- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] app(app(f,0),n) -> app(app(hd,app(app(map,f),app(app(cons,0),nil))),n) [2] app(app(map,f),nil) -> nil [3] app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,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(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)), app(app(map,f),xs)) ; app(app(map,f),nil) >= nil ; app(app(f,0),n) >= app(app(hd,app(app(map,f),app(app(cons,0),nil))),n) ; Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(app(map,f),xs) ; Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(app(cons,app(f,x)), app(app(map,f),xs)) ; Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(f,x) ; Marked_app(app(f,0),n) >= Marked_app(app(hd, app(app(map,f),app(app(cons,0),nil))), n) ; Marked_app(app(f,0),n) >= Marked_app(app(map,f),app(app(cons,0),nil)) ; Marked_app(app(f,0),n) >= Marked_app(app(cons,0),nil) ; } + Disjunctions:{ { Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(map,f),xs) ; } { Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(cons,app(f,x)), app(app(map,f),xs)) ; } { Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(f,x) ; } { Marked_app(app(f,0),n) > Marked_app(app(hd, app(app(map,f),app(app(cons,0),nil))), n) ; } { Marked_app(app(f,0),n) > Marked_app(app(map,f),app(app(cons,0),nil)) ; } { Marked_app(app(f,0),n) > Marked_app(app(cons,0),nil) ; } } === 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 : 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(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)), app(app(map,f),xs)) constraint: app(app(map,f),nil) >= nil constraint: app(app(f,0),n) >= app(app(hd,app(app(map,f),app(app(cons,0),nil))), n) constraint: Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app( app(map,f), xs) constraint: Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app( app(cons,app(f,x)), app(app(map,f),xs)) constraint: Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(f,x) constraint: Marked_app(app(f,0),n) >= Marked_app(app(hd, app(app(map,f), app(app(cons,0),nil))), n) constraint: Marked_app(app(f,0),n) >= Marked_app(app(map,f), app(app(cons,0),nil)) constraint: Marked_app(app(f,0),n) >= Marked_app(app(cons,0),nil) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)), app(app(map,f),xs)) ; app(app(map,f),nil) >= nil ; app(app(f,0),n) >= app(app(hd,app(app(map,f),app(app(cons,0),nil))),n) ; Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(app(map,f),xs) ; Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(app(cons,app(f,x)), app(app(map,f),xs)) ; Marked_app(app(f,0),n) >= Marked_app(app(hd, app(app(map,f),app(app(cons,0),nil))), n) ; Marked_app(app(f,0),n) >= Marked_app(app(map,f),app(app(cons,0),nil)) ; Marked_app(app(f,0),n) >= Marked_app(app(cons,0),nil) ; } + Disjunctions:{ { Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(map,f),xs) ; } { Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(cons,app(f,x)), app(app(map,f),xs)) ; } { Marked_app(app(f,0),n) > Marked_app(app(hd, app(app(map,f),app(app(cons,0),nil))), n) ; } { Marked_app(app(f,0),n) > Marked_app(app(map,f),app(app(cons,0),nil)) ; } { Marked_app(app(f,0),n) > Marked_app(app(cons,0),nil) ; } } === 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 : 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(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)), app(app(map,f),xs)) constraint: app(app(map,f),nil) >= nil constraint: app(app(f,0),n) >= app(app(hd,app(app(map,f),app(app(cons,0),nil))), n) constraint: Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app( app(map,f), xs) constraint: Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app( app(cons,app(f,x)), app(app(map,f),xs)) constraint: Marked_app(app(f,0),n) >= Marked_app(app(hd, app(app(map,f), app(app(cons,0),nil))), n) constraint: Marked_app(app(f,0),n) >= Marked_app(app(map,f), app(app(cons,0),nil)) constraint: Marked_app(app(f,0),n) >= Marked_app(app(cons,0),nil) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)), app(app(map,f),xs)) ; app(app(map,f),nil) >= nil ; app(app(f,0),n) >= app(app(hd,app(app(map,f),app(app(cons,0),nil))),n) ; Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app(app(map,f),xs) ; Marked_app(app(f,0),n) >= Marked_app(app(hd, app(app(map,f),app(app(cons,0),nil))), n) ; Marked_app(app(f,0),n) >= Marked_app(app(map,f),app(app(cons,0),nil)) ; Marked_app(app(f,0),n) >= Marked_app(app(cons,0),nil) ; } + Disjunctions:{ { Marked_app(app(map,f),app(app(cons,x),xs)) > Marked_app(app(map,f),xs) ; } { Marked_app(app(f,0),n) > Marked_app(app(hd, app(app(map,f),app(app(cons,0),nil))), n) ; } { Marked_app(app(f,0),n) > Marked_app(app(map,f),app(app(cons,0),nil)) ; } { Marked_app(app(f,0),n) > Marked_app(app(cons,0),nil) ; } } === 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 === 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(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)), app(app(map,f),xs)) constraint: app(app(map,f),nil) >= nil constraint: app(app(f,0),n) >= app(app(hd,app(app(map,f),app(app(cons,0),nil))), n) constraint: Marked_app(app(map,f),app(app(cons,x),xs)) >= Marked_app( app(map,f), xs) constraint: Marked_app(app(f,0),n) >= Marked_app(app(hd, app(app(map,f), app(app(cons,0),nil))), n) constraint: Marked_app(app(f,0),n) >= Marked_app(app(map,f), app(app(cons,0),nil)) constraint: Marked_app(app(f,0),n) >= Marked_app(app(cons,0),nil) APPLY CRITERIA (Graph splitting) Found 2 components: { --> } { --> } APPLY CRITERIA (Subterm criterion) ST: Marked_app -> 2 APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)), app(app(map,f),xs)) ; app(app(map,f),nil) >= nil ; app(app(f,0),n) >= app(app(hd,app(app(map,f),app(app(cons,0),nil))),n) ; Marked_app(app(f,0),n) >= Marked_app(app(cons,0),nil) ; } + Disjunctions:{ { Marked_app(app(f,0),n) > Marked_app(app(cons,0),nil) ; } } === 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(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)), app(app(map,f),xs)) ; app(app(map,f),nil) >= nil ; app(app(f,0),n) >= app(app(hd,app(app(map,f),app(app(cons,0),nil))),n) ; Marked_app(app(f,0),n) > Marked_app(app(cons,0),nil) ; } APPLY CRITERIA (SOLVE_ORD) Trying to solve the following constraints: { app(app(map,f),app(app(cons,x),xs)) >= app(app(cons,app(f,x)), app(app(map,f),xs)) ; app(app(map,f),nil) >= nil ; app(app(f,0),n) >= app(app(hd,app(app(map,f),app(app(cons,0),nil))),n) ; Marked_app(app(f,0),n) > Marked_app(app(cons,0),nil) ; } + Disjunctions:{ } === TIMER virtual : 10.000000 === Entering poly_solver === 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.(10 bt (0) [6]) === TIMER virtual : 15.000000 === Entering poly_solver === 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 === 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 101.127559 seconds (real time) Cime Exit Status: 0