- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] app(f,app(f,x)) -> app(g,app(f,x)) [2] app(g,app(g,x)) -> app(f,x) [3] app(app(map,fun),nil) -> nil [4] app(app(map,fun),app(app(cons,x),xs)) -> app(app(cons,app(fun,x)),app(app(map,fun),xs)) [5] app(app(filter,fun),nil) -> nil [6] app(app(filter,fun),app(app(cons,x),xs)) -> app(app(app(app(filter2,app(fun,x)),fun),x),xs) [7] app(app(app(app(filter2,true),fun),x),xs) -> app(app(cons,x),app(app(filter,fun),xs)) [8] app(app(app(app(filter2,false),fun),x),xs) -> app(app(filter,fun),xs) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 2 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { app(app(app(app(filter2,true),fun),x),xs) >= app(app(cons,x), app(app(filter,fun),xs)) ; app(app(app(app(filter2,false),fun),x),xs) >= app(app(filter,fun),xs) ; app(app(map,fun),app(app(cons,x),xs)) >= app(app(cons,app(fun,x)), app(app(map,fun),xs)) ; app(app(map,fun),nil) >= nil ; app(app(filter,fun),app(app(cons,x),xs)) >= app(app(app(app(filter2, app(fun,x)), fun),x),xs) ; app(app(filter,fun),nil) >= nil ; app(g,app(g,x)) >= app(f,x) ; app(f,app(f,x)) >= app(g,app(f,x)) ; Marked_app(app(app(app(filter2,true),fun),x),xs) >= Marked_app(app(cons,x), app(app(filter,fun),xs)) ; Marked_app(app(app(app(filter2,true),fun),x),xs) >= Marked_app(app( filter, fun), xs) ; Marked_app(app(app(app(filter2,false),fun),x),xs) >= Marked_app(app( filter, fun), xs) ; Marked_app(app(map,fun),app(app(cons,x),xs)) >= Marked_app(app(map,fun),xs) ; Marked_app(app(map,fun),app(app(cons,x),xs)) >= Marked_app(app(cons, app(fun,x)), app(app(map,fun),xs)) ; Marked_app(app(map,fun),app(app(cons,x),xs)) >= Marked_app(fun,x) ; Marked_app(app(filter,fun),app(app(cons,x),xs)) >= Marked_app(app(app( app( filter2, app(fun,x)), fun), x),xs) ; Marked_app(app(filter,fun),app(app(cons,x),xs)) >= Marked_app(app(app( filter2, app(fun,x)), fun), x) ; Marked_app(app(filter,fun),app(app(cons,x),xs)) >= Marked_app(app(filter2, app(fun,x)), fun) ; Marked_app(app(filter,fun),app(app(cons,x),xs)) >= Marked_app(fun,x) ; } + Disjunctions:{ { Marked_app(app(app(app(filter2,true),fun),x),xs) > Marked_app(app(cons,x), app(app(filter,fun),xs)) ; } { Marked_app(app(app(app(filter2,true),fun),x),xs) > Marked_app(app(filter,fun), xs) ; } { Marked_app(app(app(app(filter2,false),fun),x),xs) > Marked_app(app( filter, fun), xs) ; } { Marked_app(app(map,fun),app(app(cons,x),xs)) > Marked_app(app(map,fun),xs) ; } { Marked_app(app(map,fun),app(app(cons,x),xs)) > Marked_app(app(cons, app(fun,x)), app(app(map,fun),xs)) ; } { Marked_app(app(map,fun),app(app(cons,x),xs)) > Marked_app(fun,x) ; } { Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(app(app( app( filter2, app(fun,x)), fun), x),xs) ; } { Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(app(app( filter2, app(fun,x)), fun), x) ; } { Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(app(filter2, app(fun,x)), fun) ; } { Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(fun,x) ; } } === 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 : 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 === 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 === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. No solution found for these constraints. APPLY CRITERIA (Simple graph) Found the following constraints: { app(app(app(app(filter2,true),fun),x),xs) >= app(app(cons,x), app(app(filter,fun),xs)) ; app(app(app(app(filter2,false),fun),x),xs) >= app(app(filter,fun),xs) ; app(app(map,fun),app(app(cons,x),xs)) >= app(app(cons,app(fun,x)), app(app(map,fun),xs)) ; app(app(map,fun),nil) >= nil ; app(app(filter,fun),app(app(cons,x),xs)) >= app(app(app(app(filter2, app(fun,x)), fun),x),xs) ; app(app(filter,fun),nil) >= nil ; app(g,app(g,x)) >= app(f,x) ; app(f,app(f,x)) >= app(g,app(f,x)) ; Marked_app(app(app(app(filter2,true),fun),x),xs) > Marked_app(app(cons,x), app(app(filter,fun),xs)) ; Marked_app(app(app(app(filter2,true),fun),x),xs) > Marked_app(app(filter,fun), xs) ; Marked_app(app(app(app(filter2,false),fun),x),xs) > Marked_app(app( filter, fun), xs) ; Marked_app(app(map,fun),app(app(cons,x),xs)) > Marked_app(app(map,fun),xs) ; Marked_app(app(map,fun),app(app(cons,x),xs)) > Marked_app(app(cons, app(fun,x)), app(app(map,fun),xs)) ; Marked_app(app(map,fun),app(app(cons,x),xs)) > Marked_app(fun,x) ; Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(app(app( app( filter2, app(fun,x)), fun), x),xs) ; Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(app(app( filter2, app(fun,x)), fun), x) ; Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(app(filter2, app(fun,x)), fun) ; Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(fun,x) ; } APPLY CRITERIA (SOLVE_ORD) Trying to solve the following constraints: { app(app(app(app(filter2,true),fun),x),xs) >= app(app(cons,x), app(app(filter,fun),xs)) ; app(app(app(app(filter2,false),fun),x),xs) >= app(app(filter,fun),xs) ; app(app(map,fun),app(app(cons,x),xs)) >= app(app(cons,app(fun,x)), app(app(map,fun),xs)) ; app(app(map,fun),nil) >= nil ; app(app(filter,fun),app(app(cons,x),xs)) >= app(app(app(app(filter2, app(fun,x)), fun),x),xs) ; app(app(filter,fun),nil) >= nil ; app(g,app(g,x)) >= app(f,x) ; app(f,app(f,x)) >= app(g,app(f,x)) ; Marked_app(app(app(app(filter2,true),fun),x),xs) > Marked_app(app(cons,x), app(app(filter,fun),xs)) ; Marked_app(app(app(app(filter2,true),fun),x),xs) > Marked_app(app(filter,fun), xs) ; Marked_app(app(app(app(filter2,false),fun),x),xs) > Marked_app(app( filter, fun), xs) ; Marked_app(app(map,fun),app(app(cons,x),xs)) > Marked_app(app(map,fun),xs) ; Marked_app(app(map,fun),app(app(cons,x),xs)) > Marked_app(app(cons, app(fun,x)), app(app(map,fun),xs)) ; Marked_app(app(map,fun),app(app(cons,x),xs)) > Marked_app(fun,x) ; Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(app(app( app( filter2, app(fun,x)), fun), x),xs) ; Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(app(app( filter2, app(fun,x)), fun), x) ; Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(app(filter2, app(fun,x)), fun) ; Marked_app(app(filter,fun),app(app(cons,x),xs)) > Marked_app(fun,x) ; } + Disjunctions:{ } === 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 === No solution found for these parameters.(6 bt (0) [8]) === 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 === STOPING TIMER real === === STOPING TIMER virtual === No solution found for these parameters. No solution found for these constraints. APPLY CRITERIA (ID_CRIT) NOT SOLVED No proof found Cime worked for 52.167142 seconds (real time) Cime Exit Status: 0