- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] half(0) -> 0 [2] half(s(0)) -> 0 [3] half(s(s(x))) -> s(half(x)) [4] inc(0) -> 0 [5] inc(s(x)) -> s(inc(x)) [6] zero(0) -> true [7] zero(s(x)) -> false [8] p(0) -> 0 [9] p(s(x)) -> x [10] bits(x) -> bitIter(x,0) [11] bitIter(x,y) -> if(zero(x),x,inc(y)) [12] if(true,x,y) -> p(y) [13] if(false,x,y) -> bitIter(half(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: { half(0) >= 0 ; half(s(0)) >= 0 ; half(s(s(x))) >= s(half(x)) ; inc(0) >= 0 ; inc(s(x)) >= s(inc(x)) ; zero(0) >= true ; zero(s(x)) >= false ; p(0) >= 0 ; p(s(x)) >= x ; bitIter(x,y) >= if(zero(x),x,inc(y)) ; bits(x) >= bitIter(x,0) ; if(true,x,y) >= p(y) ; if(false,x,y) >= bitIter(half(x),y) ; Marked_if(false,x,y) >= Marked_bitIter(half(x),y) ; Marked_bitIter(x,y) >= Marked_if(zero(x),x,inc(y)) ; } + Disjunctions:{ { Marked_if(false,x,y) > Marked_bitIter(half(x),y) ; } { Marked_bitIter(x,y) > Marked_if(zero(x),x,inc(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 : 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: { half(0) >= 0 ; half(s(0)) >= 0 ; half(s(s(x))) >= s(half(x)) ; inc(0) >= 0 ; inc(s(x)) >= s(inc(x)) ; zero(0) >= true ; zero(s(x)) >= false ; p(0) >= 0 ; p(s(x)) >= x ; bitIter(x,y) >= if(zero(x),x,inc(y)) ; bits(x) >= bitIter(x,0) ; if(true,x,y) >= p(y) ; if(false,x,y) >= bitIter(half(x),y) ; Marked_if(false,x,y) >= Marked_bitIter(half(x),y) ; Marked_bitIter(x,y) > Marked_if(zero(x),x,inc(y)) ; } APPLY CRITERIA (SOLVE_ORD) Trying to solve the following constraints: { half(0) >= 0 ; half(s(0)) >= 0 ; half(s(s(x))) >= s(half(x)) ; inc(0) >= 0 ; inc(s(x)) >= s(inc(x)) ; zero(0) >= true ; zero(s(x)) >= false ; p(0) >= 0 ; p(s(x)) >= x ; bitIter(x,y) >= if(zero(x),x,inc(y)) ; bits(x) >= bitIter(x,0) ; if(true,x,y) >= p(y) ; if(false,x,y) >= bitIter(half(x),y) ; Marked_if(false,x,y) >= Marked_bitIter(half(x),y) ; Marked_bitIter(x,y) > Marked_if(zero(x),x,inc(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.(26460 bt (28315) [2043]) === 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 3.132758 seconds (real time) Cime Exit Status: 0