- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] ge(0,0) -> true [2] ge(s(x),0) -> ge(x,0) [3] ge(0,s(0)) -> false [4] ge(0,s(s(x))) -> ge(0,s(x)) [5] ge(s(x),s(y)) -> ge(x,y) [6] minus(0,0) -> 0 [7] minus(0,s(x)) -> minus(0,x) [8] minus(s(x),0) -> s(minus(x,0)) [9] minus(s(x),s(y)) -> minus(x,y) [10] plus(0,0) -> 0 [11] plus(0,s(x)) -> s(plus(0,x)) [12] plus(s(x),y) -> s(plus(x,y)) [13] div(x,y) -> ify(ge(y,s(0)),x,y) [14] ify(false,x,y) -> divByZeroError [15] ify(true,x,y) -> if(ge(x,y),x,y) [16] if(false,x,y) -> 0 [17] if(true,x,y) -> s(div(minus(x,y),y)) [18] div(plus(x,y),z) -> plus(div(x,z),div(y,z)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 9 components: { --> --> --> --> --> --> --> --> --> --> --> } { --> } { --> } { --> } { --> } { --> } { --> } { --> } { --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { ge(0,0) >= true ; ge(0,s(0)) >= false ; ge(0,s(s(x))) >= ge(0,s(x)) ; ge(s(x),0) >= ge(x,0) ; ge(s(x),s(y)) >= ge(x,y) ; minus(0,0) >= 0 ; minus(0,s(x)) >= minus(0,x) ; minus(s(x),0) >= s(minus(x,0)) ; minus(s(x),s(y)) >= minus(x,y) ; plus(0,0) >= 0 ; plus(0,s(x)) >= s(plus(0,x)) ; plus(s(x),y) >= s(plus(x,y)) ; ify(true,x,y) >= if(ge(x,y),x,y) ; ify(false,x,y) >= divByZeroError ; div(plus(x,y),z) >= plus(div(x,z),div(y,z)) ; div(x,y) >= ify(ge(y,s(0)),x,y) ; if(true,x,y) >= s(div(minus(x,y),y)) ; if(false,x,y) >= 0 ; Marked_div(plus(x,y),z) >= Marked_div(x,z) ; Marked_div(plus(x,y),z) >= Marked_div(y,z) ; Marked_div(x,y) >= Marked_ify(ge(y,s(0)),x,y) ; Marked_if(true,x,y) >= Marked_div(minus(x,y),y) ; Marked_ify(true,x,y) >= Marked_if(ge(x,y),x,y) ; } + Disjunctions:{ { Marked_div(plus(x,y),z) > Marked_div(x,z) ; } { Marked_div(plus(x,y),z) > Marked_div(y,z) ; } { Marked_div(x,y) > Marked_ify(ge(y,s(0)),x,y) ; } { Marked_if(true,x,y) > Marked_div(minus(x,y),y) ; } { Marked_ify(true,x,y) > Marked_if(ge(x,y),x,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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: ge(0,0) >= true constraint: ge(0,s(0)) >= false constraint: ge(0,s(s(x))) >= ge(0,s(x)) constraint: ge(s(x),0) >= ge(x,0) constraint: ge(s(x),s(y)) >= ge(x,y) constraint: minus(0,0) >= 0 constraint: minus(0,s(x)) >= minus(0,x) constraint: minus(s(x),0) >= s(minus(x,0)) constraint: minus(s(x),s(y)) >= minus(x,y) constraint: plus(0,0) >= 0 constraint: plus(0,s(x)) >= s(plus(0,x)) constraint: plus(s(x),y) >= s(plus(x,y)) constraint: ify(true,x,y) >= if(ge(x,y),x,y) constraint: ify(false,x,y) >= divByZeroError constraint: div(plus(x,y),z) >= plus(div(x,z),div(y,z)) constraint: div(x,y) >= ify(ge(y,s(0)),x,y) constraint: if(true,x,y) >= s(div(minus(x,y),y)) constraint: if(false,x,y) >= 0 constraint: Marked_div(plus(x,y),z) >= Marked_div(x,z) constraint: Marked_div(plus(x,y),z) >= Marked_div(y,z) constraint: Marked_div(x,y) >= Marked_ify(ge(y,s(0)),x,y) constraint: Marked_if(true,x,y) >= Marked_div(minus(x,y),y) constraint: Marked_ify(true,x,y) >= Marked_if(ge(x,y),x,y) APPLY CRITERIA (Subterm criterion) ST: Marked_minus -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_minus -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_minus -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_ge -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_ge -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_ge -> 2 APPLY CRITERIA (Subterm criterion) ST: Marked_plus -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_plus -> 2 APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> } APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { ge(0,0) >= true ; ge(0,s(0)) >= false ; ge(0,s(s(x))) >= ge(0,s(x)) ; ge(s(x),0) >= ge(x,0) ; ge(s(x),s(y)) >= ge(x,y) ; minus(0,0) >= 0 ; minus(0,s(x)) >= minus(0,x) ; minus(s(x),0) >= s(minus(x,0)) ; minus(s(x),s(y)) >= minus(x,y) ; plus(0,0) >= 0 ; plus(0,s(x)) >= s(plus(0,x)) ; plus(s(x),y) >= s(plus(x,y)) ; ify(true,x,y) >= if(ge(x,y),x,y) ; ify(false,x,y) >= divByZeroError ; div(plus(x,y),z) >= plus(div(x,z),div(y,z)) ; div(x,y) >= ify(ge(y,s(0)),x,y) ; if(true,x,y) >= s(div(minus(x,y),y)) ; if(false,x,y) >= 0 ; Marked_div(x,y) >= Marked_ify(ge(y,s(0)),x,y) ; Marked_if(true,x,y) >= Marked_div(minus(x,y),y) ; Marked_ify(true,x,y) >= Marked_if(ge(x,y),x,y) ; } + Disjunctions:{ { Marked_div(x,y) > Marked_ify(ge(y,s(0)),x,y) ; } { Marked_if(true,x,y) > Marked_div(minus(x,y),y) ; } { Marked_ify(true,x,y) > Marked_if(ge(x,y),x,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: { ge(0,0) >= true ; ge(0,s(0)) >= false ; ge(0,s(s(x))) >= ge(0,s(x)) ; ge(s(x),0) >= ge(x,0) ; ge(s(x),s(y)) >= ge(x,y) ; minus(0,0) >= 0 ; minus(0,s(x)) >= minus(0,x) ; minus(s(x),0) >= s(minus(x,0)) ; minus(s(x),s(y)) >= minus(x,y) ; plus(0,0) >= 0 ; plus(0,s(x)) >= s(plus(0,x)) ; plus(s(x),y) >= s(plus(x,y)) ; ify(true,x,y) >= if(ge(x,y),x,y) ; ify(false,x,y) >= divByZeroError ; div(plus(x,y),z) >= plus(div(x,z),div(y,z)) ; div(x,y) >= ify(ge(y,s(0)),x,y) ; if(true,x,y) >= s(div(minus(x,y),y)) ; if(false,x,y) >= 0 ; Marked_div(x,y) >= Marked_ify(ge(y,s(0)),x,y) ; Marked_if(true,x,y) >= Marked_div(minus(x,y),y) ; Marked_ify(true,x,y) > Marked_if(ge(x,y),x,y) ; } APPLY CRITERIA (SOLVE_ORD) Trying to solve the following constraints: { ge(0,0) >= true ; ge(0,s(0)) >= false ; ge(0,s(s(x))) >= ge(0,s(x)) ; ge(s(x),0) >= ge(x,0) ; ge(s(x),s(y)) >= ge(x,y) ; minus(0,0) >= 0 ; minus(0,s(x)) >= minus(0,x) ; minus(s(x),0) >= s(minus(x,0)) ; minus(s(x),s(y)) >= minus(x,y) ; plus(0,0) >= 0 ; plus(0,s(x)) >= s(plus(0,x)) ; plus(s(x),y) >= s(plus(x,y)) ; ify(true,x,y) >= if(ge(x,y),x,y) ; ify(false,x,y) >= divByZeroError ; div(plus(x,y),z) >= plus(div(x,z),div(y,z)) ; div(x,y) >= ify(ge(y,s(0)),x,y) ; if(true,x,y) >= s(div(minus(x,y),y)) ; if(false,x,y) >= 0 ; Marked_div(x,y) >= Marked_ify(ge(y,s(0)),x,y) ; Marked_if(true,x,y) >= Marked_div(minus(x,y),y) ; Marked_ify(true,x,y) > Marked_if(ge(x,y),x,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.(84466 bt (80990) [5153]) === 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) APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: NOT SOLVED No proof found Cime worked for 20.135814 seconds (real time) Cime Exit Status: 0