- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] minus(minus(x,y),z) -> minus(x,plus(y,z)) [2] minus(0,y) -> 0 [3] minus(x,0) -> x [4] minus(s(x),s(y)) -> minus(x,y) [5] plus(0,y) -> y [6] plus(s(x),y) -> plus(x,s(y)) [7] plus(s(x),y) -> s(plus(y,x)) [8] zero(s(x)) -> false [9] zero(0) -> true [10] p(s(x)) -> x [11] p(0) -> 0 [12] div(x,y) -> quot(x,y,0) [13] quot(s(x),s(y),z) -> quot(minus(p(ack(0,x)),y),s(y),s(z)) [14] quot(0,s(y),z) -> z [15] ack(0,x) -> s(x) [16] ack(0,x) -> plus(x,s(0)) [17] ack(s(x),0) -> ack(x,s(0)) [18] ack(s(x),s(y)) -> ack(x,ack(s(x),y)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 4 components: { --> } { --> --> --> --> } { --> --> --> --> --> --> --> --> } { --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { minus(minus(x,y),z) >= minus(x,plus(y,z)) ; minus(0,y) >= 0 ; minus(s(x),s(y)) >= minus(x,y) ; minus(x,0) >= x ; plus(0,y) >= y ; plus(s(x),y) >= plus(x,s(y)) ; plus(s(x),y) >= s(plus(y,x)) ; zero(0) >= true ; zero(s(x)) >= false ; p(0) >= 0 ; p(s(x)) >= x ; quot(0,s(y),z) >= z ; quot(s(x),s(y),z) >= quot(minus(p(ack(0,x)),y),s(y),s(z)) ; div(x,y) >= quot(x,y,0) ; ack(0,x) >= plus(x,s(0)) ; ack(0,x) >= s(x) ; ack(s(x),0) >= ack(x,s(0)) ; ack(s(x),s(y)) >= ack(x,ack(s(x),y)) ; Marked_quot(s(x),s(y),z) >= Marked_quot(minus(p(ack(0,x)),y),s(y),s(z)) ; } + Disjunctions:{ { Marked_quot(s(x),s(y),z) > Marked_quot(minus(p(ack(0,x)),y),s(y),s(z)) ; } } === 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: { minus(minus(x,y),z) >= minus(x,plus(y,z)) ; minus(0,y) >= 0 ; minus(s(x),s(y)) >= minus(x,y) ; minus(x,0) >= x ; plus(0,y) >= y ; plus(s(x),y) >= plus(x,s(y)) ; plus(s(x),y) >= s(plus(y,x)) ; zero(0) >= true ; zero(s(x)) >= false ; p(0) >= 0 ; p(s(x)) >= x ; quot(0,s(y),z) >= z ; quot(s(x),s(y),z) >= quot(minus(p(ack(0,x)),y),s(y),s(z)) ; div(x,y) >= quot(x,y,0) ; ack(0,x) >= plus(x,s(0)) ; ack(0,x) >= s(x) ; ack(s(x),0) >= ack(x,s(0)) ; ack(s(x),s(y)) >= ack(x,ack(s(x),y)) ; Marked_quot(s(x),s(y),z) > Marked_quot(minus(p(ack(0,x)),y),s(y),s(z)) ; } APPLY CRITERIA (SOLVE_ORD) Trying to solve the following constraints: { minus(minus(x,y),z) >= minus(x,plus(y,z)) ; minus(0,y) >= 0 ; minus(s(x),s(y)) >= minus(x,y) ; minus(x,0) >= x ; plus(0,y) >= y ; plus(s(x),y) >= plus(x,s(y)) ; plus(s(x),y) >= s(plus(y,x)) ; zero(0) >= true ; zero(s(x)) >= false ; p(0) >= 0 ; p(s(x)) >= x ; quot(0,s(y),z) >= z ; quot(s(x),s(y),z) >= quot(minus(p(ack(0,x)),y),s(y),s(z)) ; div(x,y) >= quot(x,y,0) ; ack(0,x) >= plus(x,s(0)) ; ack(0,x) >= s(x) ; ack(s(x),0) >= ack(x,s(0)) ; ack(s(x),s(y)) >= ack(x,ack(s(x),y)) ; Marked_quot(s(x),s(y),z) > Marked_quot(minus(p(ack(0,x)),y),s(y),s(z)) ; } + 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.(1021 bt (1125) [234]) === 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 7.510251 seconds (real time) Cime Exit Status: 0