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(U31(tt)) | → | mark(0) | (3) |
active(U41(tt,M,N)) | → | mark(plus(x(N,M),N)) | (4) |
active(and(tt,X)) | → | mark(X) | (5) |
active(isNat(0)) | → | mark(tt) | (6) |
active(isNat(plus(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (7) |
active(isNat(s(V1))) | → | mark(isNat(V1)) | (8) |
active(isNat(x(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (9) |
active(plus(N,0)) | → | mark(U11(isNat(N),N)) | (10) |
active(plus(N,s(M))) | → | mark(U21(and(isNat(M),isNat(N)),M,N)) | (11) |
active(x(N,0)) | → | mark(U31(isNat(N))) | (12) |
active(x(N,s(M))) | → | mark(U41(and(isNat(M),isNat(N)),M,N)) | (13) |
mark(U11(X1,X2)) | → | active(U11(mark(X1),X2)) | (14) |
mark(tt) | → | active(tt) | (15) |
mark(U21(X1,X2,X3)) | → | active(U21(mark(X1),X2,X3)) | (16) |
mark(s(X)) | → | active(s(mark(X))) | (17) |
mark(plus(X1,X2)) | → | active(plus(mark(X1),mark(X2))) | (18) |
mark(U31(X)) | → | active(U31(mark(X))) | (19) |
mark(0) | → | active(0) | (20) |
mark(U41(X1,X2,X3)) | → | active(U41(mark(X1),X2,X3)) | (21) |
mark(x(X1,X2)) | → | active(x(mark(X1),mark(X2))) | (22) |
mark(and(X1,X2)) | → | active(and(mark(X1),X2)) | (23) |
mark(isNat(X)) | → | active(isNat(X)) | (24) |
U11(mark(X1),X2) | → | U11(X1,X2) | (25) |
U11(X1,mark(X2)) | → | U11(X1,X2) | (26) |
U11(active(X1),X2) | → | U11(X1,X2) | (27) |
U11(X1,active(X2)) | → | U11(X1,X2) | (28) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (29) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (30) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (31) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (32) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (33) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (34) |
s(mark(X)) | → | s(X) | (35) |
s(active(X)) | → | s(X) | (36) |
plus(mark(X1),X2) | → | plus(X1,X2) | (37) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (38) |
plus(active(X1),X2) | → | plus(X1,X2) | (39) |
plus(X1,active(X2)) | → | plus(X1,X2) | (40) |
U31(mark(X)) | → | U31(X) | (41) |
U31(active(X)) | → | U31(X) | (42) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (43) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (44) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (45) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (46) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (47) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (48) |
x(mark(X1),X2) | → | x(X1,X2) | (49) |
x(X1,mark(X2)) | → | x(X1,X2) | (50) |
x(active(X1),X2) | → | x(X1,X2) | (51) |
x(X1,active(X2)) | → | x(X1,X2) | (52) |
and(mark(X1),X2) | → | and(X1,X2) | (53) |
and(X1,mark(X2)) | → | and(X1,X2) | (54) |
and(active(X1),X2) | → | and(X1,X2) | (55) |
and(X1,active(X2)) | → | and(X1,X2) | (56) |
isNat(mark(X)) | → | isNat(X) | (57) |
isNat(active(X)) | → | isNat(X) | (58) |
active#(U21(tt,M,N)) | → | s#(plus(N,M)) | (59) |
active#(U31(tt)) | → | mark#(0) | (60) |
U21#(X1,X2,mark(X3)) | → | U21#(X1,X2,X3) | (61) |
active#(plus(N,s(M))) | → | mark#(U21(and(isNat(M),isNat(N)),M,N)) | (62) |
mark#(isNat(X)) | → | active#(isNat(X)) | (63) |
mark#(U21(X1,X2,X3)) | → | active#(U21(mark(X1),X2,X3)) | (64) |
mark#(x(X1,X2)) | → | x#(mark(X1),mark(X2)) | (65) |
mark#(U11(X1,X2)) | → | U11#(mark(X1),X2) | (66) |
active#(x(N,0)) | → | isNat#(N) | (67) |
x#(X1,mark(X2)) | → | x#(X1,X2) | (68) |
active#(x(N,0)) | → | U31#(isNat(N)) | (69) |
mark#(and(X1,X2)) | → | and#(mark(X1),X2) | (70) |
mark#(plus(X1,X2)) | → | mark#(X2) | (71) |
mark#(plus(X1,X2)) | → | plus#(mark(X1),mark(X2)) | (72) |
mark#(tt) | → | active#(tt) | (73) |
mark#(s(X)) | → | mark#(X) | (74) |
mark#(U11(X1,X2)) | → | mark#(X1) | (75) |
active#(isNat(plus(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (76) |
mark#(s(X)) | → | active#(s(mark(X))) | (77) |
U21#(X1,mark(X2),X3) | → | U21#(X1,X2,X3) | (78) |
mark#(U31(X)) | → | active#(U31(mark(X))) | (79) |
U21#(active(X1),X2,X3) | → | U21#(X1,X2,X3) | (80) |
active#(plus(N,0)) | → | mark#(U11(isNat(N),N)) | (81) |
U21#(X1,active(X2),X3) | → | U21#(X1,X2,X3) | (82) |
mark#(and(X1,X2)) | → | mark#(X1) | (83) |
s#(mark(X)) | → | s#(X) | (84) |
active#(plus(N,0)) | → | U11#(isNat(N),N) | (85) |
active#(isNat(plus(V1,V2))) | → | isNat#(V1) | (86) |
mark#(x(X1,X2)) | → | mark#(X1) | (87) |
active#(x(N,0)) | → | mark#(U31(isNat(N))) | (88) |
active#(isNat(s(V1))) | → | isNat#(V1) | (89) |
U11#(mark(X1),X2) | → | U11#(X1,X2) | (90) |
U41#(X1,X2,active(X3)) | → | U41#(X1,X2,X3) | (91) |
U31#(mark(X)) | → | U31#(X) | (92) |
U41#(X1,active(X2),X3) | → | U41#(X1,X2,X3) | (93) |
mark#(plus(X1,X2)) | → | mark#(X1) | (94) |
plus#(active(X1),X2) | → | plus#(X1,X2) | (95) |
mark#(U31(X)) | → | U31#(mark(X)) | (96) |
active#(U41(tt,M,N)) | → | x#(N,M) | (97) |
active#(x(N,s(M))) | → | isNat#(N) | (98) |
U11#(active(X1),X2) | → | U11#(X1,X2) | (99) |
active#(x(N,s(M))) | → | isNat#(M) | (100) |
mark#(U41(X1,X2,X3)) | → | U41#(mark(X1),X2,X3) | (101) |
U11#(X1,mark(X2)) | → | U11#(X1,X2) | (102) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (103) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (104) |
U21#(X1,X2,active(X3)) | → | U21#(X1,X2,X3) | (105) |
and#(mark(X1),X2) | → | and#(X1,X2) | (106) |
active#(plus(N,s(M))) | → | and#(isNat(M),isNat(N)) | (107) |
s#(active(X)) | → | s#(X) | (108) |
active#(isNat(plus(V1,V2))) | → | isNat#(V2) | (109) |
active#(isNat(s(V1))) | → | mark#(isNat(V1)) | (110) |
mark#(U41(X1,X2,X3)) | → | mark#(X1) | (111) |
isNat#(active(X)) | → | isNat#(X) | (112) |
active#(and(tt,X)) | → | mark#(X) | (113) |
active#(plus(N,s(M))) | → | U21#(and(isNat(M),isNat(N)),M,N) | (114) |
mark#(0) | → | active#(0) | (115) |
x#(X1,active(X2)) | → | x#(X1,X2) | (116) |
active#(isNat(x(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (117) |
active#(x(N,s(M))) | → | mark#(U41(and(isNat(M),isNat(N)),M,N)) | (118) |
and#(X1,mark(X2)) | → | and#(X1,X2) | (119) |
U41#(active(X1),X2,X3) | → | U41#(X1,X2,X3) | (120) |
U41#(X1,X2,mark(X3)) | → | U41#(X1,X2,X3) | (121) |
plus#(mark(X1),X2) | → | plus#(X1,X2) | (122) |
active#(U41(tt,M,N)) | → | mark#(plus(x(N,M),N)) | (123) |
active#(U41(tt,M,N)) | → | plus#(x(N,M),N) | (124) |
U11#(X1,active(X2)) | → | U11#(X1,X2) | (125) |
active#(plus(N,s(M))) | → | isNat#(N) | (126) |
mark#(s(X)) | → | s#(mark(X)) | (127) |
U21#(mark(X1),X2,X3) | → | U21#(X1,X2,X3) | (128) |
and#(X1,active(X2)) | → | and#(X1,X2) | (129) |
mark#(x(X1,X2)) | → | active#(x(mark(X1),mark(X2))) | (130) |
active#(isNat(x(V1,V2))) | → | isNat#(V2) | (131) |
active#(x(N,s(M))) | → | and#(isNat(M),isNat(N)) | (132) |
isNat#(mark(X)) | → | isNat#(X) | (133) |
mark#(U21(X1,X2,X3)) | → | U21#(mark(X1),X2,X3) | (134) |
active#(U11(tt,N)) | → | mark#(N) | (135) |
active#(isNat(x(V1,V2))) | → | isNat#(V1) | (136) |
active#(plus(N,0)) | → | isNat#(N) | (137) |
and#(active(X1),X2) | → | and#(X1,X2) | (138) |
active#(plus(N,s(M))) | → | isNat#(M) | (139) |
x#(active(X1),X2) | → | x#(X1,X2) | (140) |
U41#(X1,mark(X2),X3) | → | U41#(X1,X2,X3) | (141) |
active#(isNat(x(V1,V2))) | → | and#(isNat(V1),isNat(V2)) | (142) |
mark#(U21(X1,X2,X3)) | → | mark#(X1) | (143) |
mark#(x(X1,X2)) | → | mark#(X2) | (144) |
mark#(and(X1,X2)) | → | active#(and(mark(X1),X2)) | (145) |
active#(x(N,s(M))) | → | U41#(and(isNat(M),isNat(N)),M,N) | (146) |
active#(isNat(0)) | → | mark#(tt) | (147) |
active#(U21(tt,M,N)) | → | plus#(N,M) | (148) |
mark#(U31(X)) | → | mark#(X) | (149) |
active#(U21(tt,M,N)) | → | mark#(s(plus(N,M))) | (150) |
active#(isNat(plus(V1,V2))) | → | and#(isNat(V1),isNat(V2)) | (151) |
U31#(active(X)) | → | U31#(X) | (152) |
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (153) |
U41#(mark(X1),X2,X3) | → | U41#(X1,X2,X3) | (154) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (155) |
x#(mark(X1),X2) | → | x#(X1,X2) | (156) |
plus#(X1,active(X2)) | → | plus#(X1,X2) | (157) |
The dependency pairs are split into 10 components.
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (155) |
active#(isNat(x(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (117) |
active#(and(tt,X)) | → | mark#(X) | (113) |
mark#(U41(X1,X2,X3)) | → | mark#(X1) | (111) |
active#(isNat(s(V1))) | → | mark#(isNat(V1)) | (110) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (104) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (103) |
active#(U21(tt,M,N)) | → | mark#(s(plus(N,M))) | (150) |
mark#(U31(X)) | → | mark#(X) | (149) |
mark#(and(X1,X2)) | → | active#(and(mark(X1),X2)) | (145) |
mark#(x(X1,X2)) | → | mark#(X2) | (144) |
mark#(U21(X1,X2,X3)) | → | mark#(X1) | (143) |
mark#(plus(X1,X2)) | → | mark#(X1) | (94) |
active#(x(N,0)) | → | mark#(U31(isNat(N))) | (88) |
mark#(x(X1,X2)) | → | mark#(X1) | (87) |
mark#(and(X1,X2)) | → | mark#(X1) | (83) |
active#(U11(tt,N)) | → | mark#(N) | (135) |
active#(plus(N,0)) | → | mark#(U11(isNat(N),N)) | (81) |
mark#(U31(X)) | → | active#(U31(mark(X))) | (79) |
mark#(s(X)) | → | active#(s(mark(X))) | (77) |
active#(isNat(plus(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (76) |
mark#(x(X1,X2)) | → | active#(x(mark(X1),mark(X2))) | (130) |
mark#(s(X)) | → | mark#(X) | (74) |
mark#(U11(X1,X2)) | → | mark#(X1) | (75) |
mark#(plus(X1,X2)) | → | mark#(X2) | (71) |
active#(U41(tt,M,N)) | → | mark#(plus(x(N,M),N)) | (123) |
mark#(U21(X1,X2,X3)) | → | active#(U21(mark(X1),X2,X3)) | (64) |
mark#(isNat(X)) | → | active#(isNat(X)) | (63) |
active#(plus(N,s(M))) | → | mark#(U21(and(isNat(M),isNat(N)),M,N)) | (62) |
active#(x(N,s(M))) | → | mark#(U41(and(isNat(M),isNat(N)),M,N)) | (118) |
[U21(x1, x2, x3)] | = | 36336 |
[U11(x1, x2)] | = | 36336 |
[s(x1)] | = | 35495 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | 36336 |
[plus#(x1, x2)] | = | 0 |
[x(x1, x2)] | = | 36336 |
[mark#(x1)] | = | 36336 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | 1 |
[isNat(x1)] | = | 36336 |
[plus(x1, x2)] | = | 36336 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | 1 |
[U31(x1)] | = | 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | x1 + 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 5 |
[U41(x1, x2, x3)] | = | 36336 |
[U31#(x1)] | = | 0 |
[and#(x1, x2)] | = | 0 |
mark(plus(X1,X2)) | → | active(plus(mark(X1),mark(X2))) | (18) |
x(X1,mark(X2)) | → | x(X1,X2) | (50) |
active(U41(tt,M,N)) | → | mark(plus(x(N,M),N)) | (4) |
mark(tt) | → | active(tt) | (15) |
active(isNat(s(V1))) | → | mark(isNat(V1)) | (8) |
and(X1,mark(X2)) | → | and(X1,X2) | (54) |
active(U11(tt,N)) | → | mark(N) | (1) |
active(U31(tt)) | → | mark(0) | (3) |
mark(U21(X1,X2,X3)) | → | active(U21(mark(X1),X2,X3)) | (16) |
mark(U41(X1,X2,X3)) | → | active(U41(mark(X1),X2,X3)) | (21) |
s(active(X)) | → | s(X) | (36) |
U11(X1,mark(X2)) | → | U11(X1,X2) | (26) |
mark(U31(X)) | → | active(U31(mark(X))) | (19) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (32) |
mark(s(X)) | → | active(s(mark(X))) | (17) |
U11(active(X1),X2) | → | U11(X1,X2) | (27) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (34) |
mark(x(X1,X2)) | → | active(x(mark(X1),mark(X2))) | (22) |
U11(X1,active(X2)) | → | U11(X1,X2) | (28) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (44) |
active(and(tt,X)) | → | mark(X) | (5) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (33) |
active(plus(N,0)) | → | mark(U11(isNat(N),N)) | (10) |
plus(active(X1),X2) | → | plus(X1,X2) | (39) |
active(isNat(plus(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (7) |
mark(0) | → | active(0) | (20) |
U11(mark(X1),X2) | → | U11(X1,X2) | (25) |
x(mark(X1),X2) | → | x(X1,X2) | (49) |
x(X1,active(X2)) | → | x(X1,X2) | (52) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (30) |
mark(U11(X1,X2)) | → | active(U11(mark(X1),X2)) | (14) |
and(X1,active(X2)) | → | and(X1,X2) | (56) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (31) |
active(x(N,0)) | → | mark(U31(isNat(N))) | (12) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (45) |
mark(and(X1,X2)) | → | active(and(mark(X1),X2)) | (23) |
mark(isNat(X)) | → | active(isNat(X)) | (24) |
isNat(mark(X)) | → | isNat(X) | (57) |
active(plus(N,s(M))) | → | mark(U21(and(isNat(M),isNat(N)),M,N)) | (11) |
active(isNat(x(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (9) |
active(x(N,s(M))) | → | mark(U41(and(isNat(M),isNat(N)),M,N)) | (13) |
x(active(X1),X2) | → | x(X1,X2) | (51) |
plus(X1,active(X2)) | → | plus(X1,X2) | (40) |
and(active(X1),X2) | → | and(X1,X2) | (55) |
active(isNat(0)) | → | mark(tt) | (6) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (38) |
isNat(active(X)) | → | isNat(X) | (58) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (48) |
and(mark(X1),X2) | → | and(X1,X2) | (53) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (47) |
plus(mark(X1),X2) | → | plus(X1,X2) | (37) |
U31(mark(X)) | → | U31(X) | (41) |
U31(active(X)) | → | U31(X) | (42) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (46) |
s(mark(X)) | → | s(X) | (35) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (29) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (43) |
active(U21(tt,M,N)) | → | mark(s(plus(N,M))) | (2) |
mark#(U31(X)) | → | active#(U31(mark(X))) | (79) |
mark#(s(X)) | → | active#(s(mark(X))) | (77) |
The dependency pairs are split into 1 component.
mark#(plus(X1,X2)) | → | mark#(X2) | (71) |
mark#(plus(X1,X2)) | → | mark#(X1) | (94) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (104) |
active#(U41(tt,M,N)) | → | mark#(plus(x(N,M),N)) | (123) |
active#(isNat(s(V1))) | → | mark#(isNat(V1)) | (110) |
active#(U11(tt,N)) | → | mark#(N) | (135) |
mark#(U21(X1,X2,X3)) | → | mark#(X1) | (143) |
mark#(U21(X1,X2,X3)) | → | active#(U21(mark(X1),X2,X3)) | (64) |
mark#(U41(X1,X2,X3)) | → | mark#(X1) | (111) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (155) |
mark#(U31(X)) | → | mark#(X) | (149) |
mark#(s(X)) | → | mark#(X) | (74) |
mark#(x(X1,X2)) | → | mark#(X2) | (144) |
mark#(x(X1,X2)) | → | mark#(X1) | (87) |
mark#(x(X1,X2)) | → | active#(x(mark(X1),mark(X2))) | (130) |
active#(and(tt,X)) | → | mark#(X) | (113) |
active#(plus(N,0)) | → | mark#(U11(isNat(N),N)) | (81) |
active#(isNat(plus(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (76) |
mark#(U11(X1,X2)) | → | mark#(X1) | (75) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (103) |
active#(x(N,0)) | → | mark#(U31(isNat(N))) | (88) |
mark#(and(X1,X2)) | → | mark#(X1) | (83) |
mark#(and(X1,X2)) | → | active#(and(mark(X1),X2)) | (145) |
mark#(isNat(X)) | → | active#(isNat(X)) | (63) |
active#(plus(N,s(M))) | → | mark#(U21(and(isNat(M),isNat(N)),M,N)) | (62) |
active#(isNat(x(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (117) |
active#(x(N,s(M))) | → | mark#(U41(and(isNat(M),isNat(N)),M,N)) | (118) |
active#(U21(tt,M,N)) | → | mark#(s(plus(N,M))) | (150) |
[U21(x1, x2, x3)] | = | max(x1 + 1, x2 + 21878, x3 + 0, 0) |
[U11(x1, x2)] | = | max(x1 + 1, x2 + 0, 0) |
[s(x1)] | = | x1 + 0 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[plus#(x1, x2)] | = | max(0) |
[x(x1, x2)] | = | max(x1 + 21880, x2 + 21881, 0) |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 1 |
[x#(x1, x2)] | = | max(0) |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[isNat(x1)] | = | 19430 |
[plus(x1, x2)] | = | max(x1 + 0, x2 + 21878, 0) |
[U11#(x1, x2)] | = | max(0) |
[active(x1)] | = | x1 + 0 |
[U31(x1)] | = | x1 + 591 |
[U41#(x1, x2, x3)] | = | max(0) |
[active#(x1)] | = | x1 + 0 |
[U21#(x1, x2, x3)] | = | max(0) |
[tt] | = | 19428 |
[U41(x1, x2, x3)] | = | max(x1 + 2451, x2 + 21881, x3 + 21880, 0) |
[U31#(x1)] | = | 0 |
[and#(x1, x2)] | = | max(0) |
mark(plus(X1,X2)) | → | active(plus(mark(X1),mark(X2))) | (18) |
x(X1,mark(X2)) | → | x(X1,X2) | (50) |
active(U41(tt,M,N)) | → | mark(plus(x(N,M),N)) | (4) |
mark(tt) | → | active(tt) | (15) |
active(isNat(s(V1))) | → | mark(isNat(V1)) | (8) |
and(X1,mark(X2)) | → | and(X1,X2) | (54) |
active(U11(tt,N)) | → | mark(N) | (1) |
active(U31(tt)) | → | mark(0) | (3) |
mark(U21(X1,X2,X3)) | → | active(U21(mark(X1),X2,X3)) | (16) |
mark(U41(X1,X2,X3)) | → | active(U41(mark(X1),X2,X3)) | (21) |
s(active(X)) | → | s(X) | (36) |
U11(X1,mark(X2)) | → | U11(X1,X2) | (26) |
mark(U31(X)) | → | active(U31(mark(X))) | (19) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (32) |
mark(s(X)) | → | active(s(mark(X))) | (17) |
U11(active(X1),X2) | → | U11(X1,X2) | (27) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (34) |
mark(x(X1,X2)) | → | active(x(mark(X1),mark(X2))) | (22) |
U11(X1,active(X2)) | → | U11(X1,X2) | (28) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (44) |
active(and(tt,X)) | → | mark(X) | (5) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (33) |
active(plus(N,0)) | → | mark(U11(isNat(N),N)) | (10) |
plus(active(X1),X2) | → | plus(X1,X2) | (39) |
active(isNat(plus(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (7) |
mark(0) | → | active(0) | (20) |
U11(mark(X1),X2) | → | U11(X1,X2) | (25) |
x(mark(X1),X2) | → | x(X1,X2) | (49) |
x(X1,active(X2)) | → | x(X1,X2) | (52) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (30) |
mark(U11(X1,X2)) | → | active(U11(mark(X1),X2)) | (14) |
and(X1,active(X2)) | → | and(X1,X2) | (56) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (31) |
active(x(N,0)) | → | mark(U31(isNat(N))) | (12) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (45) |
mark(and(X1,X2)) | → | active(and(mark(X1),X2)) | (23) |
mark(isNat(X)) | → | active(isNat(X)) | (24) |
isNat(mark(X)) | → | isNat(X) | (57) |
active(plus(N,s(M))) | → | mark(U21(and(isNat(M),isNat(N)),M,N)) | (11) |
active(isNat(x(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (9) |
active(x(N,s(M))) | → | mark(U41(and(isNat(M),isNat(N)),M,N)) | (13) |
x(active(X1),X2) | → | x(X1,X2) | (51) |
plus(X1,active(X2)) | → | plus(X1,X2) | (40) |
and(active(X1),X2) | → | and(X1,X2) | (55) |
active(isNat(0)) | → | mark(tt) | (6) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (38) |
isNat(active(X)) | → | isNat(X) | (58) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (48) |
and(mark(X1),X2) | → | and(X1,X2) | (53) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (47) |
plus(mark(X1),X2) | → | plus(X1,X2) | (37) |
U31(mark(X)) | → | U31(X) | (41) |
U31(active(X)) | → | U31(X) | (42) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (46) |
s(mark(X)) | → | s(X) | (35) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (29) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (43) |
active(U21(tt,M,N)) | → | mark(s(plus(N,M))) | (2) |
mark#(plus(X1,X2)) | → | mark#(X2) | (71) |
mark#(U21(X1,X2,X3)) | → | mark#(X1) | (143) |
mark#(U41(X1,X2,X3)) | → | mark#(X1) | (111) |
mark#(U31(X)) | → | mark#(X) | (149) |
mark#(x(X1,X2)) | → | mark#(X2) | (144) |
mark#(x(X1,X2)) | → | mark#(X1) | (87) |
mark#(U11(X1,X2)) | → | mark#(X1) | (75) |
active#(x(N,0)) | → | mark#(U31(isNat(N))) | (88) |
The dependency pairs are split into 1 component.
mark#(plus(X1,X2)) | → | mark#(X1) | (94) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (104) |
active#(U41(tt,M,N)) | → | mark#(plus(x(N,M),N)) | (123) |
active#(isNat(s(V1))) | → | mark#(isNat(V1)) | (110) |
active#(U11(tt,N)) | → | mark#(N) | (135) |
mark#(U21(X1,X2,X3)) | → | active#(U21(mark(X1),X2,X3)) | (64) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (155) |
mark#(s(X)) | → | mark#(X) | (74) |
mark#(x(X1,X2)) | → | active#(x(mark(X1),mark(X2))) | (130) |
active#(and(tt,X)) | → | mark#(X) | (113) |
active#(plus(N,0)) | → | mark#(U11(isNat(N),N)) | (81) |
active#(isNat(plus(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (76) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (103) |
mark#(and(X1,X2)) | → | mark#(X1) | (83) |
mark#(and(X1,X2)) | → | active#(and(mark(X1),X2)) | (145) |
mark#(isNat(X)) | → | active#(isNat(X)) | (63) |
active#(plus(N,s(M))) | → | mark#(U21(and(isNat(M),isNat(N)),M,N)) | (62) |
active#(isNat(x(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (117) |
active#(x(N,s(M))) | → | mark#(U41(and(isNat(M),isNat(N)),M,N)) | (118) |
active#(U21(tt,M,N)) | → | mark#(s(plus(N,M))) | (150) |
[U21(x1, x2, x3)] | = | max(x2 + 38781, x3 + 0, 0) |
[U11(x1, x2)] | = | max(x2 + 0, 0) |
[s(x1)] | = | x1 + 0 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | max(x1 + 0, x2 + 1, 0) |
[plus#(x1, x2)] | = | max(0) |
[x(x1, x2)] | = | max(x1 + 38781, x2 + 16336, 0) |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 22325 |
[x#(x1, x2)] | = | max(0) |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[isNat(x1)] | = | x1 + 5969 |
[plus(x1, x2)] | = | max(x1 + 0, x2 + 38781, 0) |
[U11#(x1, x2)] | = | max(0) |
[active(x1)] | = | x1 + 0 |
[U31(x1)] | = | x1 + 32812 |
[U41#(x1, x2, x3)] | = | max(0) |
[active#(x1)] | = | x1 + 0 |
[U21#(x1, x2, x3)] | = | max(0) |
[tt] | = | 17525 |
[U41(x1, x2, x3)] | = | max(x2 + 16336, x3 + 38781, 0) |
[U31#(x1)] | = | 0 |
[and#(x1, x2)] | = | max(0) |
mark(plus(X1,X2)) | → | active(plus(mark(X1),mark(X2))) | (18) |
x(X1,mark(X2)) | → | x(X1,X2) | (50) |
active(U41(tt,M,N)) | → | mark(plus(x(N,M),N)) | (4) |
mark(tt) | → | active(tt) | (15) |
active(isNat(s(V1))) | → | mark(isNat(V1)) | (8) |
and(X1,mark(X2)) | → | and(X1,X2) | (54) |
active(U11(tt,N)) | → | mark(N) | (1) |
active(U31(tt)) | → | mark(0) | (3) |
mark(U21(X1,X2,X3)) | → | active(U21(mark(X1),X2,X3)) | (16) |
mark(U41(X1,X2,X3)) | → | active(U41(mark(X1),X2,X3)) | (21) |
s(active(X)) | → | s(X) | (36) |
U11(X1,mark(X2)) | → | U11(X1,X2) | (26) |
mark(U31(X)) | → | active(U31(mark(X))) | (19) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (32) |
mark(s(X)) | → | active(s(mark(X))) | (17) |
U11(active(X1),X2) | → | U11(X1,X2) | (27) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (34) |
mark(x(X1,X2)) | → | active(x(mark(X1),mark(X2))) | (22) |
U11(X1,active(X2)) | → | U11(X1,X2) | (28) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (44) |
active(and(tt,X)) | → | mark(X) | (5) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (33) |
active(plus(N,0)) | → | mark(U11(isNat(N),N)) | (10) |
plus(active(X1),X2) | → | plus(X1,X2) | (39) |
active(isNat(plus(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (7) |
mark(0) | → | active(0) | (20) |
U11(mark(X1),X2) | → | U11(X1,X2) | (25) |
x(mark(X1),X2) | → | x(X1,X2) | (49) |
x(X1,active(X2)) | → | x(X1,X2) | (52) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (30) |
mark(U11(X1,X2)) | → | active(U11(mark(X1),X2)) | (14) |
and(X1,active(X2)) | → | and(X1,X2) | (56) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (31) |
active(x(N,0)) | → | mark(U31(isNat(N))) | (12) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (45) |
mark(and(X1,X2)) | → | active(and(mark(X1),X2)) | (23) |
mark(isNat(X)) | → | active(isNat(X)) | (24) |
isNat(mark(X)) | → | isNat(X) | (57) |
active(plus(N,s(M))) | → | mark(U21(and(isNat(M),isNat(N)),M,N)) | (11) |
active(isNat(x(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (9) |
active(x(N,s(M))) | → | mark(U41(and(isNat(M),isNat(N)),M,N)) | (13) |
x(active(X1),X2) | → | x(X1,X2) | (51) |
plus(X1,active(X2)) | → | plus(X1,X2) | (40) |
and(active(X1),X2) | → | and(X1,X2) | (55) |
active(isNat(0)) | → | mark(tt) | (6) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (38) |
isNat(active(X)) | → | isNat(X) | (58) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (48) |
and(mark(X1),X2) | → | and(X1,X2) | (53) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (47) |
plus(mark(X1),X2) | → | plus(X1,X2) | (37) |
U31(mark(X)) | → | U31(X) | (41) |
U31(active(X)) | → | U31(X) | (42) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (46) |
s(mark(X)) | → | s(X) | (35) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (29) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (43) |
active(U21(tt,M,N)) | → | mark(s(plus(N,M))) | (2) |
active#(and(tt,X)) | → | mark#(X) | (113) |
active#(isNat(x(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (117) |
The dependency pairs are split into 1 component.
mark#(plus(X1,X2)) | → | mark#(X1) | (94) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (104) |
active#(U41(tt,M,N)) | → | mark#(plus(x(N,M),N)) | (123) |
active#(isNat(s(V1))) | → | mark#(isNat(V1)) | (110) |
active#(U11(tt,N)) | → | mark#(N) | (135) |
mark#(U21(X1,X2,X3)) | → | active#(U21(mark(X1),X2,X3)) | (64) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (155) |
mark#(s(X)) | → | mark#(X) | (74) |
mark#(x(X1,X2)) | → | active#(x(mark(X1),mark(X2))) | (130) |
active#(plus(N,0)) | → | mark#(U11(isNat(N),N)) | (81) |
active#(isNat(plus(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (76) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (103) |
mark#(and(X1,X2)) | → | mark#(X1) | (83) |
mark#(and(X1,X2)) | → | active#(and(mark(X1),X2)) | (145) |
mark#(isNat(X)) | → | active#(isNat(X)) | (63) |
active#(plus(N,s(M))) | → | mark#(U21(and(isNat(M),isNat(N)),M,N)) | (62) |
active#(x(N,s(M))) | → | mark#(U41(and(isNat(M),isNat(N)),M,N)) | (118) |
active#(U21(tt,M,N)) | → | mark#(s(plus(N,M))) | (150) |
[U21(x1, x2, x3)] | = | 9049 |
[U11(x1, x2)] | = | 9049 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | 1 |
[plus#(x1, x2)] | = | 0 |
[x(x1, x2)] | = | 9049 |
[mark#(x1)] | = | 9049 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | 0 |
[isNat(x1)] | = | 9049 |
[plus(x1, x2)] | = | 9049 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | 0 |
[U31(x1)] | = | 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | x1 + 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 1 |
[U41(x1, x2, x3)] | = | 9049 |
[U31#(x1)] | = | 0 |
[and#(x1, x2)] | = | 0 |
mark(plus(X1,X2)) | → | active(plus(mark(X1),mark(X2))) | (18) |
x(X1,mark(X2)) | → | x(X1,X2) | (50) |
active(U41(tt,M,N)) | → | mark(plus(x(N,M),N)) | (4) |
mark(tt) | → | active(tt) | (15) |
active(isNat(s(V1))) | → | mark(isNat(V1)) | (8) |
and(X1,mark(X2)) | → | and(X1,X2) | (54) |
active(U11(tt,N)) | → | mark(N) | (1) |
active(U31(tt)) | → | mark(0) | (3) |
mark(U21(X1,X2,X3)) | → | active(U21(mark(X1),X2,X3)) | (16) |
mark(U41(X1,X2,X3)) | → | active(U41(mark(X1),X2,X3)) | (21) |
s(active(X)) | → | s(X) | (36) |
U11(X1,mark(X2)) | → | U11(X1,X2) | (26) |
mark(U31(X)) | → | active(U31(mark(X))) | (19) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (32) |
mark(s(X)) | → | active(s(mark(X))) | (17) |
U11(active(X1),X2) | → | U11(X1,X2) | (27) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (34) |
mark(x(X1,X2)) | → | active(x(mark(X1),mark(X2))) | (22) |
U11(X1,active(X2)) | → | U11(X1,X2) | (28) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (44) |
active(and(tt,X)) | → | mark(X) | (5) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (33) |
active(plus(N,0)) | → | mark(U11(isNat(N),N)) | (10) |
plus(active(X1),X2) | → | plus(X1,X2) | (39) |
active(isNat(plus(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (7) |
mark(0) | → | active(0) | (20) |
U11(mark(X1),X2) | → | U11(X1,X2) | (25) |
x(mark(X1),X2) | → | x(X1,X2) | (49) |
x(X1,active(X2)) | → | x(X1,X2) | (52) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (30) |
mark(U11(X1,X2)) | → | active(U11(mark(X1),X2)) | (14) |
and(X1,active(X2)) | → | and(X1,X2) | (56) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (31) |
active(x(N,0)) | → | mark(U31(isNat(N))) | (12) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (45) |
mark(and(X1,X2)) | → | active(and(mark(X1),X2)) | (23) |
mark(isNat(X)) | → | active(isNat(X)) | (24) |
isNat(mark(X)) | → | isNat(X) | (57) |
active(plus(N,s(M))) | → | mark(U21(and(isNat(M),isNat(N)),M,N)) | (11) |
active(isNat(x(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (9) |
active(x(N,s(M))) | → | mark(U41(and(isNat(M),isNat(N)),M,N)) | (13) |
x(active(X1),X2) | → | x(X1,X2) | (51) |
plus(X1,active(X2)) | → | plus(X1,X2) | (40) |
and(active(X1),X2) | → | and(X1,X2) | (55) |
active(isNat(0)) | → | mark(tt) | (6) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (38) |
isNat(active(X)) | → | isNat(X) | (58) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (48) |
and(mark(X1),X2) | → | and(X1,X2) | (53) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (47) |
plus(mark(X1),X2) | → | plus(X1,X2) | (37) |
U31(mark(X)) | → | U31(X) | (41) |
U31(active(X)) | → | U31(X) | (42) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (46) |
s(mark(X)) | → | s(X) | (35) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (29) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (43) |
active(U21(tt,M,N)) | → | mark(s(plus(N,M))) | (2) |
mark#(and(X1,X2)) | → | active#(and(mark(X1),X2)) | (145) |
The dependency pairs are split into 1 component.
mark#(plus(X1,X2)) | → | mark#(X1) | (94) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (104) |
active#(U41(tt,M,N)) | → | mark#(plus(x(N,M),N)) | (123) |
active#(isNat(s(V1))) | → | mark#(isNat(V1)) | (110) |
active#(U11(tt,N)) | → | mark#(N) | (135) |
mark#(U21(X1,X2,X3)) | → | active#(U21(mark(X1),X2,X3)) | (64) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (155) |
mark#(s(X)) | → | mark#(X) | (74) |
mark#(x(X1,X2)) | → | active#(x(mark(X1),mark(X2))) | (130) |
active#(plus(N,0)) | → | mark#(U11(isNat(N),N)) | (81) |
active#(isNat(plus(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (76) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (103) |
mark#(and(X1,X2)) | → | mark#(X1) | (83) |
mark#(isNat(X)) | → | active#(isNat(X)) | (63) |
active#(plus(N,s(M))) | → | mark#(U21(and(isNat(M),isNat(N)),M,N)) | (62) |
active#(x(N,s(M))) | → | mark#(U41(and(isNat(M),isNat(N)),M,N)) | (118) |
active#(U21(tt,M,N)) | → | mark#(s(plus(N,M))) | (150) |
π(s#) | = | 1 |
π(mark) | = | 1 |
π(active) | = | 1 |
π(active#) | = | 1 |
prec(U21) | = | 4 | status(U21) | = | [2, 3, 1] | list-extension(U21) | = | Lex | ||
prec(U11) | = | 3 | status(U11) | = | [2, 1] | list-extension(U11) | = | Lex | ||
prec(s) | = | 1 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(isNat#) | = | 0 | status(isNat#) | = | [] | list-extension(isNat#) | = | Lex | ||
prec(and) | = | 3 | status(and) | = | [2, 1] | list-extension(and) | = | Lex | ||
prec(plus#) | = | 0 | status(plus#) | = | [] | list-extension(plus#) | = | Lex | ||
prec(x) | = | 5 | status(x) | = | [2, 1] | list-extension(x) | = | Lex | ||
prec(mark#) | = | 2 | status(mark#) | = | [1] | list-extension(mark#) | = | Lex | ||
prec(0) | = | 0 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(x#) | = | 0 | status(x#) | = | [2, 1] | list-extension(x#) | = | Lex | ||
prec(isNat) | = | 3 | status(isNat) | = | [1] | list-extension(isNat) | = | Lex | ||
prec(plus) | = | 4 | status(plus) | = | [2, 1] | list-extension(plus) | = | Lex | ||
prec(U11#) | = | 0 | status(U11#) | = | [1, 2] | list-extension(U11#) | = | Lex | ||
prec(U31) | = | 4 | status(U31) | = | [] | list-extension(U31) | = | Lex | ||
prec(U41#) | = | 0 | status(U41#) | = | [1, 2, 3] | list-extension(U41#) | = | Lex | ||
prec(U21#) | = | 0 | status(U21#) | = | [3, 1] | list-extension(U21#) | = | Lex | ||
prec(tt) | = | 0 | status(tt) | = | [] | list-extension(tt) | = | Lex | ||
prec(U41) | = | 5 | status(U41) | = | [2, 3, 1] | list-extension(U41) | = | Lex | ||
prec(U31#) | = | 0 | status(U31#) | = | [] | list-extension(U31#) | = | Lex | ||
prec(and#) | = | 0 | status(and#) | = | [2, 1] | list-extension(and#) | = | 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 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[plus#(x1, x2)] | = | max(0) |
[x(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[mark#(x1)] | = | x1 + 0 |
[0] | = | 0 |
[x#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[isNat(x1)] | = | x1 + 0 |
[plus(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[U11#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[U31(x1)] | = | 0 |
[U41#(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U21#(x1, x2, x3)] | = | max(x1 + 0, x3 + 0, 0) |
[tt] | = | 0 |
[U41(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[U31#(x1)] | = | 0 |
[and#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
mark(plus(X1,X2)) | → | active(plus(mark(X1),mark(X2))) | (18) |
x(X1,mark(X2)) | → | x(X1,X2) | (50) |
active(U41(tt,M,N)) | → | mark(plus(x(N,M),N)) | (4) |
mark(tt) | → | active(tt) | (15) |
active(isNat(s(V1))) | → | mark(isNat(V1)) | (8) |
and(X1,mark(X2)) | → | and(X1,X2) | (54) |
active(U11(tt,N)) | → | mark(N) | (1) |
active(U31(tt)) | → | mark(0) | (3) |
mark(U21(X1,X2,X3)) | → | active(U21(mark(X1),X2,X3)) | (16) |
mark(U41(X1,X2,X3)) | → | active(U41(mark(X1),X2,X3)) | (21) |
s(active(X)) | → | s(X) | (36) |
U11(X1,mark(X2)) | → | U11(X1,X2) | (26) |
mark(U31(X)) | → | active(U31(mark(X))) | (19) |
U21(active(X1),X2,X3) | → | U21(X1,X2,X3) | (32) |
mark(s(X)) | → | active(s(mark(X))) | (17) |
U11(active(X1),X2) | → | U11(X1,X2) | (27) |
U21(X1,X2,active(X3)) | → | U21(X1,X2,X3) | (34) |
mark(x(X1,X2)) | → | active(x(mark(X1),mark(X2))) | (22) |
U11(X1,active(X2)) | → | U11(X1,X2) | (28) |
U41(X1,mark(X2),X3) | → | U41(X1,X2,X3) | (44) |
active(and(tt,X)) | → | mark(X) | (5) |
U21(X1,active(X2),X3) | → | U21(X1,X2,X3) | (33) |
active(plus(N,0)) | → | mark(U11(isNat(N),N)) | (10) |
plus(active(X1),X2) | → | plus(X1,X2) | (39) |
active(isNat(plus(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (7) |
mark(0) | → | active(0) | (20) |
U11(mark(X1),X2) | → | U11(X1,X2) | (25) |
x(mark(X1),X2) | → | x(X1,X2) | (49) |
x(X1,active(X2)) | → | x(X1,X2) | (52) |
U21(X1,mark(X2),X3) | → | U21(X1,X2,X3) | (30) |
mark(U11(X1,X2)) | → | active(U11(mark(X1),X2)) | (14) |
and(X1,active(X2)) | → | and(X1,X2) | (56) |
U21(X1,X2,mark(X3)) | → | U21(X1,X2,X3) | (31) |
active(x(N,0)) | → | mark(U31(isNat(N))) | (12) |
U41(X1,X2,mark(X3)) | → | U41(X1,X2,X3) | (45) |
mark(and(X1,X2)) | → | active(and(mark(X1),X2)) | (23) |
mark(isNat(X)) | → | active(isNat(X)) | (24) |
isNat(mark(X)) | → | isNat(X) | (57) |
active(plus(N,s(M))) | → | mark(U21(and(isNat(M),isNat(N)),M,N)) | (11) |
active(isNat(x(V1,V2))) | → | mark(and(isNat(V1),isNat(V2))) | (9) |
active(x(N,s(M))) | → | mark(U41(and(isNat(M),isNat(N)),M,N)) | (13) |
x(active(X1),X2) | → | x(X1,X2) | (51) |
plus(X1,active(X2)) | → | plus(X1,X2) | (40) |
and(active(X1),X2) | → | and(X1,X2) | (55) |
active(isNat(0)) | → | mark(tt) | (6) |
plus(X1,mark(X2)) | → | plus(X1,X2) | (38) |
isNat(active(X)) | → | isNat(X) | (58) |
U41(X1,X2,active(X3)) | → | U41(X1,X2,X3) | (48) |
and(mark(X1),X2) | → | and(X1,X2) | (53) |
U41(X1,active(X2),X3) | → | U41(X1,X2,X3) | (47) |
plus(mark(X1),X2) | → | plus(X1,X2) | (37) |
U31(mark(X)) | → | U31(X) | (41) |
U31(active(X)) | → | U31(X) | (42) |
U41(active(X1),X2,X3) | → | U41(X1,X2,X3) | (46) |
s(mark(X)) | → | s(X) | (35) |
U21(mark(X1),X2,X3) | → | U21(X1,X2,X3) | (29) |
U41(mark(X1),X2,X3) | → | U41(X1,X2,X3) | (43) |
active(U21(tt,M,N)) | → | mark(s(plus(N,M))) | (2) |
mark#(plus(X1,X2)) | → | mark#(X1) | (94) |
mark#(plus(X1,X2)) | → | active#(plus(mark(X1),mark(X2))) | (104) |
active#(U41(tt,M,N)) | → | mark#(plus(x(N,M),N)) | (123) |
active#(isNat(s(V1))) | → | mark#(isNat(V1)) | (110) |
active#(U11(tt,N)) | → | mark#(N) | (135) |
mark#(U21(X1,X2,X3)) | → | active#(U21(mark(X1),X2,X3)) | (64) |
mark#(U41(X1,X2,X3)) | → | active#(U41(mark(X1),X2,X3)) | (155) |
mark#(s(X)) | → | mark#(X) | (74) |
mark#(x(X1,X2)) | → | active#(x(mark(X1),mark(X2))) | (130) |
active#(plus(N,0)) | → | mark#(U11(isNat(N),N)) | (81) |
active#(isNat(plus(V1,V2))) | → | mark#(and(isNat(V1),isNat(V2))) | (76) |
mark#(U11(X1,X2)) | → | active#(U11(mark(X1),X2)) | (103) |
mark#(and(X1,X2)) | → | mark#(X1) | (83) |
mark#(isNat(X)) | → | active#(isNat(X)) | (63) |
active#(plus(N,s(M))) | → | mark#(U21(and(isNat(M),isNat(N)),M,N)) | (62) |
active#(x(N,s(M))) | → | mark#(U41(and(isNat(M),isNat(N)),M,N)) | (118) |
active#(U21(tt,M,N)) | → | mark#(s(plus(N,M))) | (150) |
The dependency pairs are split into 0 components.
and#(mark(X1),X2) | → | and#(X1,X2) | (106) |
and#(active(X1),X2) | → | and#(X1,X2) | (138) |
and#(X1,active(X2)) | → | and#(X1,X2) | (129) |
and#(X1,mark(X2)) | → | and#(X1,X2) | (119) |
[U21(x1, x2, x3)] | = | 1 |
[U11(x1, x2)] | = | 1 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | 1 |
[plus#(x1, x2)] | = | 0 |
[x(x1, x2)] | = | x2 + 1 |
[mark#(x1)] | = | 0 |
[0] | = | 0 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 3 |
[isNat(x1)] | = | 1 |
[plus(x1, x2)] | = | x1 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1)] | = | 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 0 |
[U41(x1, x2, x3)] | = | x2 + 2 |
[U31#(x1)] | = | 0 |
[and#(x1, x2)] | = | x2 + 0 |
U31(mark(X)) | → | U31(X) | (41) |
U31(active(X)) | → | U31(X) | (42) |
and#(X1,active(X2)) | → | and#(X1,X2) | (129) |
and#(X1,mark(X2)) | → | and#(X1,X2) | (119) |
The dependency pairs are split into 1 component.
and#(active(X1),X2) | → | and#(X1,X2) | (138) |
and#(mark(X1),X2) | → | and#(X1,X2) | (106) |
[U21(x1, x2, x3)] | = | 2 |
[U11(x1, x2)] | = | 2 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | 1 |
[plus#(x1, x2)] | = | 0 |
[x(x1, x2)] | = | x2 + 1 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 4 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + 2 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1)] | = | 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 0 |
[U41(x1, x2, x3)] | = | x2 + 2 |
[U31#(x1)] | = | 0 |
[and#(x1, x2)] | = | x1 + 0 |
U31(mark(X)) | → | U31(X) | (41) |
U31(active(X)) | → | U31(X) | (42) |
and#(active(X1),X2) | → | and#(X1,X2) | (138) |
and#(mark(X1),X2) | → | and#(X1,X2) | (106) |
The dependency pairs are split into 0 components.
U11#(X1,mark(X2)) | → | U11#(X1,X2) | (102) |
U11#(active(X1),X2) | → | U11#(X1,X2) | (99) |
U11#(mark(X1),X2) | → | U11#(X1,X2) | (90) |
U11#(X1,active(X2)) | → | U11#(X1,X2) | (125) |
[U21(x1, x2, x3)] | = | 3 |
[U11(x1, x2)] | = | 1 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | 1 |
[plus#(x1, x2)] | = | 0 |
[x(x1, x2)] | = | x2 + 1 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 4 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + 1 |
[U11#(x1, x2)] | = | x1 + x2 + 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1)] | = | 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 0 |
[U41(x1, x2, x3)] | = | x2 + 1 |
[U31#(x1)] | = | 0 |
[and#(x1, x2)] | = | 0 |
U31(mark(X)) | → | U31(X) | (41) |
U31(active(X)) | → | U31(X) | (42) |
U11#(X1,mark(X2)) | → | U11#(X1,X2) | (102) |
U11#(active(X1),X2) | → | U11#(X1,X2) | (99) |
U11#(mark(X1),X2) | → | U11#(X1,X2) | (90) |
U11#(X1,active(X2)) | → | U11#(X1,X2) | (125) |
The dependency pairs are split into 0 components.
s#(active(X)) | → | s#(X) | (108) |
s#(mark(X)) | → | s#(X) | (84) |
[U21(x1, x2, x3)] | = | 10949 |
[U11(x1, x2)] | = | 6447 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | 13856 |
[plus#(x1, x2)] | = | 0 |
[x(x1, x2)] | = | x2 + 8028 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | x1 + 0 |
[mark(x1)] | = | x1 + 21807 |
[isNat(x1)] | = | x1 + 21804 |
[plus(x1, x2)] | = | x1 + 3 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1)] | = | 6773 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 0 |
[U41(x1, x2, x3)] | = | x2 + 3103 |
[U31#(x1)] | = | 0 |
[and#(x1, x2)] | = | 0 |
U31(mark(X)) | → | U31(X) | (41) |
U31(active(X)) | → | U31(X) | (42) |
s#(active(X)) | → | s#(X) | (108) |
s#(mark(X)) | → | s#(X) | (84) |
The dependency pairs are split into 0 components.
U31#(active(X)) | → | U31#(X) | (152) |
U31#(mark(X)) | → | U31#(X) | (92) |
[U21(x1, x2, x3)] | = | 1 |
[U11(x1, x2)] | = | 2 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | 1 |
[plus#(x1, x2)] | = | 0 |
[x(x1, x2)] | = | x2 + 1 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 4 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1)] | = | 3 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 0 |
[U41(x1, x2, x3)] | = | x2 + 4 |
[U31#(x1)] | = | x1 + 0 |
[and#(x1, x2)] | = | 0 |
U31(mark(X)) | → | U31(X) | (41) |
U31(active(X)) | → | U31(X) | (42) |
U31#(active(X)) | → | U31#(X) | (152) |
U31#(mark(X)) | → | U31#(X) | (92) |
The dependency pairs are split into 0 components.
U41#(mark(X1),X2,X3) | → | U41#(X1,X2,X3) | (154) |
U41#(X1,active(X2),X3) | → | U41#(X1,X2,X3) | (93) |
U41#(X1,X2,active(X3)) | → | U41#(X1,X2,X3) | (91) |
U41#(X1,mark(X2),X3) | → | U41#(X1,X2,X3) | (141) |
U41#(X1,X2,mark(X3)) | → | U41#(X1,X2,X3) | (121) |
U41#(active(X1),X2,X3) | → | U41#(X1,X2,X3) | (120) |
[U21(x1, x2, x3)] | = | 1 |
[U11(x1, x2)] | = | 2 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | 1 |
[plus#(x1, x2)] | = | 0 |
[x(x1, x2)] | = | x2 + 1 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 4 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1)] | = | 1 |
[U41#(x1, x2, x3)] | = | x1 + x2 + x3 + 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 0 |
[U41(x1, x2, x3)] | = | x2 + 1 |
[U31#(x1)] | = | 0 |
[and#(x1, x2)] | = | 0 |
U31(mark(X)) | → | U31(X) | (41) |
U31(active(X)) | → | U31(X) | (42) |
U41#(mark(X1),X2,X3) | → | U41#(X1,X2,X3) | (154) |
U41#(X1,active(X2),X3) | → | U41#(X1,X2,X3) | (93) |
U41#(X1,X2,active(X3)) | → | U41#(X1,X2,X3) | (91) |
U41#(X1,mark(X2),X3) | → | U41#(X1,X2,X3) | (141) |
U41#(X1,X2,mark(X3)) | → | U41#(X1,X2,X3) | (121) |
U41#(active(X1),X2,X3) | → | U41#(X1,X2,X3) | (120) |
The dependency pairs are split into 0 components.
isNat#(active(X)) | → | isNat#(X) | (112) |
isNat#(mark(X)) | → | isNat#(X) | (133) |
[U21(x1, x2, x3)] | = | 2 |
[U11(x1, x2)] | = | 2 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | x1 + 0 |
[and(x1, x2)] | = | 1 |
[plus#(x1, x2)] | = | 0 |
[x(x1, x2)] | = | x2 + 1 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 4 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1)] | = | 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 0 |
[U41(x1, x2, x3)] | = | x2 + 3 |
[U31#(x1)] | = | 0 |
[and#(x1, x2)] | = | 0 |
U31(mark(X)) | → | U31(X) | (41) |
U31(active(X)) | → | U31(X) | (42) |
isNat#(active(X)) | → | isNat#(X) | (112) |
isNat#(mark(X)) | → | isNat#(X) | (133) |
The dependency pairs are split into 0 components.
U21#(X1,X2,active(X3)) | → | U21#(X1,X2,X3) | (105) |
U21#(X1,active(X2),X3) | → | U21#(X1,X2,X3) | (82) |
U21#(active(X1),X2,X3) | → | U21#(X1,X2,X3) | (80) |
U21#(X1,mark(X2),X3) | → | U21#(X1,X2,X3) | (78) |
U21#(mark(X1),X2,X3) | → | U21#(X1,X2,X3) | (128) |
U21#(X1,X2,mark(X3)) | → | U21#(X1,X2,X3) | (61) |
[U21(x1, x2, x3)] | = | 1 |
[U11(x1, x2)] | = | 1 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | 2 |
[plus#(x1, x2)] | = | 0 |
[x(x1, x2)] | = | x2 + 1 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 4 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x1 + 3 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1)] | = | 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | x2 + x3 + 0 |
[tt] | = | 0 |
[U41(x1, x2, x3)] | = | x2 + 1 |
[U31#(x1)] | = | 0 |
[and#(x1, x2)] | = | 0 |
U31(mark(X)) | → | U31(X) | (41) |
U31(active(X)) | → | U31(X) | (42) |
U21#(X1,X2,active(X3)) | → | U21#(X1,X2,X3) | (105) |
U21#(X1,active(X2),X3) | → | U21#(X1,X2,X3) | (82) |
U21#(X1,mark(X2),X3) | → | U21#(X1,X2,X3) | (78) |
U21#(X1,X2,mark(X3)) | → | U21#(X1,X2,X3) | (61) |
The dependency pairs are split into 1 component.
U21#(active(X1),X2,X3) | → | U21#(X1,X2,X3) | (80) |
U21#(mark(X1),X2,X3) | → | U21#(X1,X2,X3) | (128) |
[U21(x1, x2, x3)] | = | 2488 |
[U11(x1, x2)] | = | 410 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | 1142 |
[plus#(x1, x2)] | = | 0 |
[x(x1, x2)] | = | x2 + 1 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 4513 |
[isNat(x1)] | = | x1 + 2101 |
[plus(x1, x2)] | = | x1 + 1 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1)] | = | 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | x1 + 0 |
[tt] | = | 0 |
[U41(x1, x2, x3)] | = | x2 + 28 |
[U31#(x1)] | = | 0 |
[and#(x1, x2)] | = | 0 |
U31(mark(X)) | → | U31(X) | (41) |
U31(active(X)) | → | U31(X) | (42) |
U21#(active(X1),X2,X3) | → | U21#(X1,X2,X3) | (80) |
U21#(mark(X1),X2,X3) | → | U21#(X1,X2,X3) | (128) |
The dependency pairs are split into 0 components.
x#(mark(X1),X2) | → | x#(X1,X2) | (156) |
x#(X1,active(X2)) | → | x#(X1,X2) | (116) |
x#(active(X1),X2) | → | x#(X1,X2) | (140) |
x#(X1,mark(X2)) | → | x#(X1,X2) | (68) |
[U21(x1, x2, x3)] | = | 19314 |
[U11(x1, x2)] | = | 23959 |
[s(x1)] | = | 1 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | 1 |
[plus#(x1, x2)] | = | 0 |
[x(x1, x2)] | = | x2 + 15155 |
[mark#(x1)] | = | 0 |
[0] | = | 37883 |
[x#(x1, x2)] | = | x2 + 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 54021 |
[isNat(x1)] | = | x1 + 16136 |
[plus(x1, x2)] | = | x1 + 8752 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1)] | = | 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 0 |
[U41(x1, x2, x3)] | = | x2 + 12692 |
[U31#(x1)] | = | 0 |
[and#(x1, x2)] | = | 0 |
U31(mark(X)) | → | U31(X) | (41) |
U31(active(X)) | → | U31(X) | (42) |
x#(X1,active(X2)) | → | x#(X1,X2) | (116) |
x#(X1,mark(X2)) | → | x#(X1,X2) | (68) |
The dependency pairs are split into 1 component.
x#(mark(X1),X2) | → | x#(X1,X2) | (156) |
x#(active(X1),X2) | → | x#(X1,X2) | (140) |
[U21(x1, x2, x3)] | = | x1 + 1 |
[U11(x1, x2)] | = | x1 + 44033 |
[s(x1)] | = | x1 + 29823 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | 13862 |
[plus#(x1, x2)] | = | 0 |
[x(x1, x2)] | = | x2 + 16019 |
[mark#(x1)] | = | 0 |
[0] | = | 10026 |
[x#(x1, x2)] | = | x1 + 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 73356 |
[isNat(x1)] | = | x1 + 3901 |
[plus(x1, x2)] | = | x2 + 2061 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1)] | = | x1 + 14809 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 29321 |
[U41(x1, x2, x3)] | = | x1 + x2 + 13780 |
[U31#(x1)] | = | 0 |
[and#(x1, x2)] | = | 0 |
x#(mark(X1),X2) | → | x#(X1,X2) | (156) |
x#(active(X1),X2) | → | x#(X1,X2) | (140) |
The dependency pairs are split into 0 components.
plus#(X1,active(X2)) | → | plus#(X1,X2) | (157) |
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (153) |
plus#(active(X1),X2) | → | plus#(X1,X2) | (95) |
plus#(mark(X1),X2) | → | plus#(X1,X2) | (122) |
[U21(x1, x2, x3)] | = | x1 + 2 |
[U11(x1, x2)] | = | x1 + 1 |
[s(x1)] | = | x1 + 1 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | x1 + x2 + 1 |
[plus#(x1, x2)] | = | x1 + 0 |
[x(x1, x2)] | = | x1 + 2 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 4 |
[isNat(x1)] | = | x1 + 1 |
[plus(x1, x2)] | = | x2 + 2 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 1 |
[U31(x1)] | = | x1 + 1 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 1 |
[U41(x1, x2, x3)] | = | x1 + x3 + 1 |
[U31#(x1)] | = | 0 |
[and#(x1, x2)] | = | 0 |
plus#(active(X1),X2) | → | plus#(X1,X2) | (95) |
plus#(mark(X1),X2) | → | plus#(X1,X2) | (122) |
The dependency pairs are split into 1 component.
plus#(X1,active(X2)) | → | plus#(X1,X2) | (157) |
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (153) |
[U21(x1, x2, x3)] | = | x1 + 22315 |
[U11(x1, x2)] | = | x1 + x2 + 47469 |
[s(x1)] | = | 3162 |
[isNat#(x1)] | = | 0 |
[and(x1, x2)] | = | x2 + 17603 |
[plus#(x1, x2)] | = | x2 + 0 |
[x(x1, x2)] | = | x1 + x2 + 7135 |
[mark#(x1)] | = | 0 |
[0] | = | 1 |
[x#(x1, x2)] | = | 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 47476 |
[isNat(x1)] | = | 1 |
[plus(x1, x2)] | = | x2 + 25 |
[U11#(x1, x2)] | = | 0 |
[active(x1)] | = | x1 + 5 |
[U31(x1)] | = | x1 + 1602 |
[U41#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
[U21#(x1, x2, x3)] | = | 0 |
[tt] | = | 1 |
[U41(x1, x2, x3)] | = | x1 + x2 + x3 + 11413 |
[U31#(x1)] | = | 0 |
[and#(x1, x2)] | = | 0 |
plus#(X1,active(X2)) | → | plus#(X1,X2) | (157) |
plus#(X1,mark(X2)) | → | plus#(X1,X2) | (153) |
The dependency pairs are split into 0 components.