- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] numbers -> d(0) [2] d(x) -> if(le(x,nr),x) [3] if(true,x) -> cons(x,d(s(x))) [4] if(false,x) -> nil [5] le(0,y) -> true [6] le(s(x),0) -> false [7] le(s(x),s(y)) -> le(x,y) [8] nr -> ack(s(s(s(s(s(s(0)))))),0) [9] ack(0,x) -> s(x) [10] ack(s(x),0) -> ack(x,s(0)) [11] ack(s(x),s(y)) -> ack(x,ack(s(x),y)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 3 components: { --> --> } { --> } { --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { d(x) >= if(le(x,nr),x) ; numbers >= d(0) ; if(true,x) >= cons(x,d(s(x))) ; if(false,x) >= nil ; le(0,y) >= true ; le(s(x),0) >= false ; le(s(x),s(y)) >= le(x,y) ; nr >= ack(s(s(s(s(s(s(0)))))),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_if(true,x) >= Marked_d(s(x)) ; Marked_d(x) >= Marked_if(le(x,nr),x) ; } + Disjunctions:{ { Marked_if(true,x) > Marked_d(s(x)) ; } { Marked_d(x) > Marked_if(le(x,nr),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 : 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 timeout reached === STOPING TIMER virtual === No solution found for these parameters. No solution found for these constraints. APPLY CRITERIA (Simple graph) Found the following constraints: { d(x) >= if(le(x,nr),x) ; numbers >= d(0) ; if(true,x) >= cons(x,d(s(x))) ; if(false,x) >= nil ; le(0,y) >= true ; le(s(x),0) >= false ; le(s(x),s(y)) >= le(x,y) ; nr >= ack(s(s(s(s(s(s(0)))))),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_if(true,x) >= Marked_d(s(x)) ; Marked_d(x) > Marked_if(le(x,nr),x) ; } APPLY CRITERIA (SOLVE_ORD) Trying to solve the following constraints: { d(x) >= if(le(x,nr),x) ; numbers >= d(0) ; if(true,x) >= cons(x,d(s(x))) ; if(false,x) >= nil ; le(0,y) >= true ; le(s(x),0) >= false ; le(s(x),s(y)) >= le(x,y) ; nr >= ack(s(s(s(s(s(s(0)))))),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_if(true,x) >= Marked_d(s(x)) ; Marked_d(x) > Marked_if(le(x,nr),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.(5613 bt (5261) [640]) === 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 timeout reached === 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 139.784443 seconds (real time) Cime Exit Status: 0