- : 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] le(0,y) -> true [5] le(s(x),0) -> false [6] le(s(x),s(y)) -> le(x,y) [7] inc(0) -> 0 [8] inc(s(x)) -> s(inc(x)) [9] log(x) -> log2(x,0) [10] log2(x,y) -> if(le(x,s(0)),x,inc(y)) [11] if(true,x,s(y)) -> y [12] if(false,x,y) -> log2(half(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: { half(0) >= 0 ; half(s(0)) >= 0 ; half(s(s(x))) >= s(half(x)) ; le(0,y) >= true ; le(s(x),0) >= false ; le(s(x),s(y)) >= le(x,y) ; inc(0) >= 0 ; inc(s(x)) >= s(inc(x)) ; log2(x,y) >= if(le(x,s(0)),x,inc(y)) ; log(x) >= log2(x,0) ; if(true,x,s(y)) >= y ; if(false,x,y) >= log2(half(x),y) ; Marked_if(false,x,y) >= Marked_log2(half(x),y) ; Marked_log2(x,y) >= Marked_if(le(x,s(0)),x,inc(y)) ; } + Disjunctions:{ { Marked_if(false,x,y) > Marked_log2(half(x),y) ; } { Marked_log2(x,y) > Marked_if(le(x,s(0)),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)) ; le(0,y) >= true ; le(s(x),0) >= false ; le(s(x),s(y)) >= le(x,y) ; inc(0) >= 0 ; inc(s(x)) >= s(inc(x)) ; log2(x,y) >= if(le(x,s(0)),x,inc(y)) ; log(x) >= log2(x,0) ; if(true,x,s(y)) >= y ; if(false,x,y) >= log2(half(x),y) ; Marked_if(false,x,y) >= Marked_log2(half(x),y) ; Marked_log2(x,y) > Marked_if(le(x,s(0)),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)) ; le(0,y) >= true ; le(s(x),0) >= false ; le(s(x),s(y)) >= le(x,y) ; inc(0) >= 0 ; inc(s(x)) >= s(inc(x)) ; log2(x,y) >= if(le(x,s(0)),x,inc(y)) ; log(x) >= log2(x,0) ; if(true,x,s(y)) >= y ; if(false,x,y) >= log2(half(x),y) ; Marked_if(false,x,y) >= Marked_log2(half(x),y) ; Marked_log2(x,y) > Marked_if(le(x,s(0)),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.(21739 bt (21477) [970]) === 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 5.878908 seconds (real time) Cime Exit Status: 0