- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] p(0) -> 0 [2] p(s(x)) -> x [3] plus(x,0) -> x [4] plus(0,y) -> y [5] plus(s(x),y) -> s(plus(x,y)) [6] plus(s(x),y) -> s(plus(p(s(x)),y)) [7] plus(x,s(y)) -> s(plus(x,p(s(y)))) [8] times(0,y) -> 0 [9] times(s(0),y) -> y [10] times(s(x),y) -> plus(y,times(x,y)) [11] div(0,y) -> 0 [12] div(x,y) -> quot(x,y,y) [13] quot(0,s(y),z) -> 0 [14] quot(s(x),s(y),z) -> quot(x,y,z) [15] quot(x,0,s(z)) -> s(div(x,s(z))) [16] div(div(x,y),z) -> div(x,times(y,z)) [17] eq(0,0) -> true [18] eq(s(x),0) -> false [19] eq(0,s(y)) -> false [20] eq(s(x),s(y)) -> eq(x,y) [21] divides(y,x) -> eq(x,times(div(x,y),y)) [22] prime(s(s(x))) -> pr(s(s(x)),s(x)) [23] pr(x,s(0)) -> true [24] pr(x,s(s(y))) -> if(divides(s(s(y)),x),x,s(y)) [25] if(true,x,y) -> false [26] if(false,x,y) -> pr(x,y) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 5 components: { --> --> } { --> } { --> --> --> --> --> --> --> --> } { --> } { --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_if -> 3 Marked_pr -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_eq -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_quot -> 1 Marked_div -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_times -> 1 APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { p(0) >= 0 ; p(s(x)) >= x ; plus(0,y) >= y ; plus(s(x),y) >= s(plus(p(s(x)),y)) ; plus(s(x),y) >= s(plus(x,y)) ; plus(x,0) >= x ; plus(x,s(y)) >= s(plus(x,p(s(y)))) ; times(0,y) >= 0 ; times(s(0),y) >= y ; times(s(x),y) >= plus(y,times(x,y)) ; div(0,y) >= 0 ; div(div(x,y),z) >= div(x,times(y,z)) ; div(x,y) >= quot(x,y,y) ; quot(0,s(y),z) >= 0 ; quot(s(x),s(y),z) >= quot(x,y,z) ; quot(x,0,s(z)) >= s(div(x,s(z))) ; eq(0,0) >= true ; eq(0,s(y)) >= false ; eq(s(x),0) >= false ; eq(s(x),s(y)) >= eq(x,y) ; divides(y,x) >= eq(x,times(div(x,y),y)) ; pr(x,s(0)) >= true ; pr(x,s(s(y))) >= if(divides(s(s(y)),x),x,s(y)) ; prime(s(s(x))) >= pr(s(s(x)),s(x)) ; if(true,x,y) >= false ; if(false,x,y) >= pr(x,y) ; Marked_plus(s(x),y) >= Marked_plus(p(s(x)),y) ; Marked_plus(s(x),y) >= Marked_plus(x,y) ; Marked_plus(x,s(y)) >= Marked_plus(x,p(s(y))) ; } + Disjunctions:{ { Marked_plus(s(x),y) > Marked_plus(p(s(x)),y) ; } { Marked_plus(s(x),y) > Marked_plus(x,y) ; } { Marked_plus(x,s(y)) > Marked_plus(x,p(s(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 : 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: { p(0) >= 0 ; p(s(x)) >= x ; plus(0,y) >= y ; plus(s(x),y) >= s(plus(p(s(x)),y)) ; plus(s(x),y) >= s(plus(x,y)) ; plus(x,0) >= x ; plus(x,s(y)) >= s(plus(x,p(s(y)))) ; times(0,y) >= 0 ; times(s(0),y) >= y ; times(s(x),y) >= plus(y,times(x,y)) ; div(0,y) >= 0 ; div(div(x,y),z) >= div(x,times(y,z)) ; div(x,y) >= quot(x,y,y) ; quot(0,s(y),z) >= 0 ; quot(s(x),s(y),z) >= quot(x,y,z) ; quot(x,0,s(z)) >= s(div(x,s(z))) ; eq(0,0) >= true ; eq(0,s(y)) >= false ; eq(s(x),0) >= false ; eq(s(x),s(y)) >= eq(x,y) ; divides(y,x) >= eq(x,times(div(x,y),y)) ; pr(x,s(0)) >= true ; pr(x,s(s(y))) >= if(divides(s(s(y)),x),x,s(y)) ; prime(s(s(x))) >= pr(s(s(x)),s(x)) ; if(true,x,y) >= false ; if(false,x,y) >= pr(x,y) ; Marked_plus(s(x),y) > Marked_plus(p(s(x)),y) ; Marked_plus(s(x),y) > Marked_plus(x,y) ; Marked_plus(x,s(y)) > Marked_plus(x,p(s(y))) ; } APPLY CRITERIA (SOLVE_ORD) Trying to solve the following constraints: { p(0) >= 0 ; p(s(x)) >= x ; plus(0,y) >= y ; plus(s(x),y) >= s(plus(p(s(x)),y)) ; plus(s(x),y) >= s(plus(x,y)) ; plus(x,0) >= x ; plus(x,s(y)) >= s(plus(x,p(s(y)))) ; times(0,y) >= 0 ; times(s(0),y) >= y ; times(s(x),y) >= plus(y,times(x,y)) ; div(0,y) >= 0 ; div(div(x,y),z) >= div(x,times(y,z)) ; div(x,y) >= quot(x,y,y) ; quot(0,s(y),z) >= 0 ; quot(s(x),s(y),z) >= quot(x,y,z) ; quot(x,0,s(z)) >= s(div(x,s(z))) ; eq(0,0) >= true ; eq(0,s(y)) >= false ; eq(s(x),0) >= false ; eq(s(x),s(y)) >= eq(x,y) ; divides(y,x) >= eq(x,times(div(x,y),y)) ; pr(x,s(0)) >= true ; pr(x,s(s(y))) >= if(divides(s(s(y)),x),x,s(y)) ; prime(s(s(x))) >= pr(s(s(x)),s(x)) ; if(true,x,y) >= false ; if(false,x,y) >= pr(x,y) ; Marked_plus(s(x),y) > Marked_plus(p(s(x)),y) ; Marked_plus(s(x),y) > Marked_plus(x,y) ; Marked_plus(x,s(y)) > Marked_plus(x,p(s(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.(1474 bt (1728) [297]) === 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 4.786419 seconds (real time) Cime Exit Status: 0