The rewrite relation of the following TRS is considered.
active(minus(0,Y)) | → | mark(0) | (1) |
active(minus(s(X),s(Y))) | → | mark(minus(X,Y)) | (2) |
active(geq(X,0)) | → | mark(true) | (3) |
active(geq(0,s(Y))) | → | mark(false) | (4) |
active(geq(s(X),s(Y))) | → | mark(geq(X,Y)) | (5) |
active(div(0,s(Y))) | → | mark(0) | (6) |
active(div(s(X),s(Y))) | → | mark(if(geq(X,Y),s(div(minus(X,Y),s(Y))),0)) | (7) |
active(if(true,X,Y)) | → | mark(X) | (8) |
active(if(false,X,Y)) | → | mark(Y) | (9) |
active(s(X)) | → | s(active(X)) | (10) |
active(div(X1,X2)) | → | div(active(X1),X2) | (11) |
active(if(X1,X2,X3)) | → | if(active(X1),X2,X3) | (12) |
s(mark(X)) | → | mark(s(X)) | (13) |
div(mark(X1),X2) | → | mark(div(X1,X2)) | (14) |
if(mark(X1),X2,X3) | → | mark(if(X1,X2,X3)) | (15) |
proper(minus(X1,X2)) | → | minus(proper(X1),proper(X2)) | (16) |
proper(0) | → | ok(0) | (17) |
proper(s(X)) | → | s(proper(X)) | (18) |
proper(geq(X1,X2)) | → | geq(proper(X1),proper(X2)) | (19) |
proper(true) | → | ok(true) | (20) |
proper(false) | → | ok(false) | (21) |
proper(div(X1,X2)) | → | div(proper(X1),proper(X2)) | (22) |
proper(if(X1,X2,X3)) | → | if(proper(X1),proper(X2),proper(X3)) | (23) |
minus(ok(X1),ok(X2)) | → | ok(minus(X1,X2)) | (24) |
s(ok(X)) | → | ok(s(X)) | (25) |
geq(ok(X1),ok(X2)) | → | ok(geq(X1,X2)) | (26) |
div(ok(X1),ok(X2)) | → | ok(div(X1,X2)) | (27) |
if(ok(X1),ok(X2),ok(X3)) | → | ok(if(X1,X2,X3)) | (28) |
top(mark(X)) | → | top(proper(X)) | (29) |
top(ok(X)) | → | top(active(X)) | (30) |
top#(mark(X)) | → | top#(proper(X)) | (31) |
proper#(div(X1,X2)) | → | proper#(X2) | (32) |
proper#(minus(X1,X2)) | → | minus#(proper(X1),proper(X2)) | (33) |
proper#(minus(X1,X2)) | → | proper#(X2) | (34) |
if#(mark(X1),X2,X3) | → | if#(X1,X2,X3) | (35) |
active#(div(X1,X2)) | → | active#(X1) | (36) |
proper#(s(X)) | → | proper#(X) | (37) |
active#(if(X1,X2,X3)) | → | active#(X1) | (38) |
proper#(if(X1,X2,X3)) | → | proper#(X1) | (39) |
proper#(if(X1,X2,X3)) | → | proper#(X3) | (40) |
active#(s(X)) | → | active#(X) | (41) |
active#(s(X)) | → | s#(active(X)) | (42) |
active#(if(X1,X2,X3)) | → | if#(active(X1),X2,X3) | (43) |
proper#(geq(X1,X2)) | → | geq#(proper(X1),proper(X2)) | (44) |
div#(mark(X1),X2) | → | div#(X1,X2) | (45) |
div#(ok(X1),ok(X2)) | → | div#(X1,X2) | (46) |
active#(geq(s(X),s(Y))) | → | geq#(X,Y) | (47) |
active#(div(s(X),s(Y))) | → | s#(div(minus(X,Y),s(Y))) | (48) |
minus#(ok(X1),ok(X2)) | → | minus#(X1,X2) | (49) |
proper#(s(X)) | → | s#(proper(X)) | (50) |
proper#(if(X1,X2,X3)) | → | proper#(X2) | (51) |
proper#(geq(X1,X2)) | → | proper#(X2) | (52) |
active#(div(X1,X2)) | → | div#(active(X1),X2) | (53) |
proper#(div(X1,X2)) | → | proper#(X1) | (54) |
active#(div(s(X),s(Y))) | → | minus#(X,Y) | (55) |
geq#(ok(X1),ok(X2)) | → | geq#(X1,X2) | (56) |
proper#(div(X1,X2)) | → | div#(proper(X1),proper(X2)) | (57) |
s#(ok(X)) | → | s#(X) | (58) |
proper#(geq(X1,X2)) | → | proper#(X1) | (59) |
active#(div(s(X),s(Y))) | → | geq#(X,Y) | (60) |
if#(ok(X1),ok(X2),ok(X3)) | → | if#(X1,X2,X3) | (61) |
proper#(minus(X1,X2)) | → | proper#(X1) | (62) |
active#(div(s(X),s(Y))) | → | div#(minus(X,Y),s(Y)) | (63) |
top#(ok(X)) | → | active#(X) | (64) |
top#(mark(X)) | → | proper#(X) | (65) |
active#(minus(s(X),s(Y))) | → | minus#(X,Y) | (66) |
proper#(if(X1,X2,X3)) | → | if#(proper(X1),proper(X2),proper(X3)) | (67) |
top#(ok(X)) | → | top#(active(X)) | (68) |
s#(mark(X)) | → | s#(X) | (69) |
active#(div(s(X),s(Y))) | → | if#(geq(X,Y),s(div(minus(X,Y),s(Y))),0) | (70) |
The dependency pairs are split into 8 components.
top#(ok(X)) | → | top#(active(X)) | (68) |
top#(mark(X)) | → | top#(proper(X)) | (31) |
π(div#) | = | 1 |
π(top#) | = | 1 |
π(proper) | = | 1 |
π(ok) | = | 1 |
π(minus#) | = | 1 |
π(active) | = | 1 |
prec(s) | = | 5 | status(s) | = | [1] | list-extension(s) | = | Lex | ||
prec(minus) | = | 4 | status(minus) | = | [1] | list-extension(minus) | = | Lex | ||
prec(geq#) | = | 0 | status(geq#) | = | [1, 2] | list-extension(geq#) | = | Lex | ||
prec(top) | = | 0 | status(top) | = | [] | list-extension(top) | = | Lex | ||
prec(false) | = | 0 | status(false) | = | [] | list-extension(false) | = | Lex | ||
prec(div) | = | 6 | status(div) | = | [1, 2] | list-extension(div) | = | Lex | ||
prec(geq) | = | 4 | status(geq) | = | [1] | list-extension(geq) | = | Lex | ||
prec(true) | = | 2 | status(true) | = | [] | list-extension(true) | = | Lex | ||
prec(0) | = | 1 | status(0) | = | [] | list-extension(0) | = | Lex | ||
prec(if) | = | 4 | status(if) | = | [3, 2, 1] | list-extension(if) | = | Lex | ||
prec(s#) | = | 0 | status(s#) | = | [] | list-extension(s#) | = | Lex | ||
prec(mark) | = | 3 | status(mark) | = | [1] | list-extension(mark) | = | Lex | ||
prec(proper#) | = | 0 | status(proper#) | = | [] | list-extension(proper#) | = | Lex | ||
prec(if#) | = | 0 | status(if#) | = | [3, 2, 1] | list-extension(if#) | = | Lex | ||
prec(active#) | = | 0 | status(active#) | = | [] | list-extension(active#) | = | Lex |
[s(x1)] | = | x1 + 0 |
[minus(x1, x2)] | = | max(x1 + 0, 0) |
[geq#(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[top(x1)] | = | 0 |
[false] | = | 0 |
[div(x1, x2)] | = | max(x1 + 0, x2 + 0, 0) |
[geq(x1, x2)] | = | max(x1 + 0, 0) |
[true] | = | 0 |
[0] | = | 0 |
[if(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[proper#(x1)] | = | 0 |
[if#(x1, x2, x3)] | = | max(x1 + 0, x2 + 0, x3 + 0, 0) |
[active#(x1)] | = | 0 |
proper(s(X)) | → | s(proper(X)) | (18) |
active(geq(0,s(Y))) | → | mark(false) | (4) |
if(mark(X1),X2,X3) | → | mark(if(X1,X2,X3)) | (15) |
active(if(true,X,Y)) | → | mark(X) | (8) |
active(minus(0,Y)) | → | mark(0) | (1) |
active(geq(X,0)) | → | mark(true) | (3) |
proper(minus(X1,X2)) | → | minus(proper(X1),proper(X2)) | (16) |
proper(false) | → | ok(false) | (21) |
geq(ok(X1),ok(X2)) | → | ok(geq(X1,X2)) | (26) |
proper(geq(X1,X2)) | → | geq(proper(X1),proper(X2)) | (19) |
proper(0) | → | ok(0) | (17) |
div(ok(X1),ok(X2)) | → | ok(div(X1,X2)) | (27) |
proper(div(X1,X2)) | → | div(proper(X1),proper(X2)) | (22) |
if(ok(X1),ok(X2),ok(X3)) | → | ok(if(X1,X2,X3)) | (28) |
active(geq(s(X),s(Y))) | → | mark(geq(X,Y)) | (5) |
active(s(X)) | → | s(active(X)) | (10) |
active(div(s(X),s(Y))) | → | mark(if(geq(X,Y),s(div(minus(X,Y),s(Y))),0)) | (7) |
proper(true) | → | ok(true) | (20) |
s(ok(X)) | → | ok(s(X)) | (25) |
div(mark(X1),X2) | → | mark(div(X1,X2)) | (14) |
active(if(X1,X2,X3)) | → | if(active(X1),X2,X3) | (12) |
proper(if(X1,X2,X3)) | → | if(proper(X1),proper(X2),proper(X3)) | (23) |
minus(ok(X1),ok(X2)) | → | ok(minus(X1,X2)) | (24) |
active(div(X1,X2)) | → | div(active(X1),X2) | (11) |
active(if(false,X,Y)) | → | mark(Y) | (9) |
s(mark(X)) | → | mark(s(X)) | (13) |
active(div(0,s(Y))) | → | mark(0) | (6) |
active(minus(s(X),s(Y))) | → | mark(minus(X,Y)) | (2) |
top#(mark(X)) | → | top#(proper(X)) | (31) |
The dependency pairs are split into 1 component.
top#(ok(X)) | → | top#(active(X)) | (68) |
[div#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 0 |
[minus(x1, x2)] | = | x1 + 0 |
[geq#(x1, x2)] | = | 0 |
[top(x1)] | = | 0 |
[false] | = | 0 |
[top#(x1)] | = | x1 + 0 |
[div(x1, x2)] | = | x1 + 0 |
[geq(x1, x2)] | = | 64419 |
[true] | = | 1 |
[proper(x1)] | = | 64419 |
[ok(x1)] | = | 64419 |
[0] | = | 1 |
[if(x1, x2, x3)] | = | x1 + 0 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | 0 |
[minus#(x1, x2)] | = | 0 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 45671 |
[if#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
proper(s(X)) | → | s(proper(X)) | (18) |
active(geq(0,s(Y))) | → | mark(false) | (4) |
if(mark(X1),X2,X3) | → | mark(if(X1,X2,X3)) | (15) |
active(if(true,X,Y)) | → | mark(X) | (8) |
active(minus(0,Y)) | → | mark(0) | (1) |
active(geq(X,0)) | → | mark(true) | (3) |
proper(minus(X1,X2)) | → | minus(proper(X1),proper(X2)) | (16) |
proper(false) | → | ok(false) | (21) |
geq(ok(X1),ok(X2)) | → | ok(geq(X1,X2)) | (26) |
proper(geq(X1,X2)) | → | geq(proper(X1),proper(X2)) | (19) |
proper(0) | → | ok(0) | (17) |
div(ok(X1),ok(X2)) | → | ok(div(X1,X2)) | (27) |
proper(div(X1,X2)) | → | div(proper(X1),proper(X2)) | (22) |
if(ok(X1),ok(X2),ok(X3)) | → | ok(if(X1,X2,X3)) | (28) |
active(geq(s(X),s(Y))) | → | mark(geq(X,Y)) | (5) |
active(s(X)) | → | s(active(X)) | (10) |
active(div(s(X),s(Y))) | → | mark(if(geq(X,Y),s(div(minus(X,Y),s(Y))),0)) | (7) |
proper(true) | → | ok(true) | (20) |
s(ok(X)) | → | ok(s(X)) | (25) |
div(mark(X1),X2) | → | mark(div(X1,X2)) | (14) |
active(if(X1,X2,X3)) | → | if(active(X1),X2,X3) | (12) |
proper(if(X1,X2,X3)) | → | if(proper(X1),proper(X2),proper(X3)) | (23) |
minus(ok(X1),ok(X2)) | → | ok(minus(X1,X2)) | (24) |
active(div(X1,X2)) | → | div(active(X1),X2) | (11) |
active(if(false,X,Y)) | → | mark(Y) | (9) |
s(mark(X)) | → | mark(s(X)) | (13) |
active(div(0,s(Y))) | → | mark(0) | (6) |
active(minus(s(X),s(Y))) | → | mark(minus(X,Y)) | (2) |
top#(ok(X)) | → | top#(active(X)) | (68) |
The dependency pairs are split into 0 components.
proper#(minus(X1,X2)) | → | proper#(X1) | (62) |
proper#(if(X1,X2,X3)) | → | proper#(X3) | (40) |
proper#(if(X1,X2,X3)) | → | proper#(X1) | (39) |
proper#(geq(X1,X2)) | → | proper#(X1) | (59) |
proper#(s(X)) | → | proper#(X) | (37) |
proper#(div(X1,X2)) | → | proper#(X1) | (54) |
proper#(minus(X1,X2)) | → | proper#(X2) | (34) |
proper#(geq(X1,X2)) | → | proper#(X2) | (52) |
proper#(if(X1,X2,X3)) | → | proper#(X2) | (51) |
proper#(div(X1,X2)) | → | proper#(X2) | (32) |
[div#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 0 |
[minus(x1, x2)] | = | x1 + x2 + 1 |
[geq#(x1, x2)] | = | 0 |
[top(x1)] | = | 0 |
[false] | = | 1 |
[top#(x1)] | = | 0 |
[div(x1, x2)] | = | x1 + x2 + 14459 |
[geq(x1, x2)] | = | x1 + x2 + 29273 |
[true] | = | 1 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 2 |
[if(x1, x2, x3)] | = | x1 + x2 + x3 + 1350 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[minus#(x1, x2)] | = | 0 |
[proper#(x1)] | = | x1 + 0 |
[active(x1)] | = | 45672 |
[if#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
active(geq(0,s(Y))) | → | mark(false) | (4) |
active(minus(0,Y)) | → | mark(0) | (1) |
active(geq(X,0)) | → | mark(true) | (3) |
active(div(0,s(Y))) | → | mark(0) | (6) |
proper#(minus(X1,X2)) | → | proper#(X1) | (62) |
proper#(if(X1,X2,X3)) | → | proper#(X3) | (40) |
proper#(if(X1,X2,X3)) | → | proper#(X1) | (39) |
proper#(geq(X1,X2)) | → | proper#(X1) | (59) |
proper#(div(X1,X2)) | → | proper#(X1) | (54) |
proper#(minus(X1,X2)) | → | proper#(X2) | (34) |
proper#(geq(X1,X2)) | → | proper#(X2) | (52) |
proper#(if(X1,X2,X3)) | → | proper#(X2) | (51) |
proper#(div(X1,X2)) | → | proper#(X2) | (32) |
The dependency pairs are split into 1 component.
proper#(s(X)) | → | proper#(X) | (37) |
[div#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[minus(x1, x2)] | = | x1 + x2 + 1 |
[geq#(x1, x2)] | = | 0 |
[top(x1)] | = | 0 |
[false] | = | 1 |
[top#(x1)] | = | 0 |
[div(x1, x2)] | = | x1 + x2 + 1 |
[geq(x1, x2)] | = | x1 + x2 + 29273 |
[true] | = | 1 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[if(x1, x2, x3)] | = | x1 + x2 + x3 + 14264 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[minus#(x1, x2)] | = | 0 |
[proper#(x1)] | = | x1 + 0 |
[active(x1)] | = | 45672 |
[if#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
active(geq(0,s(Y))) | → | mark(false) | (4) |
active(minus(0,Y)) | → | mark(0) | (1) |
active(geq(X,0)) | → | mark(true) | (3) |
active(div(0,s(Y))) | → | mark(0) | (6) |
proper#(s(X)) | → | proper#(X) | (37) |
The dependency pairs are split into 0 components.
active#(s(X)) | → | active#(X) | (41) |
active#(if(X1,X2,X3)) | → | active#(X1) | (38) |
active#(div(X1,X2)) | → | active#(X1) | (36) |
[div#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[minus(x1, x2)] | = | x1 + x2 + 1 |
[geq#(x1, x2)] | = | 0 |
[top(x1)] | = | 0 |
[false] | = | 3 |
[top#(x1)] | = | 0 |
[div(x1, x2)] | = | x1 + x2 + 1 |
[geq(x1, x2)] | = | x1 + x2 + 1 |
[true] | = | 1 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[if(x1, x2, x3)] | = | x1 + x2 + x3 + 29134 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[minus#(x1, x2)] | = | 0 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 29140 |
[if#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | x1 + 0 |
active(geq(0,s(Y))) | → | mark(false) | (4) |
active(minus(0,Y)) | → | mark(0) | (1) |
active(geq(X,0)) | → | mark(true) | (3) |
active(div(0,s(Y))) | → | mark(0) | (6) |
active#(s(X)) | → | active#(X) | (41) |
active#(if(X1,X2,X3)) | → | active#(X1) | (38) |
active#(div(X1,X2)) | → | active#(X1) | (36) |
The dependency pairs are split into 0 components.
if#(ok(X1),ok(X2),ok(X3)) | → | if#(X1,X2,X3) | (61) |
if#(mark(X1),X2,X3) | → | if#(X1,X2,X3) | (35) |
[div#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[minus(x1, x2)] | = | x1 + x2 + 1 |
[geq#(x1, x2)] | = | 0 |
[top(x1)] | = | 0 |
[false] | = | 11449 |
[top#(x1)] | = | 0 |
[div(x1, x2)] | = | x1 + x2 + 1 |
[geq(x1, x2)] | = | x1 + x2 + 1 |
[true] | = | 1 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 3308 |
[0] | = | 1 |
[if(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 0 |
[minus#(x1, x2)] | = | 0 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 29140 |
[if#(x1, x2, x3)] | = | x1 + x3 + 0 |
[active#(x1)] | = | 0 |
active(geq(0,s(Y))) | → | mark(false) | (4) |
active(minus(0,Y)) | → | mark(0) | (1) |
active(geq(X,0)) | → | mark(true) | (3) |
active(div(0,s(Y))) | → | mark(0) | (6) |
if#(ok(X1),ok(X2),ok(X3)) | → | if#(X1,X2,X3) | (61) |
The dependency pairs are split into 1 component.
if#(mark(X1),X2,X3) | → | if#(X1,X2,X3) | (35) |
[div#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[minus(x1, x2)] | = | x1 + x2 + 1 |
[geq#(x1, x2)] | = | 0 |
[top(x1)] | = | 0 |
[false] | = | 1 |
[top#(x1)] | = | 0 |
[div(x1, x2)] | = | x1 + x2 + 1 |
[geq(x1, x2)] | = | x1 + x2 + 1 |
[true] | = | 1 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[if(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[minus#(x1, x2)] | = | 0 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 29141 |
[if#(x1, x2, x3)] | = | x1 + 0 |
[active#(x1)] | = | 0 |
active(geq(0,s(Y))) | → | mark(false) | (4) |
active(minus(0,Y)) | → | mark(0) | (1) |
active(geq(X,0)) | → | mark(true) | (3) |
active(div(0,s(Y))) | → | mark(0) | (6) |
if#(mark(X1),X2,X3) | → | if#(X1,X2,X3) | (35) |
The dependency pairs are split into 0 components.
div#(ok(X1),ok(X2)) | → | div#(X1,X2) | (46) |
div#(mark(X1),X2) | → | div#(X1,X2) | (45) |
[div#(x1, x2)] | = | x2 + 0 |
[s(x1)] | = | x1 + 1 |
[minus(x1, x2)] | = | x1 + x2 + 1 |
[geq#(x1, x2)] | = | 0 |
[top(x1)] | = | 0 |
[false] | = | 1 |
[top#(x1)] | = | 0 |
[div(x1, x2)] | = | x1 + x2 + 1 |
[geq(x1, x2)] | = | x1 + x2 + 1 |
[true] | = | 1 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[if(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[minus#(x1, x2)] | = | 0 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 29141 |
[if#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
active(geq(0,s(Y))) | → | mark(false) | (4) |
active(minus(0,Y)) | → | mark(0) | (1) |
active(geq(X,0)) | → | mark(true) | (3) |
active(div(0,s(Y))) | → | mark(0) | (6) |
div#(ok(X1),ok(X2)) | → | div#(X1,X2) | (46) |
The dependency pairs are split into 1 component.
div#(mark(X1),X2) | → | div#(X1,X2) | (45) |
[div#(x1, x2)] | = | x1 + 0 |
[s(x1)] | = | x1 + 1 |
[minus(x1, x2)] | = | x1 + x2 + 1 |
[geq#(x1, x2)] | = | 0 |
[top(x1)] | = | 0 |
[false] | = | 1 |
[top#(x1)] | = | 0 |
[div(x1, x2)] | = | x1 + x2 + 42087 |
[geq(x1, x2)] | = | x1 + x2 + 28589 |
[true] | = | 1 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[if(x1, x2, x3)] | = | x1 + x2 + x3 + 1 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 9133 |
[minus#(x1, x2)] | = | 0 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 79814 |
[if#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
active(geq(0,s(Y))) | → | mark(false) | (4) |
active(minus(0,Y)) | → | mark(0) | (1) |
active(geq(X,0)) | → | mark(true) | (3) |
active(div(0,s(Y))) | → | mark(0) | (6) |
div#(mark(X1),X2) | → | div#(X1,X2) | (45) |
The dependency pairs are split into 0 components.
minus#(ok(X1),ok(X2)) | → | minus#(X1,X2) | (49) |
[div#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 543 |
[minus(x1, x2)] | = | x1 + x2 + 1 |
[geq#(x1, x2)] | = | 0 |
[top(x1)] | = | 0 |
[false] | = | 18406 |
[top#(x1)] | = | 0 |
[div(x1, x2)] | = | x1 + x2 + 1 |
[geq(x1, x2)] | = | x1 + x2 + 1 |
[true] | = | 11677 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 3 |
[if(x1, x2, x3)] | = | x1 + x2 + x3 + 24498 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[minus#(x1, x2)] | = | x2 + 0 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 42090 |
[if#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
active(geq(0,s(Y))) | → | mark(false) | (4) |
active(minus(0,Y)) | → | mark(0) | (1) |
active(geq(X,0)) | → | mark(true) | (3) |
active(div(0,s(Y))) | → | mark(0) | (6) |
minus#(ok(X1),ok(X2)) | → | minus#(X1,X2) | (49) |
The dependency pairs are split into 0 components.
geq#(ok(X1),ok(X2)) | → | geq#(X1,X2) | (56) |
[div#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[minus(x1, x2)] | = | x1 + x2 + 1 |
[geq#(x1, x2)] | = | x1 + 0 |
[top(x1)] | = | 0 |
[false] | = | 1 |
[top#(x1)] | = | 0 |
[div(x1, x2)] | = | x1 + x2 + 3137 |
[geq(x1, x2)] | = | x1 + x2 + 1 |
[true] | = | 26355 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 1 |
[0] | = | 1 |
[if(x1, x2, x3)] | = | x1 + x2 + x3 + 3699 |
[s#(x1)] | = | 0 |
[mark(x1)] | = | x1 + 1 |
[minus#(x1, x2)] | = | 0 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 42090 |
[if#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
active(geq(0,s(Y))) | → | mark(false) | (4) |
active(minus(0,Y)) | → | mark(0) | (1) |
active(geq(X,0)) | → | mark(true) | (3) |
active(div(0,s(Y))) | → | mark(0) | (6) |
geq#(ok(X1),ok(X2)) | → | geq#(X1,X2) | (56) |
The dependency pairs are split into 0 components.
s#(mark(X)) | → | s#(X) | (69) |
s#(ok(X)) | → | s#(X) | (58) |
[div#(x1, x2)] | = | 0 |
[s(x1)] | = | x1 + 1 |
[minus(x1, x2)] | = | x1 + x2 + 1 |
[geq#(x1, x2)] | = | 0 |
[top(x1)] | = | 0 |
[false] | = | 7036 |
[top#(x1)] | = | 0 |
[div(x1, x2)] | = | x1 + x2 + 11560 |
[geq(x1, x2)] | = | x1 + x2 + 1 |
[true] | = | 14668 |
[proper(x1)] | = | 1 |
[ok(x1)] | = | x1 + 11688 |
[0] | = | 1 |
[if(x1, x2, x3)] | = | x1 + x2 + x3 + 3103 |
[s#(x1)] | = | x1 + 0 |
[mark(x1)] | = | x1 + 32755 |
[minus#(x1, x2)] | = | 0 |
[proper#(x1)] | = | 0 |
[active(x1)] | = | 47423 |
[if#(x1, x2, x3)] | = | 0 |
[active#(x1)] | = | 0 |
active(geq(0,s(Y))) | → | mark(false) | (4) |
active(minus(0,Y)) | → | mark(0) | (1) |
active(geq(X,0)) | → | mark(true) | (3) |
active(div(0,s(Y))) | → | mark(0) | (6) |
s#(mark(X)) | → | s#(X) | (69) |
s#(ok(X)) | → | s#(X) | (58) |
The dependency pairs are split into 0 components.