- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] app(app(plus,0),y) -> y [2] app(app(plus,app(s,x)),y) -> app(s,app(app(plus,x),y)) [3] app(app(sumwith,f),nil) -> nil [4] app(app(sumwith,f),app(app(cons,x),xs)) -> app(app(plus,app(f,x)),app(app(sumwith,f),xs)) 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(plus,app(s,x)),y) >= app(s,app(app(plus,x),y)) ; app(app(plus,0),y) >= y ; app(app(sumwith,f),app(app(cons,x),xs)) >= app(app(plus,app(f,x)), app(app(sumwith,f),xs)) ; app(app(sumwith,f),nil) >= nil ; Marked_app(app(plus,app(s,x)),y) >= Marked_app(app(plus,x),y) ; Marked_app(app(sumwith,f),app(app(cons,x),xs)) >= Marked_app(app(plus, app(f,x)), app(app(sumwith,f),xs)) ; Marked_app(app(sumwith,f),app(app(cons,x),xs)) >= Marked_app(app(sumwith,f), xs) ; Marked_app(app(sumwith,f),app(app(cons,x),xs)) >= Marked_app(f,x) ; } + Disjunctions:{ { Marked_app(app(plus,app(s,x)),y) > Marked_app(app(plus,x),y) ; } { Marked_app(app(sumwith,f),app(app(cons,x),xs)) > Marked_app(app(plus, app(f,x)), app(app(sumwith,f),xs)) ; } { Marked_app(app(sumwith,f),app(app(cons,x),xs)) > Marked_app(app(sumwith,f), xs) ; } { Marked_app(app(sumwith,f),app(app(cons,x),xs)) > Marked_app(f,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 : 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(plus,app(s,x)),y) >= app(s,app(app(plus,x),y)) constraint: app(app(plus,0),y) >= y constraint: app(app(sumwith,f),app(app(cons,x),xs)) >= app(app(plus,app(f,x)), app(app(sumwith,f),xs)) constraint: app(app(sumwith,f),nil) >= nil constraint: Marked_app(app(plus,app(s,x)),y) >= Marked_app(app(plus,x),y) constraint: Marked_app(app(sumwith,f),app(app(cons,x),xs)) >= Marked_app( app(plus, app(f,x)), app(app( sumwith, f), xs)) constraint: Marked_app(app(sumwith,f),app(app(cons,x),xs)) >= Marked_app( app(sumwith, f),xs) constraint: Marked_app(app(sumwith,f),app(app(cons,x),xs)) >= Marked_app(f,x) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { app(app(plus,app(s,x)),y) >= app(s,app(app(plus,x),y)) ; app(app(plus,0),y) >= y ; app(app(sumwith,f),app(app(cons,x),xs)) >= app(app(plus,app(f,x)), app(app(sumwith,f),xs)) ; app(app(sumwith,f),nil) >= nil ; Marked_app(app(plus,app(s,x)),y) >= Marked_app(app(plus,x),y) ; Marked_app(app(sumwith,f),app(app(cons,x),xs)) >= Marked_app(app(plus, app(f,x)), app(app(sumwith,f),xs)) ; Marked_app(app(sumwith,f),app(app(cons,x),xs)) >= Marked_app(app(sumwith,f), xs) ; } + Disjunctions:{ { Marked_app(app(plus,app(s,x)),y) > Marked_app(app(plus,x),y) ; } { Marked_app(app(sumwith,f),app(app(cons,x),xs)) > Marked_app(app(plus, app(f,x)), app(app(sumwith,f),xs)) ; } { Marked_app(app(sumwith,f),app(app(cons,x),xs)) > Marked_app(app(sumwith,f), xs) ; } } === 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 : 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(plus,app(s,x)),y) >= app(s,app(app(plus,x),y)) constraint: app(app(plus,0),y) >= y constraint: app(app(sumwith,f),app(app(cons,x),xs)) >= app(app(plus,app(f,x)), app(app(sumwith,f),xs)) constraint: app(app(sumwith,f),nil) >= nil constraint: Marked_app(app(plus,app(s,x)),y) >= Marked_app(app(plus,x),y) constraint: Marked_app(app(sumwith,f),app(app(cons,x),xs)) >= Marked_app( app(plus, app(f,x)), app(app( sumwith, f), xs)) constraint: Marked_app(app(sumwith,f),app(app(cons,x),xs)) >= Marked_app( app(sumwith, f),xs) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { app(app(plus,app(s,x)),y) >= app(s,app(app(plus,x),y)) ; app(app(plus,0),y) >= y ; app(app(sumwith,f),app(app(cons,x),xs)) >= app(app(plus,app(f,x)), app(app(sumwith,f),xs)) ; app(app(sumwith,f),nil) >= nil ; Marked_app(app(plus,app(s,x)),y) >= Marked_app(app(plus,x),y) ; Marked_app(app(sumwith,f),app(app(cons,x),xs)) >= Marked_app(app(plus, app(f,x)), app(app(sumwith,f),xs)) ; } + Disjunctions:{ { Marked_app(app(plus,app(s,x)),y) > Marked_app(app(plus,x),y) ; } { Marked_app(app(sumwith,f),app(app(cons,x),xs)) > Marked_app(app(plus, app(f,x)), app(app(sumwith,f),xs)) ; } } === 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 : 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(plus,app(s,x)),y) >= app(s,app(app(plus,x),y)) constraint: app(app(plus,0),y) >= y constraint: app(app(sumwith,f),app(app(cons,x),xs)) >= app(app(plus,app(f,x)), app(app(sumwith,f),xs)) constraint: app(app(sumwith,f),nil) >= nil constraint: Marked_app(app(plus,app(s,x)),y) >= Marked_app(app(plus,x),y) constraint: Marked_app(app(sumwith,f),app(app(cons,x),xs)) >= Marked_app( app(plus, app(f,x)), app(app( sumwith, f), xs)) APPLY CRITERIA (Graph splitting) Found 1 components: { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { app(app(plus,app(s,x)),y) >= app(s,app(app(plus,x),y)) ; app(app(plus,0),y) >= y ; app(app(sumwith,f),app(app(cons,x),xs)) >= app(app(plus,app(f,x)), app(app(sumwith,f),xs)) ; app(app(sumwith,f),nil) >= nil ; Marked_app(app(plus,app(s,x)),y) >= Marked_app(app(plus,x),y) ; } + Disjunctions:{ { Marked_app(app(plus,app(s,x)),y) > Marked_app(app(plus,x),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 : 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(plus,app(s,x)),y) >= app(s,app(app(plus,x),y)) ; app(app(plus,0),y) >= y ; app(app(sumwith,f),app(app(cons,x),xs)) >= app(app(plus,app(f,x)), app(app(sumwith,f),xs)) ; app(app(sumwith,f),nil) >= nil ; Marked_app(app(plus,app(s,x)),y) > Marked_app(app(plus,x),y) ; } APPLY CRITERIA (SOLVE_ORD) Trying to solve the following constraints: { app(app(plus,app(s,x)),y) >= app(s,app(app(plus,x),y)) ; app(app(plus,0),y) >= y ; app(app(sumwith,f),app(app(cons,x),xs)) >= app(app(plus,app(f,x)), app(app(sumwith,f),xs)) ; app(app(sumwith,f),nil) >= nil ; Marked_app(app(plus,app(s,x)),y) > Marked_app(app(plus,x),y) ; } + 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.(4 bt (0) [5]) === 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 8.350048 seconds (real time) Cime Exit Status: 0