- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] app(app(h,z),app(e,x)) -> app(app(h,app(c,z)),app(app(d,z),x)) [2] app(app(d,z),app(app(g,0),0)) -> app(e,0) [3] app(app(d,z),app(app(g,x),y)) -> app(app(g,app(e,x)),app(app(d,z),y)) [4] app(app(d,app(c,z)),app(app(g,app(app(g,x),y)),0)) -> app(app(g,app(app(d,app(c,z)),app(app(g,x),y))),app(app(d,z),app(app(g,x),y))) [5] app(app(g,app(e,x)),app(e,y)) -> app(e,app(app(g,x),y)) [6] app(app(map,f),nil) -> nil [7] app(app(map,f),app(app(cons,x),xs)) -> app(app(cons,app(f,x)),app(app(map,f),xs)) [8] app(app(filter,f),nil) -> nil [9] app(app(filter,f),app(app(cons,x),xs)) -> app(app(app(app(filter2,app(f,x)),f),x),xs) [10] app(app(app(app(filter2,true),f),x),xs) -> app(app(cons,x),app(app(filter,f),xs)) [11] 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(h,z),app(e,x)) >= app(app(h,app(c,z)),app(app(d,z),x)) ; app(app(d,app(c,z)),app(app(g,app(app(g,x),y)),0)) >= app(app(g, app(app( d,app(c,z)), app(app(g,x),y))), app(app(d,z), app(app(g,x),y))) ; app(app(d,z),app(app(g,0),0)) >= app(e,0) ; app(app(d,z),app(app(g,x),y)) >= app(app(g,app(e,x)),app(app(d,z),y)) ; app(app(g,app(e,x)),app(e,y)) >= app(e,app(app(g,x),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 ; 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(h,z),app(e,x)) >= Marked_app(app(h,app(c,z)),app(app(d,z),x)) ; Marked_app(app(h,z),app(e,x)) >= Marked_app(app(d,z),x) ; Marked_app(app(d,app(c,z)),app(app(g,app(app(g,x),y)),0)) >= Marked_app( app(d, app(c,z)), app(app(g,x),y)) ; Marked_app(app(d,app(c,z)),app(app(g,app(app(g,x),y)),0)) >= Marked_app( app(d, z), app(app(g,x),y)) ; Marked_app(app(d,app(c,z)),app(app(g,app(app(g,x),y)),0)) >= Marked_app( app(g, app( app( d, app(c,z)), app( app(g,x), y))), app(app(d,z), app( app(g,x), y))) ; Marked_app(app(d,z),app(app(g,x),y)) >= Marked_app(app(d,z),y) ; Marked_app(app(d,z),app(app(g,x),y)) >= Marked_app(app(g,app(e,x)), app(app(d,z),y)) ; Marked_app(app(g,app(e,x)),app(e,y)) >= Marked_app(app(g,x),y) ; 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(h,z),app(e,x)) > Marked_app(app(h,app(c,z)),app(app(d,z),x)) ; } { Marked_app(app(h,z),app(e,x)) > Marked_app(app(d,z),x) ; } { Marked_app(app(d,app(c,z)),app(app(g,app(app(g,x),y)),0)) > Marked_app( app(d, app(c,z)), app(app(g,x),y)) ; } { Marked_app(app(d,app(c,z)),app(app(g,app(app(g,x),y)),0)) > Marked_app( app(d, z), app(app(g,x),y)) ; } { Marked_app(app(d,app(c,z)),app(app(g,app(app(g,x),y)),0)) > Marked_app( app(g, app(app( d, app(c,z)), app( app(g,x), y))), app(app(d,z), app(app(g,x),y))) ; } { Marked_app(app(d,z),app(app(g,x),y)) > Marked_app(app(d,z),y) ; } { Marked_app(app(d,z),app(app(g,x),y)) > Marked_app(app(g,app(e,x)), app(app(d,z),y)) ; } { Marked_app(app(g,app(e,x)),app(e,y)) > Marked_app(app(g,x),y) ; } { 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 : 15.000000 === Entering poly_solver Starting Sat solver initialization === STOPING TIMER virtual === Time out 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(h,z),app(e,x)) >= app(app(h,app(c,z)),app(app(d,z),x)) ; app(app(d,app(c,z)),app(app(g,app(app(g,x),y)),0)) >= app(app(g, app(app( d,app(c,z)), app(app(g,x),y))), app(app(d,z), app(app(g,x),y))) ; app(app(d,z),app(app(g,0),0)) >= app(e,0) ; app(app(d,z),app(app(g,x),y)) >= app(app(g,app(e,x)),app(app(d,z),y)) ; app(app(g,app(e,x)),app(e,y)) >= app(e,app(app(g,x),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 ; 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(h,z),app(e,x)) > Marked_app(app(h,app(c,z)),app(app(d,z),x)) ; Marked_app(app(h,z),app(e,x)) > Marked_app(app(d,z),x) ; Marked_app(app(d,app(c,z)),app(app(g,app(app(g,x),y)),0)) > Marked_app( app(d, app(c,z)), app(app(g,x),y)) ; Marked_app(app(d,app(c,z)),app(app(g,app(app(g,x),y)),0)) > Marked_app( app(d, z), app(app(g,x),y)) ; Marked_app(app(d,app(c,z)),app(app(g,app(app(g,x),y)),0)) > Marked_app( app(g, app(app( d, app(c,z)), app( app(g,x), y))), app(app(d,z), app(app(g,x),y))) ; Marked_app(app(d,z),app(app(g,x),y)) > Marked_app(app(d,z),y) ; Marked_app(app(d,z),app(app(g,x),y)) > Marked_app(app(g,app(e,x)), app(app(d,z),y)) ; Marked_app(app(g,app(e,x)),app(e,y)) > Marked_app(app(g,x),y) ; 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(h,z),app(e,x)) >= app(app(h,app(c,z)),app(app(d,z),x)) ; app(app(d,app(c,z)),app(app(g,app(app(g,x),y)),0)) >= app(app(g, app(app( d,app(c,z)), app(app(g,x),y))), app(app(d,z), app(app(g,x),y))) ; app(app(d,z),app(app(g,0),0)) >= app(e,0) ; app(app(d,z),app(app(g,x),y)) >= app(app(g,app(e,x)),app(app(d,z),y)) ; app(app(g,app(e,x)),app(e,y)) >= app(e,app(app(g,x),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 ; 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(h,z),app(e,x)) > Marked_app(app(h,app(c,z)),app(app(d,z),x)) ; Marked_app(app(h,z),app(e,x)) > Marked_app(app(d,z),x) ; Marked_app(app(d,app(c,z)),app(app(g,app(app(g,x),y)),0)) > Marked_app( app(d, app(c,z)), app(app(g,x),y)) ; Marked_app(app(d,app(c,z)),app(app(g,app(app(g,x),y)),0)) > Marked_app( app(d, z), app(app(g,x),y)) ; Marked_app(app(d,app(c,z)),app(app(g,app(app(g,x),y)),0)) > Marked_app( app(g, app(app( d, app(c,z)), app( app(g,x), y))), app(app(d,z), app(app(g,x),y))) ; Marked_app(app(d,z),app(app(g,x),y)) > Marked_app(app(d,z),y) ; Marked_app(app(d,z),app(app(g,x),y)) > Marked_app(app(g,app(e,x)), app(app(d,z),y)) ; Marked_app(app(g,app(e,x)),app(e,y)) > Marked_app(app(g,x),y) ; 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.(4 bt (0) [6]) === TIMER virtual : 15.000000 === Entering poly_solver Starting Sat solver initialization === STOPING TIMER virtual === Time out 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 147.612769 seconds (real time) Cime Exit Status: 0