/export/starexec/sandbox/solver/bin/starexec_run_Default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE Input TRS: 1: active(zeros()) -> mark(cons(0(),zeros())) 2: active(U11(tt(),L)) -> mark(s(length(L))) 3: active(U21(tt())) -> mark(nil()) 4: active(U31(tt(),IL,M,N)) -> mark(cons(N,take(M,IL))) 5: active(and(tt(),X)) -> mark(X) 6: active(isNat(0())) -> mark(tt()) 7: active(isNat(length(V1))) -> mark(isNatList(V1)) 8: active(isNat(s(V1))) -> mark(isNat(V1)) 9: active(isNatIList(V)) -> mark(isNatList(V)) 10: active(isNatIList(zeros())) -> mark(tt()) 11: active(isNatIList(cons(V1,V2))) -> mark(and(isNat(V1),isNatIList(V2))) 12: active(isNatList(nil())) -> mark(tt()) 13: active(isNatList(cons(V1,V2))) -> mark(and(isNat(V1),isNatList(V2))) 14: active(isNatList(take(V1,V2))) -> mark(and(isNat(V1),isNatIList(V2))) 15: active(length(nil())) -> mark(0()) 16: active(length(cons(N,L))) -> mark(U11(and(isNatList(L),isNat(N)),L)) 17: active(take(0(),IL)) -> mark(U21(isNatIList(IL))) 18: active(take(s(M),cons(N,IL))) -> mark(U31(and(isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N)) 19: mark(zeros()) -> active(zeros()) 20: mark(cons(X1,X2)) -> active(cons(mark(X1),X2)) 21: mark(0()) -> active(0()) 22: mark(U11(X1,X2)) -> active(U11(mark(X1),X2)) 23: mark(tt()) -> active(tt()) 24: mark(s(X)) -> active(s(mark(X))) 25: mark(length(X)) -> active(length(mark(X))) 26: mark(U21(X)) -> active(U21(mark(X))) 27: mark(nil()) -> active(nil()) 28: mark(U31(X1,X2,X3,X4)) -> active(U31(mark(X1),X2,X3,X4)) 29: mark(take(X1,X2)) -> active(take(mark(X1),mark(X2))) 30: mark(and(X1,X2)) -> active(and(mark(X1),X2)) 31: mark(isNat(X)) -> active(isNat(X)) 32: mark(isNatList(X)) -> active(isNatList(X)) 33: mark(isNatIList(X)) -> active(isNatIList(X)) 34: cons(mark(X1),X2) -> cons(X1,X2) 35: cons(X1,mark(X2)) -> cons(X1,X2) 36: cons(active(X1),X2) -> cons(X1,X2) 37: cons(X1,active(X2)) -> cons(X1,X2) 38: U11(mark(X1),X2) -> U11(X1,X2) 39: U11(X1,mark(X2)) -> U11(X1,X2) 40: U11(active(X1),X2) -> U11(X1,X2) 41: U11(X1,active(X2)) -> U11(X1,X2) 42: s(mark(X)) -> s(X) 43: s(active(X)) -> s(X) 44: length(mark(X)) -> length(X) 45: length(active(X)) -> length(X) 46: U21(mark(X)) -> U21(X) 47: U21(active(X)) -> U21(X) 48: U31(mark(X1),X2,X3,X4) -> U31(X1,X2,X3,X4) 49: U31(X1,mark(X2),X3,X4) -> U31(X1,X2,X3,X4) 50: U31(X1,X2,mark(X3),X4) -> U31(X1,X2,X3,X4) 51: U31(X1,X2,X3,mark(X4)) -> U31(X1,X2,X3,X4) 52: U31(active(X1),X2,X3,X4) -> U31(X1,X2,X3,X4) 53: U31(X1,active(X2),X3,X4) -> U31(X1,X2,X3,X4) 54: U31(X1,X2,active(X3),X4) -> U31(X1,X2,X3,X4) 55: U31(X1,X2,X3,active(X4)) -> U31(X1,X2,X3,X4) 56: take(mark(X1),X2) -> take(X1,X2) 57: take(X1,mark(X2)) -> take(X1,X2) 58: take(active(X1),X2) -> take(X1,X2) 59: take(X1,active(X2)) -> take(X1,X2) 60: and(mark(X1),X2) -> and(X1,X2) 61: and(X1,mark(X2)) -> and(X1,X2) 62: and(active(X1),X2) -> and(X1,X2) 63: and(X1,active(X2)) -> and(X1,X2) 64: isNat(mark(X)) -> isNat(X) 65: isNat(active(X)) -> isNat(X) 66: isNatList(mark(X)) -> isNatList(X) 67: isNatList(active(X)) -> isNatList(X) 68: isNatIList(mark(X)) -> isNatIList(X) 69: isNatIList(active(X)) -> isNatIList(X) Number of strict rules: 69 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: #s(active(X)) -> #s(X) #5: #mark(take(X1,X2)) -> #active(take(mark(X1),mark(X2))) #6: #mark(take(X1,X2)) -> #take(mark(X1),mark(X2)) #7: #mark(take(X1,X2)) -> #mark(X1) #8: #mark(take(X1,X2)) -> #mark(X2) #9: #cons(X1,mark(X2)) -> #cons(X1,X2) #10: #isNatList(mark(X)) -> #isNatList(X) #11: #U21(mark(X)) -> #U21(X) #12: #s(mark(X)) -> #s(X) #13: #U11(X1,active(X2)) -> #U11(X1,X2) #14: #cons(X1,active(X2)) -> #cons(X1,X2) #15: #U21(active(X)) -> #U21(X) #16: #U31(X1,active(X2),X3,X4) -> #U31(X1,X2,X3,X4) #17: #U31(mark(X1),X2,X3,X4) -> #U31(X1,X2,X3,X4) #18: #take(active(X1),X2) -> #take(X1,X2) #19: #and(X1,mark(X2)) -> #and(X1,X2) #20: #U11(mark(X1),X2) -> #U11(X1,X2) #21: #active(isNat(0())) -> #mark(tt()) #22: #take(X1,active(X2)) -> #take(X1,X2) #23: #U31(X1,X2,X3,active(X4)) -> #U31(X1,X2,X3,X4) #24: #isNatList(active(X)) -> #isNatList(X) #25: #U11(active(X1),X2) -> #U11(X1,X2) #26: #U31(X1,X2,X3,mark(X4)) -> #U31(X1,X2,X3,X4) #27: #active(isNatList(cons(V1,V2))) -> #mark(and(isNat(V1),isNatList(V2))) #28: #active(isNatList(cons(V1,V2))) -> #and(isNat(V1),isNatList(V2)) #29: #active(isNatList(cons(V1,V2))) -> #isNat(V1) #30: #active(isNatList(cons(V1,V2))) -> #isNatList(V2) #31: #active(isNatIList(V)) -> #mark(isNatList(V)) #32: #active(isNatIList(V)) -> #isNatList(V) #33: #active(isNatIList(cons(V1,V2))) -> #mark(and(isNat(V1),isNatIList(V2))) #34: #active(isNatIList(cons(V1,V2))) -> #and(isNat(V1),isNatIList(V2)) #35: #active(isNatIList(cons(V1,V2))) -> #isNat(V1) #36: #active(isNatIList(cons(V1,V2))) -> #isNatIList(V2) #37: #take(X1,mark(X2)) -> #take(X1,X2) #38: #mark(s(X)) -> #active(s(mark(X))) #39: #mark(s(X)) -> #s(mark(X)) #40: #mark(s(X)) -> #mark(X) #41: #mark(tt()) -> #active(tt()) #42: #length(active(X)) -> #length(X) #43: #isNatIList(active(X)) -> #isNatIList(X) #44: #active(isNatList(nil())) -> #mark(tt()) #45: #mark(isNat(X)) -> #active(isNat(X)) #46: #take(mark(X1),X2) -> #take(X1,X2) #47: #active(isNatList(take(V1,V2))) -> #mark(and(isNat(V1),isNatIList(V2))) #48: #active(isNatList(take(V1,V2))) -> #and(isNat(V1),isNatIList(V2)) #49: #active(isNatList(take(V1,V2))) -> #isNat(V1) #50: #active(isNatList(take(V1,V2))) -> #isNatIList(V2) #51: #and(active(X1),X2) -> #and(X1,X2) #52: #mark(and(X1,X2)) -> #active(and(mark(X1),X2)) #53: #mark(and(X1,X2)) -> #and(mark(X1),X2) #54: #mark(and(X1,X2)) -> #mark(X1) #55: #U31(active(X1),X2,X3,X4) -> #U31(X1,X2,X3,X4) #56: #U31(X1,mark(X2),X3,X4) -> #U31(X1,X2,X3,X4) #57: #mark(length(X)) -> #active(length(mark(X))) #58: #mark(length(X)) -> #length(mark(X)) #59: #mark(length(X)) -> #mark(X) #60: #mark(cons(X1,X2)) -> #active(cons(mark(X1),X2)) #61: #mark(cons(X1,X2)) -> #cons(mark(X1),X2) #62: #mark(cons(X1,X2)) -> #mark(X1) #63: #active(isNat(length(V1))) -> #mark(isNatList(V1)) #64: #active(isNat(length(V1))) -> #isNatList(V1) #65: #U11(X1,mark(X2)) -> #U11(X1,X2) #66: #active(isNatIList(zeros())) -> #mark(tt()) #67: #isNat(mark(X)) -> #isNat(X) #68: #mark(isNatIList(X)) -> #active(isNatIList(X)) #69: #active(and(tt(),X)) -> #mark(X) #70: #length(mark(X)) -> #length(X) #71: #isNat(active(X)) -> #isNat(X) #72: #mark(U31(X1,X2,X3,X4)) -> #active(U31(mark(X1),X2,X3,X4)) #73: #mark(U31(X1,X2,X3,X4)) -> #U31(mark(X1),X2,X3,X4) #74: #mark(U31(X1,X2,X3,X4)) -> #mark(X1) #75: #mark(U11(X1,X2)) -> #active(U11(mark(X1),X2)) #76: #mark(U11(X1,X2)) -> #U11(mark(X1),X2) #77: #mark(U11(X1,X2)) -> #mark(X1) #78: #cons(mark(X1),X2) -> #cons(X1,X2) #79: #mark(nil()) -> #active(nil()) #80: #and(mark(X1),X2) -> #and(X1,X2) #81: #active(take(0(),IL)) -> #mark(U21(isNatIList(IL))) #82: #active(take(0(),IL)) -> #U21(isNatIList(IL)) #83: #active(take(0(),IL)) -> #isNatIList(IL) #84: #mark(isNatList(X)) -> #active(isNatList(X)) #85: #mark(zeros()) -> #active(zeros()) #86: #and(X1,active(X2)) -> #and(X1,X2) #87: #mark(U21(X)) -> #active(U21(mark(X))) #88: #mark(U21(X)) -> #U21(mark(X)) #89: #mark(U21(X)) -> #mark(X) #90: #isNatIList(mark(X)) -> #isNatIList(X) #91: #cons(active(X1),X2) -> #cons(X1,X2) #92: #mark(0()) -> #active(0()) #93: #active(length(cons(N,L))) -> #mark(U11(and(isNatList(L),isNat(N)),L)) #94: #active(length(cons(N,L))) -> #U11(and(isNatList(L),isNat(N)),L) #95: #active(length(cons(N,L))) -> #and(isNatList(L),isNat(N)) #96: #active(length(cons(N,L))) -> #isNatList(L) #97: #active(length(cons(N,L))) -> #isNat(N) #98: #active(U21(tt())) -> #mark(nil()) #99: #active(zeros()) -> #mark(cons(0(),zeros())) #100: #active(zeros()) -> #cons(0(),zeros()) #101: #U31(X1,X2,active(X3),X4) -> #U31(X1,X2,X3,X4) #102: #active(isNat(s(V1))) -> #mark(isNat(V1)) #103: #active(isNat(s(V1))) -> #isNat(V1) #104: #active(length(nil())) -> #mark(0()) #105: #active(U31(tt(),IL,M,N)) -> #mark(cons(N,take(M,IL))) #106: #active(U31(tt(),IL,M,N)) -> #cons(N,take(M,IL)) #107: #active(U31(tt(),IL,M,N)) -> #take(M,IL) #108: #U31(X1,X2,mark(X3),X4) -> #U31(X1,X2,X3,X4) #109: #active(take(s(M),cons(N,IL))) -> #mark(U31(and(isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N)) #110: #active(take(s(M),cons(N,IL))) -> #U31(and(isNatIList(IL),and(isNat(M),isNat(N))),IL,M,N) #111: #active(take(s(M),cons(N,IL))) -> #and(isNatIList(IL),and(isNat(M),isNat(N))) #112: #active(take(s(M),cons(N,IL))) -> #isNatIList(IL) #113: #active(take(s(M),cons(N,IL))) -> #and(isNat(M),isNat(N)) #114: #active(take(s(M),cons(N,IL))) -> #isNat(M) #115: #active(take(s(M),cons(N,IL))) -> #isNat(N) Number of SCCs: 12, DPs: 67 SCC { #4 #12 } POLO(Sum)... succeeded. U21 w: 0 isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 #take w: 0 take 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 U31 w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 #U21 w: 0 tt w: 0 length w: 0 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #4 #12 Number of SCCs: 11, DPs: 65 SCC { #10 #24 } POLO(Sum)... succeeded. U21 w: 0 isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 #take w: 0 take 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 U31 w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 #U21 w: 0 tt w: 0 length w: 0 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #10 #24 Number of SCCs: 10, DPs: 63 SCC { #42 #70 } POLO(Sum)... succeeded. U21 w: 0 isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 #take w: 0 take 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 U31 w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 #U21 w: 0 tt w: 0 length w: 0 #length w: x1 #U31 w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #42 #70 Number of SCCs: 9, DPs: 61 SCC { #11 #15 } POLO(Sum)... succeeded. U21 w: 0 isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 #take w: 0 take 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 U31 w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 #U21 w: x1 tt w: 0 length w: 0 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #11 #15 Number of SCCs: 8, DPs: 59 SCC { #67 #71 } POLO(Sum)... succeeded. U21 w: 0 isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: x1 #take w: 0 take 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 U31 w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 #U21 w: 0 tt w: 0 length w: 0 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #67 #71 Number of SCCs: 7, DPs: 57 SCC { #43 #90 } POLO(Sum)... succeeded. U21 w: 0 isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 #take w: 0 take 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 U31 w: 0 cons w: 0 #active w: 0 #isNatIList w: x1 #U21 w: 0 tt w: 0 length w: 0 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #43 #90 Number of SCCs: 6, DPs: 55 SCC { #9 #14 #78 #91 } POLO(Sum)... succeeded. U21 w: 0 isNatList w: 0 U11 w: 0 #cons w: x2 s w: 0 #isNat w: 0 #take w: 0 take 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 U31 w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 #U21 w: 0 tt w: 0 length w: 0 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #9 #14 Number of SCCs: 6, DPs: 53 SCC { #78 #91 } POLO(Sum)... succeeded. U21 w: 0 isNatList w: 0 U11 w: 0 #cons w: x1 s w: 0 #isNat w: 0 #take w: 0 take 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 U31 w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 #U21 w: 0 tt w: 0 length w: 0 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #78 #91 Number of SCCs: 5, DPs: 51 SCC { #18 #22 #37 #46 } POLO(Sum)... succeeded. U21 w: 0 isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 #take w: x2 take 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 U31 w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 #U21 w: 0 tt w: 0 length w: 0 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #22 #37 Number of SCCs: 5, DPs: 49 SCC { #18 #46 } POLO(Sum)... succeeded. U21 w: 0 isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 #take w: x1 take 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 U31 w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 #U21 w: 0 tt w: 0 length w: 0 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #18 #46 Number of SCCs: 4, DPs: 47 SCC { #19 #51 #80 #86 } POLO(Sum)... succeeded. U21 w: 0 isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 #take w: 0 take 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 U31 w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 #U21 w: 0 tt w: 0 length w: 0 #length w: 0 #U31 w: 0 #and w: x1 USABLE RULES: { } Removed DPs: #51 #80 Number of SCCs: 4, DPs: 45 SCC { #19 #86 } POLO(Sum)... succeeded. U21 w: 0 isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 #take w: 0 take 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 U31 w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 #U21 w: 0 tt w: 0 length w: 0 #length w: 0 #U31 w: 0 #and w: x2 USABLE RULES: { } Removed DPs: #19 #86 Number of SCCs: 3, DPs: 43 SCC { #13 #20 #25 #65 } POLO(Sum)... succeeded. U21 w: 0 isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 #take w: 0 take 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: x2 active w: x1 + 1 U31 w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 #U21 w: 0 tt w: 0 length w: 0 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #13 #65 Number of SCCs: 3, DPs: 41 SCC { #20 #25 } POLO(Sum)... succeeded. U21 w: 0 isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 #take w: 0 take 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: x1 active w: x1 + 1 U31 w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 #U21 w: 0 tt w: 0 length w: 0 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { } Removed DPs: #20 #25 Number of SCCs: 2, DPs: 39 SCC { #16 #17 #23 #26 #55 #56 #101 #108 } POLO(Sum)... succeeded. U21 w: 0 isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 #take w: 0 take 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 U31 w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 #U21 w: 0 tt w: 0 length w: 0 #length w: 0 #U31 w: x2 + x3 + x4 #and w: 0 USABLE RULES: { } Removed DPs: #16 #23 #26 #56 #101 #108 Number of SCCs: 2, DPs: 33 SCC { #17 #55 } POLO(Sum)... succeeded. U21 w: 0 isNatList w: 0 U11 w: 0 #cons w: 0 s w: 0 #isNat w: 0 #take w: 0 take 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 U31 w: 0 cons w: 0 #active w: 0 #isNatIList w: 0 #U21 w: 0 tt w: 0 length w: 0 #length w: 0 #U31 w: x1 #and w: 0 USABLE RULES: { } Removed DPs: #17 #55 Number of SCCs: 1, DPs: 31 SCC { #1 #5 #7 #8 #27 #31 #33 #40 #45 #47 #52 #54 #57 #59 #62 #63 #68 #69 #72 #74 #75 #77 #81 #84 #85 #89 #93 #99 #102 #105 #109 } POLO(Sum)... succeeded. U21 w: x1 + 1 isNatList w: 0 U11 w: x1 + x2 + 1 #cons w: 0 s w: x1 #isNat w: 0 #take w: 0 take w: x1 + x2 + 2 and w: x1 + x2 isNatIList w: 0 zeros w: 1 #mark w: x1 0 w: 0 #isNatList w: 0 #s w: 0 nil w: 1 mark w: x1 isNat w: 0 #U11 w: 0 active w: x1 U31 w: x1 + x2 + x3 + x4 + 2 cons w: x1 + x2 #active w: x1 #isNatIList w: 0 #U21 w: 0 tt w: 0 length w: x1 + 1 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { 1..69 } Removed DPs: #7 #8 #59 #74 #77 #81 #89 Number of SCCs: 1, DPs: 24 SCC { #1 #5 #27 #31 #33 #40 #45 #47 #52 #54 #57 #62 #63 #68 #69 #72 #75 #84 #85 #93 #99 #102 #105 #109 } POLO(Sum)... succeeded. U21 w: 1 isNatList w: 0 U11 w: 1 #cons w: 0 s w: x1 #isNat w: 0 #take w: 0 take w: x1 + x2 + 2 and w: x1 + x2 isNatIList w: 0 zeros w: 3 #mark w: x1 0 w: 1 #isNatList w: 0 #s w: 0 nil w: 1 mark w: x1 isNat w: 0 #U11 w: 0 active w: x1 U31 w: x3 + x4 + 2 cons w: x1 + 1 #active w: x1 #isNatIList w: 0 #U21 w: 0 tt w: 0 length w: 1 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { 1..69 } Removed DPs: #62 #99 #105 #109 Number of SCCs: 1, DPs: 17 SCC { #1 #27 #31 #33 #40 #45 #47 #52 #54 #57 #63 #68 #69 #75 #84 #93 #102 } POLO(Sum)... succeeded. U21 w: 1 isNatList w: x1 U11 w: x2 #cons w: 0 s w: x1 #isNat w: 0 #take w: 0 take w: x1 + x2 + 2 and w: x1 + x2 isNatIList w: x1 + 1 zeros w: 3 #mark w: x1 0 w: 0 #isNatList w: 0 #s w: 0 nil w: 1 mark w: x1 isNat w: x1 #U11 w: 0 active w: x1 U31 w: x2 + x3 + x4 + 2 cons w: x1 + x2 #active w: x1 #isNatIList w: 0 #U21 w: 0 tt w: 0 length w: x1 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { 1..69 } Removed DPs: #31 #47 Number of SCCs: 1, DPs: 15 SCC { #1 #27 #33 #40 #45 #52 #54 #57 #63 #68 #69 #75 #84 #93 #102 } POLO(Sum)... succeeded. U21 w: 1 isNatList w: x1 + 1 U11 w: x2 + 2 #cons w: 0 s w: x1 #isNat w: 0 #take w: 0 take w: x1 + x2 + 2 and w: x1 + x2 isNatIList w: x1 + 1 zeros w: 3 #mark w: x1 0 w: 0 #isNatList w: 0 #s w: 0 nil w: 1 mark w: x1 isNat w: x1 #U11 w: 0 active w: x1 U31 w: x2 + x3 + x4 + 2 cons w: x1 + x2 #active w: x1 #isNatIList w: 0 #U21 w: 0 tt w: 0 length w: x1 + 2 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { 1..69 } Removed DPs: #63 Number of SCCs: 2, DPs: 14 SCC { #45 #102 } POLO(Sum)... succeeded. U21 w: x1 + 1 isNatList w: x1 + 6 U11 w: x2 + 3 #cons w: 0 s w: x1 + 4 #isNat w: 0 #take w: 0 take w: 5 and w: 13 isNatIList w: 5 zeros w: 1 #mark w: x1 + 1 0 w: 3 #isNatList w: 0 #s w: 0 nil w: 10 mark w: x1 + 1 isNat w: x1 + 1 #U11 w: 0 active w: x1 + 2 U31 w: x2 + x4 + 7 cons w: x1 + 9 #active w: x1 #isNatIList w: 0 #U21 w: 0 tt w: 7 length w: 1 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { 34..41 44 45 48..69 } Removed DPs: #45 #102 Number of SCCs: 1, DPs: 12 SCC { #1 #27 #33 #40 #52 #54 #57 #68 #69 #75 #84 #93 } POLO(Sum)... POLO(max)... succeeded. U21 w: 0 isNatList w: x1 + 1 U11 w: max(x2 + 1) #cons w: 0 s w: x1 #isNat w: 0 #take w: 0 take w: max(x1 + 1, x2 + 2) and w: max(x1 + 1, x2) isNatIList w: x1 + 1 zeros w: 2 #mark w: x1 + 1 0 w: 1 #isNatList w: 0 #s w: 0 nil w: 0 mark w: x1 isNat w: x1 + 1 #U11 w: 0 active w: x1 U31 w: max(x2 + 2, x3 + 1, x4 + 1) cons w: max(x1 + 1, x2) #active w: x1 + 1 #isNatIList w: 0 #U21 w: 0 tt w: 1 length w: x1 + 1 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { 1..69 } Removed DPs: #54 Number of SCCs: 1, DPs: 11 SCC { #1 #27 #33 #40 #52 #57 #68 #69 #75 #84 #93 } POLO(Sum)... succeeded. U21 w: 1 isNatList w: 3 U11 w: 1 #cons w: 0 s w: x1 #isNat w: 0 #take w: 0 take w: 5 and w: x2 isNatIList w: x1 + 5 zeros w: 1 #mark w: x1 + 2 0 w: 3 #isNatList w: 0 #s w: 0 nil w: 3 mark w: x1 + 1 isNat w: 1 #U11 w: 0 active w: x1 + 2 U31 w: x2 + x4 + 7 cons w: x2 + 4 #active w: x1 + 2 #isNatIList w: 0 #U21 w: 0 tt w: 8 length w: 1 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { 34..41 44 45 48..69 } Removed DPs: #33 Number of SCCs: 1, DPs: 9 SCC { #1 #27 #40 #52 #57 #69 #75 #84 #93 } POLO(Sum)... succeeded. U21 w: 1 isNatList w: x1 + 3 U11 w: 1 #cons w: 0 s w: x1 #isNat w: 0 #take w: 0 take w: 5 and w: x2 + 1 isNatIList w: x1 + 9 zeros w: 1 #mark w: x1 + 2 0 w: 3 #isNatList w: 0 #s w: 0 nil w: 3 mark w: x1 + 1 isNat w: 1 #U11 w: 0 active w: x1 + 2 U31 w: x2 + x4 + 7 cons w: x2 + 4 #active w: x1 + 2 #isNatIList w: 0 #U21 w: 0 tt w: 12 length w: 1 #length w: 0 #U31 w: 0 #and w: 0 USABLE RULES: { 34..41 44 45 48..69 } Removed DPs: #27 #69 Number of SCCs: 1, DPs: 5 SCC { #1 #40 #57 #75 #93 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. Finding a loop... failed.