + 1, x2, x3) from w: x1 + 7 #s w: 0 #tail w: 0 mark w: x1 sieve w: x1 + 5 #divides w: 0 #from w: 0 active w: x1 head w: x1 + 1 cons w: max(x1 + 6, x2) #if w: 0 #active w: x1 filter w: max(x1 + 4, x2) primes w: 14 #sieve w: 0 divides w: max(x1 + 2, x2 + 1) USABLE RULES: { 1..49 } Removed DPs: #21 #31 #37 #49 #59 #66 #67 #70..72 #83 #84 Number of SCCs: 1, DPs: 7 SCC { #15 #27 #35 #38 #39 #51 #57 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. Finding a loop... failed.