The rewrite relation of the following TRS is considered.
a__zeros | → | cons(0,zeros) | (1) |
a__U11(tt) | → | tt | (2) |
a__U21(tt) | → | tt | (3) |
a__U31(tt) | → | tt | (4) |
a__U41(tt,V2) | → | a__U42(a__isNatIList(V2)) | (5) |
a__U42(tt) | → | tt | (6) |
a__U51(tt,V2) | → | a__U52(a__isNatList(V2)) | (7) |
a__U52(tt) | → | tt | (8) |
a__U61(tt,L,N) | → | a__U62(a__isNat(N),L) | (9) |
a__U62(tt,L) | → | s(a__length(mark(L))) | (10) |
a__isNat(0) | → | tt | (11) |
a__isNat(length(V1)) | → | a__U11(a__isNatList(V1)) | (12) |
a__isNat(s(V1)) | → | a__U21(a__isNat(V1)) | (13) |
a__isNatIList(V) | → | a__U31(a__isNatList(V)) | (14) |
a__isNatIList(zeros) | → | tt | (15) |
a__isNatIList(cons(V1,V2)) | → | a__U41(a__isNat(V1),V2) | (16) |
a__isNatList(nil) | → | tt | (17) |
a__isNatList(cons(V1,V2)) | → | a__U51(a__isNat(V1),V2) | (18) |
a__length(nil) | → | 0 | (19) |
a__length(cons(N,L)) | → | a__U61(a__isNatList(L),L,N) | (20) |
mark(zeros) | → | a__zeros | (21) |
mark(U11(X)) | → | a__U11(mark(X)) | (22) |
mark(U21(X)) | → | a__U21(mark(X)) | (23) |
mark(U31(X)) | → | a__U31(mark(X)) | (24) |
mark(U41(X1,X2)) | → | a__U41(mark(X1),X2) | (25) |
mark(U42(X)) | → | a__U42(mark(X)) | (26) |
mark(isNatIList(X)) | → | a__isNatIList(X) | (27) |
mark(U51(X1,X2)) | → | a__U51(mark(X1),X2) | (28) |
mark(U52(X)) | → | a__U52(mark(X)) | (29) |
mark(isNatList(X)) | → | a__isNatList(X) | (30) |
mark(U61(X1,X2,X3)) | → | a__U61(mark(X1),X2,X3) | (31) |
mark(U62(X1,X2)) | → | a__U62(mark(X1),X2) | (32) |
mark(isNat(X)) | → | a__isNat(X) | (33) |
mark(length(X)) | → | a__length(mark(X)) | (34) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (35) |
mark(0) | → | 0 | (36) |
mark(tt) | → | tt | (37) |
mark(s(X)) | → | s(mark(X)) | (38) |
mark(nil) | → | nil | (39) |
a__zeros | → | zeros | (40) |
a__U11(X) | → | U11(X) | (41) |
a__U21(X) | → | U21(X) | (42) |
a__U31(X) | → | U31(X) | (43) |
a__U41(X1,X2) | → | U41(X1,X2) | (44) |
a__U42(X) | → | U42(X) | (45) |
a__isNatIList(X) | → | isNatIList(X) | (46) |
a__U51(X1,X2) | → | U51(X1,X2) | (47) |
a__U52(X) | → | U52(X) | (48) |
a__isNatList(X) | → | isNatList(X) | (49) |
a__U61(X1,X2,X3) | → | U61(X1,X2,X3) | (50) |
a__U62(X1,X2) | → | U62(X1,X2) | (51) |
a__isNat(X) | → | isNat(X) | (52) |
a__length(X) | → | length(X) | (53) |
[a__zeros] | = | 0 |
[cons(x1, x2)] | = | 1 · x1 + 2 · x2 |
[0] | = | 0 |
[zeros] | = | 0 |
[a__U11(x1)] | = | 1 · x1 |
[tt] | = | 0 |
[a__U21(x1)] | = | 1 · x1 |
[a__U31(x1)] | = | 1 · x1 |
[a__U41(x1, x2)] | = | 1 · x1 + 2 · x2 |
[a__U42(x1)] | = | 2 · x1 |
[a__isNatIList(x1)] | = | 1 · x1 |
[a__U51(x1, x2)] | = | 1 · x1 + 2 · x2 |
[a__U52(x1)] | = | 2 · x1 |
[a__isNatList(x1)] | = | 1 · x1 |
[a__U61(x1, x2, x3)] | = | 1 · x1 + 1 · x2 + 1 · x3 |
[a__U62(x1, x2)] | = | 1 · x1 + 1 · x2 |
[a__isNat(x1)] | = | 1 · x1 |
[s(x1)] | = | 1 · x1 |
[a__length(x1)] | = | 1 · x1 |
[mark(x1)] | = | 1 · x1 |
[length(x1)] | = | 1 · x1 |
[nil] | = | 1 |
[U11(x1)] | = | 1 · x1 |
[U21(x1)] | = | 1 · x1 |
[U31(x1)] | = | 1 · x1 |
[U41(x1, x2)] | = | 1 · x1 + 2 · x2 |
[U42(x1)] | = | 2 · x1 |
[isNatIList(x1)] | = | 1 · x1 |
[U51(x1, x2)] | = | 1 · x1 + 2 · x2 |
[U52(x1)] | = | 2 · x1 |
[isNatList(x1)] | = | 1 · x1 |
[U61(x1, x2, x3)] | = | 1 · x1 + 1 · x2 + 1 · x3 |
[U62(x1, x2)] | = | 1 · x1 + 1 · x2 |
[isNat(x1)] | = | 1 · x1 |
a__isNatList(nil) | → | tt | (17) |
a__length(nil) | → | 0 | (19) |
[a__zeros] | = | 0 |
[cons(x1, x2)] | = | 2 · x1 + 2 · x2 |
[0] | = | 0 |
[zeros] | = | 0 |
[a__U11(x1)] | = | 2 · x1 |
[tt] | = | 0 |
[a__U21(x1)] | = | 1 · x1 |
[a__U31(x1)] | = | 1 · x1 |
[a__U41(x1, x2)] | = | 1 · x1 + 2 · x2 |
[a__U42(x1)] | = | 2 · x1 |
[a__isNatIList(x1)] | = | 1 · x1 |
[a__U51(x1, x2)] | = | 1 · x1 + 2 · x2 |
[a__U52(x1)] | = | 2 · x1 |
[a__isNatList(x1)] | = | 1 · x1 |
[a__U61(x1, x2, x3)] | = | 1 + 2 · x1 + 2 · x2 + 2 · x3 |
[a__U62(x1, x2)] | = | 1 + 1 · x1 + 2 · x2 |
[a__isNat(x1)] | = | 2 · x1 |
[s(x1)] | = | 1 · x1 |
[a__length(x1)] | = | 1 + 2 · x1 |
[mark(x1)] | = | 1 · x1 |
[length(x1)] | = | 1 + 2 · x1 |
[U11(x1)] | = | 2 · x1 |
[U21(x1)] | = | 1 · x1 |
[U31(x1)] | = | 1 · x1 |
[U41(x1, x2)] | = | 1 · x1 + 2 · x2 |
[U42(x1)] | = | 2 · x1 |
[isNatIList(x1)] | = | 1 · x1 |
[U51(x1, x2)] | = | 1 · x1 + 2 · x2 |
[U52(x1)] | = | 2 · x1 |
[isNatList(x1)] | = | 1 · x1 |
[U61(x1, x2, x3)] | = | 1 + 2 · x1 + 2 · x2 + 2 · x3 |
[U62(x1, x2)] | = | 1 + 1 · x1 + 2 · x2 |
[isNat(x1)] | = | 2 · x1 |
[nil] | = | 0 |
a__isNat(length(V1)) | → | a__U11(a__isNatList(V1)) | (12) |
[a__zeros] | = | 0 |
[cons(x1, x2)] | = | 2 · x1 + 2 · x2 |
[0] | = | 0 |
[zeros] | = | 0 |
[a__U11(x1)] | = | 2 · x1 |
[tt] | = | 0 |
[a__U21(x1)] | = | 1 · x1 |
[a__U31(x1)] | = | 1 + 1 · x1 |
[a__U41(x1, x2)] | = | 1 + 2 · x1 + 1 · x2 |
[a__U42(x1)] | = | 1 · x1 |
[a__isNatIList(x1)] | = | 1 + 1 · x1 |
[a__U51(x1, x2)] | = | 2 · x1 + 2 · x2 |
[a__U52(x1)] | = | 2 · x1 |
[a__isNatList(x1)] | = | 1 · x1 |
[a__U61(x1, x2, x3)] | = | 2 · x1 + 2 · x2 + 2 · x3 |
[a__U62(x1, x2)] | = | 2 · x1 + 2 · x2 |
[a__isNat(x1)] | = | 1 · x1 |
[s(x1)] | = | 1 · x1 |
[a__length(x1)] | = | 2 · x1 |
[mark(x1)] | = | 1 · x1 |
[U11(x1)] | = | 2 · x1 |
[U21(x1)] | = | 1 · x1 |
[U31(x1)] | = | 1 + 1 · x1 |
[U41(x1, x2)] | = | 1 + 2 · x1 + 1 · x2 |
[U42(x1)] | = | 1 · x1 |
[isNatIList(x1)] | = | 1 + 1 · x1 |
[U51(x1, x2)] | = | 2 · x1 + 2 · x2 |
[U52(x1)] | = | 2 · x1 |
[isNatList(x1)] | = | 1 · x1 |
[U61(x1, x2, x3)] | = | 2 · x1 + 2 · x2 + 2 · x3 |
[U62(x1, x2)] | = | 2 · x1 + 2 · x2 |
[isNat(x1)] | = | 1 · x1 |
[length(x1)] | = | 2 · x1 |
[nil] | = | 0 |
a__U31(tt) | → | tt | (4) |
a__isNatIList(zeros) | → | tt | (15) |
[a__zeros] | = | 0 |
[cons(x1, x2)] | = | 2 · x1 + 2 · x2 |
[0] | = | 0 |
[zeros] | = | 0 |
[a__U11(x1)] | = | 1 + 1 · x1 |
[tt] | = | 0 |
[a__U21(x1)] | = | 1 · x1 |
[a__U41(x1, x2)] | = | 1 · x1 + 2 · x2 |
[a__U42(x1)] | = | 2 · x1 |
[a__isNatIList(x1)] | = | 1 · x1 |
[a__U51(x1, x2)] | = | 2 · x1 + 2 · x2 |
[a__U52(x1)] | = | 1 · x1 |
[a__isNatList(x1)] | = | 1 · x1 |
[a__U61(x1, x2, x3)] | = | 1 · x1 + 2 · x2 + 2 · x3 |
[a__U62(x1, x2)] | = | 1 · x1 + 2 · x2 |
[a__isNat(x1)] | = | 1 · x1 |
[s(x1)] | = | 1 · x1 |
[a__length(x1)] | = | 2 · x1 |
[mark(x1)] | = | 1 · x1 |
[a__U31(x1)] | = | 1 · x1 |
[U11(x1)] | = | 1 + 1 · x1 |
[U21(x1)] | = | 1 · x1 |
[U31(x1)] | = | 1 · x1 |
[U41(x1, x2)] | = | 1 · x1 + 2 · x2 |
[U42(x1)] | = | 2 · x1 |
[isNatIList(x1)] | = | 1 · x1 |
[U51(x1, x2)] | = | 2 · x1 + 2 · x2 |
[U52(x1)] | = | 1 · x1 |
[isNatList(x1)] | = | 1 · x1 |
[U61(x1, x2, x3)] | = | 1 · x1 + 2 · x2 + 2 · x3 |
[U62(x1, x2)] | = | 1 · x1 + 2 · x2 |
[isNat(x1)] | = | 1 · x1 |
[length(x1)] | = | 2 · x1 |
[nil] | = | 0 |
a__U11(tt) | → | tt | (2) |
[a__zeros] | = | 0 |
[cons(x1, x2)] | = | 2 · x1 + 2 · x2 |
[0] | = | 0 |
[zeros] | = | 0 |
[a__U21(x1)] | = | 1 · x1 |
[tt] | = | 0 |
[a__U41(x1, x2)] | = | 1 + 2 · x1 + 2 · x2 |
[a__U42(x1)] | = | 1 · x1 |
[a__isNatIList(x1)] | = | 1 + 1 · x1 |
[a__U51(x1, x2)] | = | 2 · x1 + 2 · x2 |
[a__U52(x1)] | = | 1 · x1 |
[a__isNatList(x1)] | = | 1 · x1 |
[a__U61(x1, x2, x3)] | = | 2 · x1 + 2 · x2 + 2 · x3 |
[a__U62(x1, x2)] | = | 2 · x1 + 2 · x2 |
[a__isNat(x1)] | = | 1 · x1 |
[s(x1)] | = | 1 · x1 |
[a__length(x1)] | = | 2 · x1 |
[mark(x1)] | = | 1 · x1 |
[a__U31(x1)] | = | 1 · x1 |
[U11(x1)] | = | 1 · x1 |
[a__U11(x1)] | = | 1 · x1 |
[U21(x1)] | = | 1 · x1 |
[U31(x1)] | = | 1 · x1 |
[U41(x1, x2)] | = | 1 + 2 · x1 + 2 · x2 |
[U42(x1)] | = | 1 · x1 |
[isNatIList(x1)] | = | 1 + 1 · x1 |
[U51(x1, x2)] | = | 2 · x1 + 2 · x2 |
[U52(x1)] | = | 1 · x1 |
[isNatList(x1)] | = | 1 · x1 |
[U61(x1, x2, x3)] | = | 2 · x1 + 2 · x2 + 2 · x3 |
[U62(x1, x2)] | = | 2 · x1 + 2 · x2 |
[isNat(x1)] | = | 1 · x1 |
[length(x1)] | = | 2 · x1 |
[nil] | = | 0 |
a__isNatIList(V) | → | a__U31(a__isNatList(V)) | (14) |
[a__zeros] | = | 1 |
[cons(x1, x2)] | = | 1 + 1 · x1 + 2 · x2 |
[0] | = | 0 |
[zeros] | = | 0 |
[a__U21(x1)] | = | 1 · x1 |
[tt] | = | 0 |
[a__U41(x1, x2)] | = | 1 · x1 + 2 · x2 |
[a__U42(x1)] | = | 1 · x1 |
[a__isNatIList(x1)] | = | 1 · x1 |
[a__U51(x1, x2)] | = | 1 · x1 + 1 · x2 |
[a__U52(x1)] | = | 1 · x1 |
[a__isNatList(x1)] | = | 1 · x1 |
[a__U61(x1, x2, x3)] | = | 1 + 1 · x1 + 1 · x2 + 1 · x3 |
[a__U62(x1, x2)] | = | 1 + 1 · x1 + 1 · x2 |
[a__isNat(x1)] | = | 1 · x1 |
[s(x1)] | = | 1 · x1 |
[a__length(x1)] | = | 1 · x1 |
[mark(x1)] | = | 1 + 1 · x1 |
[U11(x1)] | = | 1 · x1 |
[a__U11(x1)] | = | 1 · x1 |
[U21(x1)] | = | 1 · x1 |
[U31(x1)] | = | 1 · x1 |
[a__U31(x1)] | = | 1 · x1 |
[U41(x1, x2)] | = | 1 · x1 + 2 · x2 |
[U42(x1)] | = | 1 · x1 |
[isNatIList(x1)] | = | 1 · x1 |
[U51(x1, x2)] | = | 1 · x1 + 1 · x2 |
[U52(x1)] | = | 1 · x1 |
[isNatList(x1)] | = | 1 · x1 |
[U61(x1, x2, x3)] | = | 1 + 1 · x1 + 1 · x2 + 1 · x3 |
[U62(x1, x2)] | = | 1 + 1 · x1 + 1 · x2 |
[isNat(x1)] | = | 1 · x1 |
[length(x1)] | = | 1 · x1 |
[nil] | = | 1 |
a__isNatIList(cons(V1,V2)) | → | a__U41(a__isNat(V1),V2) | (16) |
a__isNatList(cons(V1,V2)) | → | a__U51(a__isNat(V1),V2) | (18) |
mark(isNatIList(X)) | → | a__isNatIList(X) | (27) |
mark(isNatList(X)) | → | a__isNatList(X) | (30) |
mark(isNat(X)) | → | a__isNat(X) | (33) |
mark(0) | → | 0 | (36) |
mark(tt) | → | tt | (37) |
mark(nil) | → | nil | (39) |
a__zeros | → | zeros | (40) |
[a__zeros] | = | 0 |
[cons(x1, x2)] | = | 2 · x1 + 2 · x2 |
[0] | = | 0 |
[zeros] | = | 0 |
[a__U21(x1)] | = | 1 · x1 |
[tt] | = | 1 |
[a__U41(x1, x2)] | = | 1 · x1 + 2 · x2 |
[a__U42(x1)] | = | 2 · x1 |
[a__isNatIList(x1)] | = | 1 · x1 |
[a__U51(x1, x2)] | = | 2 · x1 + 2 · x2 |
[a__U52(x1)] | = | 1 · x1 |
[a__isNatList(x1)] | = | 2 · x1 |
[a__U61(x1, x2, x3)] | = | 1 + 1 · x1 + 2 · x2 + 2 · x3 |
[a__U62(x1, x2)] | = | 1 · x1 + 2 · x2 |
[a__isNat(x1)] | = | 2 + 2 · x1 |
[s(x1)] | = | 1 · x1 |
[a__length(x1)] | = | 1 + 2 · x1 |
[mark(x1)] | = | 1 · x1 |
[U11(x1)] | = | 1 · x1 |
[a__U11(x1)] | = | 1 · x1 |
[U21(x1)] | = | 1 · x1 |
[U31(x1)] | = | 2 · x1 |
[a__U31(x1)] | = | 2 · x1 |
[U41(x1, x2)] | = | 1 · x1 + 2 · x2 |
[U42(x1)] | = | 2 · x1 |
[U51(x1, x2)] | = | 2 · x1 + 2 · x2 |
[U52(x1)] | = | 1 · x1 |
[U61(x1, x2, x3)] | = | 1 + 1 · x1 + 2 · x2 + 2 · x3 |
[U62(x1, x2)] | = | 1 · x1 + 2 · x2 |
[length(x1)] | = | 1 + 2 · x1 |
[isNatIList(x1)] | = | 1 · x1 |
[isNatList(x1)] | = | 2 · x1 |
[isNat(x1)] | = | 2 + 1 · x1 |
a__U41(tt,V2) | → | a__U42(a__isNatIList(V2)) | (5) |
a__U42(tt) | → | tt | (6) |
a__U51(tt,V2) | → | a__U52(a__isNatList(V2)) | (7) |
a__isNat(0) | → | tt | (11) |
[a__zeros] | = | 0 |
[cons(x1, x2)] | = | 1 · x1 + 2 · x2 |
[0] | = | 0 |
[zeros] | = | 0 |
[a__U21(x1)] | = | 1 · x1 |
[tt] | = | 0 |
[a__U52(x1)] | = | 1 · x1 |
[a__U61(x1, x2, x3)] | = | 1 · x1 + 2 · x2 + 2 · x3 |
[a__U62(x1, x2)] | = | 2 · x1 + 2 · x2 |
[a__isNat(x1)] | = | 1 · x1 |
[s(x1)] | = | 1 · x1 |
[a__length(x1)] | = | 2 · x1 |
[mark(x1)] | = | 1 · x1 |
[a__isNatList(x1)] | = | 1 · x1 |
[U11(x1)] | = | 2 · x1 |
[a__U11(x1)] | = | 2 · x1 |
[U21(x1)] | = | 1 · x1 |
[U31(x1)] | = | 1 · x1 |
[a__U31(x1)] | = | 1 · x1 |
[U41(x1, x2)] | = | 1 · x1 + 2 · x2 |
[a__U41(x1, x2)] | = | 1 · x1 + 2 · x2 |
[U42(x1)] | = | 1 · x1 |
[a__U42(x1)] | = | 1 · x1 |
[U51(x1, x2)] | = | 2 · x1 + 2 · x2 |
[a__U51(x1, x2)] | = | 2 · x1 + 2 · x2 |
[U52(x1)] | = | 1 · x1 |
[U61(x1, x2, x3)] | = | 1 · x1 + 2 · x2 + 2 · x3 |
[U62(x1, x2)] | = | 2 · x1 + 2 · x2 |
[length(x1)] | = | 2 · x1 |
[a__isNatIList(x1)] | = | 1 + 2 · x1 |
[isNatIList(x1)] | = | 2 · x1 |
[isNatList(x1)] | = | 1 · x1 |
[isNat(x1)] | = | 1 · x1 |
a__isNatIList(X) | → | isNatIList(X) | (46) |
[a__zeros] | = | 0 |
[cons(x1, x2)] | = | 2 · x1 + 2 · x2 |
[0] | = | 0 |
[zeros] | = | 0 |
[a__U21(x1)] | = | 1 · x1 |
[tt] | = | 2 |
[a__U52(x1)] | = | 1 + 2 · x1 |
[a__U61(x1, x2, x3)] | = | 1 + 2 · x1 + 2 · x2 + 2 · x3 |
[a__U62(x1, x2)] | = | 2 · x1 + 2 · x2 |
[a__isNat(x1)] | = | 1 + 1 · x1 |
[s(x1)] | = | 1 + 1 · x1 |
[a__length(x1)] | = | 2 + 2 · x1 |
[mark(x1)] | = | 1 · x1 |
[a__isNatList(x1)] | = | 1 · x1 |
[U11(x1)] | = | 2 · x1 |
[a__U11(x1)] | = | 2 · x1 |
[U21(x1)] | = | 1 · x1 |
[U31(x1)] | = | 1 · x1 |
[a__U31(x1)] | = | 1 · x1 |
[U41(x1, x2)] | = | 2 · x1 + 2 · x2 |
[a__U41(x1, x2)] | = | 2 · x1 + 2 · x2 |
[U42(x1)] | = | 2 · x1 |
[a__U42(x1)] | = | 2 · x1 |
[U51(x1, x2)] | = | 2 · x1 + 2 · x2 |
[a__U51(x1, x2)] | = | 2 · x1 + 2 · x2 |
[U52(x1)] | = | 1 + 2 · x1 |
[U61(x1, x2, x3)] | = | 1 + 2 · x1 + 2 · x2 + 2 · x3 |
[U62(x1, x2)] | = | 2 · x1 + 2 · x2 |
[length(x1)] | = | 2 + 2 · x1 |
[isNatList(x1)] | = | 1 · x1 |
[isNat(x1)] | = | 1 · x1 |
a__U52(tt) | → | tt | (8) |
a__U61(tt,L,N) | → | a__U62(a__isNat(N),L) | (9) |
a__U62(tt,L) | → | s(a__length(mark(L))) | (10) |
a__isNat(s(V1)) | → | a__U21(a__isNat(V1)) | (13) |
a__length(cons(N,L)) | → | a__U61(a__isNatList(L),L,N) | (20) |
a__isNat(X) | → | isNat(X) | (52) |
[a__zeros] | = | 0 |
[cons(x1, x2)] | = | 1 · x1 + 1 · x2 |
[0] | = | 0 |
[zeros] | = | 0 |
[a__U21(x1)] | = | 1 · x1 |
[tt] | = | 0 |
[mark(x1)] | = | 2 · x1 |
[U11(x1)] | = | 1 · x1 |
[a__U11(x1)] | = | 1 · x1 |
[U21(x1)] | = | 1 · x1 |
[U31(x1)] | = | 1 · x1 |
[a__U31(x1)] | = | 1 · x1 |
[U41(x1, x2)] | = | 1 · x1 + 1 · x2 |
[a__U41(x1, x2)] | = | 1 · x1 + 2 · x2 |
[U42(x1)] | = | 1 · x1 |
[a__U42(x1)] | = | 1 · x1 |
[U51(x1, x2)] | = | 1 · x1 + 1 · x2 |
[a__U51(x1, x2)] | = | 1 · x1 + 2 · x2 |
[U52(x1)] | = | 1 · x1 |
[a__U52(x1)] | = | 1 · x1 |
[U61(x1, x2, x3)] | = | 1 · x1 + 2 · x2 + 2 · x3 |
[a__U61(x1, x2, x3)] | = | 1 · x1 + 2 · x2 + 2 · x3 |
[U62(x1, x2)] | = | 1 · x1 + 2 · x2 |
[a__U62(x1, x2)] | = | 1 · x1 + 2 · x2 |
[length(x1)] | = | 1 · x1 |
[a__length(x1)] | = | 1 · x1 |
[s(x1)] | = | 1 · x1 |
[a__isNatList(x1)] | = | 1 + 1 · x1 |
[isNatList(x1)] | = | 1 · x1 |
a__isNatList(X) | → | isNatList(X) | (49) |
prec(a__zeros) | = | 15 | weight(a__zeros) | = | 4 | ||||
prec(0) | = | 25 | weight(0) | = | 2 | ||||
prec(zeros) | = | 26 | weight(zeros) | = | 1 | ||||
prec(tt) | = | 0 | weight(tt) | = | 1 | ||||
prec(a__U21) | = | 18 | weight(a__U21) | = | 1 | ||||
prec(mark) | = | 24 | weight(mark) | = | 3 | ||||
prec(U11) | = | 19 | weight(U11) | = | 1 | ||||
prec(a__U11) | = | 23 | weight(a__U11) | = | 1 | ||||
prec(U21) | = | 17 | weight(U21) | = | 1 | ||||
prec(U31) | = | 6 | weight(U31) | = | 1 | ||||
prec(a__U31) | = | 7 | weight(a__U31) | = | 1 | ||||
prec(U42) | = | 9 | weight(U42) | = | 1 | ||||
prec(a__U42) | = | 10 | weight(a__U42) | = | 1 | ||||
prec(U52) | = | 4 | weight(U52) | = | 1 | ||||
prec(a__U52) | = | 20 | weight(a__U52) | = | 1 | ||||
prec(length) | = | 16 | weight(length) | = | 1 | ||||
prec(a__length) | = | 21 | weight(a__length) | = | 1 | ||||
prec(s) | = | 22 | weight(s) | = | 1 | ||||
prec(cons) | = | 14 | weight(cons) | = | 1 | ||||
prec(U41) | = | 1 | weight(U41) | = | 0 | ||||
prec(a__U41) | = | 8 | weight(a__U41) | = | 0 | ||||
prec(U51) | = | 2 | weight(U51) | = | 0 | ||||
prec(a__U51) | = | 3 | weight(a__U51) | = | 0 | ||||
prec(U61) | = | 5 | weight(U61) | = | 0 | ||||
prec(a__U61) | = | 11 | weight(a__U61) | = | 0 | ||||
prec(U62) | = | 12 | weight(U62) | = | 0 | ||||
prec(a__U62) | = | 13 | weight(a__U62) | = | 0 |
a__zeros | → | cons(0,zeros) | (1) |
a__U21(tt) | → | tt | (3) |
mark(zeros) | → | a__zeros | (21) |
mark(U11(X)) | → | a__U11(mark(X)) | (22) |
mark(U21(X)) | → | a__U21(mark(X)) | (23) |
mark(U31(X)) | → | a__U31(mark(X)) | (24) |
mark(U41(X1,X2)) | → | a__U41(mark(X1),X2) | (25) |
mark(U42(X)) | → | a__U42(mark(X)) | (26) |
mark(U51(X1,X2)) | → | a__U51(mark(X1),X2) | (28) |
mark(U52(X)) | → | a__U52(mark(X)) | (29) |
mark(U61(X1,X2,X3)) | → | a__U61(mark(X1),X2,X3) | (31) |
mark(U62(X1,X2)) | → | a__U62(mark(X1),X2) | (32) |
mark(length(X)) | → | a__length(mark(X)) | (34) |
mark(cons(X1,X2)) | → | cons(mark(X1),X2) | (35) |
mark(s(X)) | → | s(mark(X)) | (38) |
a__U11(X) | → | U11(X) | (41) |
a__U21(X) | → | U21(X) | (42) |
a__U31(X) | → | U31(X) | (43) |
a__U41(X1,X2) | → | U41(X1,X2) | (44) |
a__U42(X) | → | U42(X) | (45) |
a__U51(X1,X2) | → | U51(X1,X2) | (47) |
a__U52(X) | → | U52(X) | (48) |
a__U61(X1,X2,X3) | → | U61(X1,X2,X3) | (50) |
a__U62(X1,X2) | → | U62(X1,X2) | (51) |
a__length(X) | → | length(X) | (53) |
There are no rules in the TRS. Hence, it is terminating.