The rewrite relation of the following TRS is considered.
There are 101 ruless (increase limit for explicit display).
There are 182 ruless (increase limit for explicit display).
The dependency pairs are split into 21 components.
top#(ok(X)) | → | top#(active(X)) | (252) |
top#(mark(X)) | → | top#(proper(X)) | (139) |
π(U32#) | = | 2 |
π(isNatKind) | = | 1 |
π(isNat#) | = | 1 |
π(plus#) | = | 1 |
π(top#) | = | 1 |
π(proper) | = | 1 |
π(ok) | = | 1 |
π(s#) | = | 1 |
π(isNat) | = | 1 |
π(active) | = | 1 |
π(active#) | = | 1 |
π(U71#) | = | 2 |
π(and#) | = | 2 |
prec(U21) | = | 2 | status(U21) | = | [2, 1] | list-extension(U21) | = | Lex | ||
prec(U11) | = | 3 | status(U11) | = | [2, 3, 1] | list-extension(U11) | = | Lex | ||
prec(s) | = | 5 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(U71) | = | 7 | status(U71) | = | [2, 3, 1] | list-extension(U71) | = | Lex | ||
prec(top) | = | 0 | status(top) | = | [] | list-extension(top) | = | Lex | ||
prec(and) | = | 3 | status(and) | = | [2, 1] | list-extension(and) | = | Lex | ||
prec(U13#) | = | 0 | status(U13#) | = | [] | list-extension(U13#) | = | Lex | ||
prec(U12) | = | 3 | status(U12) | = | [1, 2] | list-extension(U12) | = | Lex | ||
prec(U33#) | = | 0 | status(U33#) | = | [] | list-extension(U33#) | = | Lex | ||
prec(x) | = | 7 | status(x) | = | [2, 1] | list-extension(x) | = | Lex | ||
prec(U12#) | = | 0 | status(U12#) | = | [] | list-extension(U12#) | = | Lex | ||
prec(0) | = | 3 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(x#) | = | 0 | status(x#) | = | [1, 2] | list-extension(x#) | = | Lex | ||
prec(mark) | = | 0 | status(mark) | = | [1] | list-extension(mark) | = | Lex | ||
prec(U32) | = | 3 | status(U32) | = | [1, 2] | list-extension(U32) | = | Lex | ||
prec(U33) | = | 2 | status(U33) | = | [1] | list-extension(U33) | = | Lex | ||
prec(proper#) | = | 0 | status(proper#) | = | [] | list-extension(proper#) | = | Lex | ||
prec(plus) | = | 6 | status(plus) | = | [1, 2] | list-extension(plus) | = | Lex | ||
prec(U61) | = | 3 | status(U61) | = | [1] | list-extension(U61) | = | Lex | ||
prec(U51#) | = | 0 | status(U51#) | = | [2, 3, 1] | list-extension(U51#) | = | Lex | ||
prec(U11#) | = | 0 | status(U11#) | = | [3, 2] | list-extension(U11#) | = | Lex | ||
prec(U31) | = | 4 | status(U31) | = | [2, 1, 3] | list-extension(U31) | = | Lex | ||
prec(U41#) | = | 0 | status(U41#) | = | [2, 1] | list-extension(U41#) | = | Lex | ||
prec(U21#) | = | 0 | status(U21#) | = | [1, 2] | list-extension(U21#) | = | Lex | ||
prec(U22#) | = | 0 | status(U22#) | = | [] | list-extension(U22#) | = | Lex | ||
prec(tt) | = | 0 | status(tt) | = | [] | list-extension(tt) | = | Lex | ||
prec(U13) | = | 1 | status(U13) | = | [1] | list-extension(U13) | = | Lex | ||
prec(U22) | = | 0 | status(U22) | = | [1] | list-extension(U22) | = | Lex | ||
prec(U51) | = | 6 | status(U51) | = | [3, 2, 1] | list-extension(U51) | = | Lex | ||
prec(isNatKind#) | = | 0 | status(isNatKind#) | = | [] | list-extension(isNatKind#) | = | Lex | ||
prec(U41) | = | 5 | status(U41) | = | [2, 1] | list-extension(U41) | = | Lex | ||
prec(U31#) | = | 0 | status(U31#) | = | [2, 1, 3] | list-extension(U31#) | = | Lex | ||
prec(U61#) | = | 0 | status(U61#) | = | [] | list-extension(U61#) | = | Lex |
[U21(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[U11(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[s(x1)] | = | x1 + 0 |
[U71(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[U12#(x1, x2)] | = | max(0) |
[0] | = | 0 |
[x#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[mark(x1)] | = | x1 + 0 |
[U32(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[U33(x1)] | = | x1 + 0 |
[proper#(x1)] | = | 0 |
[plus(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[U61(x1)] | = | x1 + 0 |
[U51#(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U11#(x1, x2, x3)] | = | max(x2 + 0, x3 + 0, 0) |
[U31(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U41#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[U21#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[U22#(x1)] | = | 0 |
[tt] | = | 0 |
[U13(x1)] | = | x1 + 0 |
[U22(x1)] | = | x1 + 0 |
[U51(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[U31#(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U61#(x1)] | = | 0 |
active(isNatKind(0)) | → | mark(tt) | (18) |
U32(mark(X1),X2) | → | mark(U32(X1,X2)) | (50) |
proper(and(X1,X2)) | → | and(proper(X1),proper(X2)) | (80) |
active(U21(tt,V1)) | → | mark(U22(isNat(V1))) | (4) |
active(isNat(plus(V1,V2))) | → | mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2)) | (15) |
active(U33(tt)) | → | mark(tt) | (8) |
s(mark(X)) | → | mark(s(X)) | (54) |
active(U11(tt,V1,V2)) | → | mark(U12(isNat(V1),V2)) | (1) |
proper(0) | → | ok(0) | (77) |
active(U13(tt)) | → | mark(tt) | (3) |
active(isNat(s(V1))) | → | mark(U21(isNatKind(V1),V1)) | (16) |
active(isNatKind(x(V1,V2))) | → | mark(and(isNatKind(V1),isNatKind(V2))) | (21) |
active(s(X)) | → | s(active(X)) | (36) |
proper(U22(X)) | → | U22(proper(X)) | (68) |
U13(ok(X)) | → | ok(U13(X)) | (85) |
active(U11(X1,X2,X3)) | → | U11(active(X1),X2,X3) | (26) |
proper(tt) | → | ok(tt) | (63) |
active(isNatKind(plus(V1,V2))) | → | mark(and(isNatKind(V1),isNatKind(V2))) | (19) |
active(U32(X1,X2)) | → | U32(active(X1),X2) | (32) |
active(isNat(x(V1,V2))) | → | mark(U31(and(isNatKind(V1),isNatKind(V2)),V1,V2)) | (17) |
x(X1,mark(X2)) | → | mark(x(X1,X2)) | (60) |
active(U12(X1,X2)) | → | U12(active(X1),X2) | (27) |
U22(ok(X)) | → | ok(U22(X)) | (87) |
isNat(ok(X)) | → | ok(isNat(X)) | (84) |
active(U41(X1,X2)) | → | U41(active(X1),X2) | (34) |
active(plus(N,0)) | → | mark(U41(and(isNat(N),isNatKind(N)),N)) | (22) |
active(U13(X)) | → | U13(active(X)) | (28) |
proper(isNat(X)) | → | isNat(proper(X)) | (65) |
U11(mark(X1),X2,X3) | → | mark(U11(X1,X2,X3)) | (44) |
active(U22(tt)) | → | mark(tt) | (5) |
proper(U41(X1,X2)) | → | U41(proper(X1),proper(X2)) | (72) |
active(U33(X)) | → | U33(active(X)) | (33) |
proper(U12(X1,X2)) | → | U12(proper(X1),proper(X2)) | (64) |
s(ok(X)) | → | ok(s(X)) | (93) |
U51(ok(X1),ok(X2),ok(X3)) | → | ok(U51(X1,X2,X3)) | (92) |
active(U51(tt,M,N)) | → | mark(s(plus(N,M))) | (10) |
active(U61(X)) | → | U61(active(X)) | (39) |
active(U32(tt,V2)) | → | mark(U33(isNat(V2))) | (7) |
U31(ok(X1),ok(X2),ok(X3)) | → | ok(U31(X1,X2,X3)) | (88) |
active(isNatKind(s(V1))) | → | mark(isNatKind(V1)) | (20) |
active(x(N,s(M))) | → | mark(U71(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)) | (25) |
U31(mark(X1),X2,X3) | → | mark(U31(X1,X2,X3)) | (49) |
U41(mark(X1),X2) | → | mark(U41(X1,X2)) | (52) |
active(U22(X)) | → | U22(active(X)) | (30) |
proper(U11(X1,X2,X3)) | → | U11(proper(X1),proper(X2),proper(X3)) | (62) |
active(isNat(0)) | → | mark(tt) | (14) |
U11(ok(X1),ok(X2),ok(X3)) | → | ok(U11(X1,X2,X3)) | (82) |
U32(ok(X1),ok(X2)) | → | ok(U32(X1,X2)) | (89) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (56) |
proper(x(X1,X2)) | → | x(proper(X1),proper(X2)) | (79) |
active(U31(X1,X2,X3)) | → | U31(active(X1),X2,X3) | (31) |
active(U71(tt,M,N)) | → | mark(plus(x(N,M),N)) | (12) |
proper(U31(X1,X2,X3)) | → | U31(proper(X1),proper(X2),proper(X3)) | (69) |
U71(ok(X1),ok(X2),ok(X3)) | → | ok(U71(X1,X2,X3)) | (96) |
U12(mark(X1),X2) | → | mark(U12(X1,X2)) | (45) |
proper(U71(X1,X2,X3)) | → | U71(proper(X1),proper(X2),proper(X3)) | (78) |
proper(isNatKind(X)) | → | isNatKind(proper(X)) | (81) |
active(plus(N,s(M))) | → | mark(U51(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)) | (23) |
proper(U32(X1,X2)) | → | U32(proper(X1),proper(X2)) | (70) |
active(x(N,0)) | → | mark(U61(and(isNat(N),isNatKind(N)))) | (24) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (94) |
proper(U61(X)) | → | U61(proper(X)) | (76) |
U61(mark(X)) | → | mark(U61(X)) | (57) |
and(ok(X1),ok(X2)) | → | ok(and(X1,X2)) | (98) |
active(U61(tt)) | → | mark(0) | (11) |
active(U41(tt,N)) | → | mark(N) | (9) |
active(and(tt,X)) | → | mark(X) | (13) |
U33(mark(X)) | → | mark(U33(X)) | (51) |
U33(ok(X)) | → | ok(U33(X)) | (90) |
active(U71(X1,X2,X3)) | → | U71(active(X1),X2,X3) | (40) |
proper(U21(X1,X2)) | → | U21(proper(X1),proper(X2)) | (67) |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (55) |
x(mark(X1),X2) | → | mark(x(X1,X2)) | (59) |
active(U31(tt,V1,V2)) | → | mark(U32(isNat(V1),V2)) | (6) |
active(plus(X1,X2)) | → | plus(X1,active(X2)) | (38) |
and(mark(X1),X2) | → | mark(and(X1,X2)) | (61) |
U71(mark(X1),X2,X3) | → | mark(U71(X1,X2,X3)) | (58) |
proper(s(X)) | → | s(proper(X)) | (74) |
proper(plus(X1,X2)) | → | plus(proper(X1),proper(X2)) | (75) |
U22(mark(X)) | → | mark(U22(X)) | (48) |
proper(U33(X)) | → | U33(proper(X)) | (71) |
U51(mark(X1),X2,X3) | → | mark(U51(X1,X2,X3)) | (53) |
U21(mark(X1),X2) | → | mark(U21(X1,X2)) | (47) |
proper(U51(X1,X2,X3)) | → | U51(proper(X1),proper(X2),proper(X3)) | (73) |
U41(ok(X1),ok(X2)) | → | ok(U41(X1,X2)) | (91) |
x(ok(X1),ok(X2)) | → | ok(x(X1,X2)) | (97) |
isNatKind(ok(X)) | → | ok(isNatKind(X)) | (99) |
active(plus(X1,X2)) | → | plus(active(X1),X2) | (37) |
active(x(X1,X2)) | → | x(active(X1),X2) | (41) |
U61(ok(X)) | → | ok(U61(X)) | (95) |
active(x(X1,X2)) | → | x(X1,active(X2)) | (42) |
U13(mark(X)) | → | mark(U13(X)) | (46) |
proper(U13(X)) | → | U13(proper(X)) | (66) |
U12(ok(X1),ok(X2)) | → | ok(U12(X1,X2)) | (83) |
active(U51(X1,X2,X3)) | → | U51(active(X1),X2,X3) | (35) |
active(U21(X1,X2)) | → | U21(active(X1),X2) | (29) |
active(and(X1,X2)) | → | and(active(X1),X2) | (43) |
U21(ok(X1),ok(X2)) | → | ok(U21(X1,X2)) | (86) |
active(U12(tt,V2)) | → | mark(U13(isNat(V2))) | (2) |
top#(mark(X)) | → | top#(proper(X)) | (139) |
The dependency pairs are split into 1 component.
top#(ok(X)) | → | top#(active(X)) | (252) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | x1 + 0 |
[U21(x1, x2)] | = | x2 + 0 |
[U11(x1, x2, x3)] | = | x3 + 0 |
[s(x1)] | = | x1 + 0 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + 0 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 0 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | x1 + 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | x1 + 0 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | x1 + 0 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 3 |
[ok(x1)] | = | x1 + 2 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | 0 |
[U32(x1, x2)] | = | x2 + 0 |
[U33(x1)] | = | x1 + 0 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | x1 + 0 |
[plus(x1, x2)] | = | x1 + 0 |
[U61(x1)] | = | x1 + 0 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1, x2, x3)] | = | x1 + 0 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | x1 + 0 |
[U22(x1)] | = | x1 + 0 |
[U51(x1, x2, x3)] | = | x3 + 0 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x1 + 0 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
active(isNatKind(0)) | → | mark(tt) | (18) |
U32(mark(X1),X2) | → | mark(U32(X1,X2)) | (50) |
proper(and(X1,X2)) | → | and(proper(X1),proper(X2)) | (80) |
active(U21(tt,V1)) | → | mark(U22(isNat(V1))) | (4) |
active(isNat(plus(V1,V2))) | → | mark(U11(and(isNatKind(V1),isNatKind(V2)),V1,V2)) | (15) |
active(U33(tt)) | → | mark(tt) | (8) |
s(mark(X)) | → | mark(s(X)) | (54) |
active(U11(tt,V1,V2)) | → | mark(U12(isNat(V1),V2)) | (1) |
proper(0) | → | ok(0) | (77) |
active(U13(tt)) | → | mark(tt) | (3) |
active(isNat(s(V1))) | → | mark(U21(isNatKind(V1),V1)) | (16) |
active(isNatKind(x(V1,V2))) | → | mark(and(isNatKind(V1),isNatKind(V2))) | (21) |
active(s(X)) | → | s(active(X)) | (36) |
proper(U22(X)) | → | U22(proper(X)) | (68) |
U13(ok(X)) | → | ok(U13(X)) | (85) |
active(U11(X1,X2,X3)) | → | U11(active(X1),X2,X3) | (26) |
proper(tt) | → | ok(tt) | (63) |
active(isNatKind(plus(V1,V2))) | → | mark(and(isNatKind(V1),isNatKind(V2))) | (19) |
active(U32(X1,X2)) | → | U32(active(X1),X2) | (32) |
active(isNat(x(V1,V2))) | → | mark(U31(and(isNatKind(V1),isNatKind(V2)),V1,V2)) | (17) |
x(X1,mark(X2)) | → | mark(x(X1,X2)) | (60) |
active(U12(X1,X2)) | → | U12(active(X1),X2) | (27) |
U22(ok(X)) | → | ok(U22(X)) | (87) |
isNat(ok(X)) | → | ok(isNat(X)) | (84) |
active(U41(X1,X2)) | → | U41(active(X1),X2) | (34) |
active(plus(N,0)) | → | mark(U41(and(isNat(N),isNatKind(N)),N)) | (22) |
active(U13(X)) | → | U13(active(X)) | (28) |
proper(isNat(X)) | → | isNat(proper(X)) | (65) |
U11(mark(X1),X2,X3) | → | mark(U11(X1,X2,X3)) | (44) |
active(U22(tt)) | → | mark(tt) | (5) |
proper(U41(X1,X2)) | → | U41(proper(X1),proper(X2)) | (72) |
active(U33(X)) | → | U33(active(X)) | (33) |
proper(U12(X1,X2)) | → | U12(proper(X1),proper(X2)) | (64) |
s(ok(X)) | → | ok(s(X)) | (93) |
U51(ok(X1),ok(X2),ok(X3)) | → | ok(U51(X1,X2,X3)) | (92) |
active(U51(tt,M,N)) | → | mark(s(plus(N,M))) | (10) |
active(U61(X)) | → | U61(active(X)) | (39) |
active(U32(tt,V2)) | → | mark(U33(isNat(V2))) | (7) |
U31(ok(X1),ok(X2),ok(X3)) | → | ok(U31(X1,X2,X3)) | (88) |
active(isNatKind(s(V1))) | → | mark(isNatKind(V1)) | (20) |
active(x(N,s(M))) | → | mark(U71(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)) | (25) |
U31(mark(X1),X2,X3) | → | mark(U31(X1,X2,X3)) | (49) |
U41(mark(X1),X2) | → | mark(U41(X1,X2)) | (52) |
active(U22(X)) | → | U22(active(X)) | (30) |
proper(U11(X1,X2,X3)) | → | U11(proper(X1),proper(X2),proper(X3)) | (62) |
active(isNat(0)) | → | mark(tt) | (14) |
U11(ok(X1),ok(X2),ok(X3)) | → | ok(U11(X1,X2,X3)) | (82) |
U32(ok(X1),ok(X2)) | → | ok(U32(X1,X2)) | (89) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (56) |
proper(x(X1,X2)) | → | x(proper(X1),proper(X2)) | (79) |
active(U31(X1,X2,X3)) | → | U31(active(X1),X2,X3) | (31) |
active(U71(tt,M,N)) | → | mark(plus(x(N,M),N)) | (12) |
proper(U31(X1,X2,X3)) | → | U31(proper(X1),proper(X2),proper(X3)) | (69) |
U71(ok(X1),ok(X2),ok(X3)) | → | ok(U71(X1,X2,X3)) | (96) |
U12(mark(X1),X2) | → | mark(U12(X1,X2)) | (45) |
proper(U71(X1,X2,X3)) | → | U71(proper(X1),proper(X2),proper(X3)) | (78) |
proper(isNatKind(X)) | → | isNatKind(proper(X)) | (81) |
active(plus(N,s(M))) | → | mark(U51(and(and(isNat(M),isNatKind(M)),and(isNat(N),isNatKind(N))),M,N)) | (23) |
proper(U32(X1,X2)) | → | U32(proper(X1),proper(X2)) | (70) |
active(x(N,0)) | → | mark(U61(and(isNat(N),isNatKind(N)))) | (24) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (94) |
proper(U61(X)) | → | U61(proper(X)) | (76) |
U61(mark(X)) | → | mark(U61(X)) | (57) |
and(ok(X1),ok(X2)) | → | ok(and(X1,X2)) | (98) |
active(U61(tt)) | → | mark(0) | (11) |
active(U41(tt,N)) | → | mark(N) | (9) |
active(and(tt,X)) | → | mark(X) | (13) |
U33(mark(X)) | → | mark(U33(X)) | (51) |
U33(ok(X)) | → | ok(U33(X)) | (90) |
active(U71(X1,X2,X3)) | → | U71(active(X1),X2,X3) | (40) |
proper(U21(X1,X2)) | → | U21(proper(X1),proper(X2)) | (67) |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (55) |
x(mark(X1),X2) | → | mark(x(X1,X2)) | (59) |
active(U31(tt,V1,V2)) | → | mark(U32(isNat(V1),V2)) | (6) |
active(plus(X1,X2)) | → | plus(X1,active(X2)) | (38) |
and(mark(X1),X2) | → | mark(and(X1,X2)) | (61) |
U71(mark(X1),X2,X3) | → | mark(U71(X1,X2,X3)) | (58) |
proper(s(X)) | → | s(proper(X)) | (74) |
proper(plus(X1,X2)) | → | plus(proper(X1),proper(X2)) | (75) |
U22(mark(X)) | → | mark(U22(X)) | (48) |
proper(U33(X)) | → | U33(proper(X)) | (71) |
U51(mark(X1),X2,X3) | → | mark(U51(X1,X2,X3)) | (53) |
U21(mark(X1),X2) | → | mark(U21(X1,X2)) | (47) |
proper(U51(X1,X2,X3)) | → | U51(proper(X1),proper(X2),proper(X3)) | (73) |
U41(ok(X1),ok(X2)) | → | ok(U41(X1,X2)) | (91) |
x(ok(X1),ok(X2)) | → | ok(x(X1,X2)) | (97) |
isNatKind(ok(X)) | → | ok(isNatKind(X)) | (99) |
active(plus(X1,X2)) | → | plus(active(X1),X2) | (37) |
active(x(X1,X2)) | → | x(active(X1),X2) | (41) |
U61(ok(X)) | → | ok(U61(X)) | (95) |
active(x(X1,X2)) | → | x(X1,active(X2)) | (42) |
U13(mark(X)) | → | mark(U13(X)) | (46) |
proper(U13(X)) | → | U13(proper(X)) | (66) |
U12(ok(X1),ok(X2)) | → | ok(U12(X1,X2)) | (83) |
active(U51(X1,X2,X3)) | → | U51(active(X1),X2,X3) | (35) |
active(U21(X1,X2)) | → | U21(active(X1),X2) | (29) |
active(and(X1,X2)) | → | and(active(X1),X2) | (43) |
U21(ok(X1),ok(X2)) | → | ok(U21(X1,X2)) | (86) |
active(U12(tt,V2)) | → | mark(U13(isNat(V2))) | (2) |
top#(ok(X)) | → | top#(active(X)) | (252) |
The dependency pairs are split into 0 components.
proper#(U41(X1,X2)) | → | proper#(X1) | (199) |
proper#(U41(X1,X2)) | → | proper#(X2) | (196) |
proper#(U51(X1,X2,X3)) | → | proper#(X1) | (195) |
proper#(U31(X1,X2,X3)) | → | proper#(X1) | (187) |
proper#(isNat(X)) | → | proper#(X) | (186) |
proper#(and(X1,X2)) | → | proper#(X1) | (273) |
proper#(U61(X)) | → | proper#(X) | (184) |
proper#(U33(X)) | → | proper#(X) | (181) |
proper#(U13(X)) | → | proper#(X) | (180) |
proper#(U71(X1,X2,X3)) | → | proper#(X3) | (175) |
proper#(U12(X1,X2)) | → | proper#(X1) | (265) |
proper#(U71(X1,X2,X3)) | → | proper#(X2) | (262) |
proper#(U71(X1,X2,X3)) | → | proper#(X1) | (164) |
proper#(and(X1,X2)) | → | proper#(X2) | (253) |
proper#(U11(X1,X2,X3)) | → | proper#(X3) | (251) |
proper#(U11(X1,X2,X3)) | → | proper#(X1) | (161) |
proper#(U51(X1,X2,X3)) | → | proper#(X2) | (250) |
proper#(U32(X1,X2)) | → | proper#(X1) | (247) |
proper#(U12(X1,X2)) | → | proper#(X2) | (245) |
proper#(U51(X1,X2,X3)) | → | proper#(X3) | (232) |
proper#(U31(X1,X2,X3)) | → | proper#(X3) | (229) |
proper#(isNatKind(X)) | → | proper#(X) | (134) |
proper#(plus(X1,X2)) | → | proper#(X1) | (227) |
proper#(U21(X1,X2)) | → | proper#(X2) | (129) |
proper#(U21(X1,X2)) | → | proper#(X1) | (123) |
proper#(U22(X)) | → | proper#(X) | (217) |
proper#(U11(X1,X2,X3)) | → | proper#(X2) | (118) |
proper#(s(X)) | → | proper#(X) | (116) |
proper#(U32(X1,X2)) | → | proper#(X2) | (214) |
proper#(x(X1,X2)) | → | proper#(X2) | (213) |
proper#(x(X1,X2)) | → | proper#(X1) | (210) |
proper#(U31(X1,X2,X3)) | → | proper#(X2) | (107) |
proper#(plus(X1,X2)) | → | proper#(X2) | (106) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | x1 + 1 |
[U21(x1, x2)] | = | x1 + x2 + 1 |
[U11(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[s(x1)] | = | x1 + 9 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + x3 + 5 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 1 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | x1 + x2 + 1 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | x1 + x2 + 3 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | x1 + 12820 |
[ok(x1)] | = | 1192 |
[0] | = | 2 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[U32(x1, x2)] | = | x1 + x2 + 1 |
[U33(x1)] | = | x1 + 1 |
[proper#(x1)] | = | x1 + 0 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + x2 + 3 |
[U61(x1)] | = | x1 + 1 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[U31(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | x1 + 1 |
[U22(x1)] | = | x1 + 1 |
[U51(x1, x2, x3)] | = | x1 + x2 + x3 + 11 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x1 + x2 + 1 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
active(isNatKind(0)) | → | mark(tt) | (18) |
U32(mark(X1),X2) | → | mark(U32(X1,X2)) | (50) |
active(U21(tt,V1)) | → | mark(U22(isNat(V1))) | (4) |
active(U33(tt)) | → | mark(tt) | (8) |
s(mark(X)) | → | mark(s(X)) | (54) |
active(U11(tt,V1,V2)) | → | mark(U12(isNat(V1),V2)) | (1) |
proper(0) | → | ok(0) | (77) |
active(U13(tt)) | → | mark(tt) | (3) |
active(isNatKind(x(V1,V2))) | → | mark(and(isNatKind(V1),isNatKind(V2))) | (21) |
U13(ok(X)) | → | ok(U13(X)) | (85) |
proper(tt) | → | ok(tt) | (63) |
active(isNatKind(plus(V1,V2))) | → | mark(and(isNatKind(V1),isNatKind(V2))) | (19) |
x(X1,mark(X2)) | → | mark(x(X1,X2)) | (60) |
U22(ok(X)) | → | ok(U22(X)) | (87) |
isNat(ok(X)) | → | ok(isNat(X)) | (84) |
U11(mark(X1),X2,X3) | → | mark(U11(X1,X2,X3)) | (44) |
active(U22(tt)) | → | mark(tt) | (5) |
s(ok(X)) | → | ok(s(X)) | (93) |
active(U51(tt,M,N)) | → | mark(s(plus(N,M))) | (10) |
active(U32(tt,V2)) | → | mark(U33(isNat(V2))) | (7) |
U31(ok(X1),ok(X2),ok(X3)) | → | ok(U31(X1,X2,X3)) | (88) |
active(isNatKind(s(V1))) | → | mark(isNatKind(V1)) | (20) |
U31(mark(X1),X2,X3) | → | mark(U31(X1,X2,X3)) | (49) |
U41(mark(X1),X2) | → | mark(U41(X1,X2)) | (52) |
active(isNat(0)) | → | mark(tt) | (14) |
U11(ok(X1),ok(X2),ok(X3)) | → | ok(U11(X1,X2,X3)) | (82) |
U32(ok(X1),ok(X2)) | → | ok(U32(X1,X2)) | (89) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (56) |
U71(ok(X1),ok(X2),ok(X3)) | → | ok(U71(X1,X2,X3)) | (96) |
U12(mark(X1),X2) | → | mark(U12(X1,X2)) | (45) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (94) |
U61(mark(X)) | → | mark(U61(X)) | (57) |
and(ok(X1),ok(X2)) | → | ok(and(X1,X2)) | (98) |
active(U61(tt)) | → | mark(0) | (11) |
active(U41(tt,N)) | → | mark(N) | (9) |
active(and(tt,X)) | → | mark(X) | (13) |
U33(mark(X)) | → | mark(U33(X)) | (51) |
U33(ok(X)) | → | ok(U33(X)) | (90) |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (55) |
x(mark(X1),X2) | → | mark(x(X1,X2)) | (59) |
active(U31(tt,V1,V2)) | → | mark(U32(isNat(V1),V2)) | (6) |
and(mark(X1),X2) | → | mark(and(X1,X2)) | (61) |
U71(mark(X1),X2,X3) | → | mark(U71(X1,X2,X3)) | (58) |
U22(mark(X)) | → | mark(U22(X)) | (48) |
U21(mark(X1),X2) | → | mark(U21(X1,X2)) | (47) |
U41(ok(X1),ok(X2)) | → | ok(U41(X1,X2)) | (91) |
x(ok(X1),ok(X2)) | → | ok(x(X1,X2)) | (97) |
isNatKind(ok(X)) | → | ok(isNatKind(X)) | (99) |
U61(ok(X)) | → | ok(U61(X)) | (95) |
U13(mark(X)) | → | mark(U13(X)) | (46) |
U12(ok(X1),ok(X2)) | → | ok(U12(X1,X2)) | (83) |
U21(ok(X1),ok(X2)) | → | ok(U21(X1,X2)) | (86) |
active(U12(tt,V2)) | → | mark(U13(isNat(V2))) | (2) |
proper#(U41(X1,X2)) | → | proper#(X1) | (199) |
proper#(U41(X1,X2)) | → | proper#(X2) | (196) |
proper#(U51(X1,X2,X3)) | → | proper#(X1) | (195) |
proper#(U31(X1,X2,X3)) | → | proper#(X1) | (187) |
proper#(isNat(X)) | → | proper#(X) | (186) |
proper#(and(X1,X2)) | → | proper#(X1) | (273) |
proper#(U61(X)) | → | proper#(X) | (184) |
proper#(U33(X)) | → | proper#(X) | (181) |
proper#(U13(X)) | → | proper#(X) | (180) |
proper#(U71(X1,X2,X3)) | → | proper#(X3) | (175) |
proper#(U12(X1,X2)) | → | proper#(X1) | (265) |
proper#(U71(X1,X2,X3)) | → | proper#(X2) | (262) |
proper#(U71(X1,X2,X3)) | → | proper#(X1) | (164) |
proper#(and(X1,X2)) | → | proper#(X2) | (253) |
proper#(U11(X1,X2,X3)) | → | proper#(X3) | (251) |
proper#(U11(X1,X2,X3)) | → | proper#(X1) | (161) |
proper#(U51(X1,X2,X3)) | → | proper#(X2) | (250) |
proper#(U32(X1,X2)) | → | proper#(X1) | (247) |
proper#(U12(X1,X2)) | → | proper#(X2) | (245) |
proper#(U51(X1,X2,X3)) | → | proper#(X3) | (232) |
proper#(U31(X1,X2,X3)) | → | proper#(X3) | (229) |
proper#(isNatKind(X)) | → | proper#(X) | (134) |
proper#(plus(X1,X2)) | → | proper#(X1) | (227) |
proper#(U21(X1,X2)) | → | proper#(X2) | (129) |
proper#(U21(X1,X2)) | → | proper#(X1) | (123) |
proper#(U22(X)) | → | proper#(X) | (217) |
proper#(U11(X1,X2,X3)) | → | proper#(X2) | (118) |
proper#(s(X)) | → | proper#(X) | (116) |
proper#(U32(X1,X2)) | → | proper#(X2) | (214) |
proper#(x(X1,X2)) | → | proper#(X2) | (213) |
proper#(x(X1,X2)) | → | proper#(X1) | (210) |
proper#(U31(X1,X2,X3)) | → | proper#(X2) | (107) |
proper#(plus(X1,X2)) | → | proper#(X2) | (106) |
The dependency pairs are split into 0 components.
active#(x(X1,X2)) | → | active#(X1) | (282) |
active#(U71(X1,X2,X3)) | → | active#(X1) | (281) |
active#(U22(X)) | → | active#(X) | (276) |
active#(U12(X1,X2)) | → | active#(X1) | (275) |
active#(x(X1,X2)) | → | active#(X2) | (274) |
active#(s(X)) | → | active#(X) | (182) |
active#(U41(X1,X2)) | → | active#(X1) | (271) |
active#(U32(X1,X2)) | → | active#(X1) | (269) |
active#(U61(X)) | → | active#(X) | (174) |
active#(U51(X1,X2,X3)) | → | active#(X1) | (159) |
active#(U13(X)) | → | active#(X) | (248) |
active#(U31(X1,X2,X3)) | → | active#(X1) | (154) |
active#(U11(X1,X2,X3)) | → | active#(X1) | (231) |
active#(U33(X)) | → | active#(X) | (225) |
active#(and(X1,X2)) | → | active#(X1) | (219) |
active#(plus(X1,X2)) | → | active#(X2) | (115) |
active#(U21(X1,X2)) | → | active#(X1) | (205) |
active#(plus(X1,X2)) | → | active#(X1) | (200) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | x1 + 1 |
[U21(x1, x2)] | = | x1 + x2 + 6 |
[U11(x1, x2, x3)] | = | x1 + x2 + x3 + 322 |
[s(x1)] | = | x1 + 2443 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + x3 + 496 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 1 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | x1 + x2 + 1 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | x1 + x2 + 3 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | 1 |
[0] | = | 3 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[U32(x1, x2)] | = | x1 + x2 + 1 |
[U33(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + x2 + 494 |
[U61(x1)] | = | x1 + 2 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[U31(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | x1 + 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | x1 + 1 |
[U22(x1)] | = | x1 + 4 |
[U51(x1, x2, x3)] | = | x1 + x2 + x3 + 3001 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x1 + x2 + 1 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
active(isNatKind(0)) | → | mark(tt) | (18) |
U32(mark(X1),X2) | → | mark(U32(X1,X2)) | (50) |
active(U21(tt,V1)) | → | mark(U22(isNat(V1))) | (4) |
active(U33(tt)) | → | mark(tt) | (8) |
s(mark(X)) | → | mark(s(X)) | (54) |
active(U11(tt,V1,V2)) | → | mark(U12(isNat(V1),V2)) | (1) |
proper(0) | → | ok(0) | (77) |
active(U13(tt)) | → | mark(tt) | (3) |
active(isNatKind(x(V1,V2))) | → | mark(and(isNatKind(V1),isNatKind(V2))) | (21) |
U13(ok(X)) | → | ok(U13(X)) | (85) |
proper(tt) | → | ok(tt) | (63) |
active(isNatKind(plus(V1,V2))) | → | mark(and(isNatKind(V1),isNatKind(V2))) | (19) |
x(X1,mark(X2)) | → | mark(x(X1,X2)) | (60) |
U22(ok(X)) | → | ok(U22(X)) | (87) |
isNat(ok(X)) | → | ok(isNat(X)) | (84) |
U11(mark(X1),X2,X3) | → | mark(U11(X1,X2,X3)) | (44) |
active(U22(tt)) | → | mark(tt) | (5) |
s(ok(X)) | → | ok(s(X)) | (93) |
active(U51(tt,M,N)) | → | mark(s(plus(N,M))) | (10) |
active(U32(tt,V2)) | → | mark(U33(isNat(V2))) | (7) |
U31(ok(X1),ok(X2),ok(X3)) | → | ok(U31(X1,X2,X3)) | (88) |
active(isNatKind(s(V1))) | → | mark(isNatKind(V1)) | (20) |
U31(mark(X1),X2,X3) | → | mark(U31(X1,X2,X3)) | (49) |
U41(mark(X1),X2) | → | mark(U41(X1,X2)) | (52) |
active(isNat(0)) | → | mark(tt) | (14) |
U11(ok(X1),ok(X2),ok(X3)) | → | ok(U11(X1,X2,X3)) | (82) |
U32(ok(X1),ok(X2)) | → | ok(U32(X1,X2)) | (89) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (56) |
U71(ok(X1),ok(X2),ok(X3)) | → | ok(U71(X1,X2,X3)) | (96) |
U12(mark(X1),X2) | → | mark(U12(X1,X2)) | (45) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (94) |
U61(mark(X)) | → | mark(U61(X)) | (57) |
and(ok(X1),ok(X2)) | → | ok(and(X1,X2)) | (98) |
active(U61(tt)) | → | mark(0) | (11) |
active(U41(tt,N)) | → | mark(N) | (9) |
active(and(tt,X)) | → | mark(X) | (13) |
U33(mark(X)) | → | mark(U33(X)) | (51) |
U33(ok(X)) | → | ok(U33(X)) | (90) |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (55) |
x(mark(X1),X2) | → | mark(x(X1,X2)) | (59) |
active(U31(tt,V1,V2)) | → | mark(U32(isNat(V1),V2)) | (6) |
and(mark(X1),X2) | → | mark(and(X1,X2)) | (61) |
U71(mark(X1),X2,X3) | → | mark(U71(X1,X2,X3)) | (58) |
U22(mark(X)) | → | mark(U22(X)) | (48) |
U21(mark(X1),X2) | → | mark(U21(X1,X2)) | (47) |
U41(ok(X1),ok(X2)) | → | ok(U41(X1,X2)) | (91) |
x(ok(X1),ok(X2)) | → | ok(x(X1,X2)) | (97) |
isNatKind(ok(X)) | → | ok(isNatKind(X)) | (99) |
U61(ok(X)) | → | ok(U61(X)) | (95) |
U13(mark(X)) | → | mark(U13(X)) | (46) |
U12(ok(X1),ok(X2)) | → | ok(U12(X1,X2)) | (83) |
U21(ok(X1),ok(X2)) | → | ok(U21(X1,X2)) | (86) |
active(U12(tt,V2)) | → | mark(U13(isNat(V2))) | (2) |
active#(x(X1,X2)) | → | active#(X1) | (282) |
active#(U71(X1,X2,X3)) | → | active#(X1) | (281) |
active#(U22(X)) | → | active#(X) | (276) |
active#(U12(X1,X2)) | → | active#(X1) | (275) |
active#(x(X1,X2)) | → | active#(X2) | (274) |
active#(s(X)) | → | active#(X) | (182) |
active#(U41(X1,X2)) | → | active#(X1) | (271) |
active#(U32(X1,X2)) | → | active#(X1) | (269) |
active#(U61(X)) | → | active#(X) | (174) |
active#(U51(X1,X2,X3)) | → | active#(X1) | (159) |
active#(U13(X)) | → | active#(X) | (248) |
active#(U31(X1,X2,X3)) | → | active#(X1) | (154) |
active#(U11(X1,X2,X3)) | → | active#(X1) | (231) |
active#(U33(X)) | → | active#(X) | (225) |
active#(and(X1,X2)) | → | active#(X1) | (219) |
active#(plus(X1,X2)) | → | active#(X2) | (115) |
active#(U21(X1,X2)) | → | active#(X1) | (205) |
active#(plus(X1,X2)) | → | active#(X1) | (200) |
The dependency pairs are split into 0 components.
U51#(ok(X1),ok(X2),ok(X3)) | → | U51#(X1,X2,X3) | (272) |
U51#(mark(X1),X2,X3) | → | U51#(X1,X2,X3) | (105) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | 1 |
[U21(x1, x2)] | = | x1 + x2 + 0 |
[U11(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[s(x1)] | = | x1 + 3 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + x3 + 0 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + 0 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | x2 + 1 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | x1 + x2 + 1 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[U32(x1, x2)] | = | x2 + 2 |
[U33(x1)] | = | 1 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x2 + 0 |
[U61(x1)] | = | x1 + 1 |
[U51#(x1, x2, x3)] | = | x1 + x2 + x3 + 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 3 |
[U31(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | x1 + 1 |
[U22(x1)] | = | x1 + 0 |
[U51(x1, x2, x3)] | = | x1 + x2 + x3 + 13779 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x2 + 1 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
active(isNatKind(0)) | → | mark(tt) | (18) |
active(U33(tt)) | → | mark(tt) | (8) |
s(mark(X)) | → | mark(s(X)) | (54) |
proper(0) | → | ok(0) | (77) |
active(U13(tt)) | → | mark(tt) | (3) |
U13(ok(X)) | → | ok(U13(X)) | (85) |
proper(tt) | → | ok(tt) | (63) |
x(X1,mark(X2)) | → | mark(x(X1,X2)) | (60) |
U22(ok(X)) | → | ok(U22(X)) | (87) |
isNat(ok(X)) | → | ok(isNat(X)) | (84) |
U11(mark(X1),X2,X3) | → | mark(U11(X1,X2,X3)) | (44) |
active(U22(tt)) | → | mark(tt) | (5) |
s(ok(X)) | → | ok(s(X)) | (93) |
U31(ok(X1),ok(X2),ok(X3)) | → | ok(U31(X1,X2,X3)) | (88) |
U31(mark(X1),X2,X3) | → | mark(U31(X1,X2,X3)) | (49) |
active(isNat(0)) | → | mark(tt) | (14) |
U11(ok(X1),ok(X2),ok(X3)) | → | ok(U11(X1,X2,X3)) | (82) |
U71(ok(X1),ok(X2),ok(X3)) | → | ok(U71(X1,X2,X3)) | (96) |
U61(mark(X)) | → | mark(U61(X)) | (57) |
active(U61(tt)) | → | mark(0) | (11) |
x(mark(X1),X2) | → | mark(x(X1,X2)) | (59) |
U71(mark(X1),X2,X3) | → | mark(U71(X1,X2,X3)) | (58) |
U22(mark(X)) | → | mark(U22(X)) | (48) |
x(ok(X1),ok(X2)) | → | ok(x(X1,X2)) | (97) |
U61(ok(X)) | → | ok(U61(X)) | (95) |
U13(mark(X)) | → | mark(U13(X)) | (46) |
U51#(ok(X1),ok(X2),ok(X3)) | → | U51#(X1,X2,X3) | (272) |
U51#(mark(X1),X2,X3) | → | U51#(X1,X2,X3) | (105) |
The dependency pairs are split into 0 components.
x#(X1,mark(X2)) | → | x#(X1,X2) | (155) |
x#(ok(X1),ok(X2)) | → | x#(X1,X2) | (224) |
x#(mark(X1),X2) | → | x#(X1,X2) | (220) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | x1 + 1 |
[U21(x1, x2)] | = | 29346 |
[U11(x1, x2, x3)] | = | 27135 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + x3 + 17534 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 1 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | 2 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | x1 + x2 + 1 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 7942 |
[x#(x1, x2)] | = | x1 + 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 10310 |
[U32(x1, x2)] | = | x1 + x2 + 32056 |
[U33(x1)] | = | x1 + 43646 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | x1 + 25029 |
[plus(x1, x2)] | = | x2 + 20438 |
[U61(x1)] | = | x1 + 1 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | x3 + 5723 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | 2 |
[U22(x1)] | = | 8731 |
[U51(x1, x2, x3)] | = | x1 + x2 + 58195 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x2 + 24762 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
x#(ok(X1),ok(X2)) | → | x#(X1,X2) | (224) |
x#(mark(X1),X2) | → | x#(X1,X2) | (220) |
The dependency pairs are split into 1 component.
x#(X1,mark(X2)) | → | x#(X1,X2) | (155) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | 2 |
[U21(x1, x2)] | = | 2 |
[U11(x1, x2, x3)] | = | 2 |
[s(x1)] | = | 3 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x2 + x3 + 2 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + 20804 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | x2 + 12146 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | x1 + 17838 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | 3 |
[0] | = | 1 |
[x#(x1, x2)] | = | x2 + 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 2 |
[U32(x1, x2)] | = | 2 |
[U33(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x2 + 2 |
[U61(x1)] | = | x1 + 1 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | x1 + x3 + 5722 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | 2 |
[U22(x1)] | = | 2 |
[U51(x1, x2, x3)] | = | 2 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x2 + 2 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
isNat(ok(X)) | → | ok(isNat(X)) | (84) |
and(ok(X1),ok(X2)) | → | ok(and(X1,X2)) | (98) |
and(mark(X1),X2) | → | mark(and(X1,X2)) | (61) |
x#(X1,mark(X2)) | → | x#(X1,X2) | (155) |
The dependency pairs are split into 0 components.
U71#(ok(X1),ok(X2),ok(X3)) | → | U71#(X1,X2,X3) | (280) |
U71#(mark(X1),X2,X3) | → | U71#(X1,X2,X3) | (141) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | 1 |
[U21(x1, x2)] | = | x1 + x2 + 36870 |
[U11(x1, x2, x3)] | = | 11681 |
[s(x1)] | = | x1 + 0 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + x3 + 195 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 1 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | x1 + 27878 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | x2 + 111395 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 2 |
[0] | = | 481 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | 111395 |
[U32(x1, x2)] | = | x1 + x2 + 33552 |
[U33(x1)] | = | 9312 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 1 |
[plus(x1, x2)] | = | 1 |
[U61(x1)] | = | 111395 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | x1 + 35333 |
[U31(x1, x2, x3)] | = | x2 + x3 + 111395 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 39191 |
[U71#(x1, x2, x3)] | = | x2 + 0 |
[U13(x1)] | = | x1 + 32021 |
[U22(x1)] | = | x1 + 32257 |
[U51(x1, x2, x3)] | = | 16527 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x2 + 32223 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
and(ok(X1),ok(X2)) | → | ok(and(X1,X2)) | (98) |
and(mark(X1),X2) | → | mark(and(X1,X2)) | (61) |
U71#(ok(X1),ok(X2),ok(X3)) | → | U71#(X1,X2,X3) | (280) |
The dependency pairs are split into 1 component.
U71#(mark(X1),X2,X3) | → | U71#(X1,X2,X3) | (141) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | 1 |
[U21(x1, x2)] | = | x1 + x2 + 1 |
[U11(x1, x2, x3)] | = | 1 |
[s(x1)] | = | x1 + 24377 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + 1 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 0 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | x1 + 2 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | x2 + 0 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 2 |
[0] | = | 9924 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 3 |
[U32(x1, x2)] | = | x1 + x2 + 1 |
[U33(x1)] | = | 1 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 1 |
[plus(x1, x2)] | = | 1 |
[U61(x1)] | = | 1 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1, x2, x3)] | = | x2 + x3 + 1 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | x1 + 0 |
[U13(x1)] | = | x1 + 1 |
[U22(x1)] | = | x1 + 0 |
[U51(x1, x2, x3)] | = | 910 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x2 + 1 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
and(ok(X1),ok(X2)) | → | ok(and(X1,X2)) | (98) |
and(mark(X1),X2) | → | mark(and(X1,X2)) | (61) |
U71#(mark(X1),X2,X3) | → | U71#(X1,X2,X3) | (141) |
The dependency pairs are split into 0 components.
U61#(mark(X)) | → | U61#(X) | (266) |
U61#(ok(X)) | → | U61#(X) | (259) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | 1 |
[U21(x1, x2)] | = | x1 + x2 + 1 |
[U11(x1, x2, x3)] | = | x1 + 1 |
[s(x1)] | = | x1 + 45888 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + 2 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 1 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | x1 + 1 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | x2 + 0 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 2 |
[0] | = | 3740 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 3 |
[U32(x1, x2)] | = | x1 + x2 + 1 |
[U33(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 1 |
[plus(x1, x2)] | = | 1 |
[U61(x1)] | = | 1 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1, x2, x3)] | = | x2 + x3 + 1 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 0 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | x1 + 1 |
[U22(x1)] | = | x1 + 1 |
[U51(x1, x2, x3)] | = | 1 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x2 + 1 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | x1 + 0 |
and(ok(X1),ok(X2)) | → | ok(and(X1,X2)) | (98) |
and(mark(X1),X2) | → | mark(and(X1,X2)) | (61) |
U61#(mark(X)) | → | U61#(X) | (266) |
U61#(ok(X)) | → | U61#(X) | (259) |
The dependency pairs are split into 0 components.
plus#(mark(X1),X2) | → | plus#(X1,X2) | (176) |
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (167) |
plus#(ok(X1),ok(X2)) | → | plus#(X1,X2) | (163) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | 1 |
[U21(x1, x2)] | = | x1 + x2 + 1 |
[U11(x1, x2, x3)] | = | x1 + 1 |
[s(x1)] | = | x1 + 176066 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + 1 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 44015 |
[plus#(x1, x2)] | = | x2 + 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | x1 + 1 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | x2 + 0 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 2 |
[0] | = | 44017 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 82079 |
[U32(x1, x2)] | = | x1 + x2 + 1 |
[U33(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 1 |
[plus(x1, x2)] | = | 1 |
[U61(x1)] | = | 1 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | x1 + 38063 |
[U31(x1, x2, x3)] | = | x2 + x3 + 1 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 0 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | x1 + 1 |
[U22(x1)] | = | x1 + 7506 |
[U51(x1, x2, x3)] | = | 1671 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x2 + 2189 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
and(ok(X1),ok(X2)) | → | ok(and(X1,X2)) | (98) |
and(mark(X1),X2) | → | mark(and(X1,X2)) | (61) |
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (167) |
plus#(ok(X1),ok(X2)) | → | plus#(X1,X2) | (163) |
The dependency pairs are split into 1 component.
plus#(mark(X1),X2) | → | plus#(X1,X2) | (176) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | 1 |
[U21(x1, x2)] | = | x1 + 1 |
[U11(x1, x2, x3)] | = | 1 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + 2 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 1 |
[plus#(x1, x2)] | = | x1 + 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | x1 + 0 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | 25801 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 0 |
[0] | = | 2 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 6774 |
[U32(x1, x2)] | = | x1 + 1 |
[U33(x1)] | = | 2 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 1 |
[plus(x1, x2)] | = | 1 |
[U61(x1)] | = | 1 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1, x2, x3)] | = | x2 + x3 + 1 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 6771 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | 1 |
[U22(x1)] | = | x1 + 0 |
[U51(x1, x2, x3)] | = | 1 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | 1 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
isNat(ok(X)) | → | ok(isNat(X)) | (84) |
isNatKind(ok(X)) | → | ok(isNatKind(X)) | (99) |
plus#(mark(X1),X2) | → | plus#(X1,X2) | (176) |
The dependency pairs are split into 0 components.
U33#(mark(X)) | → | U33#(X) | (193) |
U33#(ok(X)) | → | U33#(X) | (157) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | x1 + 22620 |
[U21(x1, x2)] | = | x1 + 19902 |
[U11(x1, x2, x3)] | = | 1460 |
[s(x1)] | = | x1 + 20980 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + x3 + 21079 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 1 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | x1 + 8662 |
[U33#(x1)] | = | x1 + 0 |
[x(x1, x2)] | = | 6728 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 14684 |
[U32(x1, x2)] | = | x1 + x2 + 1 |
[U33(x1)] | = | 19288 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + 28264 |
[U61(x1)] | = | x1 + 1 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | x2 + x3 + 17954 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 26209 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | x1 + 2281 |
[U22(x1)] | = | 10326 |
[U51(x1, x2, x3)] | = | x1 + 1 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x1 + x2 + 22244 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
U33#(mark(X)) | → | U33#(X) | (193) |
U33#(ok(X)) | → | U33#(X) | (157) |
The dependency pairs are split into 0 components.
U13#(ok(X)) | → | U13#(X) | (267) |
U13#(mark(X)) | → | U13#(X) | (158) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | x1 + 22620 |
[U21(x1, x2)] | = | 26 |
[U11(x1, x2, x3)] | = | 24780 |
[s(x1)] | = | x1 + 20980 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 9467 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | x1 + 0 |
[U12(x1, x2)] | = | 18352 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | 6728 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 4 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 13029 |
[U32(x1, x2)] | = | x1 + x2 + 37838 |
[U33(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 23715 |
[plus(x1, x2)] | = | x1 + 2 |
[U61(x1)] | = | 29145 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | x2 + x3 + 24419 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | x1 + 1 |
[U22(x1)] | = | 22317 |
[U51(x1, x2, x3)] | = | 31299 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x2 + 48098 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
U13#(ok(X)) | → | U13#(X) | (267) |
U13#(mark(X)) | → | U13#(X) | (158) |
The dependency pairs are split into 0 components.
U41#(mark(X1),X2) | → | U41#(X1,X2) | (277) |
U41#(ok(X1),ok(X2)) | → | U41#(X1,X2) | (171) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | x1 + 27603 |
[U21(x1, x2)] | = | 2 |
[U11(x1, x2, x3)] | = | 2 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + x3 + 33889 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 2 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | 4618 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | 2 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 12224 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 2 |
[U32(x1, x2)] | = | x1 + x2 + 1 |
[U33(x1)] | = | x1 + 17094 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 23715 |
[plus(x1, x2)] | = | x1 + 6459 |
[U61(x1)] | = | 2 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | x2 + x3 + 8938 |
[U41#(x1, x2)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | x1 + 1 |
[U22(x1)] | = | 2 |
[U51(x1, x2, x3)] | = | 2 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x2 + 2 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
U41#(mark(X1),X2) | → | U41#(X1,X2) | (277) |
U41#(ok(X1),ok(X2)) | → | U41#(X1,X2) | (171) |
The dependency pairs are split into 0 components.
U31#(mark(X1),X2,X3) | → | U31#(X1,X2,X3) | (279) |
U31#(ok(X1),ok(X2),ok(X3)) | → | U31#(X1,X2,X3) | (117) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | x1 + 27603 |
[U21(x1, x2)] | = | 2 |
[U11(x1, x2, x3)] | = | 2 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + x3 + 36928 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 2 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | 29245 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | 2 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 31891 |
[U32(x1, x2)] | = | x1 + x2 + 1 |
[U33(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 2 |
[plus(x1, x2)] | = | x1 + 6459 |
[U61(x1)] | = | 2 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | x2 + x3 + 29490 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | x1 + 1 |
[U22(x1)] | = | 2 |
[U51(x1, x2, x3)] | = | 2 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x2 + 2 |
[U31#(x1, x2, x3)] | = | x3 + 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
U31#(ok(X1),ok(X2),ok(X3)) | → | U31#(X1,X2,X3) | (117) |
The dependency pairs are split into 1 component.
U31#(mark(X1),X2,X3) | → | U31#(X1,X2,X3) | (279) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | x1 + 1 |
[U21(x1, x2)] | = | 2 |
[U11(x1, x2, x3)] | = | 2 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + x3 + 22520 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 14350 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | 25058 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | 2 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 31891 |
[U32(x1, x2)] | = | x1 + x2 + 1 |
[U33(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 2 |
[plus(x1, x2)] | = | x1 + 2 |
[U61(x1)] | = | 2 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | x2 + x3 + 1310 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | x1 + 1 |
[U22(x1)] | = | 2 |
[U51(x1, x2, x3)] | = | 2 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x2 + 31861 |
[U31#(x1, x2, x3)] | = | x1 + 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
U31#(mark(X1),X2,X3) | → | U31#(X1,X2,X3) | (279) |
The dependency pairs are split into 0 components.
U32#(mark(X1),X2) | → | U32#(X1,X2) | (283) |
U32#(ok(X1),ok(X2)) | → | U32#(X1,X2) | (114) |
[U32#(x1, x2)] | = | x1 + 0 |
[isNatKind(x1)] | = | x1 + 1 |
[U21(x1, x2)] | = | 2 |
[U11(x1, x2, x3)] | = | 2 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + x3 + 567 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 28641 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | 16185 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | 2 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 4 |
[0] | = | 53236 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 31891 |
[U32(x1, x2)] | = | x1 + x2 + 1 |
[U33(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 2 |
[plus(x1, x2)] | = | x1 + 2 |
[U61(x1)] | = | 2 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | x2 + x3 + 24739 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | x1 + 1 |
[U22(x1)] | = | 2 |
[U51(x1, x2, x3)] | = | 2 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x2 + 31861 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
U32#(mark(X1),X2) | → | U32#(X1,X2) | (283) |
U32#(ok(X1),ok(X2)) | → | U32#(X1,X2) | (114) |
The dependency pairs are split into 0 components.
s#(ok(X)) | → | s#(X) | (254) |
s#(mark(X)) | → | s#(X) | (240) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | x1 + 1 |
[U21(x1, x2)] | = | 3123 |
[U11(x1, x2, x3)] | = | 31518 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + x3 + 32874 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 6711 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | 32388 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | 2 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 28715 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | x1 + 0 |
[mark(x1)] | = | x1 + 31891 |
[U32(x1, x2)] | = | x1 + x2 + 13823 |
[U33(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 2 |
[plus(x1, x2)] | = | x1 + 21741 |
[U61(x1)] | = | 9713 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | x2 + x3 + 28021 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | x1 + 1 |
[U22(x1)] | = | 27773 |
[U51(x1, x2, x3)] | = | 24832 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x2 + 60261 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
s#(ok(X)) | → | s#(X) | (254) |
s#(mark(X)) | → | s#(X) | (240) |
The dependency pairs are split into 0 components.
U21#(ok(X1),ok(X2)) | → | U21#(X1,X2) | (260) |
U21#(mark(X1),X2) | → | U21#(X1,X2) | (223) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | x1 + 1 |
[U21(x1, x2)] | = | 2 |
[U11(x1, x2, x3)] | = | 2 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 2 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | 7182 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | 2 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 13666 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1084 |
[U32(x1, x2)] | = | x1 + x2 + 1 |
[U33(x1)] | = | x1 + 10708 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 2 |
[plus(x1, x2)] | = | x1 + 21741 |
[U61(x1)] | = | 6795 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | x2 + x3 + 7193 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | x2 + 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | x1 + 1 |
[U22(x1)] | = | 27773 |
[U51(x1, x2, x3)] | = | 29648 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x2 + 2 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
U21#(ok(X1),ok(X2)) | → | U21#(X1,X2) | (260) |
The dependency pairs are split into 1 component.
U21#(mark(X1),X2) | → | U21#(X1,X2) | (223) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | x1 + 1 |
[U21(x1, x2)] | = | 2 |
[U11(x1, x2, x3)] | = | 2 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 8625 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | 23398 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | 2 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 17594 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1084 |
[U32(x1, x2)] | = | x1 + x2 + 1 |
[U33(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 2 |
[plus(x1, x2)] | = | x1 + 2 |
[U61(x1)] | = | 2 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | x2 + x3 + 15882 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | x1 + 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | x1 + 1 |
[U22(x1)] | = | 27773 |
[U51(x1, x2, x3)] | = | 2 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x2 + 2771 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
U21#(mark(X1),X2) | → | U21#(X1,X2) | (223) |
The dependency pairs are split into 0 components.
U12#(mark(X1),X2) | → | U12#(X1,X2) | (183) |
U12#(ok(X1),ok(X2)) | → | U12#(X1,X2) | (209) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | x1 + 1 |
[U21(x1, x2)] | = | 2 |
[U11(x1, x2, x3)] | = | 163 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + x3 + 22526 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 29087 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | 20244 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | 2 |
[U12#(x1, x2)] | = | x2 + 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 52208 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 7498 |
[U32(x1, x2)] | = | x1 + x2 + 1 |
[U33(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 2 |
[plus(x1, x2)] | = | x1 + 2 |
[U61(x1)] | = | 2 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | x2 + x3 + 25656 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | x1 + 26143 |
[U22(x1)] | = | 9983 |
[U51(x1, x2, x3)] | = | 2 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x2 + 6762 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
U12#(ok(X1),ok(X2)) | → | U12#(X1,X2) | (209) |
The dependency pairs are split into 1 component.
U12#(mark(X1),X2) | → | U12#(X1,X2) | (183) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | x1 + 6513 |
[U21(x1, x2)] | = | 2 |
[U11(x1, x2, x3)] | = | 2 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 2 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | 29888 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | 2 |
[U12#(x1, x2)] | = | x1 + 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 27531 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 7498 |
[U32(x1, x2)] | = | x1 + x2 + 1 |
[U33(x1)] | = | x1 + 1 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 2 |
[plus(x1, x2)] | = | x1 + 21180 |
[U61(x1)] | = | 2 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | x2 + x3 + 2 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | x1 + 1 |
[U22(x1)] | = | 22050 |
[U51(x1, x2, x3)] | = | 3583 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x2 + 19666 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
U12#(mark(X1),X2) | → | U12#(X1,X2) | (183) |
The dependency pairs are split into 0 components.
U11#(ok(X1),ok(X2),ok(X3)) | → | U11#(X1,X2,X3) | (177) |
U11#(mark(X1),X2,X3) | → | U11#(X1,X2,X3) | (256) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | x1 + 1 |
[U21(x1, x2)] | = | x2 + 2 |
[U11(x1, x2, x3)] | = | 7331 |
[s(x1)] | = | 4558 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x2 + x3 + 6609 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 17847 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | 5272 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | x1 + 7086 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | 7498 |
[U32(x1, x2)] | = | 6610 |
[U33(x1)] | = | 3619 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | x1 + 2290 |
[plus(x1, x2)] | = | 2 |
[U61(x1)] | = | 6225 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | x2 + x3 + 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | 1777 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | x1 + 1 |
[U22(x1)] | = | 57 |
[U51(x1, x2, x3)] | = | x2 + x3 + 1401 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | 7497 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
isNat(ok(X)) | → | ok(isNat(X)) | (84) |
and(ok(X1),ok(X2)) | → | ok(and(X1,X2)) | (98) |
and(mark(X1),X2) | → | mark(and(X1,X2)) | (61) |
isNatKind(ok(X)) | → | ok(isNatKind(X)) | (99) |
U11#(ok(X1),ok(X2),ok(X3)) | → | U11#(X1,X2,X3) | (177) |
The dependency pairs are split into 1 component.
U11#(mark(X1),X2,X3) | → | U11#(X1,X2,X3) | (256) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | 2 |
[U21(x1, x2)] | = | 2 |
[U11(x1, x2, x3)] | = | 2 |
[s(x1)] | = | 2 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x2 + x3 + 2 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 2 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | 2 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | 7086 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | 3 |
[0] | = | 49099 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 7498 |
[U32(x1, x2)] | = | 2 |
[U33(x1)] | = | 2 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 2 |
[plus(x1, x2)] | = | 2 |
[U61(x1)] | = | 2 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | x1 + 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | 2 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 38828 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | 2 |
[U22(x1)] | = | 2 |
[U51(x1, x2, x3)] | = | x1 + 39183 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | 24367 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
U11#(mark(X1),X2,X3) | → | U11#(X1,X2,X3) | (256) |
The dependency pairs are split into 0 components.
and#(ok(X1),ok(X2)) | → | and#(X1,X2) | (124) |
and#(mark(X1),X2) | → | and#(X1,X2) | (206) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | 2 |
[U21(x1, x2)] | = | 21100 |
[U11(x1, x2, x3)] | = | 15925 |
[s(x1)] | = | 2 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x2 + x3 + 31043 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 25229 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | 22086 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | 12165 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 49099 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 7498 |
[U32(x1, x2)] | = | 2 |
[U33(x1)] | = | 31989 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 26055 |
[plus(x1, x2)] | = | 25053 |
[U61(x1)] | = | 3115 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | 2 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | 11009 |
[U22(x1)] | = | 2 |
[U51(x1, x2, x3)] | = | x1 + 1 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x1 + 18666 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | x1 + x2 + 0 |
[U61#(x1)] | = | 0 |
and#(ok(X1),ok(X2)) | → | and#(X1,X2) | (124) |
and#(mark(X1),X2) | → | and#(X1,X2) | (206) |
The dependency pairs are split into 0 components.
isNatKind#(ok(X)) | → | isNatKind#(X) | (258) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | 2 |
[U21(x1, x2)] | = | 2 |
[U11(x1, x2, x3)] | = | 5153 |
[s(x1)] | = | 2 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x2 + x3 + 29910 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 2 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | 22086 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | 10428 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 1576 |
[0] | = | 31095 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 7202 |
[U32(x1, x2)] | = | 31206 |
[U33(x1)] | = | 2 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 26055 |
[plus(x1, x2)] | = | 2 |
[U61(x1)] | = | 7359 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | 2 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | 2 |
[U22(x1)] | = | 20787 |
[U51(x1, x2, x3)] | = | x1 + 1 |
[isNatKind#(x1)] | = | x1 + 0 |
[U41(x1, x2)] | = | x1 + 1 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
isNatKind#(ok(X)) | → | isNatKind#(X) | (258) |
The dependency pairs are split into 0 components.
U22#(ok(X)) | → | U22#(X) | (244) |
U22#(mark(X)) | → | U22#(X) | (242) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | 2 |
[U21(x1, x2)] | = | 9480 |
[U11(x1, x2, x3)] | = | 23473 |
[s(x1)] | = | 2 |
[isNat#(x1)] | = | 0 |
[U71(x1, x2, x3)] | = | x2 + x3 + 4452 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 30385 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | 14667 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | 18671 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 1576 |
[0] | = | 24875 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 7202 |
[U32(x1, x2)] | = | 27910 |
[U33(x1)] | = | 26478 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 26055 |
[plus(x1, x2)] | = | 2 |
[U61(x1)] | = | 2909 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | 2 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | x1 + 0 |
[tt] | = | 1 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | 2 |
[U22(x1)] | = | 48799 |
[U51(x1, x2, x3)] | = | x1 + 25606 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x1 + 12472 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
U22#(ok(X)) | → | U22#(X) | (244) |
U22#(mark(X)) | → | U22#(X) | (242) |
The dependency pairs are split into 0 components.
isNat#(ok(X)) | → | isNat#(X) | (235) |
[U32#(x1, x2)] | = | 0 |
[isNatKind(x1)] | = | 2 |
[U21(x1, x2)] | = | 2 |
[U11(x1, x2, x3)] | = | 2 |
[s(x1)] | = | 5861 |
[isNat#(x1)] | = | x1 + 0 |
[U71(x1, x2, x3)] | = | x2 + x3 + 9380 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 2 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[U13#(x1)] | = | 0 |
[U12(x1, x2)] | = | 2 |
[U33#(x1)] | = | 0 |
[x(x1, x2)] | = | 2 |
[U12#(x1, x2)] | = | 0 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 1576 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 2 |
[U32(x1, x2)] | = | 9452 |
[U33(x1)] | = | 2 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | 26055 |
[plus(x1, x2)] | = | 2 |
[U61(x1)] | = | 2 |
[U51#(x1, x2, x3)] | = | 0 |
[U11#(x1, x2, x3)] | = | 0 |
[active(x1)] | = | 1 |
[U31(x1, x2, x3)] | = | 2 |
[U41#(x1, x2)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2)] | = | 0 |
[U22#(x1)] | = | 0 |
[tt] | = | 35869 |
[U71#(x1, x2, x3)] | = | 0 |
[U13(x1)] | = | 2 |
[U22(x1)] | = | 2 |
[U51(x1, x2, x3)] | = | x1 + 1 |
[isNatKind#(x1)] | = | 0 |
[U41(x1, x2)] | = | x1 + 31187 |
[U31#(x1, x2, x3)] | = | 0 |
[and#(x1, x2)] | = | 0 |
[U61#(x1)] | = | 0 |
isNat#(ok(X)) | → | isNat#(X) | (235) |
The dependency pairs are split into 0 components.