1.31/1.33 YES 1.31/1.33 1.31/1.33 Problem 1: 1.31/1.33 1.31/1.33 (VAR s x) 1.31/1.33 (STRATEGY CONTEXTSENSITIVE 1.31/1.33 (*top*_0 1) 1.31/1.33 (M_1) 1.31/1.33 (cons_1) 1.31/1.33 (cons_10) 1.31/1.33 (cons_11) 1.31/1.33 (cons_2) 1.31/1.33 (cons_3) 1.31/1.33 (cons_4) 1.31/1.33 (cons_5) 1.31/1.33 (cons_6) 1.31/1.33 (cons_7) 1.31/1.33 (cons_8) 1.31/1.33 (cons_9) 1.31/1.33 (h_0 1) 1.31/1.33 (tail_0 1) 1.31/1.33 (tail_1) 1.31/1.33 (0_0) 1.31/1.33 (1_0) 1.31/1.33 (garbage_collection_0) 1.31/1.33 (h_1) 1.31/1.33 ) 1.31/1.33 (RULES 1.31/1.33 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 ) 1.31/1.33 1.31/1.33 Problem 1: 1.31/1.33 1.31/1.33 Dependency Pairs Processor: 1.31/1.33 -> Pairs: 1.31/1.33 *TOP*_0(tail_1(cons_1(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_1(x,s))) -> s 1.31/1.33 *TOP*_0(tail_1(cons_10(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_10(x,s))) -> s 1.31/1.33 *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_11(x,s))) -> s 1.31/1.33 *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_5(x,s))) -> s 1.31/1.33 *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_6(x,s))) -> s 1.31/1.33 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_1(0_0,s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) 1.31/1.33 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_1(1_0,s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) 1.31/1.33 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_10(1_0,s))) -> CONS_10(1_0,cons_2(0_0,h_1(s))) 1.31/1.33 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_11(1_0,s))) -> CONS_10(1_0,cons_3(0_0,h_1(s))) 1.31/1.33 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_2(0_0,s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) 1.31/1.33 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_3(0_0,s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) 1.31/1.33 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_4(0_0,s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) 1.31/1.33 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_5(0_0,s))) -> CONS_6(0_0,cons_7(1_0,h_1(s))) 1.31/1.33 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_6(0_0,s))) -> CONS_6(0_0,cons_8(1_0,h_1(s))) 1.31/1.33 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_7(1_0,s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) 1.31/1.33 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_8(1_0,s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) 1.31/1.33 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_9(1_0,s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) 1.31/1.33 H_0(tail_1(cons_1(x,s))) -> H_0(s) 1.31/1.33 H_0(tail_1(cons_1(x,s))) -> s 1.31/1.33 TAIL_0(tail_1(cons_1(x,s))) -> TAIL_1(s) 1.31/1.33 TAIL_0(tail_1(cons_10(x,s))) -> TAIL_1(s) 1.31/1.33 TAIL_0(tail_1(cons_11(x,s))) -> TAIL_1(s) 1.31/1.33 TAIL_0(tail_1(cons_5(x,s))) -> TAIL_1(s) 1.31/1.33 TAIL_0(tail_1(cons_6(x,s))) -> TAIL_1(s) 1.31/1.33 TAIL_1(cons_1(x,s)) -> s 1.31/1.33 TAIL_1(cons_2(x,s)) -> s 1.31/1.33 TAIL_1(cons_3(x,s)) -> s 1.31/1.33 TAIL_1(cons_4(x,s)) -> s 1.31/1.33 TAIL_1(cons_7(x,s)) -> s 1.31/1.33 TAIL_1(cons_8(x,s)) -> s 1.31/1.33 TAIL_1(cons_9(x,s)) -> s 1.31/1.33 -> Rules: 1.31/1.33 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 -> Unhiding Rules: 1.31/1.33 cons_1(0_0,h_0(s)) -> CONS_1(0_0,h_0(s)) 1.31/1.33 cons_1(0_0,tail_0(M_1)) -> CONS_1(0_0,tail_0(M_1)) 1.31/1.33 cons_1(1_0,h_0(s)) -> CONS_1(1_0,h_0(s)) 1.31/1.33 cons_10(1_0,cons_1(0_0,h_0(s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) 1.31/1.33 cons_10(1_0,cons_2(0_0,h_1(s))) -> CONS_10(1_0,cons_2(0_0,h_1(s))) 1.31/1.33 cons_10(1_0,cons_3(0_0,h_1(s))) -> CONS_10(1_0,cons_3(0_0,h_1(s))) 1.31/1.33 cons_2(0_0,h_1(s)) -> CONS_2(0_0,h_1(s)) 1.31/1.33 cons_3(0_0,h_1(s)) -> CONS_3(0_0,h_1(s)) 1.31/1.33 cons_6(0_0,cons_1(1_0,h_0(s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) 1.31/1.33 cons_6(0_0,cons_7(1_0,h_1(s))) -> CONS_6(0_0,cons_7(1_0,h_1(s))) 1.31/1.33 cons_6(0_0,cons_8(1_0,h_1(s))) -> CONS_6(0_0,cons_8(1_0,h_1(s))) 1.31/1.33 cons_7(1_0,h_1(s)) -> CONS_7(1_0,h_1(s)) 1.31/1.33 cons_8(1_0,h_1(s)) -> CONS_8(1_0,h_1(s)) 1.31/1.33 1.31/1.33 Problem 1: 1.31/1.33 1.31/1.33 SCC Processor: 1.31/1.33 -> Pairs: 1.31/1.33 *TOP*_0(tail_1(cons_1(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_1(x,s))) -> s 1.31/1.33 *TOP*_0(tail_1(cons_10(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_10(x,s))) -> s 1.31/1.33 *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_11(x,s))) -> s 1.31/1.33 *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_5(x,s))) -> s 1.31/1.33 *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_6(x,s))) -> s 1.31/1.33 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_1(0_0,s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) 1.31/1.33 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_1(1_0,s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) 1.31/1.33 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_10(1_0,s))) -> CONS_10(1_0,cons_2(0_0,h_1(s))) 1.31/1.33 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_11(1_0,s))) -> CONS_10(1_0,cons_3(0_0,h_1(s))) 1.31/1.33 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_2(0_0,s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) 1.31/1.33 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_3(0_0,s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) 1.31/1.33 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_4(0_0,s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) 1.31/1.33 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_5(0_0,s))) -> CONS_6(0_0,cons_7(1_0,h_1(s))) 1.31/1.33 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_6(0_0,s))) -> CONS_6(0_0,cons_8(1_0,h_1(s))) 1.31/1.33 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_7(1_0,s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) 1.31/1.33 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_8(1_0,s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) 1.31/1.33 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_9(1_0,s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) 1.31/1.33 H_0(tail_1(cons_1(x,s))) -> H_0(s) 1.31/1.33 H_0(tail_1(cons_1(x,s))) -> s 1.31/1.33 TAIL_0(tail_1(cons_1(x,s))) -> TAIL_1(s) 1.31/1.33 TAIL_0(tail_1(cons_10(x,s))) -> TAIL_1(s) 1.31/1.33 TAIL_0(tail_1(cons_11(x,s))) -> TAIL_1(s) 1.31/1.33 TAIL_0(tail_1(cons_5(x,s))) -> TAIL_1(s) 1.31/1.33 TAIL_0(tail_1(cons_6(x,s))) -> TAIL_1(s) 1.31/1.33 TAIL_1(cons_1(x,s)) -> s 1.31/1.33 TAIL_1(cons_2(x,s)) -> s 1.31/1.33 TAIL_1(cons_3(x,s)) -> s 1.31/1.33 TAIL_1(cons_4(x,s)) -> s 1.31/1.33 TAIL_1(cons_7(x,s)) -> s 1.31/1.33 TAIL_1(cons_8(x,s)) -> s 1.31/1.33 TAIL_1(cons_9(x,s)) -> s 1.31/1.33 -> Rules: 1.31/1.33 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 -> Unhiding rules: 1.31/1.33 cons_1(0_0,h_0(s)) -> CONS_1(0_0,h_0(s)) 1.31/1.33 cons_1(0_0,tail_0(M_1)) -> CONS_1(0_0,tail_0(M_1)) 1.31/1.33 cons_1(1_0,h_0(s)) -> CONS_1(1_0,h_0(s)) 1.31/1.33 cons_10(1_0,cons_1(0_0,h_0(s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) 1.31/1.33 cons_10(1_0,cons_2(0_0,h_1(s))) -> CONS_10(1_0,cons_2(0_0,h_1(s))) 1.31/1.33 cons_10(1_0,cons_3(0_0,h_1(s))) -> CONS_10(1_0,cons_3(0_0,h_1(s))) 1.31/1.33 cons_2(0_0,h_1(s)) -> CONS_2(0_0,h_1(s)) 1.31/1.33 cons_3(0_0,h_1(s)) -> CONS_3(0_0,h_1(s)) 1.31/1.33 cons_6(0_0,cons_1(1_0,h_0(s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) 1.31/1.33 cons_6(0_0,cons_7(1_0,h_1(s))) -> CONS_6(0_0,cons_7(1_0,h_1(s))) 1.31/1.33 cons_6(0_0,cons_8(1_0,h_1(s))) -> CONS_6(0_0,cons_8(1_0,h_1(s))) 1.31/1.33 cons_7(1_0,h_1(s)) -> CONS_7(1_0,h_1(s)) 1.31/1.33 cons_8(1_0,h_1(s)) -> CONS_8(1_0,h_1(s)) 1.31/1.33 ->Strongly Connected Components: 1.31/1.33 ->->Cycle: 1.31/1.33 ->->-> Pairs: 1.31/1.33 H_0(tail_1(cons_1(x,s))) -> H_0(s) 1.31/1.33 ->->-> Rules: 1.31/1.33 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 ->->-> Unhiding rules: 1.31/1.33 Empty 1.31/1.33 ->->Cycle: 1.31/1.33 ->->-> Pairs: 1.31/1.33 *TOP*_0(tail_1(cons_1(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_10(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 ->->-> Rules: 1.31/1.33 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 ->->-> Unhiding rules: 1.31/1.33 Empty 1.31/1.33 1.31/1.33 1.31/1.33 The problem is decomposed in 2 subproblems. 1.31/1.33 1.31/1.33 Problem 1.1: 1.31/1.33 1.31/1.33 Reduction Pairs Processor: 1.31/1.33 -> Pairs: 1.31/1.33 H_0(tail_1(cons_1(x,s))) -> H_0(s) 1.31/1.33 -> Rules: 1.31/1.33 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 -> Unhiding rules: 1.31/1.33 Empty 1.31/1.33 -> Usable rules: 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 ->Interpretation type: 1.31/1.33 Linear 1.31/1.33 ->Coefficients: 1.31/1.33 Natural Numbers 1.31/1.33 ->Dimension: 1.31/1.33 1 1.31/1.33 ->Bound: 1.31/1.33 2 1.31/1.33 ->Interpretation: 1.31/1.33 1.31/1.33 [M_1] = 2 1.31/1.33 [cons_1](X1,X2) = 2.X2 1.31/1.33 [cons_10](X1,X2) = 2.X1 + X2 + 1 1.31/1.33 [cons_11](X1,X2) = 2.X1 + 2.X2 + 2 1.31/1.33 [cons_2](X1,X2) = 2.X1 + 2.X2 1.31/1.33 [cons_3](X1,X2) = X1 + X2 + 2 1.31/1.33 [cons_4](X1,X2) = X1 + 2.X2 + 1 1.31/1.33 [cons_5](X1,X2) = 2.X2 + 2 1.31/1.33 [cons_6](X1,X2) = 2.X1 + X2 1.31/1.33 [cons_7](X1,X2) = 2.X1 + X2 + 2 1.31/1.33 [cons_8](X1,X2) = 2.X2 + 1 1.31/1.33 [cons_9](X1,X2) = X2 + 2 1.31/1.33 [h_0](X) = 2 1.31/1.33 [tail_0](X) = 2.X + 2 1.31/1.33 [tail_1](X) = X + 1 1.31/1.33 [0_0] = 0 1.31/1.33 [1_0] = 0 1.31/1.33 [garbage_collection_0] = 0 1.31/1.33 [h_1](X) = 2 1.31/1.33 [H_0](X) = 2.X 1.31/1.33 1.31/1.33 Problem 1.1: 1.31/1.33 1.31/1.33 Basic Processor: 1.31/1.33 -> Pairs: 1.31/1.33 Empty 1.31/1.33 -> Rules: 1.31/1.33 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 -> Unhiding rules: 1.31/1.33 Empty 1.31/1.33 -> Result: 1.31/1.33 Set P is empty 1.31/1.33 1.31/1.33 The problem is finite. 1.31/1.33 1.31/1.33 Problem 1.2: 1.31/1.33 1.31/1.33 Reduction Pairs Processor: 1.31/1.33 -> Pairs: 1.31/1.33 *TOP*_0(tail_1(cons_1(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_10(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 -> Rules: 1.31/1.33 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 -> Unhiding rules: 1.31/1.33 Empty 1.31/1.33 -> Usable rules: 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 ->Interpretation type: 1.31/1.33 Linear 1.31/1.33 ->Coefficients: 1.31/1.33 Natural Numbers 1.31/1.33 ->Dimension: 1.31/1.33 1 1.31/1.33 ->Bound: 1.31/1.33 2 1.31/1.33 ->Interpretation: 1.31/1.33 1.31/1.33 [M_1] = 2 1.31/1.33 [cons_1](X1,X2) = X2 1.31/1.33 [cons_10](X1,X2) = X2 1.31/1.33 [cons_11](X1,X2) = X1 + 2.X2 1.31/1.33 [cons_2](X1,X2) = 2.X1 + X2 1.31/1.33 [cons_3](X1,X2) = X1 + X2 1.31/1.33 [cons_4](X1,X2) = 2.X1 + 2.X2 + 2 1.31/1.33 [cons_5](X1,X2) = X1 + 2.X2 1.31/1.33 [cons_6](X1,X2) = 2.X1 + X2 1.31/1.33 [cons_7](X1,X2) = 2.X1 + X2 1.31/1.33 [cons_8](X1,X2) = 2.X1 + X2 1.31/1.33 [cons_9](X1,X2) = X1 + X2 1.31/1.33 [h_0](X) = 1 1.31/1.33 [tail_0](X) = 2.X 1.31/1.33 [tail_1](X) = X + 1 1.31/1.33 [0_0] = 0 1.31/1.33 [1_0] = 0 1.31/1.33 [garbage_collection_0] = 0 1.31/1.33 [h_1](X) = 1 1.31/1.33 [*TOP*_0](X) = 2.X 1.31/1.33 1.31/1.33 Problem 1.2: 1.31/1.33 1.31/1.33 SCC Processor: 1.31/1.33 -> Pairs: 1.31/1.33 *TOP*_0(tail_1(cons_10(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 -> Rules: 1.31/1.33 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 -> Unhiding rules: 1.31/1.33 Empty 1.31/1.33 ->Strongly Connected Components: 1.31/1.33 ->->Cycle: 1.31/1.33 ->->-> Pairs: 1.31/1.33 *TOP*_0(tail_1(cons_10(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 ->->-> Rules: 1.31/1.33 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 ->->-> Unhiding rules: 1.31/1.33 Empty 1.31/1.33 1.31/1.33 Problem 1.2: 1.31/1.33 1.31/1.33 Reduction Pairs Processor: 1.31/1.33 -> Pairs: 1.31/1.33 *TOP*_0(tail_1(cons_10(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 -> Rules: 1.31/1.33 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 -> Unhiding rules: 1.31/1.33 Empty 1.31/1.33 -> Usable rules: 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 ->Interpretation type: 1.31/1.33 Linear 1.31/1.33 ->Coefficients: 1.31/1.33 Natural Numbers 1.31/1.33 ->Dimension: 1.31/1.33 1 1.31/1.33 ->Bound: 1.31/1.33 2 1.31/1.33 ->Interpretation: 1.31/1.33 1.31/1.33 [M_1] = 2 1.31/1.33 [cons_1](X1,X2) = X2 1.31/1.33 [cons_10](X1,X2) = X2 1.31/1.33 [cons_11](X1,X2) = 2.X1 + 2.X2 + 2 1.31/1.33 [cons_2](X1,X2) = 2.X1 + X2 1.31/1.33 [cons_3](X1,X2) = 2.X1 + X2 1.31/1.33 [cons_4](X1,X2) = X1 + 2.X2 + 2 1.31/1.33 [cons_5](X1,X2) = X1 + 2.X2 + 2 1.31/1.33 [cons_6](X1,X2) = X1 + X2 1.31/1.33 [cons_7](X1,X2) = 2.X1 + X2 1.31/1.33 [cons_8](X1,X2) = X2 1.31/1.33 [cons_9](X1,X2) = X1 + 2.X2 + 1 1.31/1.33 [h_0](X) = 2 1.31/1.33 [tail_0](X) = 2.X + 2 1.31/1.33 [tail_1](X) = X + 1 1.31/1.33 [0_0] = 0 1.31/1.33 [1_0] = 0 1.31/1.33 [garbage_collection_0] = 0 1.31/1.33 [h_1](X) = 2 1.31/1.33 [*TOP*_0](X) = 2.X 1.31/1.33 1.31/1.33 Problem 1.2: 1.31/1.33 1.31/1.33 SCC Processor: 1.31/1.33 -> Pairs: 1.31/1.33 *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 -> Rules: 1.31/1.33 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 -> Unhiding rules: 1.31/1.33 Empty 1.31/1.33 ->Strongly Connected Components: 1.31/1.33 ->->Cycle: 1.31/1.33 ->->-> Pairs: 1.31/1.33 *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 ->->-> Rules: 1.31/1.33 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 ->->-> Unhiding rules: 1.31/1.33 Empty 1.31/1.33 1.31/1.33 Problem 1.2: 1.31/1.33 1.31/1.33 Reduction Pairs Processor: 1.31/1.33 -> Pairs: 1.31/1.33 *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 -> Rules: 1.31/1.33 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 -> Unhiding rules: 1.31/1.33 Empty 1.31/1.33 -> Usable rules: 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 ->Interpretation type: 1.31/1.33 Linear 1.31/1.33 ->Coefficients: 1.31/1.33 Natural Numbers 1.31/1.33 ->Dimension: 1.31/1.33 1 1.31/1.33 ->Bound: 1.31/1.33 2 1.31/1.33 ->Interpretation: 1.31/1.33 1.31/1.33 [M_1] = 0 1.31/1.33 [cons_1](X1,X2) = X2 1.31/1.33 [cons_10](X1,X2) = X2 1.31/1.33 [cons_11](X1,X2) = 2.X1 + 2.X2 + 2 1.31/1.33 [cons_2](X1,X2) = X2 1.31/1.33 [cons_3](X1,X2) = 2.X1 + X2 + 2 1.31/1.33 [cons_4](X1,X2) = 2.X2 + 2 1.31/1.33 [cons_5](X1,X2) = 2.X1 + 2.X2 + 2 1.31/1.33 [cons_6](X1,X2) = X2 1.31/1.33 [cons_7](X1,X2) = X1 + 2.X2 + 1 1.31/1.33 [cons_8](X1,X2) = X1 + X2 1.31/1.33 [cons_9](X1,X2) = 2.X2 + 1 1.31/1.33 [h_0](X) = 2.X 1.31/1.33 [tail_0](X) = 2.X 1.31/1.33 [tail_1](X) = 2.X 1.31/1.33 [0_0] = 0 1.31/1.33 [1_0] = 0 1.31/1.33 [garbage_collection_0] = 0 1.31/1.33 [h_1](X) = 2.X 1.31/1.33 [*TOP*_0](X) = 2.X 1.31/1.33 1.31/1.33 Problem 1.2: 1.31/1.33 1.31/1.33 SCC Processor: 1.31/1.33 -> Pairs: 1.31/1.33 *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 -> Rules: 1.31/1.33 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 -> Unhiding rules: 1.31/1.33 Empty 1.31/1.33 ->Strongly Connected Components: 1.31/1.33 ->->Cycle: 1.31/1.33 ->->-> Pairs: 1.31/1.33 *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 ->->-> Rules: 1.31/1.33 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_1(cons_1(x,s)) -> s 1.31/1.33 tail_1(cons_2(x,s)) -> s 1.31/1.33 tail_1(cons_3(x,s)) -> s 1.31/1.33 tail_1(cons_4(x,s)) -> s 1.31/1.33 tail_1(cons_7(x,s)) -> s 1.31/1.33 tail_1(cons_8(x,s)) -> s 1.31/1.33 tail_1(cons_9(x,s)) -> s 1.31/1.33 ->->-> Unhiding rules: 1.31/1.33 Empty 1.31/1.33 1.31/1.33 Problem 1.2: 1.31/1.33 1.31/1.33 Reduction Pairs Processor: 1.31/1.33 -> Pairs: 1.31/1.33 *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) 1.31/1.33 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 -> Rules: 1.31/1.33 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.33 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.33 cons_1(x,s) -> garbage_collection_0 1.31/1.33 cons_10(x,s) -> garbage_collection_0 1.31/1.33 cons_11(x,s) -> garbage_collection_0 1.31/1.33 cons_2(x,s) -> garbage_collection_0 1.31/1.33 cons_3(x,s) -> garbage_collection_0 1.31/1.33 cons_4(x,s) -> garbage_collection_0 1.31/1.33 cons_5(x,s) -> garbage_collection_0 1.31/1.33 cons_6(x,s) -> garbage_collection_0 1.31/1.33 cons_7(x,s) -> garbage_collection_0 1.31/1.33 cons_8(x,s) -> garbage_collection_0 1.31/1.33 cons_9(x,s) -> garbage_collection_0 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.33 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.33 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.33 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.33 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.33 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.33 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.33 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 -> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 -> Usable rules: 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 ->Interpretation type: 1.31/1.34 Linear 1.31/1.34 ->Coefficients: 1.31/1.34 Natural Numbers 1.31/1.34 ->Dimension: 1.31/1.34 1 1.31/1.34 ->Bound: 1.31/1.34 2 1.31/1.34 ->Interpretation: 1.31/1.34 1.31/1.34 [M_1] = 2 1.31/1.34 [cons_1](X1,X2) = X2 1.31/1.34 [cons_10](X1,X2) = X2 1.31/1.34 [cons_11](X1,X2) = 2.X1 + 2.X2 1.31/1.34 [cons_2](X1,X2) = X2 1.31/1.34 [cons_3](X1,X2) = X2 1.31/1.34 [cons_4](X1,X2) = 2.X1 + 2.X2 + 1 1.31/1.34 [cons_5](X1,X2) = X2 1.31/1.34 [cons_6](X1,X2) = X2 1.31/1.34 [cons_7](X1,X2) = X2 1.31/1.34 [cons_8](X1,X2) = X2 1.31/1.34 [cons_9](X1,X2) = X1 + 2.X2 + 1 1.31/1.34 [h_0](X) = 2 1.31/1.34 [tail_0](X) = 2.X + 2 1.31/1.34 [tail_1](X) = 2.X + 2 1.31/1.34 [0_0] = 0 1.31/1.34 [1_0] = 2 1.31/1.34 [garbage_collection_0] = 0 1.31/1.34 [h_1](X) = 2 1.31/1.34 [*TOP*_0](X) = 2.X 1.31/1.34 1.31/1.34 Problem 1.2: 1.31/1.34 1.31/1.34 SCC Processor: 1.31/1.34 -> Pairs: 1.31/1.34 *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) 1.31/1.34 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 -> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 -> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 ->Strongly Connected Components: 1.31/1.34 ->->Cycle: 1.31/1.34 ->->-> Pairs: 1.31/1.34 *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) 1.31/1.34 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 ->->-> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 ->->-> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 1.31/1.34 Problem 1.2: 1.31/1.34 1.31/1.34 Reduction Pairs Processor: 1.31/1.34 -> Pairs: 1.31/1.34 *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) 1.31/1.34 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 -> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 -> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 -> Usable rules: 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 ->Interpretation type: 1.31/1.34 Linear 1.31/1.34 ->Coefficients: 1.31/1.34 Natural Numbers 1.31/1.34 ->Dimension: 1.31/1.34 1 1.31/1.34 ->Bound: 1.31/1.34 2 1.31/1.34 ->Interpretation: 1.31/1.34 1.31/1.34 [M_1] = 2 1.31/1.34 [cons_1](X1,X2) = 2.X1 + X2 1.31/1.34 [cons_10](X1,X2) = X2 1.31/1.34 [cons_11](X1,X2) = X1 + 2.X2 1.31/1.34 [cons_2](X1,X2) = 2.X1 + X2 1.31/1.34 [cons_3](X1,X2) = 2.X1 + X2 1.31/1.34 [cons_4](X1,X2) = 2.X1 + X2 + 2 1.31/1.34 [cons_5](X1,X2) = 2.X1 + X2 + 2 1.31/1.34 [cons_6](X1,X2) = 2.X1 + X2 1.31/1.34 [cons_7](X1,X2) = 2.X1 + X2 1.31/1.34 [cons_8](X1,X2) = X2 1.31/1.34 [cons_9](X1,X2) = 2.X1 + X2 + 2 1.31/1.34 [h_0](X) = 2 1.31/1.34 [tail_0](X) = 2.X + 2 1.31/1.34 [tail_1](X) = 2.X + 2 1.31/1.34 [0_0] = 0 1.31/1.34 [1_0] = 0 1.31/1.34 [garbage_collection_0] = 0 1.31/1.34 [h_1](X) = 2 1.31/1.34 [*TOP*_0](X) = 2.X 1.31/1.34 1.31/1.34 Problem 1.2: 1.31/1.34 1.31/1.34 SCC Processor: 1.31/1.34 -> Pairs: 1.31/1.34 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 -> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 -> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 ->Strongly Connected Components: 1.31/1.34 ->->Cycle: 1.31/1.34 ->->-> Pairs: 1.31/1.34 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 ->->-> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 ->->-> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 1.31/1.34 Problem 1.2: 1.31/1.34 1.31/1.34 Reduction Pairs Processor: 1.31/1.34 -> Pairs: 1.31/1.34 *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 -> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 -> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 -> Usable rules: 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 ->Interpretation type: 1.31/1.34 Linear 1.31/1.34 ->Coefficients: 1.31/1.34 Natural Numbers 1.31/1.34 ->Dimension: 1.31/1.34 1 1.31/1.34 ->Bound: 1.31/1.34 2 1.31/1.34 ->Interpretation: 1.31/1.34 1.31/1.34 [cons_1](X1,X2) = 2.X2 + 1 1.31/1.34 [cons_10](X1,X2) = 2.X1 + 2.X2 + 2 1.31/1.34 [cons_11](X1,X2) = 2 1.31/1.34 [cons_2](X1,X2) = 2 1.31/1.34 [cons_3](X1,X2) = 2 1.31/1.34 [cons_4](X1,X2) = 1 1.31/1.34 [cons_5](X1,X2) = 2.X1 + 2 1.31/1.34 [cons_6](X1,X2) = 2.X2 + 1 1.31/1.34 [cons_7](X1,X2) = 2.X1 + 2 1.31/1.34 [cons_8](X1,X2) = 2.X1 + 1 1.31/1.34 [cons_9](X1,X2) = 2.X2 + 1 1.31/1.34 [h_0](X) = 0 1.31/1.34 [0_0] = 2 1.31/1.34 [1_0] = 0 1.31/1.34 [garbage_collection_0] = 1 1.31/1.34 [h_1](X) = 2.X + 2 1.31/1.34 [*TOP*_0](X) = X 1.31/1.34 1.31/1.34 Problem 1.2: 1.31/1.34 1.31/1.34 SCC Processor: 1.31/1.34 -> Pairs: 1.31/1.34 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 -> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 -> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 ->Strongly Connected Components: 1.31/1.34 ->->Cycle: 1.31/1.34 ->->-> Pairs: 1.31/1.34 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 ->->-> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 ->->-> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 1.31/1.34 Problem 1.2: 1.31/1.34 1.31/1.34 Reduction Pairs Processor: 1.31/1.34 -> Pairs: 1.31/1.34 *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 -> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 -> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 -> Usable rules: 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 ->Interpretation type: 1.31/1.34 Linear 1.31/1.34 ->Coefficients: 1.31/1.34 Natural Numbers 1.31/1.34 ->Dimension: 1.31/1.34 1 1.31/1.34 ->Bound: 1.31/1.34 2 1.31/1.34 ->Interpretation: 1.31/1.34 1.31/1.34 [cons_1](X1,X2) = 2.X1 + 2.X2 1.31/1.34 [cons_10](X1,X2) = X1 1.31/1.34 [cons_11](X1,X2) = 2.X1 + 2.X2 + 2 1.31/1.34 [cons_2](X1,X2) = 2.X1 + 2 1.31/1.34 [cons_3](X1,X2) = 2.X1 + 2.X2 + 2 1.31/1.34 [cons_4](X1,X2) = X1 + 2.X2 + 2 1.31/1.34 [cons_5](X1,X2) = 2.X1 + 2.X2 + 2 1.31/1.34 [cons_6](X1,X2) = X1 + 2.X2 + 2 1.31/1.34 [cons_7](X1,X2) = 2.X1 + X2 + 2 1.31/1.34 [cons_8](X1,X2) = 2.X1 + 2 1.31/1.34 [cons_9](X1,X2) = 2.X2 1.31/1.34 [h_0](X) = 0 1.31/1.34 [0_0] = 2 1.31/1.34 [1_0] = 0 1.31/1.34 [garbage_collection_0] = 0 1.31/1.34 [h_1](X) = 2.X + 1 1.31/1.34 [*TOP*_0](X) = 2.X 1.31/1.34 1.31/1.34 Problem 1.2: 1.31/1.34 1.31/1.34 SCC Processor: 1.31/1.34 -> Pairs: 1.31/1.34 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 -> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 -> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 ->Strongly Connected Components: 1.31/1.34 ->->Cycle: 1.31/1.34 ->->-> Pairs: 1.31/1.34 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 ->->-> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 ->->-> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 1.31/1.34 Problem 1.2: 1.31/1.34 1.31/1.34 Reduction Pairs Processor: 1.31/1.34 -> Pairs: 1.31/1.34 *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 -> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 -> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 -> Usable rules: 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 ->Interpretation type: 1.31/1.34 Linear 1.31/1.34 ->Coefficients: 1.31/1.34 Natural Numbers 1.31/1.34 ->Dimension: 1.31/1.34 1 1.31/1.34 ->Bound: 1.31/1.34 2 1.31/1.34 ->Interpretation: 1.31/1.34 1.31/1.34 [cons_1](X1,X2) = 2.X1 + 2 1.31/1.34 [cons_10](X1,X2) = X1 1.31/1.34 [cons_11](X1,X2) = 2.X1 + 2.X2 1.31/1.34 [cons_2](X1,X2) = 2.X2 + 2 1.31/1.34 [cons_3](X1,X2) = X1 + 2.X2 + 2 1.31/1.34 [cons_4](X1,X2) = 2.X1 + 2.X2 + 2 1.31/1.34 [cons_5](X1,X2) = 2.X2 + 2 1.31/1.34 [cons_6](X1,X2) = 2.X1 + 1 1.31/1.34 [cons_7](X1,X2) = 2 1.31/1.34 [cons_8](X1,X2) = 2.X1 + 2.X2 1.31/1.34 [cons_9](X1,X2) = 2.X2 + 2 1.31/1.34 [h_0](X) = 2.X + 2 1.31/1.34 [0_0] = 1 1.31/1.34 [1_0] = 2 1.31/1.34 [garbage_collection_0] = 0 1.31/1.34 [h_1](X) = 2.X 1.31/1.34 [*TOP*_0](X) = 2.X 1.31/1.34 1.31/1.34 Problem 1.2: 1.31/1.34 1.31/1.34 SCC Processor: 1.31/1.34 -> Pairs: 1.31/1.34 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 -> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 -> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 ->Strongly Connected Components: 1.31/1.34 ->->Cycle: 1.31/1.34 ->->-> Pairs: 1.31/1.34 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 ->->-> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 ->->-> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 1.31/1.34 Problem 1.2: 1.31/1.34 1.31/1.34 Reduction Pairs Processor: 1.31/1.34 -> Pairs: 1.31/1.34 *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 -> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 -> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 -> Usable rules: 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 ->Interpretation type: 1.31/1.34 Linear 1.31/1.34 ->Coefficients: 1.31/1.34 Natural Numbers 1.31/1.34 ->Dimension: 1.31/1.34 1 1.31/1.34 ->Bound: 1.31/1.34 2 1.31/1.34 ->Interpretation: 1.31/1.34 1.31/1.34 [cons_1](X1,X2) = X2 1.31/1.34 [cons_10](X1,X2) = 2 1.31/1.34 [cons_11](X1,X2) = 2.X2 + 2 1.31/1.34 [cons_2](X1,X2) = X1 + 2.X2 + 1 1.31/1.34 [cons_3](X1,X2) = 2.X1 + 2.X2 + 1 1.31/1.34 [cons_4](X1,X2) = 2.X2 + 2 1.31/1.34 [cons_5](X1,X2) = X1 + 2.X2 + 2 1.31/1.34 [cons_6](X1,X2) = 2.X1 + 2.X2 + 2 1.31/1.34 [cons_7](X1,X2) = 2.X1 + 2 1.31/1.34 [cons_8](X1,X2) = 2.X1 + X2 1.31/1.34 [cons_9](X1,X2) = X2 1.31/1.34 [h_0](X) = 0 1.31/1.34 [0_0] = 2 1.31/1.34 [1_0] = 0 1.31/1.34 [garbage_collection_0] = 2 1.31/1.34 [h_1](X) = 2.X + 2 1.31/1.34 [*TOP*_0](X) = X 1.31/1.34 1.31/1.34 Problem 1.2: 1.31/1.34 1.31/1.34 SCC Processor: 1.31/1.34 -> Pairs: 1.31/1.34 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 -> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 -> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 ->Strongly Connected Components: 1.31/1.34 ->->Cycle: 1.31/1.34 ->->-> Pairs: 1.31/1.34 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 ->->-> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 ->->-> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 1.31/1.34 Problem 1.2: 1.31/1.34 1.31/1.34 Reduction Pairs Processor: 1.31/1.34 -> Pairs: 1.31/1.34 *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 -> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 -> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 -> Usable rules: 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 ->Interpretation type: 1.31/1.34 Linear 1.31/1.34 ->Coefficients: 1.31/1.34 Natural Numbers 1.31/1.34 ->Dimension: 1.31/1.34 1 1.31/1.34 ->Bound: 1.31/1.34 2 1.31/1.34 ->Interpretation: 1.31/1.34 1.31/1.34 [cons_1](X1,X2) = 2.X1 + 2 1.31/1.34 [cons_10](X1,X2) = 2.X2 + 2 1.31/1.34 [cons_2](X1,X2) = 2.X2 + 2 1.31/1.34 [cons_3](X1,X2) = X1 + 2.X2 1.31/1.34 [cons_4](X1,X2) = 2 1.31/1.34 [cons_5](X1,X2) = X1 + 2.X2 + 2 1.31/1.34 [cons_6](X1,X2) = 2.X1 + 2 1.31/1.34 [cons_7](X1,X2) = 2.X1 + 2.X2 + 2 1.31/1.34 [cons_8](X1,X2) = 2 1.31/1.34 [cons_9](X1,X2) = X1 + X2 + 2 1.31/1.34 [h_0](X) = 2.X + 2 1.31/1.34 [0_0] = 0 1.31/1.34 [1_0] = 2 1.31/1.34 [garbage_collection_0] = 2 1.31/1.34 [h_1](X) = 2.X + 2 1.31/1.34 [*TOP*_0](X) = X 1.31/1.34 1.31/1.34 Problem 1.2: 1.31/1.34 1.31/1.34 SCC Processor: 1.31/1.34 -> Pairs: 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 -> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.34 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.34 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 tail_1(cons_1(x,s)) -> s 1.31/1.34 tail_1(cons_2(x,s)) -> s 1.31/1.34 tail_1(cons_3(x,s)) -> s 1.31/1.34 tail_1(cons_4(x,s)) -> s 1.31/1.34 tail_1(cons_7(x,s)) -> s 1.31/1.34 tail_1(cons_8(x,s)) -> s 1.31/1.34 tail_1(cons_9(x,s)) -> s 1.31/1.34 -> Unhiding rules: 1.31/1.34 Empty 1.31/1.34 ->Strongly Connected Components: 1.31/1.34 ->->Cycle: 1.31/1.34 ->->-> Pairs: 1.31/1.34 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 ->->-> Rules: 1.31/1.34 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.34 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.34 cons_1(x,s) -> garbage_collection_0 1.31/1.34 cons_10(x,s) -> garbage_collection_0 1.31/1.34 cons_11(x,s) -> garbage_collection_0 1.31/1.34 cons_2(x,s) -> garbage_collection_0 1.31/1.34 cons_3(x,s) -> garbage_collection_0 1.31/1.34 cons_4(x,s) -> garbage_collection_0 1.31/1.34 cons_5(x,s) -> garbage_collection_0 1.31/1.34 cons_6(x,s) -> garbage_collection_0 1.31/1.34 cons_7(x,s) -> garbage_collection_0 1.31/1.34 cons_8(x,s) -> garbage_collection_0 1.31/1.34 cons_9(x,s) -> garbage_collection_0 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.34 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.34 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.34 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.34 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.34 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 ->->-> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 1.31/1.35 Problem 1.2: 1.31/1.35 1.31/1.35 Reduction Pairs Processor: 1.31/1.35 -> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 -> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 -> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 -> Usable rules: 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 ->Interpretation type: 1.31/1.35 Linear 1.31/1.35 ->Coefficients: 1.31/1.35 Natural Numbers 1.31/1.35 ->Dimension: 1.31/1.35 1 1.31/1.35 ->Bound: 1.31/1.35 2 1.31/1.35 ->Interpretation: 1.31/1.35 1.31/1.35 [cons_1](X1,X2) = 2.X1 + 1 1.31/1.35 [cons_10](X1,X2) = X1 + 2.X2 + 2 1.31/1.35 [cons_3](X1,X2) = X1 + X2 + 2 1.31/1.35 [cons_4](X1,X2) = 2.X1 1.31/1.35 [cons_5](X1,X2) = 2 1.31/1.35 [cons_6](X1,X2) = 2.X1 + 2 1.31/1.35 [cons_7](X1,X2) = 2.X1 + X2 + 2 1.31/1.35 [cons_8](X1,X2) = 2.X1 + 2 1.31/1.35 [cons_9](X1,X2) = 2.X1 + X2 + 2 1.31/1.35 [h_0](X) = X + 2 1.31/1.35 [0_0] = 0 1.31/1.35 [1_0] = 2 1.31/1.35 [garbage_collection_0] = 2 1.31/1.35 [h_1](X) = 2.X + 2 1.31/1.35 [*TOP*_0](X) = 2.X 1.31/1.35 1.31/1.35 Problem 1.2: 1.31/1.35 1.31/1.35 SCC Processor: 1.31/1.35 -> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 -> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 -> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 ->Strongly Connected Components: 1.31/1.35 ->->Cycle: 1.31/1.35 ->->-> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 ->->-> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 ->->-> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 1.31/1.35 Problem 1.2: 1.31/1.35 1.31/1.35 Reduction Pairs Processor: 1.31/1.35 -> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 -> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 -> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 -> Usable rules: 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 ->Interpretation type: 1.31/1.35 Linear 1.31/1.35 ->Coefficients: 1.31/1.35 Natural Numbers 1.31/1.35 ->Dimension: 1.31/1.35 1 1.31/1.35 ->Bound: 1.31/1.35 2 1.31/1.35 ->Interpretation: 1.31/1.35 1.31/1.35 [cons_1](X1,X2) = 0 1.31/1.35 [cons_10](X1,X2) = 2 1.31/1.35 [cons_4](X1,X2) = 2.X1 + 2.X2 + 2 1.31/1.35 [cons_5](X1,X2) = 2.X1 + 2 1.31/1.35 [cons_6](X1,X2) = 2.X1 + X2 + 2 1.31/1.35 [cons_7](X1,X2) = X1 + 1 1.31/1.35 [cons_8](X1,X2) = 0 1.31/1.35 [cons_9](X1,X2) = 2.X1 + X2 1.31/1.35 [h_0](X) = 2.X + 1 1.31/1.35 [0_0] = 0 1.31/1.35 [1_0] = 1 1.31/1.35 [garbage_collection_0] = 1 1.31/1.35 [h_1](X) = 2.X + 2 1.31/1.35 [*TOP*_0](X) = 2.X 1.31/1.35 1.31/1.35 Problem 1.2: 1.31/1.35 1.31/1.35 SCC Processor: 1.31/1.35 -> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 -> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 -> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 ->Strongly Connected Components: 1.31/1.35 ->->Cycle: 1.31/1.35 ->->-> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 ->->-> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 ->->-> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 1.31/1.35 Problem 1.2: 1.31/1.35 1.31/1.35 Reduction Pairs Processor: 1.31/1.35 -> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 -> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 -> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 -> Usable rules: 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 ->Interpretation type: 1.31/1.35 Linear 1.31/1.35 ->Coefficients: 1.31/1.35 Natural Numbers 1.31/1.35 ->Dimension: 1.31/1.35 1 1.31/1.35 ->Bound: 1.31/1.35 2 1.31/1.35 ->Interpretation: 1.31/1.35 1.31/1.35 [cons_1](X1,X2) = 2.X2 1.31/1.35 [cons_10](X1,X2) = 2.X1 1.31/1.35 [cons_5](X1,X2) = X1 + 2.X2 + 2 1.31/1.35 [cons_6](X1,X2) = 2.X1 + 1 1.31/1.35 [cons_7](X1,X2) = 2.X1 + 1 1.31/1.35 [cons_8](X1,X2) = X1 + 2 1.31/1.35 [cons_9](X1,X2) = 2.X1 + 2.X2 1.31/1.35 [h_0](X) = X + 1 1.31/1.35 [0_0] = 2 1.31/1.35 [1_0] = 0 1.31/1.35 [garbage_collection_0] = 0 1.31/1.35 [h_1](X) = 2.X 1.31/1.35 [*TOP*_0](X) = 2.X 1.31/1.35 1.31/1.35 Problem 1.2: 1.31/1.35 1.31/1.35 SCC Processor: 1.31/1.35 -> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 -> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 -> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 ->Strongly Connected Components: 1.31/1.35 ->->Cycle: 1.31/1.35 ->->-> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 ->->-> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 ->->-> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 1.31/1.35 Problem 1.2: 1.31/1.35 1.31/1.35 Reduction Pairs Processor: 1.31/1.35 -> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 -> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 -> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 -> Usable rules: 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 ->Interpretation type: 1.31/1.35 Linear 1.31/1.35 ->Coefficients: 1.31/1.35 Natural Numbers 1.31/1.35 ->Dimension: 1.31/1.35 1 1.31/1.35 ->Bound: 1.31/1.35 2 1.31/1.35 ->Interpretation: 1.31/1.35 1.31/1.35 [cons_1](X1,X2) = 2.X1 + 2.X2 1.31/1.35 [cons_10](X1,X2) = X1 + 2.X2 1.31/1.35 [cons_6](X1,X2) = 1 1.31/1.35 [cons_7](X1,X2) = X1 + 2.X2 + 2 1.31/1.35 [cons_8](X1,X2) = 2.X1 + 2 1.31/1.35 [cons_9](X1,X2) = 2.X1 + 2.X2 + 2 1.31/1.35 [h_0](X) = 0 1.31/1.35 [0_0] = 0 1.31/1.35 [1_0] = 2 1.31/1.35 [garbage_collection_0] = 0 1.31/1.35 [h_1](X) = 2 1.31/1.35 [*TOP*_0](X) = 2.X 1.31/1.35 1.31/1.35 Problem 1.2: 1.31/1.35 1.31/1.35 SCC Processor: 1.31/1.35 -> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 -> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 -> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 ->Strongly Connected Components: 1.31/1.35 ->->Cycle: 1.31/1.35 ->->-> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 ->->-> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 ->->-> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 1.31/1.35 Problem 1.2: 1.31/1.35 1.31/1.35 Reduction Pairs Processor: 1.31/1.35 -> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 -> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 -> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 -> Usable rules: 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 ->Interpretation type: 1.31/1.35 Linear 1.31/1.35 ->Coefficients: 1.31/1.35 Natural Numbers 1.31/1.35 ->Dimension: 1.31/1.35 1 1.31/1.35 ->Bound: 1.31/1.35 2 1.31/1.35 ->Interpretation: 1.31/1.35 1.31/1.35 [cons_1](X1,X2) = 0 1.31/1.35 [cons_10](X1,X2) = 2.X2 + 1 1.31/1.35 [cons_7](X1,X2) = 2.X1 + 2.X2 + 1 1.31/1.35 [cons_8](X1,X2) = 2.X2 1.31/1.35 [cons_9](X1,X2) = X2 1.31/1.35 [h_0](X) = 2.X 1.31/1.35 [0_0] = 0 1.31/1.35 [1_0] = 0 1.31/1.35 [garbage_collection_0] = 1 1.31/1.35 [h_1](X) = 2 1.31/1.35 [*TOP*_0](X) = X 1.31/1.35 1.31/1.35 Problem 1.2: 1.31/1.35 1.31/1.35 SCC Processor: 1.31/1.35 -> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 -> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 -> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 ->Strongly Connected Components: 1.31/1.35 ->->Cycle: 1.31/1.35 ->->-> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 ->->-> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 ->->-> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 1.31/1.35 Problem 1.2: 1.31/1.35 1.31/1.35 Reduction Pairs Processor: 1.31/1.35 -> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 -> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 -> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 -> Usable rules: 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 ->Interpretation type: 1.31/1.35 Linear 1.31/1.35 ->Coefficients: 1.31/1.35 Natural Numbers 1.31/1.35 ->Dimension: 1.31/1.35 1 1.31/1.35 ->Bound: 1.31/1.35 2 1.31/1.35 ->Interpretation: 1.31/1.35 1.31/1.35 [cons_1](X1,X2) = X2 1.31/1.35 [cons_10](X1,X2) = 2.X1 + 2.X2 + 1 1.31/1.35 [cons_8](X1,X2) = 2.X2 + 2 1.31/1.35 [cons_9](X1,X2) = 2 1.31/1.35 [h_0](X) = 1 1.31/1.35 [0_0] = 2 1.31/1.35 [1_0] = 0 1.31/1.35 [garbage_collection_0] = 0 1.31/1.35 [h_1](X) = 2.X + 1 1.31/1.35 [*TOP*_0](X) = X 1.31/1.35 1.31/1.35 Problem 1.2: 1.31/1.35 1.31/1.35 SCC Processor: 1.31/1.35 -> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 -> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 -> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 ->Strongly Connected Components: 1.31/1.35 ->->Cycle: 1.31/1.35 ->->-> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 ->->-> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 ->->-> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 1.31/1.35 Problem 1.2: 1.31/1.35 1.31/1.35 Reduction Pairs Processor: 1.31/1.35 -> Pairs: 1.31/1.35 *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 -> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 -> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 -> Usable rules: 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 ->Interpretation type: 1.31/1.35 Linear 1.31/1.35 ->Coefficients: 1.31/1.35 Natural Numbers 1.31/1.35 ->Dimension: 1.31/1.35 1 1.31/1.35 ->Bound: 1.31/1.35 2 1.31/1.35 ->Interpretation: 1.31/1.35 1.31/1.35 [cons_1](X1,X2) = X2 + 1 1.31/1.35 [cons_10](X1,X2) = 2.X1 + 2.X2 + 1 1.31/1.35 [cons_9](X1,X2) = 2.X2 + 2 1.31/1.35 [h_0](X) = 2.X 1.31/1.35 [0_0] = 2 1.31/1.35 [1_0] = 1 1.31/1.35 [garbage_collection_0] = 1 1.31/1.35 [h_1](X) = 2.X + 2 1.31/1.35 [*TOP*_0](X) = 2.X 1.31/1.35 1.31/1.35 Problem 1.2: 1.31/1.35 1.31/1.35 Basic Processor: 1.31/1.35 -> Pairs: 1.31/1.35 Empty 1.31/1.35 -> Rules: 1.31/1.35 *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) 1.31/1.35 *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 M_1 -> h_1(cons_1(0_0,tail_0(M_1))) 1.31/1.35 cons_1(x,s) -> garbage_collection_0 1.31/1.35 cons_10(x,s) -> garbage_collection_0 1.31/1.35 cons_11(x,s) -> garbage_collection_0 1.31/1.35 cons_2(x,s) -> garbage_collection_0 1.31/1.35 cons_3(x,s) -> garbage_collection_0 1.31/1.35 cons_4(x,s) -> garbage_collection_0 1.31/1.35 cons_5(x,s) -> garbage_collection_0 1.31/1.35 cons_6(x,s) -> garbage_collection_0 1.31/1.35 cons_7(x,s) -> garbage_collection_0 1.31/1.35 cons_8(x,s) -> garbage_collection_0 1.31/1.35 cons_9(x,s) -> garbage_collection_0 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_0(s) 1.31/1.35 h_0(tail_1(cons_1(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_10(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_11(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_5(x,s))) -> h_1(s) 1.31/1.35 h_0(tail_1(cons_6(x,s))) -> h_1(s) 1.31/1.35 h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(tail_1(cons_1(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_10(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_11(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_5(x,s))) -> tail_1(s) 1.31/1.35 tail_0(tail_1(cons_6(x,s))) -> tail_1(s) 1.31/1.35 tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) 1.31/1.35 tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) 1.31/1.35 tail_1(cons_1(x,s)) -> s 1.31/1.35 tail_1(cons_2(x,s)) -> s 1.31/1.35 tail_1(cons_3(x,s)) -> s 1.31/1.35 tail_1(cons_4(x,s)) -> s 1.31/1.35 tail_1(cons_7(x,s)) -> s 1.31/1.35 tail_1(cons_8(x,s)) -> s 1.31/1.35 tail_1(cons_9(x,s)) -> s 1.31/1.35 -> Unhiding rules: 1.31/1.35 Empty 1.31/1.35 -> Result: 1.31/1.35 Set P is empty 1.31/1.35 1.31/1.35 The problem is finite. 1.31/1.35 EOF