/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR s x) (STRATEGY CONTEXTSENSITIVE (*top*_0 1) (M_1) (cons_1) (cons_10) (cons_11) (cons_2) (cons_3) (cons_4) (cons_5) (cons_6) (cons_7) (cons_8) (cons_9) (h_0 1) (tail_0 1) (tail_1) (0_0) (1_0) (garbage_collection_0) (h_1) ) (RULES *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ) Problem 1: Dependency Pairs Processor: -> Pairs: *TOP*_0(tail_1(cons_1(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_1(x,s))) -> s *TOP*_0(tail_1(cons_10(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_10(x,s))) -> s *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_11(x,s))) -> s *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_5(x,s))) -> s *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_6(x,s))) -> s *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(0_0,s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> CONS_10(1_0,cons_2(0_0,h_1(s))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> CONS_10(1_0,cons_3(0_0,h_1(s))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> CONS_6(0_0,cons_7(1_0,h_1(s))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> CONS_6(0_0,cons_8(1_0,h_1(s))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) H_0(tail_1(cons_1(x,s))) -> H_0(s) H_0(tail_1(cons_1(x,s))) -> s TAIL_0(tail_1(cons_1(x,s))) -> TAIL_1(s) TAIL_0(tail_1(cons_10(x,s))) -> TAIL_1(s) TAIL_0(tail_1(cons_11(x,s))) -> TAIL_1(s) TAIL_0(tail_1(cons_5(x,s))) -> TAIL_1(s) TAIL_0(tail_1(cons_6(x,s))) -> TAIL_1(s) TAIL_1(cons_1(x,s)) -> s TAIL_1(cons_2(x,s)) -> s TAIL_1(cons_3(x,s)) -> s TAIL_1(cons_4(x,s)) -> s TAIL_1(cons_7(x,s)) -> s TAIL_1(cons_8(x,s)) -> s TAIL_1(cons_9(x,s)) -> s -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding Rules: cons_1(0_0,h_0(s)) -> CONS_1(0_0,h_0(s)) cons_1(0_0,tail_0(M_1)) -> CONS_1(0_0,tail_0(M_1)) cons_1(1_0,h_0(s)) -> CONS_1(1_0,h_0(s)) cons_10(1_0,cons_1(0_0,h_0(s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) cons_10(1_0,cons_2(0_0,h_1(s))) -> CONS_10(1_0,cons_2(0_0,h_1(s))) cons_10(1_0,cons_3(0_0,h_1(s))) -> CONS_10(1_0,cons_3(0_0,h_1(s))) cons_2(0_0,h_1(s)) -> CONS_2(0_0,h_1(s)) cons_3(0_0,h_1(s)) -> CONS_3(0_0,h_1(s)) cons_6(0_0,cons_1(1_0,h_0(s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) cons_6(0_0,cons_7(1_0,h_1(s))) -> CONS_6(0_0,cons_7(1_0,h_1(s))) cons_6(0_0,cons_8(1_0,h_1(s))) -> CONS_6(0_0,cons_8(1_0,h_1(s))) cons_7(1_0,h_1(s)) -> CONS_7(1_0,h_1(s)) cons_8(1_0,h_1(s)) -> CONS_8(1_0,h_1(s)) Problem 1: SCC Processor: -> Pairs: *TOP*_0(tail_1(cons_1(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_1(x,s))) -> s *TOP*_0(tail_1(cons_10(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_10(x,s))) -> s *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_11(x,s))) -> s *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_5(x,s))) -> s *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_6(x,s))) -> s *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(0_0,s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> CONS_10(1_0,cons_2(0_0,h_1(s))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> CONS_10(1_0,cons_3(0_0,h_1(s))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> CONS_6(0_0,cons_7(1_0,h_1(s))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> CONS_6(0_0,cons_8(1_0,h_1(s))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) H_0(tail_1(cons_1(x,s))) -> H_0(s) H_0(tail_1(cons_1(x,s))) -> s TAIL_0(tail_1(cons_1(x,s))) -> TAIL_1(s) TAIL_0(tail_1(cons_10(x,s))) -> TAIL_1(s) TAIL_0(tail_1(cons_11(x,s))) -> TAIL_1(s) TAIL_0(tail_1(cons_5(x,s))) -> TAIL_1(s) TAIL_0(tail_1(cons_6(x,s))) -> TAIL_1(s) TAIL_1(cons_1(x,s)) -> s TAIL_1(cons_2(x,s)) -> s TAIL_1(cons_3(x,s)) -> s TAIL_1(cons_4(x,s)) -> s TAIL_1(cons_7(x,s)) -> s TAIL_1(cons_8(x,s)) -> s TAIL_1(cons_9(x,s)) -> s -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: cons_1(0_0,h_0(s)) -> CONS_1(0_0,h_0(s)) cons_1(0_0,tail_0(M_1)) -> CONS_1(0_0,tail_0(M_1)) cons_1(1_0,h_0(s)) -> CONS_1(1_0,h_0(s)) cons_10(1_0,cons_1(0_0,h_0(s))) -> CONS_10(1_0,cons_1(0_0,h_0(s))) cons_10(1_0,cons_2(0_0,h_1(s))) -> CONS_10(1_0,cons_2(0_0,h_1(s))) cons_10(1_0,cons_3(0_0,h_1(s))) -> CONS_10(1_0,cons_3(0_0,h_1(s))) cons_2(0_0,h_1(s)) -> CONS_2(0_0,h_1(s)) cons_3(0_0,h_1(s)) -> CONS_3(0_0,h_1(s)) cons_6(0_0,cons_1(1_0,h_0(s))) -> CONS_6(0_0,cons_1(1_0,h_0(s))) cons_6(0_0,cons_7(1_0,h_1(s))) -> CONS_6(0_0,cons_7(1_0,h_1(s))) cons_6(0_0,cons_8(1_0,h_1(s))) -> CONS_6(0_0,cons_8(1_0,h_1(s))) cons_7(1_0,h_1(s)) -> CONS_7(1_0,h_1(s)) cons_8(1_0,h_1(s)) -> CONS_8(1_0,h_1(s)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: H_0(tail_1(cons_1(x,s))) -> H_0(s) ->->-> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->->-> Unhiding rules: Empty ->->Cycle: ->->-> Pairs: *TOP*_0(tail_1(cons_1(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_10(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) ->->-> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->->-> Unhiding rules: Empty The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pairs Processor: -> Pairs: H_0(tail_1(cons_1(x,s))) -> H_0(s) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Usable rules: M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [M_1] = 2 [cons_1](X1,X2) = 2.X2 [cons_10](X1,X2) = 2.X1 + X2 + 1 [cons_11](X1,X2) = 2.X1 + 2.X2 + 2 [cons_2](X1,X2) = 2.X1 + 2.X2 [cons_3](X1,X2) = X1 + X2 + 2 [cons_4](X1,X2) = X1 + 2.X2 + 1 [cons_5](X1,X2) = 2.X2 + 2 [cons_6](X1,X2) = 2.X1 + X2 [cons_7](X1,X2) = 2.X1 + X2 + 2 [cons_8](X1,X2) = 2.X2 + 1 [cons_9](X1,X2) = X2 + 2 [h_0](X) = 2 [tail_0](X) = 2.X + 2 [tail_1](X) = X + 1 [0_0] = 0 [1_0] = 0 [garbage_collection_0] = 0 [h_1](X) = 2 [H_0](X) = 2.X Problem 1.1: Basic Processor: -> Pairs: Empty -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Result: Set P is empty The problem is finite. Problem 1.2: Reduction Pairs Processor: -> Pairs: *TOP*_0(tail_1(cons_1(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_10(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Usable rules: M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [M_1] = 2 [cons_1](X1,X2) = X2 [cons_10](X1,X2) = X2 [cons_11](X1,X2) = X1 + 2.X2 [cons_2](X1,X2) = 2.X1 + X2 [cons_3](X1,X2) = X1 + X2 [cons_4](X1,X2) = 2.X1 + 2.X2 + 2 [cons_5](X1,X2) = X1 + 2.X2 [cons_6](X1,X2) = 2.X1 + X2 [cons_7](X1,X2) = 2.X1 + X2 [cons_8](X1,X2) = 2.X1 + X2 [cons_9](X1,X2) = X1 + X2 [h_0](X) = 1 [tail_0](X) = 2.X [tail_1](X) = X + 1 [0_0] = 0 [1_0] = 0 [garbage_collection_0] = 0 [h_1](X) = 1 [*TOP*_0](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: *TOP*_0(tail_1(cons_10(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: *TOP*_0(tail_1(cons_10(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) ->->-> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->->-> Unhiding rules: Empty Problem 1.2: Reduction Pairs Processor: -> Pairs: *TOP*_0(tail_1(cons_10(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Usable rules: M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [M_1] = 2 [cons_1](X1,X2) = X2 [cons_10](X1,X2) = X2 [cons_11](X1,X2) = 2.X1 + 2.X2 + 2 [cons_2](X1,X2) = 2.X1 + X2 [cons_3](X1,X2) = 2.X1 + X2 [cons_4](X1,X2) = X1 + 2.X2 + 2 [cons_5](X1,X2) = X1 + 2.X2 + 2 [cons_6](X1,X2) = X1 + X2 [cons_7](X1,X2) = 2.X1 + X2 [cons_8](X1,X2) = X2 [cons_9](X1,X2) = X1 + 2.X2 + 1 [h_0](X) = 2 [tail_0](X) = 2.X + 2 [tail_1](X) = X + 1 [0_0] = 0 [1_0] = 0 [garbage_collection_0] = 0 [h_1](X) = 2 [*TOP*_0](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) ->->-> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->->-> Unhiding rules: Empty Problem 1.2: Reduction Pairs Processor: -> Pairs: *TOP*_0(tail_1(cons_11(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Usable rules: M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [M_1] = 0 [cons_1](X1,X2) = X2 [cons_10](X1,X2) = X2 [cons_11](X1,X2) = 2.X1 + 2.X2 + 2 [cons_2](X1,X2) = X2 [cons_3](X1,X2) = 2.X1 + X2 + 2 [cons_4](X1,X2) = 2.X2 + 2 [cons_5](X1,X2) = 2.X1 + 2.X2 + 2 [cons_6](X1,X2) = X2 [cons_7](X1,X2) = X1 + 2.X2 + 1 [cons_8](X1,X2) = X1 + X2 [cons_9](X1,X2) = 2.X2 + 1 [h_0](X) = 2.X [tail_0](X) = 2.X [tail_1](X) = 2.X [0_0] = 0 [1_0] = 0 [garbage_collection_0] = 0 [h_1](X) = 2.X [*TOP*_0](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) ->->-> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->->-> Unhiding rules: Empty Problem 1.2: Reduction Pairs Processor: -> Pairs: *TOP*_0(tail_1(cons_5(x,s))) -> *TOP*_0(s) *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Usable rules: M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [M_1] = 2 [cons_1](X1,X2) = X2 [cons_10](X1,X2) = X2 [cons_11](X1,X2) = 2.X1 + 2.X2 [cons_2](X1,X2) = X2 [cons_3](X1,X2) = X2 [cons_4](X1,X2) = 2.X1 + 2.X2 + 1 [cons_5](X1,X2) = X2 [cons_6](X1,X2) = X2 [cons_7](X1,X2) = X2 [cons_8](X1,X2) = X2 [cons_9](X1,X2) = X1 + 2.X2 + 1 [h_0](X) = 2 [tail_0](X) = 2.X + 2 [tail_1](X) = 2.X + 2 [0_0] = 0 [1_0] = 2 [garbage_collection_0] = 0 [h_1](X) = 2 [*TOP*_0](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) ->->-> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->->-> Unhiding rules: Empty Problem 1.2: Reduction Pairs Processor: -> Pairs: *TOP*_0(tail_1(cons_6(x,s))) -> *TOP*_0(s) *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Usable rules: M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [M_1] = 2 [cons_1](X1,X2) = 2.X1 + X2 [cons_10](X1,X2) = X2 [cons_11](X1,X2) = X1 + 2.X2 [cons_2](X1,X2) = 2.X1 + X2 [cons_3](X1,X2) = 2.X1 + X2 [cons_4](X1,X2) = 2.X1 + X2 + 2 [cons_5](X1,X2) = 2.X1 + X2 + 2 [cons_6](X1,X2) = 2.X1 + X2 [cons_7](X1,X2) = 2.X1 + X2 [cons_8](X1,X2) = X2 [cons_9](X1,X2) = 2.X1 + X2 + 2 [h_0](X) = 2 [tail_0](X) = 2.X + 2 [tail_1](X) = 2.X + 2 [0_0] = 0 [1_0] = 0 [garbage_collection_0] = 0 [h_1](X) = 2 [*TOP*_0](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) ->->-> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->->-> Unhiding rules: Empty Problem 1.2: Reduction Pairs Processor: -> Pairs: *TOP*_0(h_1(cons_1(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Usable rules: cons_10(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [cons_1](X1,X2) = 2.X2 + 1 [cons_10](X1,X2) = 2.X1 + 2.X2 + 2 [cons_11](X1,X2) = 2 [cons_2](X1,X2) = 2 [cons_3](X1,X2) = 2 [cons_4](X1,X2) = 1 [cons_5](X1,X2) = 2.X1 + 2 [cons_6](X1,X2) = 2.X2 + 1 [cons_7](X1,X2) = 2.X1 + 2 [cons_8](X1,X2) = 2.X1 + 1 [cons_9](X1,X2) = 2.X2 + 1 [h_0](X) = 0 [0_0] = 2 [1_0] = 0 [garbage_collection_0] = 1 [h_1](X) = 2.X + 2 [*TOP*_0](X) = X Problem 1.2: SCC Processor: -> Pairs: *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) ->->-> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->->-> Unhiding rules: Empty Problem 1.2: Reduction Pairs Processor: -> Pairs: *TOP*_0(h_1(cons_1(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Usable rules: cons_10(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [cons_1](X1,X2) = 2.X1 + 2.X2 [cons_10](X1,X2) = X1 [cons_11](X1,X2) = 2.X1 + 2.X2 + 2 [cons_2](X1,X2) = 2.X1 + 2 [cons_3](X1,X2) = 2.X1 + 2.X2 + 2 [cons_4](X1,X2) = X1 + 2.X2 + 2 [cons_5](X1,X2) = 2.X1 + 2.X2 + 2 [cons_6](X1,X2) = X1 + 2.X2 + 2 [cons_7](X1,X2) = 2.X1 + X2 + 2 [cons_8](X1,X2) = 2.X1 + 2 [cons_9](X1,X2) = 2.X2 [h_0](X) = 0 [0_0] = 2 [1_0] = 0 [garbage_collection_0] = 0 [h_1](X) = 2.X + 1 [*TOP*_0](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) ->->-> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->->-> Unhiding rules: Empty Problem 1.2: Reduction Pairs Processor: -> Pairs: *TOP*_0(h_1(cons_10(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Usable rules: cons_10(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [cons_1](X1,X2) = 2.X1 + 2 [cons_10](X1,X2) = X1 [cons_11](X1,X2) = 2.X1 + 2.X2 [cons_2](X1,X2) = 2.X2 + 2 [cons_3](X1,X2) = X1 + 2.X2 + 2 [cons_4](X1,X2) = 2.X1 + 2.X2 + 2 [cons_5](X1,X2) = 2.X2 + 2 [cons_6](X1,X2) = 2.X1 + 1 [cons_7](X1,X2) = 2 [cons_8](X1,X2) = 2.X1 + 2.X2 [cons_9](X1,X2) = 2.X2 + 2 [h_0](X) = 2.X + 2 [0_0] = 1 [1_0] = 2 [garbage_collection_0] = 0 [h_1](X) = 2.X [*TOP*_0](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) ->->-> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->->-> Unhiding rules: Empty Problem 1.2: Reduction Pairs Processor: -> Pairs: *TOP*_0(h_1(cons_11(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Usable rules: cons_10(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [cons_1](X1,X2) = X2 [cons_10](X1,X2) = 2 [cons_11](X1,X2) = 2.X2 + 2 [cons_2](X1,X2) = X1 + 2.X2 + 1 [cons_3](X1,X2) = 2.X1 + 2.X2 + 1 [cons_4](X1,X2) = 2.X2 + 2 [cons_5](X1,X2) = X1 + 2.X2 + 2 [cons_6](X1,X2) = 2.X1 + 2.X2 + 2 [cons_7](X1,X2) = 2.X1 + 2 [cons_8](X1,X2) = 2.X1 + X2 [cons_9](X1,X2) = X2 [h_0](X) = 0 [0_0] = 2 [1_0] = 0 [garbage_collection_0] = 2 [h_1](X) = 2.X + 2 [*TOP*_0](X) = X Problem 1.2: SCC Processor: -> Pairs: *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) ->->-> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->->-> Unhiding rules: Empty Problem 1.2: Reduction Pairs Processor: -> Pairs: *TOP*_0(h_1(cons_2(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Usable rules: cons_10(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [cons_1](X1,X2) = 2.X1 + 2 [cons_10](X1,X2) = 2.X2 + 2 [cons_2](X1,X2) = 2.X2 + 2 [cons_3](X1,X2) = X1 + 2.X2 [cons_4](X1,X2) = 2 [cons_5](X1,X2) = X1 + 2.X2 + 2 [cons_6](X1,X2) = 2.X1 + 2 [cons_7](X1,X2) = 2.X1 + 2.X2 + 2 [cons_8](X1,X2) = 2 [cons_9](X1,X2) = X1 + X2 + 2 [h_0](X) = 2.X + 2 [0_0] = 0 [1_0] = 2 [garbage_collection_0] = 2 [h_1](X) = 2.X + 2 [*TOP*_0](X) = X Problem 1.2: SCC Processor: -> Pairs: *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) ->->-> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->->-> Unhiding rules: Empty Problem 1.2: Reduction Pairs Processor: -> Pairs: *TOP*_0(h_1(cons_3(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Usable rules: cons_10(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [cons_1](X1,X2) = 2.X1 + 1 [cons_10](X1,X2) = X1 + 2.X2 + 2 [cons_3](X1,X2) = X1 + X2 + 2 [cons_4](X1,X2) = 2.X1 [cons_5](X1,X2) = 2 [cons_6](X1,X2) = 2.X1 + 2 [cons_7](X1,X2) = 2.X1 + X2 + 2 [cons_8](X1,X2) = 2.X1 + 2 [cons_9](X1,X2) = 2.X1 + X2 + 2 [h_0](X) = X + 2 [0_0] = 0 [1_0] = 2 [garbage_collection_0] = 2 [h_1](X) = 2.X + 2 [*TOP*_0](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) ->->-> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->->-> Unhiding rules: Empty Problem 1.2: Reduction Pairs Processor: -> Pairs: *TOP*_0(h_1(cons_4(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Usable rules: cons_10(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [cons_1](X1,X2) = 0 [cons_10](X1,X2) = 2 [cons_4](X1,X2) = 2.X1 + 2.X2 + 2 [cons_5](X1,X2) = 2.X1 + 2 [cons_6](X1,X2) = 2.X1 + X2 + 2 [cons_7](X1,X2) = X1 + 1 [cons_8](X1,X2) = 0 [cons_9](X1,X2) = 2.X1 + X2 [h_0](X) = 2.X + 1 [0_0] = 0 [1_0] = 1 [garbage_collection_0] = 1 [h_1](X) = 2.X + 2 [*TOP*_0](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) ->->-> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->->-> Unhiding rules: Empty Problem 1.2: Reduction Pairs Processor: -> Pairs: *TOP*_0(h_1(cons_5(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Usable rules: cons_10(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [cons_1](X1,X2) = 2.X2 [cons_10](X1,X2) = 2.X1 [cons_5](X1,X2) = X1 + 2.X2 + 2 [cons_6](X1,X2) = 2.X1 + 1 [cons_7](X1,X2) = 2.X1 + 1 [cons_8](X1,X2) = X1 + 2 [cons_9](X1,X2) = 2.X1 + 2.X2 [h_0](X) = X + 1 [0_0] = 2 [1_0] = 0 [garbage_collection_0] = 0 [h_1](X) = 2.X [*TOP*_0](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) ->->-> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->->-> Unhiding rules: Empty Problem 1.2: Reduction Pairs Processor: -> Pairs: *TOP*_0(h_1(cons_6(0_0,s))) -> *TOP*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Usable rules: cons_10(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [cons_1](X1,X2) = 2.X1 + 2.X2 [cons_10](X1,X2) = X1 + 2.X2 [cons_6](X1,X2) = 1 [cons_7](X1,X2) = X1 + 2.X2 + 2 [cons_8](X1,X2) = 2.X1 + 2 [cons_9](X1,X2) = 2.X1 + 2.X2 + 2 [h_0](X) = 0 [0_0] = 0 [1_0] = 2 [garbage_collection_0] = 0 [h_1](X) = 2 [*TOP*_0](X) = 2.X Problem 1.2: SCC Processor: -> Pairs: *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) ->->-> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->->-> Unhiding rules: Empty Problem 1.2: Reduction Pairs Processor: -> Pairs: *TOP*_0(h_1(cons_7(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Usable rules: cons_10(x,s) -> garbage_collection_0 ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [cons_1](X1,X2) = 0 [cons_10](X1,X2) = 2.X2 + 1 [cons_7](X1,X2) = 2.X1 + 2.X2 + 1 [cons_8](X1,X2) = 2.X2 [cons_9](X1,X2) = X2 [h_0](X) = 2.X [0_0] = 0 [1_0] = 0 [garbage_collection_0] = 1 [h_1](X) = 2 [*TOP*_0](X) = X Problem 1.2: SCC Processor: -> Pairs: *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) ->->-> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->->-> Unhiding rules: Empty Problem 1.2: Reduction Pairs Processor: -> Pairs: *TOP*_0(h_1(cons_8(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Usable rules: cons_10(x,s) -> garbage_collection_0 ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [cons_1](X1,X2) = X2 [cons_10](X1,X2) = 2.X1 + 2.X2 + 1 [cons_8](X1,X2) = 2.X2 + 2 [cons_9](X1,X2) = 2 [h_0](X) = 1 [0_0] = 2 [1_0] = 0 [garbage_collection_0] = 0 [h_1](X) = 2.X + 1 [*TOP*_0](X) = X Problem 1.2: SCC Processor: -> Pairs: *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) ->->-> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s ->->-> Unhiding rules: Empty Problem 1.2: Reduction Pairs Processor: -> Pairs: *TOP*_0(h_1(cons_9(1_0,s))) -> *TOP*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Usable rules: cons_10(x,s) -> garbage_collection_0 ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [cons_1](X1,X2) = X2 + 1 [cons_10](X1,X2) = 2.X1 + 2.X2 + 1 [cons_9](X1,X2) = 2.X2 + 2 [h_0](X) = 2.X [0_0] = 2 [1_0] = 1 [garbage_collection_0] = 1 [h_1](X) = 2.X + 2 [*TOP*_0](X) = 2.X Problem 1.2: Basic Processor: -> Pairs: Empty -> Rules: *top*_0(tail_1(cons_1(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_10(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_11(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_5(x,s))) -> *top*_0(s) *top*_0(tail_1(cons_6(x,s))) -> *top*_0(s) *top*_0(h_1(cons_1(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_1(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_10(1_0,s))) -> *top*_0(cons_10(1_0,cons_2(0_0,h_1(s)))) *top*_0(h_1(cons_11(1_0,s))) -> *top*_0(cons_10(1_0,cons_3(0_0,h_1(s)))) *top*_0(h_1(cons_2(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_3(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_4(0_0,s))) -> *top*_0(cons_6(0_0,cons_1(1_0,h_0(s)))) *top*_0(h_1(cons_5(0_0,s))) -> *top*_0(cons_6(0_0,cons_7(1_0,h_1(s)))) *top*_0(h_1(cons_6(0_0,s))) -> *top*_0(cons_6(0_0,cons_8(1_0,h_1(s)))) *top*_0(h_1(cons_7(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_8(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) *top*_0(h_1(cons_9(1_0,s))) -> *top*_0(cons_10(1_0,cons_1(0_0,h_0(s)))) M_1 -> h_1(cons_1(0_0,tail_0(M_1))) cons_1(x,s) -> garbage_collection_0 cons_10(x,s) -> garbage_collection_0 cons_11(x,s) -> garbage_collection_0 cons_2(x,s) -> garbage_collection_0 cons_3(x,s) -> garbage_collection_0 cons_4(x,s) -> garbage_collection_0 cons_5(x,s) -> garbage_collection_0 cons_6(x,s) -> garbage_collection_0 cons_7(x,s) -> garbage_collection_0 cons_8(x,s) -> garbage_collection_0 cons_9(x,s) -> garbage_collection_0 h_0(tail_1(cons_1(x,s))) -> h_0(s) h_0(tail_1(cons_1(x,s))) -> h_1(s) h_0(tail_1(cons_10(x,s))) -> h_1(s) h_0(tail_1(cons_11(x,s))) -> h_1(s) h_0(tail_1(cons_5(x,s))) -> h_1(s) h_0(tail_1(cons_6(x,s))) -> h_1(s) h_0(h_1(cons_1(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_1(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_10(1_0,s))) -> h_1(cons_10(1_0,cons_2(0_0,h_1(s)))) h_0(h_1(cons_11(1_0,s))) -> h_1(cons_10(1_0,cons_3(0_0,h_1(s)))) h_0(h_1(cons_2(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_3(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_4(0_0,s))) -> h_1(cons_6(0_0,cons_1(1_0,h_0(s)))) h_0(h_1(cons_5(0_0,s))) -> h_1(cons_6(0_0,cons_7(1_0,h_1(s)))) h_0(h_1(cons_6(0_0,s))) -> h_1(cons_6(0_0,cons_8(1_0,h_1(s)))) h_0(h_1(cons_7(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_8(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) h_0(h_1(cons_9(1_0,s))) -> h_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(tail_1(cons_1(x,s))) -> tail_1(s) tail_0(tail_1(cons_10(x,s))) -> tail_1(s) tail_0(tail_1(cons_11(x,s))) -> tail_1(s) tail_0(tail_1(cons_5(x,s))) -> tail_1(s) tail_0(tail_1(cons_6(x,s))) -> tail_1(s) tail_0(h_1(cons_1(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_1(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_10(1_0,s))) -> tail_1(cons_10(1_0,cons_2(0_0,h_1(s)))) tail_0(h_1(cons_11(1_0,s))) -> tail_1(cons_10(1_0,cons_3(0_0,h_1(s)))) tail_0(h_1(cons_2(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_3(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_4(0_0,s))) -> tail_1(cons_6(0_0,cons_1(1_0,h_0(s)))) tail_0(h_1(cons_5(0_0,s))) -> tail_1(cons_6(0_0,cons_7(1_0,h_1(s)))) tail_0(h_1(cons_6(0_0,s))) -> tail_1(cons_6(0_0,cons_8(1_0,h_1(s)))) tail_0(h_1(cons_7(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_8(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_0(h_1(cons_9(1_0,s))) -> tail_1(cons_10(1_0,cons_1(0_0,h_0(s)))) tail_1(cons_1(x,s)) -> s tail_1(cons_2(x,s)) -> s tail_1(cons_3(x,s)) -> s tail_1(cons_4(x,s)) -> s tail_1(cons_7(x,s)) -> s tail_1(cons_8(x,s)) -> s tail_1(cons_9(x,s)) -> s -> Unhiding rules: Empty -> Result: Set P is empty The problem is finite.