- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] app(app(neq,0),0) -> false [2] app(app(neq,0),app(s,y)) -> true [3] app(app(neq,app(s,x)),0) -> true [4] app(app(neq,app(s,x)),app(s,y)) -> app(app(neq,x),y) [5] app(app(filter,f),nil) -> nil [6] app(app(filter,f),app(app(cons,y),ys)) -> app(app(app(filtersub,app(f,y)),f),app(app(cons,y),ys)) [7] app(app(app(filtersub,true),f),app(app(cons,y),ys)) -> app(app(cons,y),app(app(filter,f),ys)) [8] app(app(app(filtersub,false),f),app(app(cons,y),ys)) -> app(app(filter,f),ys) [9] nonzero -> app(filter,app(neq,0)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { app(app(app(filtersub,false),f),app(app(cons,y),ys)) >= app(app(filter,f),ys) ; app(app(app(filtersub,true),f),app(app(cons,y),ys)) >= app(app(cons,y), app(app(filter,f),ys)) ; app(app(neq,app(s,x)),app(s,y)) >= app(app(neq,x),y) ; app(app(neq,app(s,x)),0) >= true ; app(app(neq,0),app(s,y)) >= true ; app(app(neq,0),0) >= false ; app(app(filter,f),app(app(cons,y),ys)) >= app(app(app(filtersub,app(f,y)),f), app(app(cons,y),ys)) ; app(app(filter,f),nil) >= nil ; nonzero >= app(filter,app(neq,0)) ; Marked_app(app(app(filtersub,false),f),app(app(cons,y),ys)) >= Marked_app( app( filter, f), ys) ; Marked_app(app(app(filtersub,true),f),app(app(cons,y),ys)) >= Marked_app( app( filter, f), ys) ; Marked_app(app(app(filtersub,true),f),app(app(cons,y),ys)) >= Marked_app( app( cons, y), app( app( filter, f), ys)) ; Marked_app(app(neq,app(s,x)),app(s,y)) >= Marked_app(app(neq,x),y) ; Marked_app(app(filter,f),app(app(cons,y),ys)) >= Marked_app(app(app( filtersub, app(f,y)), f), app(app(cons,y),ys)) ; Marked_app(app(filter,f),app(app(cons,y),ys)) >= Marked_app(app(filtersub, app(f,y)), f) ; Marked_app(app(filter,f),app(app(cons,y),ys)) >= Marked_app(f,y) ; } + Disjunctions:{ { Marked_app(app(app(filtersub,false),f),app(app(cons,y),ys)) > Marked_app( app( filter, f), ys) ; } { Marked_app(app(app(filtersub,true),f),app(app(cons,y),ys)) > Marked_app( app(filter, f),ys) ; } { Marked_app(app(app(filtersub,true),f),app(app(cons,y),ys)) > Marked_app( app(cons, y), app(app( filter, f), ys)) ; } { Marked_app(app(neq,app(s,x)),app(s,y)) > Marked_app(app(neq,x),y) ; } { Marked_app(app(filter,f),app(app(cons,y),ys)) > Marked_app(app(app( filtersub, app(f,y)), f), app(app(cons,y),ys)) ; } { Marked_app(app(filter,f),app(app(cons,y),ys)) > Marked_app(app(filtersub, app(f,y)), f) ; } { Marked_app(app(filter,f),app(app(cons,y),ys)) > Marked_app(f,y) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: app(app(app(filtersub,false),f),app(app(cons,y),ys)) >= app( app( filter, f), ys) constraint: app(app(app(filtersub,true),f),app(app(cons,y),ys)) >= app( app( cons, y), app( app( filter, f), ys)) constraint: app(app(neq,app(s,x)),app(s,y)) >= app(app(neq,x),y) constraint: app(app(neq,app(s,x)),0) >= true constraint: app(app(neq,0),app(s,y)) >= true constraint: app(app(neq,0),0) >= false constraint: app(app(filter,f),app(app(cons,y),ys)) >= app(app(app(filtersub, app(f,y)), f), app(app(cons,y),ys)) constraint: app(app(filter,f),nil) >= nil constraint: nonzero >= app(filter,app(neq,0)) constraint: Marked_app(app(app(filtersub,false),f),app(app(cons,y),ys)) >= Marked_app(app(filter,f),ys) constraint: Marked_app(app(app(filtersub,true),f),app(app(cons,y),ys)) >= Marked_app(app(filter,f),ys) constraint: Marked_app(app(app(filtersub,true),f),app(app(cons,y),ys)) >= Marked_app(app(cons,y),app(app(filter,f),ys)) constraint: Marked_app(app(neq,app(s,x)),app(s,y)) >= Marked_app(app(neq,x),y) constraint: Marked_app(app(filter,f),app(app(cons,y),ys)) >= Marked_app( app(app( filtersub, app(f,y)), f), app(app(cons,y), ys)) constraint: Marked_app(app(filter,f),app(app(cons,y),ys)) >= Marked_app( app(filtersub, app(f,y)), f) constraint: Marked_app(app(filter,f),app(app(cons,y),ys)) >= Marked_app(f,y) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { app(app(app(filtersub,false),f),app(app(cons,y),ys)) >= app(app(filter,f),ys) ; app(app(app(filtersub,true),f),app(app(cons,y),ys)) >= app(app(cons,y), app(app(filter,f),ys)) ; app(app(neq,app(s,x)),app(s,y)) >= app(app(neq,x),y) ; app(app(neq,app(s,x)),0) >= true ; app(app(neq,0),app(s,y)) >= true ; app(app(neq,0),0) >= false ; app(app(filter,f),app(app(cons,y),ys)) >= app(app(app(filtersub,app(f,y)),f), app(app(cons,y),ys)) ; app(app(filter,f),nil) >= nil ; nonzero >= app(filter,app(neq,0)) ; Marked_app(app(app(filtersub,false),f),app(app(cons,y),ys)) >= Marked_app( app( filter, f), ys) ; Marked_app(app(app(filtersub,true),f),app(app(cons,y),ys)) >= Marked_app( app( filter, f), ys) ; Marked_app(app(app(filtersub,true),f),app(app(cons,y),ys)) >= Marked_app( app( cons, y), app( app( filter, f), ys)) ; Marked_app(app(neq,app(s,x)),app(s,y)) >= Marked_app(app(neq,x),y) ; Marked_app(app(filter,f),app(app(cons,y),ys)) >= Marked_app(app(app( filtersub, app(f,y)), f), app(app(cons,y),ys)) ; Marked_app(app(filter,f),app(app(cons,y),ys)) >= Marked_app(app(filtersub, app(f,y)), f) ; } + Disjunctions:{ { Marked_app(app(app(filtersub,false),f),app(app(cons,y),ys)) > Marked_app( app( filter, f), ys) ; } { Marked_app(app(app(filtersub,true),f),app(app(cons,y),ys)) > Marked_app( app(filter, f),ys) ; } { Marked_app(app(app(filtersub,true),f),app(app(cons,y),ys)) > Marked_app( app(cons, y), app(app( filter, f), ys)) ; } { Marked_app(app(neq,app(s,x)),app(s,y)) > Marked_app(app(neq,x),y) ; } { Marked_app(app(filter,f),app(app(cons,y),ys)) > Marked_app(app(app( filtersub, app(f,y)), f), app(app(cons,y),ys)) ; } { Marked_app(app(filter,f),app(app(cons,y),ys)) > Marked_app(app(filtersub, app(f,y)), f) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: app(app(app(filtersub,false),f),app(app(cons,y),ys)) >= app( app( filter, f), ys) constraint: app(app(app(filtersub,true),f),app(app(cons,y),ys)) >= app( app( cons, y), app( app( filter, f), ys)) constraint: app(app(neq,app(s,x)),app(s,y)) >= app(app(neq,x),y) constraint: app(app(neq,app(s,x)),0) >= true constraint: app(app(neq,0),app(s,y)) >= true constraint: app(app(neq,0),0) >= false constraint: app(app(filter,f),app(app(cons,y),ys)) >= app(app(app(filtersub, app(f,y)), f), app(app(cons,y),ys)) constraint: app(app(filter,f),nil) >= nil constraint: nonzero >= app(filter,app(neq,0)) constraint: Marked_app(app(app(filtersub,false),f),app(app(cons,y),ys)) >= Marked_app(app(filter,f),ys) constraint: Marked_app(app(app(filtersub,true),f),app(app(cons,y),ys)) >= Marked_app(app(filter,f),ys) constraint: Marked_app(app(app(filtersub,true),f),app(app(cons,y),ys)) >= Marked_app(app(cons,y),app(app(filter,f),ys)) constraint: Marked_app(app(neq,app(s,x)),app(s,y)) >= Marked_app(app(neq,x),y) constraint: Marked_app(app(filter,f),app(app(cons,y),ys)) >= Marked_app( app(app( filtersub, app(f,y)), f), app(app(cons,y), ys)) constraint: Marked_app(app(filter,f),app(app(cons,y),ys)) >= Marked_app( app(filtersub, app(f,y)), f) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { app(app(app(filtersub,false),f),app(app(cons,y),ys)) >= app(app(filter,f),ys) ; app(app(app(filtersub,true),f),app(app(cons,y),ys)) >= app(app(cons,y), app(app(filter,f),ys)) ; app(app(neq,app(s,x)),app(s,y)) >= app(app(neq,x),y) ; app(app(neq,app(s,x)),0) >= true ; app(app(neq,0),app(s,y)) >= true ; app(app(neq,0),0) >= false ; app(app(filter,f),app(app(cons,y),ys)) >= app(app(app(filtersub,app(f,y)),f), app(app(cons,y),ys)) ; app(app(filter,f),nil) >= nil ; nonzero >= app(filter,app(neq,0)) ; Marked_app(app(app(filtersub,false),f),app(app(cons,y),ys)) >= Marked_app( app( filter, f), ys) ; Marked_app(app(app(filtersub,true),f),app(app(cons,y),ys)) >= Marked_app( app( filter, f), ys) ; Marked_app(app(neq,app(s,x)),app(s,y)) >= Marked_app(app(neq,x),y) ; Marked_app(app(filter,f),app(app(cons,y),ys)) >= Marked_app(app(app( filtersub, app(f,y)), f), app(app(cons,y),ys)) ; Marked_app(app(filter,f),app(app(cons,y),ys)) >= Marked_app(app(filtersub, app(f,y)), f) ; } + Disjunctions:{ { Marked_app(app(app(filtersub,false),f),app(app(cons,y),ys)) > Marked_app( app( filter, f), ys) ; } { Marked_app(app(app(filtersub,true),f),app(app(cons,y),ys)) > Marked_app( app(filter, f),ys) ; } { Marked_app(app(neq,app(s,x)),app(s,y)) > Marked_app(app(neq,x),y) ; } { Marked_app(app(filter,f),app(app(cons,y),ys)) > Marked_app(app(app( filtersub, app(f,y)), f), app(app(cons,y),ys)) ; } { Marked_app(app(filter,f),app(app(cons,y),ys)) > Marked_app(app(filtersub, app(f,y)), f) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: app(app(app(filtersub,false),f),app(app(cons,y),ys)) >= app( app( filter, f), ys) constraint: app(app(app(filtersub,true),f),app(app(cons,y),ys)) >= app( app( cons, y), app( app( filter, f), ys)) constraint: app(app(neq,app(s,x)),app(s,y)) >= app(app(neq,x),y) constraint: app(app(neq,app(s,x)),0) >= true constraint: app(app(neq,0),app(s,y)) >= true constraint: app(app(neq,0),0) >= false constraint: app(app(filter,f),app(app(cons,y),ys)) >= app(app(app(filtersub, app(f,y)), f), app(app(cons,y),ys)) constraint: app(app(filter,f),nil) >= nil constraint: nonzero >= app(filter,app(neq,0)) constraint: Marked_app(app(app(filtersub,false),f),app(app(cons,y),ys)) >= Marked_app(app(filter,f),ys) constraint: Marked_app(app(app(filtersub,true),f),app(app(cons,y),ys)) >= Marked_app(app(filter,f),ys) constraint: Marked_app(app(neq,app(s,x)),app(s,y)) >= Marked_app(app(neq,x),y) constraint: Marked_app(app(filter,f),app(app(cons,y),ys)) >= Marked_app( app(app( filtersub, app(f,y)), f), app(app(cons,y), ys)) constraint: Marked_app(app(filter,f),app(app(cons,y),ys)) >= Marked_app( app(filtersub, app(f,y)), f) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_app -> 2 APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { app(app(app(filtersub,false),f),app(app(cons,y),ys)) >= app(app(filter,f),ys) ; app(app(app(filtersub,true),f),app(app(cons,y),ys)) >= app(app(cons,y), app(app(filter,f),ys)) ; app(app(neq,app(s,x)),app(s,y)) >= app(app(neq,x),y) ; app(app(neq,app(s,x)),0) >= true ; app(app(neq,0),app(s,y)) >= true ; app(app(neq,0),0) >= false ; app(app(filter,f),app(app(cons,y),ys)) >= app(app(app(filtersub,app(f,y)),f), app(app(cons,y),ys)) ; app(app(filter,f),nil) >= nil ; nonzero >= app(filter,app(neq,0)) ; Marked_app(app(filter,f),app(app(cons,y),ys)) >= Marked_app(app(app( filtersub, app(f,y)), f), app(app(cons,y),ys)) ; } + Disjunctions:{ { Marked_app(app(filter,f),app(app(cons,y),ys)) > Marked_app(app(app( filtersub, app(f,y)), f), app(app(cons,y),ys)) ; } } === TIMER virtual : 10.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 10.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. Entering rpo_solver === TIMER virtual : 25.000000 === Search parameters: AFS type: 2 ; time limit: 25.. === STOPING TIMER virtual === === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 15.000000 === === STOPING TIMER real === Sat solver returned === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. === TIMER virtual : 50.000000 === trying sub matrices of size: 1 Matrix interpretation constraints generated. Search parameters: LINEAR MATRIX 3x3 (strict=1x1) ; time limit: 50.. Termination constraints generated. Starting Sat solver initialization Calling Sat solver... === STOPING TIMER virtual === === TIMER real : 50.000000 === === STOPING TIMER real === Sat solver returned Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: app(app(app(filtersub,false),f),app(app(cons,y),ys)) >= app( app( filter, f), ys) constraint: app(app(app(filtersub,true),f),app(app(cons,y),ys)) >= app( app( cons, y), app( app( filter, f), ys)) constraint: app(app(neq,app(s,x)),app(s,y)) >= app(app(neq,x),y) constraint: app(app(neq,app(s,x)),0) >= true constraint: app(app(neq,0),app(s,y)) >= true constraint: app(app(neq,0),0) >= false constraint: app(app(filter,f),app(app(cons,y),ys)) >= app(app(app(filtersub, app(f,y)), f), app(app(cons,y),ys)) constraint: app(app(filter,f),nil) >= nil constraint: nonzero >= app(filter,app(neq,0)) constraint: Marked_app(app(filter,f),app(app(cons,y),ys)) >= Marked_app( app(app( filtersub, app(f,y)), f), app(app(cons,y), ys)) APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] app(app(neq,0),0) -> false [2] app(app(neq,0),app(s,y)) -> true [3] app(app(neq,app(s,x)),0) -> true [4] app(app(neq,app(s,x)),app(s,y)) -> app(app(neq,x),y) [5] app(app(filter,f),nil) -> nil [6] app(app(filter,f),app(app(cons,y),ys)) -> app(app(app(filtersub,app(f,y)),f),app(app(cons,y),ys)) [7] app(app(app(filtersub,true),f),app(app(cons,y),ys)) -> app(app(cons,y),app(app(filter,f),ys)) [8] app(app(app(filtersub,false),f),app(app(cons,y),ys)) -> app(app(filter,f),ys) [9] nonzero -> app(filter,app(neq,0)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ false ] () = 0; [ filtersub ] () = 0; [ true ] () = 0; [ Marked_app ] (X0,X1) = 1*X0; [ neq ] () = 0; [ nonzero ] () = 2; [ nil ] () = 0; [ app ] (X0,X1) = 1*X1*X0 + 1; [ cons ] () = 0; [ s ] () = 2; [ 0 ] () = 0; [ filter ] () = 1; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ false ] () = 0; [ filtersub ] () = 2; [ true ] () = 0; [ Marked_app ] (X0,X1) = 2*X0; [ neq ] () = 0; [ nonzero ] () = 3; [ nil ] () = 0; [ app ] (X0,X1) = 1*X0; [ cons ] () = 0; [ s ] () = 0; [ 0 ] () = 0; [ filter ] () = 2; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: CG using polynomial interpretation = [ false ] () = 0; [ filtersub ] () = 1; [ true ] () = 0; [ Marked_app ] (X0,X1) = 1*X0; [ neq ] () = 0; [ nonzero ] () = 3; [ nil ] () = 0; [ app ] (X0,X1) = 1*X0 + 1; [ cons ] () = 0; [ s ] () = 0; [ 0 ] () = 0; [ filter ] () = 2; removing [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ORD [ Solution found: Matrix polynomial interpretation (strict sub matrices size: 1x1) = [ false ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ filtersub ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ true ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ Marked_app ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 0 , 1 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ neq ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ nonzero ] () = [ [ 1 , 0 , 1 ] [ 0 , 1 , 0 ] [ 1 , 0 , 0 ] ]; [ nil ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ app ] (X0,X1) = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]*X1 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 1 , 0 , 0 ] ]*X0 + [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ cons ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ s ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ 0 ] () = [ [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; [ filter ] () = [ [ 1 , 0 , 0 ] [ 0 , 0 , 0 ] [ 0 , 0 , 0 ] ]; ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} ]} Cime worked for 15.503626 seconds (real time) Cime Exit Status: 0