- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] app(app(le,0),y) -> true [2] app(app(le,app(s,x)),0) -> false [3] app(app(le,app(s,x)),app(s,y)) -> app(app(le,x),y) [4] app(pred,app(s,x)) -> x [5] app(app(minus,x),0) -> x [6] app(app(minus,x),app(s,y)) -> app(pred,app(app(minus,x),y)) [7] app(app(gcd,0),y) -> y [8] app(app(gcd,app(s,x)),0) -> app(s,x) [9] app(app(gcd,app(s,x)),app(s,y)) -> app(app(app(if_gcd,app(app(le,y),x)),app(s,x)),app(s,y)) [10] app(app(app(if_gcd,true),app(s,x)),app(s,y)) -> app(app(gcd,app(app(minus,x),y)),app(s,y)) [11] app(app(app(if_gcd,false),app(s,x)),app(s,y)) -> app(app(gcd,app(app(minus,y),x)),app(s,x)) [12] app(app(map,f),nil) -> nil [13] app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) [14] app(app(filter,f),nil) -> nil [15] app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(app(filter2,app(f,x)),f),x),xs) [16] app(app(app(app(filter2,true),f),x),xs) -> app(app(cons,x),app(app(filter,f),xs)) [17] app(app(app(app(filter2,false),f),x),xs) -> app(app(filter,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(app(app(filter2,true),f),x),xs) >= app(app(cons,x), app(app(filter,f),xs)) ; app(app(app(app(filter2,false),f),x),xs) >= app(app(filter,f),xs) ; app(app(app(if_gcd,true),app(s,x)),app(s,y)) >= app(app(gcd, app(app(minus,x),y)), app(s,y)) ; app(app(app(if_gcd,false),app(s,x)),app(s,y)) >= app(app(gcd, app(app(minus,y),x)), app(s,x)) ; app(app(le,app(s,x)),app(s,y)) >= app(app(le,x),y) ; app(app(le,app(s,x)),0) >= false ; app(app(le,0),y) >= true ; app(app(minus,x),app(s,y)) >= app(pred,app(app(minus,x),y)) ; app(app(minus,x),0) >= x ; app(app(gcd,app(s,x)),app(s,y)) >= app(app(app(if_gcd,app(app(le,y),x)), app(s,x)),app(s,y)) ; app(app(gcd,app(s,x)),0) >= app(s,x) ; app(app(gcd,0),y) >= y ; 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(filter,f),app(app(cons,x),xs)) >= app(app(app(app(filter2,app(f,x)), f),x),xs) ; app(app(filter,f),nil) >= nil ; app(pred,app(s,x)) >= x ; Marked_app(app(app(app(filter2,true),f),x),xs) >= Marked_app(app(cons,x), app(app(filter,f),xs)) ; Marked_app(app(app(app(filter2,true),f),x),xs) >= Marked_app(app(filter,f), xs) ; Marked_app(app(app(app(filter2,false),f),x),xs) >= Marked_app(app(filter,f), xs) ; Marked_app(app(app(if_gcd,true),app(s,x)),app(s,y)) >= Marked_app(app( minus, x), y) ; Marked_app(app(app(if_gcd,true),app(s,x)),app(s,y)) >= Marked_app(app( gcd, app( app( minus, x), y)), app(s,y)) ; Marked_app(app(app(if_gcd,false),app(s,x)),app(s,y)) >= Marked_app( app(minus, y),x) ; Marked_app(app(app(if_gcd,false),app(s,x)),app(s,y)) >= Marked_app( app(gcd, app(app(minus,y),x)), app(s,x)) ; Marked_app(app(le,app(s,x)),app(s,y)) >= Marked_app(app(le,x),y) ; Marked_app(app(minus,x),app(s,y)) >= Marked_app(app(minus,x),y) ; Marked_app(app(gcd,app(s,x)),app(s,y)) >= Marked_app(app(app(if_gcd, app(app(le,y),x)), app(s,x)),app(s,y)) ; Marked_app(app(gcd,app(s,x)),app(s,y)) >= Marked_app(app(le,y),x) ; Marked_app(app(gcd,app(s,x)),app(s,y)) >= Marked_app(app(if_gcd, app(app(le,y),x)), app(s,x)) ; 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(filter,f),app(app(cons,x),xs)) >= Marked_app(app(app( app( filter2, app(f,x)), f), x),xs) ; Marked_app(app(filter,f),app(app(cons,x),xs)) >= Marked_app(app(app( filter2, app(f,x)), f),x) ; Marked_app(app(filter,f),app(app(cons,x),xs)) >= Marked_app(app(filter2, app(f,x)), f) ; Marked_app(app(filter,f),app(app(cons,x),xs)) >= Marked_app(f,x) ; } + Disjunctions:{ { Marked_app(app(app(app(filter2,true),f),x),xs) > Marked_app(app(cons,x), app(app(filter,f),xs)) ; } { Marked_app(app(app(app(filter2,true),f),x),xs) > Marked_app(app(filter,f),xs) ; } { Marked_app(app(app(app(filter2,false),f),x),xs) > Marked_app(app(filter,f), xs) ; } { Marked_app(app(app(if_gcd,true),app(s,x)),app(s,y)) > Marked_app(app(minus,x), y) ; } { Marked_app(app(app(if_gcd,true),app(s,x)),app(s,y)) > Marked_app(app( gcd, app( app( minus, x), y)), app(s,y)) ; } { Marked_app(app(app(if_gcd,false),app(s,x)),app(s,y)) > Marked_app(app( minus, y), x) ; } { Marked_app(app(app(if_gcd,false),app(s,x)),app(s,y)) > Marked_app(app( gcd, app( app( minus, y), x)), app(s,x)) ; } { Marked_app(app(le,app(s,x)),app(s,y)) > Marked_app(app(le,x),y) ; } { Marked_app(app(minus,x),app(s,y)) > Marked_app(app(minus,x),y) ; } { Marked_app(app(gcd,app(s,x)),app(s,y)) > Marked_app(app(app(if_gcd, app(app(le,y),x)), app(s,x)),app(s,y)) ; } { Marked_app(app(gcd,app(s,x)),app(s,y)) > Marked_app(app(le,y),x) ; } { Marked_app(app(gcd,app(s,x)),app(s,y)) > Marked_app(app(if_gcd, app(app(le,y),x)), app(s,x)) ; } { 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(filter,f),app(app(cons,x),xs)) > Marked_app(app(app( app( filter2, app(f,x)), f), x),xs) ; } { Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(app(app( filter2, app(f,x)), f),x) ; } { Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(app(filter2, app(f,x)), f) ; } { Marked_app(app(filter,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 : 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 : 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),f),x),xs) >= app(app(cons,x), app(app(filter,f),xs)) ; app(app(app(app(filter2,false),f),x),xs) >= app(app(filter,f),xs) ; app(app(app(if_gcd,true),app(s,x)),app(s,y)) >= app(app(gcd, app(app(minus,x),y)), app(s,y)) ; app(app(app(if_gcd,false),app(s,x)),app(s,y)) >= app(app(gcd, app(app(minus,y),x)), app(s,x)) ; app(app(le,app(s,x)),app(s,y)) >= app(app(le,x),y) ; app(app(le,app(s,x)),0) >= false ; app(app(le,0),y) >= true ; app(app(minus,x),app(s,y)) >= app(pred,app(app(minus,x),y)) ; app(app(minus,x),0) >= x ; app(app(gcd,app(s,x)),app(s,y)) >= app(app(app(if_gcd,app(app(le,y),x)), app(s,x)),app(s,y)) ; app(app(gcd,app(s,x)),0) >= app(s,x) ; app(app(gcd,0),y) >= y ; 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(filter,f),app(app(cons,x),xs)) >= app(app(app(app(filter2,app(f,x)), f),x),xs) ; app(app(filter,f),nil) >= nil ; app(pred,app(s,x)) >= x ; Marked_app(app(app(app(filter2,true),f),x),xs) > Marked_app(app(cons,x), app(app(filter,f),xs)) ; Marked_app(app(app(app(filter2,true),f),x),xs) > Marked_app(app(filter,f),xs) ; Marked_app(app(app(app(filter2,false),f),x),xs) > Marked_app(app(filter,f), xs) ; Marked_app(app(app(if_gcd,true),app(s,x)),app(s,y)) > Marked_app(app(minus,x), y) ; Marked_app(app(app(if_gcd,true),app(s,x)),app(s,y)) > Marked_app(app( gcd, app( app( minus, x), y)), app(s,y)) ; Marked_app(app(app(if_gcd,false),app(s,x)),app(s,y)) > Marked_app(app( minus, y), x) ; Marked_app(app(app(if_gcd,false),app(s,x)),app(s,y)) > Marked_app(app( gcd, app( app( minus, y), x)), app(s,x)) ; Marked_app(app(le,app(s,x)),app(s,y)) > Marked_app(app(le,x),y) ; Marked_app(app(minus,x),app(s,y)) > Marked_app(app(minus,x),y) ; Marked_app(app(gcd,app(s,x)),app(s,y)) > Marked_app(app(app(if_gcd, app(app(le,y),x)), app(s,x)),app(s,y)) ; Marked_app(app(gcd,app(s,x)),app(s,y)) > Marked_app(app(le,y),x) ; Marked_app(app(gcd,app(s,x)),app(s,y)) > Marked_app(app(if_gcd, app(app(le,y),x)), app(s,x)) ; 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(filter,f),app(app(cons,x),xs)) > Marked_app(app(app( app( filter2, app(f,x)), f), x),xs) ; Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(app(app( filter2, app(f,x)), f),x) ; Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(app(filter2, app(f,x)), f) ; Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(f,x) ; } APPLY CRITERIA (SOLVE_ORD) Trying to solve the following constraints: { app(app(app(app(filter2,true),f),x),xs) >= app(app(cons,x), app(app(filter,f),xs)) ; app(app(app(app(filter2,false),f),x),xs) >= app(app(filter,f),xs) ; app(app(app(if_gcd,true),app(s,x)),app(s,y)) >= app(app(gcd, app(app(minus,x),y)), app(s,y)) ; app(app(app(if_gcd,false),app(s,x)),app(s,y)) >= app(app(gcd, app(app(minus,y),x)), app(s,x)) ; app(app(le,app(s,x)),app(s,y)) >= app(app(le,x),y) ; app(app(le,app(s,x)),0) >= false ; app(app(le,0),y) >= true ; app(app(minus,x),app(s,y)) >= app(pred,app(app(minus,x),y)) ; app(app(minus,x),0) >= x ; app(app(gcd,app(s,x)),app(s,y)) >= app(app(app(if_gcd,app(app(le,y),x)), app(s,x)),app(s,y)) ; app(app(gcd,app(s,x)),0) >= app(s,x) ; app(app(gcd,0),y) >= y ; 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(filter,f),app(app(cons,x),xs)) >= app(app(app(app(filter2,app(f,x)), f),x),xs) ; app(app(filter,f),nil) >= nil ; app(pred,app(s,x)) >= x ; Marked_app(app(app(app(filter2,true),f),x),xs) > Marked_app(app(cons,x), app(app(filter,f),xs)) ; Marked_app(app(app(app(filter2,true),f),x),xs) > Marked_app(app(filter,f),xs) ; Marked_app(app(app(app(filter2,false),f),x),xs) > Marked_app(app(filter,f), xs) ; Marked_app(app(app(if_gcd,true),app(s,x)),app(s,y)) > Marked_app(app(minus,x), y) ; Marked_app(app(app(if_gcd,true),app(s,x)),app(s,y)) > Marked_app(app( gcd, app( app( minus, x), y)), app(s,y)) ; Marked_app(app(app(if_gcd,false),app(s,x)),app(s,y)) > Marked_app(app( minus, y), x) ; Marked_app(app(app(if_gcd,false),app(s,x)),app(s,y)) > Marked_app(app( gcd, app( app( minus, y), x)), app(s,x)) ; Marked_app(app(le,app(s,x)),app(s,y)) > Marked_app(app(le,x),y) ; Marked_app(app(minus,x),app(s,y)) > Marked_app(app(minus,x),y) ; Marked_app(app(gcd,app(s,x)),app(s,y)) > Marked_app(app(app(if_gcd, app(app(le,y),x)), app(s,x)),app(s,y)) ; Marked_app(app(gcd,app(s,x)),app(s,y)) > Marked_app(app(le,y),x) ; Marked_app(app(gcd,app(s,x)),app(s,y)) > Marked_app(app(if_gcd, app(app(le,y),x)), app(s,x)) ; 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(filter,f),app(app(cons,x),xs)) > Marked_app(app(app( app( filter2, app(f,x)), f), x),xs) ; Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(app(app( filter2, app(f,x)), f),x) ; Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(app(filter2, app(f,x)), f) ; Marked_app(app(filter,f),app(app(cons,x),xs)) > Marked_app(f,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 102.445547 seconds (real time) Cime Exit Status: 0