The rewrite relation of the following TRS is considered.
p(0) | → | 0 | (1) |
p(s(X)) | → | X | (2) |
leq(0,Y) | → | true | (3) |
leq(s(X),0) | → | false | (4) |
leq(s(X),s(Y)) | → | leq(X,Y) | (5) |
if(true,X,Y) | → | activate(X) | (6) |
if(false,X,Y) | → | activate(Y) | (7) |
diff(X,Y) | → | if(leq(X,Y),n__0,n__s(diff(p(X),Y))) | (8) |
0 | → | n__0 | (9) |
s(X) | → | n__s(X) | (10) |
activate(n__0) | → | 0 | (11) |
activate(n__s(X)) | → | s(X) | (12) |
activate(X) | → | X | (13) |
leq#(s(X),s(Y)) | → | leq#(X,Y) | (14) |
if#(true,X,Y) | → | activate#(X) | (15) |
if#(false,X,Y) | → | activate#(Y) | (16) |
diff#(X,Y) | → | if#(leq(X,Y),n__0,n__s(diff(p(X),Y))) | (17) |
diff#(X,Y) | → | leq#(X,Y) | (18) |
diff#(X,Y) | → | diff#(p(X),Y) | (19) |
diff#(X,Y) | → | p#(X) | (20) |
activate#(n__0) | → | 0# | (21) |
activate#(n__s(X)) | → | s#(X) | (22) |
leq#(s(X),s(Y)) | → | leq#(X,Y) | (14) |
if#(true,X,Y) | → | activate#(X) | (15) |
if#(false,X,Y) | → | activate#(Y) | (16) |
diff#(X,Y) | → | if#(leq(X,Y),n__0,n__s(diff(p(X),Y))) | (17) |
diff#(X,Y) | → | leq#(X,Y) | (18) |
diff#(X,Y) | → | p#(X) | (20) |
activate#(n__0) | → | 0# | (21) |
activate#(n__s(X)) | → | s#(X) | (22) |
leq(0,Y) | → | true | (3) |
leq(s(X),0) | → | false | (4) |
leq(s(X),s(Y)) | → | leq(X,Y) | (5) |
if(true,X,Y) | → | activate(X) | (6) |
if(false,X,Y) | → | activate(Y) | (7) |
diff(X,Y) | → | if(leq(X,Y),n__0,n__s(diff(p(X),Y))) | (8) |
s(X) | → | n__s(X) | (10) |
activate(n__0) | → | 0 | (11) |
activate(n__s(X)) | → | s(X) | (12) |
activate(X) | → | X | (13) |
p(s(X)) | → | X | (2) |
0 | → | n__0 | (9) |
p(0) |
t0 | = | diff#(X,Y) |
→P | diff#(p(X),Y) | |
= | t1 |