/export/starexec/sandbox2/solver/bin/starexec_run_hrs /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES ******** General Schema criterion ******** Found constructors: 0, 1, cos, sin Checking type order >>OK Checking positivity of constructors >>OK Checking function dependency >>OK Checking (1) d(%X.X,Y) => 0 (fun d>0) >>True Checking (2) d(%Y.%Y,U) => 1 (fun d>1) >>True Checking (3) d(%Z.minus(H[%Z]),W) => minus(d(%U.H[%U],W)) (fun d>minus) (fun d=d) subterm comparison of args w. LR LR (meta H)[is acc in %Z.minus(H[%Z]),W] [is positive in minus(H[%Z])] [is acc in H[%Z]] (meta W)[is acc in %Z.minus(H[%Z]),W] [is positive in minus(H[%Z])] [is acc in W] >>True Checking (4) d(%V.pls(J[%V],F1[%V]),Y1) => pls(d(%F.J[%F],Y1),d(%W.F1[%W],Y1)) (fun d>pls) (fun d=d) subterm comparison of args w. LR LR (meta J)[is acc in %V.pls(J[%V],F1[%V]),Y1] [is positive in pls(J[%V],F1[%V])] [is acc in J[%V]] (meta Y1)[is acc in %V.pls(J[%V],F1[%V]),Y1] [is positive in pls(J[%V],F1[%V])] [is acc in Y1] (fun d=d) subterm comparison of args w. LR LR (meta F1)[is acc in %V.pls(J[%V],F1[%V]),Y1] [is positive in pls(J[%V],F1[%V])] [is acc in F1[%V]] (meta Y1)[is acc in %V.pls(J[%V],F1[%V]),Y1] [is positive in pls(J[%V],F1[%V])] [is acc in Y1] >>True Checking (5) d(%G.mul(G1[%G],H1[%G]),W1) => pls(mul(d(%I.G1[%I],W1),H1[W1]),mul(G1[W1],d(%H.H1[%H],W1))) (fun d>pls) (fun d>mul) (fun d=d) subterm comparison of args w. LR LR (meta G1)[is acc in %G.mul(G1[%G],H1[%G]),W1] [is positive in mul(G1[%G],H1[%G])] [is acc in G1[%G]] (meta W1)[is acc in %G.mul(G1[%G],H1[%G]),W1] [is positive in mul(G1[%G],H1[%G])] [is acc in W1] (meta H1)[is acc in %G.mul(G1[%G],H1[%G]),W1] [is positive in mul(G1[%G],H1[%G])] [is acc in H1[%G]] (meta W1)[is acc in %G.mul(G1[%G],H1[%G]),W1] [is positive in mul(G1[%G],H1[%G])] [is acc in W1] (fun d>mul) (meta G1)[is acc in %G.mul(G1[%G],H1[%G]),W1] [is positive in mul(G1[%G],H1[%G])] [is acc in G1[%G]] (meta W1)[is acc in %G.mul(G1[%G],H1[%G]),W1] [is positive in mul(G1[%G],H1[%G])] [is acc in W1] (fun d=d) subterm comparison of args w. LR LR (meta H1)[is acc in %G.mul(G1[%G],H1[%G]),W1] [is positive in mul(G1[%G],H1[%G])] [is acc in H1[%G]] (meta W1)[is acc in %G.mul(G1[%G],H1[%G]),W1] [is positive in mul(G1[%G],H1[%G])] [is acc in W1] >>True Checking (6) d(%J.sin(J1[%J]),X2) => mul(cos(X2),d(%P.J1[%P],X2)) (fun d>mul) (fun d>cos) (meta X2)[is acc in %J.sin(J1[%J]),X2] [is positive in sin(J1[%J])] [is acc in X2] (fun d=d) subterm comparison of args w. LR LR (meta J1)[is acc in %J.sin(J1[%J]),X2] [is positive in sin(J1[%J])] [is acc in J1[%J]] (meta X2)[is acc in %J.sin(J1[%J]),X2] [is positive in sin(J1[%J])] [is acc in X2] >>True Checking (7) d(%Q.cos(Z2[%Q]),U2) => mul(minus(sin(U2)),d(%R.Z2[%R],U2)) (fun d>mul) (fun d>minus) (fun d>sin) (meta U2)[is acc in %Q.cos(Z2[%Q]),U2] [is positive in cos(Z2[%Q])] [is acc in U2] (fun d=d) subterm comparison of args w. LR LR (meta Z2)[is acc in %Q.cos(Z2[%Q]),U2] [is positive in cos(Z2[%Q])] [is acc in Z2[%Q]] (meta U2)[is acc in %Q.cos(Z2[%Q]),U2] [is positive in cos(Z2[%Q])] [is acc in U2] >>True Checking (8) minus(0) => 0 (fun minus>0) >>True Checking (9) mul(0,V2) => 0 (fun mul>0) >>True Checking (10) mul(W2,0) => 0 (fun mul>0) >>True Checking (11) pls(0,P2) => P2 (meta P2)[is acc in 0,P2] [is positive in 0] [is acc in P2] >>True #SN! ******** Signature ******** 0 : R 1 : R cos : R -> R d : ((R -> R),R) -> R minus : R -> R mul : (R,R) -> R pls : (R,R) -> R sin : R -> R ******** Computation Rules ******** (1) d(%X.X,Y) => 0 (2) d(%Y.%Y,U) => 1 (3) d(%Z.minus(H[%Z]),W) => minus(d(%U.H[%U],W)) (4) d(%V.pls(J[%V],F1[%V]),Y1) => pls(d(%F.J[%F],Y1),d(%W.F1[%W],Y1)) (5) d(%G.mul(G1[%G],H1[%G]),W1) => pls(mul(d(%I.G1[%I],W1),H1[W1]),mul(G1[W1],d(%H.H1[%H],W1))) (6) d(%J.sin(J1[%J]),X2) => mul(cos(X2),d(%P.J1[%P],X2)) (7) d(%Q.cos(Z2[%Q]),U2) => mul(minus(sin(U2)),d(%R.Z2[%R],U2)) (8) minus(0) => 0 (9) mul(0,V2) => 0 (10) mul(W2,0) => 0 (11) pls(0,P2) => P2 YES