The rewrite relation of the following TRS is considered.
active(U11(tt,N)) | → | mark(N) | (1) |
active(U21(tt,M,N)) | → | mark(s(plus(N,M))) | (2) |
active(and(tt,X)) | → | mark(X) | (3) |
active(isNat(0)) | → | mark(tt) | (4) |
active(isNat(plus(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (5) |
active(isNat(s(V1))) | → | mark(isNat(V1)) | (6) |
active(plus(N,0)) | → | mark(U11(isNat(N),N)) | (7) |
active(plus(N,s(M))) | → | mark(U21(and(isNat(M),isNat(N)),M,N)) | (8) |
active(U11(X1,X2)) | → | U11(active(X1),X2) | (9) |
active(U21(X1,X2,X3)) | → | U21(active(X1),X2,X3) | (10) |
active(s(X)) | → | s(active(X)) | (11) |
active(plus(X1,X2)) | → | plus(active(X1),X2) | (12) |
active(plus(X1,X2)) | → | plus(X1,active(X2)) | (13) |
active(and(X1,X2)) | → | and(active(X1),X2) | (14) |
U11(mark(X1),X2) | → | mark(U11(X1,X2)) | (15) |
U21(mark(X1),X2,X3) | → | mark(U21(X1,X2,X3)) | (16) |
s(mark(X)) | → | mark(s(X)) | (17) |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (18) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (19) |
and(mark(X1),X2) | → | mark(and(X1,X2)) | (20) |
proper(U11(X1,X2)) | → | U11(proper(X1),proper(X2)) | (21) |
proper(tt) | → | ok(tt) | (22) |
proper(U21(X1,X2,X3)) | → | U21(proper(X1),proper(X2),proper(X3)) | (23) |
proper(s(X)) | → | s(proper(X)) | (24) |
proper(plus(X1,X2)) | → | plus(proper(X1),proper(X2)) | (25) |
proper(and(X1,X2)) | → | and(proper(X1),proper(X2)) | (26) |
proper(isNat(X)) | → | isNat(proper(X)) | (27) |
proper(0) | → | ok(0) | (28) |
U11(ok(X1),ok(X2)) | → | ok(U11(X1,X2)) | (29) |
U21(ok(X1),ok(X2),ok(X3)) | → | ok(U21(X1,X2,X3)) | (30) |
s(ok(X)) | → | ok(s(X)) | (31) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (32) |
and(ok(X1),ok(X2)) | → | ok(and(X1,X2)) | (33) |
isNat(ok(X)) | → | ok(isNat(X)) | (34) |
top(mark(X)) | → | top(proper(X)) | (35) |
top(ok(X)) | → | top(active(X)) | (36) |
active#(U21(tt,M,N)) | → | plus#(N,M) | (37) |
proper#(and(X1,X2)) | → | and#(proper(X1),proper(X2)) | (38) |
active#(plus(N,0)) | → | U11#(isNat(N),N) | (39) |
active#(isNat(plus(V1,V2))) | → | isNat#(V1) | (40) |
top#(ok(X)) | → | top#(active(X)) | (41) |
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (42) |
plus#(ok(X1),ok(X2)) | → | plus#(X1,X2) | (43) |
isNat#(ok(X)) | → | isNat#(X) | (44) |
top#(ok(X)) | → | active#(X) | (45) |
active#(plus(N,s(M))) | → | and#(isNat(M),isNat(N)) | (46) |
proper#(U11(X1,X2)) | → | U11#(proper(X1),proper(X2)) | (47) |
proper#(isNat(X)) | → | isNat#(proper(X)) | (48) |
active#(isNat(s(V1))) | → | isNat#(V1) | (49) |
active#(plus(N,s(M))) | → | isNat#(N) | (50) |
s#(mark(X)) | → | s#(X) | (51) |
U21#(mark(X1),X2,X3) | → | U21#(X1,X2,X3) | (52) |
proper#(s(X)) | → | s#(proper(X)) | (53) |
active#(U11(X1,X2)) | → | U11#(active(X1),X2) | (54) |
active#(s(X)) | → | s#(active(X)) | (55) |
plus#(mark(X1),X2) | → | plus#(X1,X2) | (56) |
U21#(ok(X1),ok(X2),ok(X3)) | → | U21#(X1,X2,X3) | (57) |
active#(and(X1,X2)) | → | active#(X1) | (58) |
proper#(and(X1,X2)) | → | proper#(X2) | (59) |
active#(s(X)) | → | active#(X) | (60) |
active#(U21(X1,X2,X3)) | → | U21#(active(X1),X2,X3) | (61) |
U11#(mark(X1),X2) | → | U11#(X1,X2) | (62) |
proper#(s(X)) | → | proper#(X) | (63) |
active#(plus(N,0)) | → | isNat#(N) | (64) |
active#(plus(N,s(M))) | → | U21#(and(isNat(M),isNat(N)),M,N) | (65) |
proper#(U11(X1,X2)) | → | proper#(X1) | (66) |
proper#(plus(X1,X2)) | → | plus#(proper(X1),proper(X2)) | (67) |
active#(plus(X1,X2)) | → | active#(X1) | (68) |
active#(plus(X1,X2)) | → | plus#(X1,active(X2)) | (69) |
proper#(isNat(X)) | → | proper#(X) | (70) |
active#(U11(X1,X2)) | → | active#(X1) | (71) |
and#(ok(X1),ok(X2)) | → | and#(X1,X2) | (72) |
top#(mark(X)) | → | proper#(X) | (73) |
proper#(and(X1,X2)) | → | proper#(X1) | (74) |
and#(mark(X1),X2) | → | and#(X1,X2) | (75) |
active#(and(X1,X2)) | → | and#(active(X1),X2) | (76) |
active#(isNat(plus(V1,V2))) | → | and#(isNat(V1),isNat(V2)) | (77) |
proper#(plus(X1,X2)) | → | proper#(X2) | (78) |
proper#(U21(X1,X2,X3)) | → | proper#(X2) | (79) |
active#(U21(X1,X2,X3)) | → | active#(X1) | (80) |
active#(plus(X1,X2)) | → | plus#(active(X1),X2) | (81) |
proper#(plus(X1,X2)) | → | proper#(X1) | (82) |
active#(isNat(plus(V1,V2))) | → | isNat#(V2) | (83) |
s#(ok(X)) | → | s#(X) | (84) |
proper#(U21(X1,X2,X3)) | → | proper#(X1) | (85) |
U11#(ok(X1),ok(X2)) | → | U11#(X1,X2) | (86) |
active#(U21(tt,M,N)) | → | s#(plus(N,M)) | (87) |
active#(plus(N,s(M))) | → | isNat#(M) | (88) |
active#(plus(X1,X2)) | → | active#(X2) | (89) |
proper#(U21(X1,X2,X3)) | → | U21#(proper(X1),proper(X2),proper(X3)) | (90) |
top#(mark(X)) | → | top#(proper(X)) | (91) |
proper#(U11(X1,X2)) | → | proper#(X2) | (92) |
proper#(U21(X1,X2,X3)) | → | proper#(X3) | (93) |
The dependency pairs are split into 9 components.
top#(mark(X)) | → | top#(proper(X)) | (91) |
top#(ok(X)) | → | top#(active(X)) | (41) |
π(isNat#) | = | 1 |
π(top#) | = | 1 |
π(proper) | = | 1 |
π(ok) | = | 1 |
π(proper#) | = | 1 |
π(isNat) | = | 1 |
π(active) | = | 1 |
π(and#) | = | 2 |
prec(U21) | = | 5 | status(U21) | = | [3, 2, 1] | list-extension(U21) | = | Lex | ||
prec(U11) | = | 4 | status(U11) | = | [2, 1] | list-extension(U11) | = | Lex | ||
prec(s) | = | 1 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(top) | = | 0 | status(top) | = | [] | list-extension(top) | = | Lex | ||
prec(and) | = | 1 | status(and) | = | [2, 1] | list-extension(and) | = | Lex | ||
prec(plus#) | = | 0 | status(plus#) | = | [2, 1] | list-extension(plus#) | = | Lex | ||
prec(0) | = | 3 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(s#) | = | 0 | status(s#) | = | [] | list-extension(s#) | = | Lex | ||
prec(mark) | = | 0 | status(mark) | = | [1] | list-extension(mark) | = | Lex | ||
prec(plus) | = | 5 | status(plus) | = | [1, 2] | list-extension(plus) | = | Lex | ||
prec(U11#) | = | 0 | status(U11#) | = | [1, 2] | list-extension(U11#) | = | Lex | ||
prec(active#) | = | 0 | status(active#) | = | [] | list-extension(active#) | = | Lex | ||
prec(U21#) | = | 0 | status(U21#) | = | [2, 3, 1] | list-extension(U21#) | = | Lex | ||
prec(tt) | = | 2 | status(tt) | = | [] | list-extension(tt) | = | Lex |
[U21(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U11(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[s(x1)] | = | x1 + 0 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[plus#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[0] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[plus(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[U11#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[tt] | = | 0 |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (18) |
active(isNat(0)) | → | mark(tt) | (4) |
U11(mark(X1),X2) | → | mark(U11(X1,X2)) | (15) |
active(plus(N,s(M))) | → | mark(U21(and(isNat(M),isNat(N)),M,N)) | (8) |
active(U11(tt,N)) | → | mark(N) | (1) |
active(and(tt,X)) | → | mark(X) | (3) |
U21(mark(X1),X2,X3) | → | mark(U21(X1,X2,X3)) | (16) |
proper(U11(X1,X2)) | → | U11(proper(X1),proper(X2)) | (21) |
proper(and(X1,X2)) | → | and(proper(X1),proper(X2)) | (26) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (19) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (32) |
s(mark(X)) | → | mark(s(X)) | (17) |
proper(isNat(X)) | → | isNat(proper(X)) | (27) |
isNat(ok(X)) | → | ok(isNat(X)) | (34) |
proper(tt) | → | ok(tt) | (22) |
proper(0) | → | ok(0) | (28) |
active(isNat(plus(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (5) |
and(ok(X1),ok(X2)) | → | ok(and(X1,X2)) | (33) |
active(U21(X1,X2,X3)) | → | U21(active(X1),X2,X3) | (10) |
active(plus(N,0)) | → | mark(U11(isNat(N),N)) | (7) |
and(mark(X1),X2) | → | mark(and(X1,X2)) | (20) |
proper(plus(X1,X2)) | → | plus(proper(X1),proper(X2)) | (25) |
U21(ok(X1),ok(X2),ok(X3)) | → | ok(U21(X1,X2,X3)) | (30) |
active(and(X1,X2)) | → | and(active(X1),X2) | (14) |
s(ok(X)) | → | ok(s(X)) | (31) |
active(plus(X1,X2)) | → | plus(active(X1),X2) | (12) |
proper(U21(X1,X2,X3)) | → | U21(proper(X1),proper(X2),proper(X3)) | (23) |
proper(s(X)) | → | s(proper(X)) | (24) |
active(s(X)) | → | s(active(X)) | (11) |
active(U11(X1,X2)) | → | U11(active(X1),X2) | (9) |
active(plus(X1,X2)) | → | plus(X1,active(X2)) | (13) |
active(isNat(s(V1))) | → | mark(isNat(V1)) | (6) |
U11(ok(X1),ok(X2)) | → | ok(U11(X1,X2)) | (29) |
active(U21(tt,M,N)) | → | mark(s(plus(N,M))) | (2) |
top#(mark(X)) | → | top#(proper(X)) | (91) |
The dependency pairs are split into 1 component.
top#(ok(X)) | → | top#(active(X)) | (41) |
[U21(x1, x2, x3)] | = | x3 + 0 |
[U11(x1, x2)] | = | x2 + 0 |
[s(x1)] | = | x1 + 0 |
[isNat#(x1)] | = | 0 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 0 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | x1 + 0 |
[proper(x1)] | = | 3 |
[ok(x1)] | = | x1 + 2 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | 0 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | x1 + 0 |
[plus(x1, x2)] | = | x1 + 0 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 1 |
[and#(x1, x2)] | = | 0 |
plus(mark(X1),X2) | → | mark(plus(X1,X2)) | (18) |
active(isNat(0)) | → | mark(tt) | (4) |
U11(mark(X1),X2) | → | mark(U11(X1,X2)) | (15) |
active(plus(N,s(M))) | → | mark(U21(and(isNat(M),isNat(N)),M,N)) | (8) |
active(U11(tt,N)) | → | mark(N) | (1) |
active(and(tt,X)) | → | mark(X) | (3) |
U21(mark(X1),X2,X3) | → | mark(U21(X1,X2,X3)) | (16) |
proper(U11(X1,X2)) | → | U11(proper(X1),proper(X2)) | (21) |
proper(and(X1,X2)) | → | and(proper(X1),proper(X2)) | (26) |
plus(X1,mark(X2)) | → | mark(plus(X1,X2)) | (19) |
plus(ok(X1),ok(X2)) | → | ok(plus(X1,X2)) | (32) |
s(mark(X)) | → | mark(s(X)) | (17) |
proper(isNat(X)) | → | isNat(proper(X)) | (27) |
isNat(ok(X)) | → | ok(isNat(X)) | (34) |
proper(tt) | → | ok(tt) | (22) |
proper(0) | → | ok(0) | (28) |
active(isNat(plus(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (5) |
and(ok(X1),ok(X2)) | → | ok(and(X1,X2)) | (33) |
active(U21(X1,X2,X3)) | → | U21(active(X1),X2,X3) | (10) |
active(plus(N,0)) | → | mark(U11(isNat(N),N)) | (7) |
and(mark(X1),X2) | → | mark(and(X1,X2)) | (20) |
proper(plus(X1,X2)) | → | plus(proper(X1),proper(X2)) | (25) |
U21(ok(X1),ok(X2),ok(X3)) | → | ok(U21(X1,X2,X3)) | (30) |
active(and(X1,X2)) | → | and(active(X1),X2) | (14) |
s(ok(X)) | → | ok(s(X)) | (31) |
active(plus(X1,X2)) | → | plus(active(X1),X2) | (12) |
proper(U21(X1,X2,X3)) | → | U21(proper(X1),proper(X2),proper(X3)) | (23) |
proper(s(X)) | → | s(proper(X)) | (24) |
active(s(X)) | → | s(active(X)) | (11) |
active(U11(X1,X2)) | → | U11(active(X1),X2) | (9) |
active(plus(X1,X2)) | → | plus(X1,active(X2)) | (13) |
active(isNat(s(V1))) | → | mark(isNat(V1)) | (6) |
U11(ok(X1),ok(X2)) | → | ok(U11(X1,X2)) | (29) |
active(U21(tt,M,N)) | → | mark(s(plus(N,M))) | (2) |
top#(ok(X)) | → | top#(active(X)) | (41) |
The dependency pairs are split into 0 components.
proper#(U21(X1,X2,X3)) | → | proper#(X3) | (93) |
proper#(U11(X1,X2)) | → | proper#(X2) | (92) |
proper#(U11(X1,X2)) | → | proper#(X1) | (66) |
proper#(s(X)) | → | proper#(X) | (63) |
proper#(and(X1,X2)) | → | proper#(X2) | (59) |
proper#(U21(X1,X2,X3)) | → | proper#(X1) | (85) |
proper#(plus(X1,X2)) | → | proper#(X1) | (82) |
proper#(U21(X1,X2,X3)) | → | proper#(X2) | (79) |
proper#(plus(X1,X2)) | → | proper#(X2) | (78) |
proper#(and(X1,X2)) | → | proper#(X1) | (74) |
proper#(isNat(X)) | → | proper#(X) | (70) |
[U21(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[U11(x1, x2)] | = | x1 + x2 + 1 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 1 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 2 |
[0] | = | 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[proper#(x1)] | = | x1 + 0 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 1 |
[and#(x1, x2)] | = | 0 |
proper#(U21(X1,X2,X3)) | → | proper#(X3) | (93) |
proper#(U11(X1,X2)) | → | proper#(X2) | (92) |
proper#(U11(X1,X2)) | → | proper#(X1) | (66) |
proper#(s(X)) | → | proper#(X) | (63) |
proper#(and(X1,X2)) | → | proper#(X2) | (59) |
proper#(U21(X1,X2,X3)) | → | proper#(X1) | (85) |
proper#(plus(X1,X2)) | → | proper#(X1) | (82) |
proper#(U21(X1,X2,X3)) | → | proper#(X2) | (79) |
proper#(plus(X1,X2)) | → | proper#(X2) | (78) |
proper#(and(X1,X2)) | → | proper#(X1) | (74) |
proper#(isNat(X)) | → | proper#(X) | (70) |
The dependency pairs are split into 0 components.
active#(s(X)) | → | active#(X) | (60) |
active#(plus(X1,X2)) | → | active#(X2) | (89) |
active#(and(X1,X2)) | → | active#(X1) | (58) |
active#(U21(X1,X2,X3)) | → | active#(X1) | (80) |
active#(U11(X1,X2)) | → | active#(X1) | (71) |
active#(plus(X1,X2)) | → | active#(X1) | (68) |
[U21(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[U11(x1, x2)] | = | x1 + x2 + 1 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 1 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 2 |
[0] | = | 18624 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | 0 |
[active#(x1)] | = | x1 + 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 1 |
[and#(x1, x2)] | = | 0 |
active#(s(X)) | → | active#(X) | (60) |
active#(plus(X1,X2)) | → | active#(X2) | (89) |
active#(and(X1,X2)) | → | active#(X1) | (58) |
active#(U21(X1,X2,X3)) | → | active#(X1) | (80) |
active#(U11(X1,X2)) | → | active#(X1) | (71) |
active#(plus(X1,X2)) | → | active#(X1) | (68) |
The dependency pairs are split into 0 components.
s#(ok(X)) | → | s#(X) | (84) |
s#(mark(X)) | → | s#(X) | (51) |
[U21(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[U11(x1, x2)] | = | x1 + x2 + 29596 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 38482 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 2 |
[0] | = | 1 |
[s#(x1)] | = | x1 + 0 |
[mark(x1)] | = | x1 + 0 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + x2 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 1 |
[and#(x1, x2)] | = | 0 |
s#(ok(X)) | → | s#(X) | (84) |
The dependency pairs are split into 1 component.
s#(mark(X)) | → | s#(X) | (51) |
[U21(x1, x2, x3)] | = | x1 + x2 + 1 |
[U11(x1, x2)] | = | x1 + x2 + 14023 |
[s(x1)] | = | x1 + 0 |
[isNat#(x1)] | = | 0 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 1 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 2 |
[0] | = | 0 |
[s#(x1)] | = | x1 + 0 |
[mark(x1)] | = | x1 + 23071 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | x1 + 0 |
[plus(x1, x2)] | = | x1 + x2 + 0 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 23069 |
[and#(x1, x2)] | = | 0 |
s#(mark(X)) | → | s#(X) | (51) |
The dependency pairs are split into 0 components.
plus#(mark(X1),X2) | → | plus#(X1,X2) | (56) |
plus#(ok(X1),ok(X2)) | → | plus#(X1,X2) | (43) |
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (42) |
[U21(x1, x2, x3)] | = | x1 + x2 + 1 |
[U11(x1, x2)] | = | x1 + x2 + 2 |
[s(x1)] | = | x1 + 0 |
[isNat#(x1)] | = | 0 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 1 |
[plus#(x1, x2)] | = | x1 + x2 + 0 |
[top#(x1)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 2 |
[0] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 11299 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | x1 + 0 |
[plus(x1, x2)] | = | x1 + x2 + 0 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 11297 |
[and#(x1, x2)] | = | 0 |
plus#(mark(X1),X2) | → | plus#(X1,X2) | (56) |
plus#(ok(X1),ok(X2)) | → | plus#(X1,X2) | (43) |
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (42) |
The dependency pairs are split into 0 components.
U11#(mark(X1),X2) | → | U11#(X1,X2) | (62) |
U11#(ok(X1),ok(X2)) | → | U11#(X1,X2) | (86) |
[U21(x1, x2, x3)] | = | x1 + x2 + 1 |
[U11(x1, x2)] | = | x1 + x2 + 28472 |
[s(x1)] | = | x1 + 0 |
[isNat#(x1)] | = | 0 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 1 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 2 |
[0] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 56908 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | x1 + 0 |
[plus(x1, x2)] | = | x1 + x2 + 0 |
[U11#(x1, x2)] | = | x2 + 0 |
[active(x1)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 56906 |
[and#(x1, x2)] | = | 0 |
U11#(ok(X1),ok(X2)) | → | U11#(X1,X2) | (86) |
The dependency pairs are split into 1 component.
U11#(mark(X1),X2) | → | U11#(X1,X2) | (62) |
[U21(x1, x2, x3)] | = | x1 + x2 + 1 |
[U11(x1, x2)] | = | x1 + x2 + 2 |
[s(x1)] | = | x1 + 0 |
[isNat#(x1)] | = | 0 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 1 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 2 |
[0] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 3 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | x1 + 0 |
[plus(x1, x2)] | = | x1 + x2 + 0 |
[U11#(x1, x2)] | = | x1 + 0 |
[active(x1)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 1 |
[and#(x1, x2)] | = | 0 |
U11#(mark(X1),X2) | → | U11#(X1,X2) | (62) |
The dependency pairs are split into 0 components.
U21#(ok(X1),ok(X2),ok(X3)) | → | U21#(X1,X2,X3) | (57) |
U21#(mark(X1),X2,X3) | → | U21#(X1,X2,X3) | (52) |
[U21(x1, x2, x3)] | = | x1 + x2 + 1 |
[U11(x1, x2)] | = | x1 + x2 + 2 |
[s(x1)] | = | x1 + 0 |
[isNat#(x1)] | = | 0 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 1 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 2 |
[0] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 7110 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | x1 + 0 |
[plus(x1, x2)] | = | x1 + x2 + 0 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | x2 + x3 + 0 |
[tt] | = | 7108 |
[and#(x1, x2)] | = | 0 |
U21#(ok(X1),ok(X2),ok(X3)) | → | U21#(X1,X2,X3) | (57) |
The dependency pairs are split into 1 component.
U21#(mark(X1),X2,X3) | → | U21#(X1,X2,X3) | (52) |
[U21(x1, x2, x3)] | = | x1 + x2 + 1 |
[U11(x1, x2)] | = | x1 + x2 + 2 |
[s(x1)] | = | x1 + 0 |
[isNat#(x1)] | = | 0 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 1 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 2 |
[0] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 31365 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | x1 + 0 |
[plus(x1, x2)] | = | x1 + x2 + 0 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | x1 + 0 |
[tt] | = | 31363 |
[and#(x1, x2)] | = | 0 |
U21#(mark(X1),X2,X3) | → | U21#(X1,X2,X3) | (52) |
The dependency pairs are split into 0 components.
and#(mark(X1),X2) | → | and#(X1,X2) | (75) |
and#(ok(X1),ok(X2)) | → | and#(X1,X2) | (72) |
[U21(x1, x2, x3)] | = | x1 + x2 + 1 |
[U11(x1, x2)] | = | x1 + x2 + 2 |
[s(x1)] | = | x1 + 0 |
[isNat#(x1)] | = | 0 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 1 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 2 |
[0] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 3 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | x1 + 0 |
[plus(x1, x2)] | = | x1 + x2 + 0 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 1 |
[and#(x1, x2)] | = | x1 + 0 |
and#(mark(X1),X2) | → | and#(X1,X2) | (75) |
and#(ok(X1),ok(X2)) | → | and#(X1,X2) | (72) |
The dependency pairs are split into 0 components.
isNat#(ok(X)) | → | isNat#(X) | (44) |
[U21(x1, x2, x3)] | = | x1 + x2 + 1 |
[U11(x1, x2)] | = | x1 + x2 + 2 |
[s(x1)] | = | x1 + 0 |
[isNat#(x1)] | = | x1 + 0 |
[top(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 1 |
[plus#(x1, x2)] | = | 0 |
[top#(x1)] | = | 0 |
[proper(x1)] | = | x1 + 1 |
[ok(x1)] | = | x1 + 2 |
[0] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 3 |
[proper#(x1)] | = | 0 |
[isNat(x1)] | = | x1 + 0 |
[plus(x1, x2)] | = | x1 + x2 + 0 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 1 |
[and#(x1, x2)] | = | 0 |
isNat#(ok(X)) | → | isNat#(X) | (44) |
The dependency pairs are split into 0 components.