/export/starexec/sandbox2/solver/bin/starexec_run_Default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Input TRS: 1: active(zeros()) -> mark(cons(0(),zeros())) 2: active(U11(tt(),L)) -> mark(s(length(L))) 3: active(and(tt(),X)) -> mark(X) 4: active(isNat(0())) -> mark(tt()) 5: active(isNat(length(V1))) -> mark(isNatList(V1)) 6: active(isNat(s(V1))) -> mark(isNat(V1)) 7: active(isNatIList(V)) -> mark(isNatList(V)) 8: active(isNatIList(zeros())) -> mark(tt()) 9: active(isNatIList(cons(V1,V2))) -> mark(and(isNat(V1),isNatIList(V2))) 10: active(isNatList(nil())) -> mark(tt()) 11: active(isNatList(cons(V1,V2))) -> mark(and(isNat(V1),isNatList(V2))) 12: active(length(nil())) -> mark(0()) 13: active(length(cons(N,L))) -> mark(U11(and(isNatList(L),isNat(N)),L)) 14: mark(zeros()) -> active(zeros()) 15: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) 16: mark(0()) -> active(0()) 17: mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) 18: mark(tt()) -> active(tt()) 19: mark(s(X)) -> active(s(mark(X))) 20: mark(length(X)) -> active(length(mark(X))) 21: mark(and(X1,X2)) -> active(and(mark(X1),X2)) 22: mark(isNat(X)) -> active(isNat(X)) 23: mark(isNatList(X)) -> active(isNatList(X)) 24: mark(isNatIList(X)) -> active(isNatIList(X)) 25: mark(nil()) -> active(nil()) 26: cons(mark(X1),X2) -> cons(X1,X2) 27: cons(X1,mark(X2)) -> cons(X1,X2) 28: cons(active(X1),X2) -> cons(X1,X2) 29: cons(X1,active(X2)) -> cons(X1,X2) 30: U11(mark(X1),X2) -> U11(X1,X2) 31: U11(X1,mark(X2)) -> U11(X1,X2) 32: U11(active(X1),X2) -> U11(X1,X2) 33: U11(X1,active(X2)) -> U11(X1,X2) 34: s(mark(X)) -> s(X) 35: s(active(X)) -> s(X) 36: length(mark(X)) -> length(X) 37: length(active(X)) -> length(X) 38: and(mark(X1),X2) -> and(X1,X2) 39: and(X1,mark(X2)) -> and(X1,X2) 40: and(active(X1),X2) -> and(X1,X2) 41: and(X1,active(X2)) -> and(X1,X2) 42: isNat(mark(X)) -> isNat(X) 43: isNat(active(X)) -> isNat(X) 44: isNatList(mark(X)) -> isNatList(X) 45: isNatList(active(X)) -> isNatList(X) 46: isNatIList(mark(X)) -> isNatIList(X) 47: isNatIList(active(X)) -> isNatIList(X) Number of strict rules: 47 Direct POLO(bPol) ... removes: 8 5 10 7 12 isNatList w: x1 U11 w: x1 + 2 * x2 + 1 s w: x1 and w: x1 + x2 isNatIList w: x1 + 6 zeros w: 0 0 w: 0 nil w: 1 mark w: x1 isNat w: x1 active w: x1 cons w: x1 + 2 * x2 tt w: 0 length w: 2 * x1 + 1 Number of strict rules: 42 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #active(U11(tt(),L)) -> #mark(s(length(L))) #2: #active(U11(tt(),L)) -> #s(length(L)) #3: #active(U11(tt(),L)) -> #length(L) #4: #isNat(active(X)) -> #isNat(X) #5: #cons(X1,active(X2)) -> #cons(X1,X2) #6: #s(active(X)) -> #s(X) #7: #isNatIList(mark(X)) -> #isNatIList(X) #8: #isNat(mark(X)) -> #isNat(X) #9: #and(X1,active(X2)) -> #and(X1,X2) #10: #length(active(X)) -> #length(X) #11: #isNatIList(active(X)) -> #isNatIList(X) #12: #and(mark(X1),X2) -> #and(X1,X2) #13: #active(isNat(s(V1))) -> #mark(isNat(V1)) #14: #active(isNat(s(V1))) -> #isNat(V1) #15: #and(active(X1),X2) -> #and(X1,X2) #16: #active(length(cons(N,L))) -> #mark(U11(and(isNatList(L),isNat(N)),L)) #17: #active(length(cons(N,L))) -> #U11(and(isNatList(L),isNat(N)),L) #18: #active(length(cons(N,L))) -> #and(isNatList(L),isNat(N)) #19: #active(length(cons(N,L))) -> #isNatList(L) #20: #active(length(cons(N,L))) -> #isNat(N) #21: #active(isNatIList(cons(V1,V2))) -> #mark(and(isNat(V1),isNatIList(V2))) #22: #active(isNatIList(cons(V1,V2))) -> #and(isNat(V1),isNatIList(V2)) #23: #active(isNatIList(cons(V1,V2))) -> #isNat(V1) #24: #active(isNatIList(cons(V1,V2))) -> #isNatIList(V2) #25: #active(isNatList(cons(V1,V2))) -> #mark(and(isNat(V1),isNatList(V2))) #26: #active(isNatList(cons(V1,V2))) -> #and(isNat(V1),isNatList(V2)) #27: #active(isNatList(cons(V1,V2))) -> #isNat(V1) #28: #active(isNatList(cons(V1,V2))) -> #isNatList(V2) #29: #mark(isNatIList(X)) -> #active(isNatIList(X)) #30: #mark(isNatList(X)) -> #active(isNatList(X)) #31: #isNatList(active(X)) -> #isNatList(X) #32: #U11(X1,mark(X2)) -> #U11(X1,X2) #33: #mark(zeros()) -> #active(zeros()) #34: #U11(mark(X1),X2) -> #U11(X1,X2) #35: #mark(nil()) -> #active(nil()) #36: #mark(length(X)) -> #active(length(mark(X))) #37: #mark(length(X)) -> #length(mark(X)) #38: #mark(length(X)) -> #mark(X) #39: #and(X1,mark(X2)) -> #and(X1,X2) #40: #U11(X1,active(X2)) -> #U11(X1,X2) #41: #isNatList(mark(X)) -> #isNatList(X) #42: #cons(active(X1),X2) -> #cons(X1,X2) #43: #mark(isNat(X)) -> #active(isNat(X)) #44: #s(mark(X)) -> #s(X) #45: #cons(X1,mark(X2)) -> #cons(X1,X2) #46: #mark(U11(X1,X2)) -> #active(U11(mark(X1),X2)) #47: #mark(U11(X1,X2)) -> #U11(mark(X1),X2) #48: #mark(U11(X1,X2)) -> #mark(X1) #49: #U11(active(X1),X2) -> #U11(X1,X2) #50: #mark(s(X)) -> #active(s(mark(X))) #51: #mark(s(X)) -> #s(mark(X)) #52: #mark(s(X)) -> #mark(X) #53: #cons(mark(X1),X2) -> #cons(X1,X2) #54: #length(mark(X)) -> #length(X) #55: #mark(and(X1,X2)) -> #active(and(mark(X1),X2)) #56: #mark(and(X1,X2)) -> #and(mark(X1),X2) #57: #mark(and(X1,X2)) -> #mark(X1) #58: #mark(0()) -> #active(0()) #59: #active(and(tt(),X)) -> #mark(X) #60: #active(zeros()) -> #mark(cons(0(),zeros())) #61: #active(zeros()) -> #cons(0(),zeros()) #62: #mark(cons(X1,X2)) -> #active(cons(mark(X1),X2)) #63: #mark(cons(X1,X2)) -> #cons(mark(X1),X2) #64: #mark(cons(X1,X2)) -> #mark(X1) #65: #active(isNat(0())) -> #mark(tt()) #66: #mark(tt()) -> #active(tt()) Number of SCCs: 10, DPs: 41 SCC { #31 #41 } POLO(Sum)... succeeded. isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 and w: 0 isNatIList w: 0 zeros w: 0 #mark w: 0 0 w: 0 #isNatList w: x1 #s w: 0 nil w: 0 mark w: x1 + 1 isNat w: 0 #U11 w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #isNatIList w: 0 tt w: 0 length w: 0 #length w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #31 #41 Number of SCCs: 9, DPs: 39 SCC { #10 #54 } POLO(Sum)... succeeded. isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 and w: 0 isNatIList w: 0 zeros w: 0 #mark w: 0 0 w: 0 #isNatList w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 isNat w: 0 #U11 w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #isNatIList w: 0 tt w: 0 length w: 0 #length w: x1 #and w: 0 USABLE RULES: { } Removed DPs: #10 #54 Number of SCCs: 8, DPs: 37 SCC { #6 #44 } POLO(Sum)... succeeded. isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 and w: 0 isNatIList w: 0 zeros w: 0 #mark w: 0 0 w: 0 #isNatList w: 0 #s w: x1 nil w: 0 mark w: x1 + 1 isNat w: 0 #U11 w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #isNatIList w: 0 tt w: 0 length w: 0 #length w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #6 #44 Number of SCCs: 7, DPs: 35 SCC { #7 #11 } POLO(Sum)... succeeded. isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 and w: 0 isNatIList w: 0 zeros w: 0 #mark w: 0 0 w: 0 #isNatList w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 isNat w: 0 #U11 w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #isNatIList w: x1 tt w: 0 length w: 0 #length w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #7 #11 Number of SCCs: 6, DPs: 33 SCC { #4 #8 } POLO(Sum)... succeeded. isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: x1 and w: 0 isNatIList w: 0 zeros w: 0 #mark w: 0 0 w: 0 #isNatList w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 isNat w: 0 #U11 w: 0 active w: x1 + 1 cons w: 0 #active w: 0 #isNatIList w: 0 tt w: 0 length w: 0 #length w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #4 #8 Number of SCCs: 5, DPs: 31 SCC { #13 #43 } POLO(Sum)... succeeded. isNatList w: 0 U11 w: 0 #cons w: 0 s w: x1 + 2 #isNat w: 0 and w: 0 isNatIList w: 0 zeros w: 0 #mark w: x1 + 1 0 w: 0 #isNatList w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 isNat w: x1 + 1 #U11 w: 0 active w: x1 + 1 cons w: 0 #active w: x1 #isNatIList w: 0 tt w: 0 length w: 0 #length w: 0 #and w: 0 USABLE RULES: { 42 43 } Removed DPs: #13 #43 Number of SCCs: 4, DPs: 29 SCC { #32 #34 #40 #49 } POLO(Sum)... succeeded. isNatList w: 0 U11 w: 0 #cons w: 0 s w: 2 #isNat w: 0 and w: 0 isNatIList w: 0 zeros w: 0 #mark w: x1 + 1 0 w: 0 #isNatList w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 isNat w: x1 + 1 #U11 w: x1 + x2 active w: x1 + 1 cons w: 0 #active w: x1 #isNatIList w: 0 tt w: 0 length w: 0 #length w: 0 #and w: 0 USABLE RULES: { 42 43 } Removed DPs: #32 #34 #40 #49 Number of SCCs: 3, DPs: 25 SCC { #9 #12 #15 #39 } POLO(Sum)... succeeded. isNatList w: 0 U11 w: 0 #cons w: 0 s w: 2 #isNat w: 0 and w: 0 isNatIList w: 0 zeros w: 0 #mark w: x1 + 1 0 w: 0 #isNatList w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 isNat w: x1 + 1 #U11 w: 0 active w: x1 + 1 cons w: 0 #active w: x1 #isNatIList w: 0 tt w: 0 length w: 0 #length w: 0 #and w: x1 + x2 USABLE RULES: { 42 43 } Removed DPs: #9 #12 #15 #39 Number of SCCs: 2, DPs: 21 SCC { #5 #42 #45 #53 } POLO(Sum)... succeeded. isNatList w: 0 U11 w: 0 #cons w: x1 + x2 s w: 2 #isNat w: 0 and w: 0 isNatIList w: 0 zeros w: 0 #mark w: x1 + 1 0 w: 0 #isNatList w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 isNat w: x1 + 1 #U11 w: 0 active w: x1 + 1 cons w: 0 #active w: x1 #isNatIList w: 0 tt w: 0 length w: 0 #length w: 0 #and w: 0 USABLE RULES: { 42 43 } Removed DPs: #5 #42 #45 #53 Number of SCCs: 1, DPs: 17 SCC { #1 #16 #21 #25 #29 #30 #33 #36 #38 #46 #48 #52 #55 #57 #59 #60 #64 } POLO(Sum)... succeeded. isNatList w: 0 U11 w: x1 + x2 + 1 #cons w: 0 s w: x1 #isNat w: 0 and w: x1 + x2 isNatIList w: 1 zeros w: 1 #mark w: x1 + 2 0 w: 0 #isNatList w: 0 #s w: 0 nil w: 1 mark w: x1 isNat w: 0 #U11 w: 0 active w: x1 cons w: x1 + x2 #active w: x1 + 2 #isNatIList w: 0 tt w: 0 length w: x1 + 1 #length w: 0 #and w: 0 USABLE RULES: { 1..4 6 9 11 13..47 } Removed DPs: #38 #48 Number of SCCs: 1, DPs: 15 SCC { #1 #16 #21 #25 #29 #30 #33 #36 #46 #52 #55 #57 #59 #60 #64 } POLO(Sum)... succeeded. isNatList w: 0 U11 w: 1 #cons w: 0 s w: x1 #isNat w: 0 and w: x1 + x2 isNatIList w: 1 zeros w: 1 #mark w: x1 + 2 0 w: 0 #isNatList w: 0 #s w: 0 nil w: 1 mark w: x1 isNat w: 0 #U11 w: 0 active w: x1 cons w: x1 #active w: x1 + 2 #isNatIList w: 0 tt w: 0 length w: 1 #length w: 0 #and w: 0 USABLE RULES: { 1..4 6 9 11 13..47 } Removed DPs: #60 Number of SCCs: 1, DPs: 13 SCC { #1 #16 #21 #25 #29 #30 #36 #46 #52 #55 #57 #59 #64 } POLO(Sum)... succeeded. isNatList w: 1 U11 w: 1 #cons w: 0 s w: x1 #isNat w: 0 and w: x1 + x2 isNatIList w: 1 zeros w: 2 #mark w: x1 + 2 0 w: 0 #isNatList w: 0 #s w: 0 nil w: 1 mark w: x1 isNat w: 0 #U11 w: 0 active w: x1 cons w: x1 + 1 #active w: x1 + 2 #isNatIList w: 0 tt w: 0 length w: 1 #length w: 0 #and w: 0 USABLE RULES: { 1..4 6 9 11 13..47 } Removed DPs: #64 Number of SCCs: 1, DPs: 12 SCC { #1 #16 #21 #25 #29 #30 #36 #46 #52 #55 #57 #59 } POLO(Sum)... POLO(max)... succeeded. isNatList w: x1 + 1 U11 w: max(x1 + 1, x2 + 4) #cons w: 0 s w: x1 #isNat w: 0 and w: max(x1 + 1, x2) isNatIList w: 6 zeros w: 5 #mark w: x1 0 w: 1 #isNatList w: 0 #s w: 0 nil w: 1 mark w: x1 isNat w: 4 #U11 w: 0 active w: x1 cons w: max(x1 + 4, x2) #active w: x1 #isNatIList w: 0 tt w: 1 length w: x1 + 4 #length w: 0 #and w: 0 USABLE RULES: { 1..4 6 9 11 13..47 } Removed DPs: #57 Number of SCCs: 1, DPs: 11 SCC { #1 #16 #21 #25 #29 #30 #36 #46 #52 #55 #59 } POLO(Sum)... succeeded. isNatList w: x1 + 1 U11 w: 1 #cons w: 0 s w: x1 #isNat w: 0 and w: x2 + 1 isNatIList w: x1 + 1 zeros w: 1 #mark w: x1 + 2 0 w: 1 #isNatList w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 isNat w: x1 + 1 #U11 w: 0 active w: x1 + 2 cons w: x2 + 2 #active w: x1 + 2 #isNatIList w: 0 tt w: 4 length w: 1 #length w: 0 #and w: 0 USABLE RULES: { 26..33 36..47 } Removed DPs: #21 #25 #59 Number of SCCs: 1, DPs: 5 SCC { #1 #16 #36 #46 #52 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. isNatList w: 1 U11 w: max(x1 - 2, 0) #cons w: max(x2 - 1, 0) s w: max(x1, 0) #isNat w: max(x1 - 1, 0) and w: max(x1 + x2 - 3, 0) isNatIList w: 0 zeros w: 9 #mark w: max(x1 + 3, 0) 0 w: 2 #isNatList w: 0 #s w: max(x1 - 1, 0) nil w: 1 mark w: max(x1, 0) isNat w: 3 #U11 w: 0 active w: max(x1, 0) cons w: 9 #active w: max(x1 + 3, 0) #isNatIList w: max(x1 - 1, 0) tt w: 3 length w: 0 #length w: max(x1 - 1, 0) #and w: 0 USABLE RULES: { 1..4 6 9 11 13..47 } Removed DPs: #1 Number of SCCs: 1, DPs: 1 SCC { #52 } POLO(Sum)... succeeded. isNatList w: 1 U11 w: 4 #cons w: 0 s w: x1 + 1 #isNat w: 0 and w: 3 isNatIList w: x1 + 1 zeros w: 2 #mark w: x1 + 1 0 w: 3 #isNatList w: 0 #s w: 0 nil w: 0 mark w: x1 + 1 isNat w: x1 + 1 #U11 w: 0 active w: x1 + 2 cons w: x1 + 1 #active w: 0 #isNatIList w: 0 tt w: 6 length w: 5 #length w: 0 #and w: 0 USABLE RULES: { 30..33 36 37 42 43 } Removed DPs: #52 Number of SCCs: 0, DPs: 0