MAYBE Input TRS: 1: zeros() -> cons(0(),n__zeros()) 2: U11(tt()) -> tt() 3: U21(tt()) -> tt() 4: U31(tt()) -> tt() 5: U41(tt(),V2) -> U42(isNatIList(activate(V2))) 6: U42(tt()) -> tt() 7: U51(tt(),V2) -> U52(isNatList(activate(V2))) 8: U52(tt()) -> tt() 9: U61(tt(),V2) -> U62(isNatIList(activate(V2))) 10: U62(tt()) -> tt() 11: U71(tt(),L,N) -> U72(isNat(activate(N)),activate(L)) 12: U72(tt(),L) -> s(length(activate(L))) 13: U81(tt()) -> nil() 14: U91(tt(),IL,M,N) -> U92(isNat(activate(M)),activate(IL),activate(M),activate(N)) 15: U92(tt(),IL,M,N) -> U93(isNat(activate(N)),activate(IL),activate(M),activate(N)) 16: U93(tt(),IL,M,N) -> cons(activate(N),n__take(activate(M),activate(IL))) 17: isNat(n__0()) -> tt() 18: isNat(n__length(V1)) -> U11(isNatList(activate(V1))) 19: isNat(n__s(V1)) -> U21(isNat(activate(V1))) 20: isNatIList(V) -> U31(isNatList(activate(V))) 21: isNatIList(n__zeros()) -> tt() 22: isNatIList(n__cons(V1,V2)) -> U41(isNat(activate(V1)),activate(V2)) 23: isNatList(n__nil()) -> tt() 24: isNatList(n__cons(V1,V2)) -> U51(isNat(activate(V1)),activate(V2)) 25: isNatList(n__take(V1,V2)) -> U61(isNat(activate(V1)),activate(V2)) 26: length(nil()) -> 0() 27: length(cons(N,L)) -> U71(isNatList(activate(L)),activate(L),N) 28: take(0(),IL) -> U81(isNatIList(IL)) 29: take(s(M),cons(N,IL)) -> U91(isNatIList(activate(IL)),activate(IL),M,N) 30: zeros() -> n__zeros() 31: take(X1,X2) -> n__take(X1,X2) 32: 0() -> n__0() 33: length(X) -> n__length(X) 34: s(X) -> n__s(X) 35: cons(X1,X2) -> n__cons(X1,X2) 36: nil() -> n__nil() 37: activate(n__zeros()) -> zeros() 38: activate(n__take(X1,X2)) -> take(X1,X2) 39: activate(n__0()) -> 0() 40: activate(n__length(X)) -> length(X) 41: activate(n__s(X)) -> s(X) 42: activate(n__cons(X1,X2)) -> cons(X1,X2) 43: activate(n__nil()) -> nil() 44: activate(X) -> X Number of strict rules: 44 Direct POLO(bPol) ... failed. Uncurrying ... failed. Dependency Pairs: #1: #activate(n__nil()) -> #nil() #2: #take(s(M),cons(N,IL)) -> #U91(isNatIList(activate(IL)),activate(IL),M,N) #3: #take(s(M),cons(N,IL)) -> #isNatIList(activate(IL)) #4: #take(s(M),cons(N,IL)) -> #activate(IL) #5: #take(s(M),cons(N,IL)) -> #activate(IL) #6: #activate(n__cons(X1,X2)) -> #cons(X1,X2) #7: #activate(n__s(X)) -> #s(X) #8: #activate(n__zeros()) -> #zeros() #9: #activate(n__take(X1,X2)) -> #take(X1,X2) #10: #activate(n__length(X)) -> #length(X) #11: #U81(tt()) -> #nil() #12: #U61(tt(),V2) -> #U62(isNatIList(activate(V2))) #13: #U61(tt(),V2) -> #isNatIList(activate(V2)) #14: #U61(tt(),V2) -> #activate(V2) #15: #U71(tt(),L,N) -> #U72(isNat(activate(N)),activate(L)) #16: #U71(tt(),L,N) -> #isNat(activate(N)) #17: #U71(tt(),L,N) -> #activate(N) #18: #U71(tt(),L,N) -> #activate(L) #19: #isNatList(n__cons(V1,V2)) -> #U51(isNat(activate(V1)),activate(V2)) #20: #isNatList(n__cons(V1,V2)) -> #isNat(activate(V1)) #21: #isNatList(n__cons(V1,V2)) -> #activate(V1) #22: #isNatList(n__cons(V1,V2)) -> #activate(V2) #23: #U72(tt(),L) -> #s(length(activate(L))) #24: #U72(tt(),L) -> #length(activate(L)) #25: #U72(tt(),L) -> #activate(L) #26: #U91(tt(),IL,M,N) -> #U92(isNat(activate(M)),activate(IL),activate(M),activate(N)) #27: #U91(tt(),IL,M,N) -> #isNat(activate(M)) #28: #U91(tt(),IL,M,N) -> #activate(M) #29: #U91(tt(),IL,M,N) -> #activate(IL) #30: #U91(tt(),IL,M,N) -> #activate(M) #31: #U91(tt(),IL,M,N) -> #activate(N) #32: #isNatList(n__take(V1,V2)) -> #U61(isNat(activate(V1)),activate(V2)) #33: #isNatList(n__take(V1,V2)) -> #isNat(activate(V1)) #34: #isNatList(n__take(V1,V2)) -> #activate(V1) #35: #isNatList(n__take(V1,V2)) -> #activate(V2) #36: #isNatIList(V) -> #U31(isNatList(activate(V))) #37: #isNatIList(V) -> #isNatList(activate(V)) #38: #isNatIList(V) -> #activate(V) #39: #U51(tt(),V2) -> #U52(isNatList(activate(V2))) #40: #U51(tt(),V2) -> #isNatList(activate(V2)) #41: #U51(tt(),V2) -> #activate(V2) #42: #activate(n__0()) -> #0() #43: #U41(tt(),V2) -> #U42(isNatIList(activate(V2))) #44: #U41(tt(),V2) -> #isNatIList(activate(V2)) #45: #U41(tt(),V2) -> #activate(V2) #46: #take(0(),IL) -> #U81(isNatIList(IL)) #47: #take(0(),IL) -> #isNatIList(IL) #48: #isNatIList(n__cons(V1,V2)) -> #U41(isNat(activate(V1)),activate(V2)) #49: #isNatIList(n__cons(V1,V2)) -> #isNat(activate(V1)) #50: #isNatIList(n__cons(V1,V2)) -> #activate(V1) #51: #isNatIList(n__cons(V1,V2)) -> #activate(V2) #52: #length(cons(N,L)) -> #U71(isNatList(activate(L)),activate(L),N) #53: #length(cons(N,L)) -> #isNatList(activate(L)) #54: #length(cons(N,L)) -> #activate(L) #55: #length(cons(N,L)) -> #activate(L) #56: #isNat(n__s(V1)) -> #U21(isNat(activate(V1))) #57: #isNat(n__s(V1)) -> #isNat(activate(V1)) #58: #isNat(n__s(V1)) -> #activate(V1) #59: #length(nil()) -> #0() #60: #U93(tt(),IL,M,N) -> #cons(activate(N),n__take(activate(M),activate(IL))) #61: #U93(tt(),IL,M,N) -> #activate(N) #62: #U93(tt(),IL,M,N) -> #activate(M) #63: #U93(tt(),IL,M,N) -> #activate(IL) #64: #zeros() -> #cons(0(),n__zeros()) #65: #zeros() -> #0() #66: #U92(tt(),IL,M,N) -> #U93(isNat(activate(N)),activate(IL),activate(M),activate(N)) #67: #U92(tt(),IL,M,N) -> #isNat(activate(N)) #68: #U92(tt(),IL,M,N) -> #activate(N) #69: #U92(tt(),IL,M,N) -> #activate(IL) #70: #U92(tt(),IL,M,N) -> #activate(M) #71: #U92(tt(),IL,M,N) -> #activate(N) #72: #isNat(n__length(V1)) -> #U11(isNatList(activate(V1))) #73: #isNat(n__length(V1)) -> #isNatList(activate(V1)) #74: #isNat(n__length(V1)) -> #activate(V1) Number of SCCs: 1, DPs: 56 SCC { #2..5 #9 #10 #13..22 #24..35 #37 #38 #40 #41 #44 #45 #47..55 #57 #58 #61..63 #66..71 #73 #74 } POLO(Sum)... succeeded. #0 w: 0 #U72 w: x2 + 9417 U21 w: 2 isNatList w: 1 U11 w: 2 #cons w: 0 s w: x1 #isNat w: x1 + 1 #take w: x1 + x2 + 14101 U42 w: x1 + 2 U91 w: x2 + x3 + x4 + 14102 activate w: x1 take w: x1 + x2 + 14102 U71 w: x2 + 9418 #U81 w: 0 #U92 w: x2 + x3 + x4 + 2 n__zeros w: 1 isNatIList w: x1 + 1 #U93 w: x2 + x3 + x4 + 1 #activate w: x1 U93 w: x2 + x3 + x4 + 14102 U72 w: x2 + 9418 zeros w: 1 n__nil w: 13214 #U52 w: 0 n__s w: x1 #U42 w: 0 #U62 w: 0 0 w: 0 #zeros w: 0 n__take w: x1 + x2 + 14102 #isNatList w: x1 + 9416 #s w: 0 n__cons w: x1 + x2 nil w: 13214 U62 w: 2 #nil w: 0 n__0 w: 0 n__length w: x1 + 9418 isNat w: 1 U52 w: x1 + 4 U61 w: x1 + 5 #U51 w: x2 + 9416 #U11 w: 0 U31 w: 2 U92 w: x2 + x3 + x4 + 14102 #U41 w: x2 + 14100 cons w: x1 + x2 #isNatIList w: x1 + 14100 #U21 w: 0 U81 w: 13214 tt w: 3 #U71 w: x2 + x3 + 9417 U51 w: x1 + x2 + 1 length w: x1 + 9418 #length w: x1 + 9417 U41 w: 2 #U31 w: 0 #U91 w: x2 + x3 + x4 + 14100 #U61 w: x2 + 23517 USABLE RULES: { 1 11..16 26..44 } Removed DPs: #2..5 #9 #10 #13 #14 #16..18 #20..22 #25..35 #37 #38 #41 #45 #47 #49..51 #53..55 #58 #61..63 #66..71 #73 #74 Number of SCCs: 4, DPs: 8 SCC { #57 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... succeeded. #0 w: [0;0] #U72 w: [0;0] U21 w: [7460;22394] isNatList w: [0,0;1,0] * x1 + [7461;18] U11 w: [7482;22394] #cons w: [0;0] s w: x1 + [7458;14937] #isNat w: [1,1;0,0] * x1 #take w: [0;0] U42 w: [4;22394] U91 w: [0,0;1,1] * x2 + [0,0;1,1] * x3 + [0,0;0,1] * x4 + [22377;22870] activate w: x1 + [0;2] take w: [0,0;1,1] * x1 + [0,0;0,1] * x2 + [22377;476] U71 w: [1,1;1,1] * x1 + [0,1;1,1] * x2 #U81 w: [0;0] #U92 w: [0;0] n__zeros w: [0;1] isNatIList w: [0,1;0,1] * x1 + [1;1] #U93 w: [0;0] #activate w: [0;0] U93 w: [0,0;1,1] * x2 + [0,0;1,1] * x3 + [0,0;0,1] * x4 + [22377;22858] U72 w: [0,1;1,1] * x2 + [14940;29854] zeros w: [0;3] n__nil w: [22377;394] #U52 w: [0;0] n__s w: x1 + [7458;14935] #U42 w: [0;0] #U62 w: [0;0] 0 w: [1;1] #zeros w: [0;0] n__take w: [0,0;1,1] * x1 + [0,0;0,1] * x2 + [22377;474] #isNatList w: [0;0] #s w: [0;0] n__cons w: [0,0;0,1] * x1 + [1,0;1,1] * x2 + [0;1] nil w: [22377;396] U62 w: [7461;22395] #nil w: [0;0] n__0 w: [1;1] n__length w: [0,1;1,1] * x1 + [7480;14913] isNat w: [1,0;1,1] * x1 + [1;0] U52 w: [0,0;0,1] * x1 + [7461;0] U61 w: [7461;22395] #U51 w: [0;0] #U11 w: [0;0] U31 w: [1,0;0,0] * x1 + [0;22394] U92 w: [0,0;1,1] * x2 + [0,0;1,1] * x3 + [0,0;0,1] * x4 + [22377;22864] #U41 w: [0;0] cons w: [0,0;0,1] * x1 + [1,0;1,1] * x2 + [0;1] #isNatIList w: [0;0] #U21 w: [0;0] U81 w: [22377;478] tt w: [7461;22395] #U71 w: [0;0] U51 w: [0,0;1,0] * x2 + [7461;18] length w: [0,1;1,1] * x1 + [7480;14915] #length w: [0;0] U41 w: [0,0;0,1] * x1 + [3;1] #U31 w: [0;0] #U91 w: [0;0] #U61 w: [0;0] USABLE RULES: { 1 7..16 23..44 } Removed DPs: #57 Number of SCCs: 3, DPs: 7 SCC { #44 #48 } POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. Finding a loop... failed.