- : unit = () - : unit = () h : heuristic = - : unit = () APPLY CRITERIA (Marked dependency pairs) TRS termination of: [1] 0(#) -> # [2] +(#,x) -> x [3] +(x,#) -> x [4] +(0(x),0(y)) -> 0(+(x,y)) [5] +(0(x),1(y)) -> 1(+(x,y)) [6] +(1(x),0(y)) -> 1(+(x,y)) [7] +(0(x),j(y)) -> j(+(x,y)) [8] +(j(x),0(y)) -> j(+(x,y)) [9] +(1(x),1(y)) -> j(+(+(x,y),1(#))) [10] +(j(x),j(y)) -> 1(+(+(x,y),j(#))) [11] +(1(x),j(y)) -> 0(+(x,y)) [12] +(j(x),1(y)) -> 0(+(x,y)) [13] +(+(x,y),z) -> +(x,+(y,z)) [14] opp(#) -> # [15] opp(0(x)) -> 0(opp(x)) [16] opp(1(x)) -> j(opp(x)) [17] opp(j(x)) -> 1(opp(x)) [18] -(x,y) -> +(x,opp(y)) [19] *(#,x) -> # [20] *(0(x),y) -> 0( *(x,y)) [21] *(1(x),y) -> +(0( *(x,y)),y) [22] *(j(x),y) -> -(0( *(x,y)),y) [23] *( *(x,y),z) -> *(x, *(y,z)) [24] *(+(x,y),z) -> +( *(x,z), *(y,z)) [25] *(x,+(y,z)) -> +( *(x,y), *(x,z)) Sub problem: guided: DP termination of: END GUIDED APPLY CRITERIA (Graph splitting) Found 3 components: { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> } { --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_* -> 1 APPLY CRITERIA (Subterm criterion) ST: Marked_opp -> 1 APPLY CRITERIA (Subterm criterion) APPLY CRITERIA (Choosing graph) Trying to solve the following constraints: { 0(#) >= # ; +(#,x) >= x ; +(0(x),0(y)) >= 0(+(x,y)) ; +(0(x),1(y)) >= 1(+(x,y)) ; +(0(x),j(y)) >= j(+(x,y)) ; +(+(x,y),z) >= +(x,+(y,z)) ; +(1(x),0(y)) >= 1(+(x,y)) ; +(1(x),1(y)) >= j(+(+(x,y),1(#))) ; +(1(x),j(y)) >= 0(+(x,y)) ; +(j(x),0(y)) >= j(+(x,y)) ; +(j(x),1(y)) >= 0(+(x,y)) ; +(j(x),j(y)) >= 1(+(+(x,y),j(#))) ; +(x,#) >= x ; opp(#) >= # ; opp(0(x)) >= 0(opp(x)) ; opp(1(x)) >= j(opp(x)) ; opp(j(x)) >= 1(opp(x)) ; -(x,y) >= +(x,opp(y)) ; *(#,x) >= # ; *(0(x),y) >= 0( *(x,y)) ; *(+(x,y),z) >= +( *(x,z), *(y,z)) ; *(1(x),y) >= +(0( *(x,y)),y) ; *(j(x),y) >= -(0( *(x,y)),y) ; *( *(x,y),z) >= *(x, *(y,z)) ; *(x,+(y,z)) >= +( *(x,y), *(x,z)) ; Marked_+(0(x),0(y)) >= Marked_+(x,y) ; Marked_+(0(x),1(y)) >= Marked_+(x,y) ; Marked_+(0(x),j(y)) >= Marked_+(x,y) ; Marked_+(+(x,y),z) >= Marked_+(y,z) ; Marked_+(+(x,y),z) >= Marked_+(x,+(y,z)) ; Marked_+(1(x),0(y)) >= Marked_+(x,y) ; Marked_+(1(x),1(y)) >= Marked_+(+(x,y),1(#)) ; Marked_+(1(x),1(y)) >= Marked_+(x,y) ; Marked_+(1(x),j(y)) >= Marked_+(x,y) ; Marked_+(j(x),0(y)) >= Marked_+(x,y) ; Marked_+(j(x),1(y)) >= Marked_+(x,y) ; Marked_+(j(x),j(y)) >= Marked_+(+(x,y),j(#)) ; Marked_+(j(x),j(y)) >= Marked_+(x,y) ; } + Disjunctions:{ { Marked_+(0(x),0(y)) > Marked_+(x,y) ; } { Marked_+(0(x),1(y)) > Marked_+(x,y) ; } { Marked_+(0(x),j(y)) > Marked_+(x,y) ; } { Marked_+(+(x,y),z) > Marked_+(y,z) ; } { Marked_+(+(x,y),z) > Marked_+(x,+(y,z)) ; } { Marked_+(1(x),0(y)) > Marked_+(x,y) ; } { Marked_+(1(x),1(y)) > Marked_+(+(x,y),1(#)) ; } { Marked_+(1(x),1(y)) > Marked_+(x,y) ; } { Marked_+(1(x),j(y)) > Marked_+(x,y) ; } { Marked_+(j(x),0(y)) > Marked_+(x,y) ; } { Marked_+(j(x),1(y)) > Marked_+(x,y) ; } { Marked_+(j(x),j(y)) > Marked_+(+(x,y),j(#)) ; } { Marked_+(j(x),j(y)) > Marked_+(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 : 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 : 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 : 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 : 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 Sat solver result read === STOPING TIMER real === === STOPING TIMER virtual === constraint: 0(#) >= # constraint: +(#,x) >= x constraint: +(0(x),0(y)) >= 0(+(x,y)) constraint: +(0(x),1(y)) >= 1(+(x,y)) constraint: +(0(x),j(y)) >= j(+(x,y)) constraint: +(+(x,y),z) >= +(x,+(y,z)) constraint: +(1(x),0(y)) >= 1(+(x,y)) constraint: +(1(x),1(y)) >= j(+(+(x,y),1(#))) constraint: +(1(x),j(y)) >= 0(+(x,y)) constraint: +(j(x),0(y)) >= j(+(x,y)) constraint: +(j(x),1(y)) >= 0(+(x,y)) constraint: +(j(x),j(y)) >= 1(+(+(x,y),j(#))) constraint: +(x,#) >= x constraint: opp(#) >= # constraint: opp(0(x)) >= 0(opp(x)) constraint: opp(1(x)) >= j(opp(x)) constraint: opp(j(x)) >= 1(opp(x)) constraint: -(x,y) >= +(x,opp(y)) constraint: *(#,x) >= # constraint: *(0(x),y) >= 0( *(x,y)) constraint: *(+(x,y),z) >= +( *(x,z), *(y,z)) constraint: *(1(x),y) >= +(0( *(x,y)),y) constraint: *(j(x),y) >= -(0( *(x,y)),y) constraint: *( *(x,y),z) >= *(x, *(y,z)) constraint: *(x,+(y,z)) >= +( *(x,y), *(x,z)) constraint: Marked_+(0(x),0(y)) >= Marked_+(x,y) constraint: Marked_+(0(x),1(y)) >= Marked_+(x,y) constraint: Marked_+(0(x),j(y)) >= Marked_+(x,y) constraint: Marked_+(+(x,y),z) >= Marked_+(y,z) constraint: Marked_+(+(x,y),z) >= Marked_+(x,+(y,z)) constraint: Marked_+(1(x),0(y)) >= Marked_+(x,y) constraint: Marked_+(1(x),1(y)) >= Marked_+(+(x,y),1(#)) constraint: Marked_+(1(x),1(y)) >= Marked_+(x,y) constraint: Marked_+(1(x),j(y)) >= Marked_+(x,y) constraint: Marked_+(j(x),0(y)) >= Marked_+(x,y) constraint: Marked_+(j(x),1(y)) >= Marked_+(x,y) constraint: Marked_+(j(x),j(y)) >= Marked_+(+(x,y),j(#)) constraint: Marked_+(j(x),j(y)) >= Marked_+(x,y) APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_* -> 2 APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 0 components: APPLY CRITERIA (Graph splitting) Found 1 components: { --> --> --> --> --> --> --> --> --> } APPLY CRITERIA (Subterm criterion) ST: Marked_+ -> 1 APPLY CRITERIA (Graph splitting) Found 0 components: SOLVED { TRS termination of: [1] 0(#) -> # [2] +(#,x) -> x [3] +(x,#) -> x [4] +(0(x),0(y)) -> 0(+(x,y)) [5] +(0(x),1(y)) -> 1(+(x,y)) [6] +(1(x),0(y)) -> 1(+(x,y)) [7] +(0(x),j(y)) -> j(+(x,y)) [8] +(j(x),0(y)) -> j(+(x,y)) [9] +(1(x),1(y)) -> j(+(+(x,y),1(#))) [10] +(j(x),j(y)) -> 1(+(+(x,y),j(#))) [11] +(1(x),j(y)) -> 0(+(x,y)) [12] +(j(x),1(y)) -> 0(+(x,y)) [13] +(+(x,y),z) -> +(x,+(y,z)) [14] opp(#) -> # [15] opp(0(x)) -> 0(opp(x)) [16] opp(1(x)) -> j(opp(x)) [17] opp(j(x)) -> 1(opp(x)) [18] -(x,y) -> +(x,opp(y)) [19] *(#,x) -> # [20] *(0(x),y) -> 0( *(x,y)) [21] *(1(x),y) -> +(0( *(x,y)),y) [22] *(j(x),y) -> -(0( *(x,y)),y) [23] *( *(x,y),z) -> *(x, *(y,z)) [24] *(+(x,y),z) -> +( *(x,z), *(y,z)) [25] *(x,+(y,z)) -> +( *(x,y), *(x,z)) , CRITERION: MDP [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} { DP termination of: , CRITERION: CG using polynomial interpretation = [ # ] () = 0; [ j ] (X0) = 1*X0 + 1; [ + ] (X0,X1) = 1*X1 + 1*X0; [ - ] (X0,X1) = 2*X1 + 1*X0; [ 0 ] (X0) = 1*X0; [ Marked_+ ] (X0,X1) = 2*X1 + 2*X0; [ opp ] (X0) = 2*X0; [ 1 ] (X0) = 1*X0 + 1; [ * ] (X0,X1) = 2*X1*X0; removing < Marked_+(0(x),j(y)),Marked_+(x,y)>< Marked_+(1(x),1(y)),Marked_+(+(x,y),1(#))>< Marked_+(j(x),j(y)),Marked_+(+(x,y),j(#))>< Marked_+(1(x),j(y)),Marked_+(x,y)> [ { DP termination of: , CRITERION: SG [ { DP termination of: , CRITERION: ST [ { DP termination of: , CRITERION: SG [ ]} ]} ]} ]} ]} ]} Cime worked for 1.100086 seconds (real time) Cime Exit Status: 0