22.66/11.03	YES
22.66/11.08	proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
22.66/11.08	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
22.66/11.08	
22.66/11.08	
22.66/11.08	Termination of the given CSR could be proven:
22.66/11.08	
22.66/11.08	(0) CSR
22.66/11.08	(1) CSRRRRProof [EQUIVALENT, 415 ms]
22.66/11.08	(2) CSR
22.66/11.08	(3) CSRRRRProof [EQUIVALENT, 253 ms]
22.66/11.08	(4) CSR
22.66/11.08	(5) CSRRRRProof [EQUIVALENT, 85 ms]
22.66/11.08	(6) CSR
22.66/11.08	(7) CSRRRRProof [EQUIVALENT, 74 ms]
22.66/11.08	(8) CSR
22.66/11.08	(9) CSRRRRProof [EQUIVALENT, 16 ms]
22.66/11.08	(10) CSR
22.66/11.08	(11) CSRRRRProof [EQUIVALENT, 46 ms]
22.66/11.08	(12) CSR
22.66/11.08	(13) CSRRRRProof [EQUIVALENT, 40 ms]
22.66/11.08	(14) CSR
22.66/11.08	(15) CSRRRRProof [EQUIVALENT, 38 ms]
22.66/11.08	(16) CSR
22.66/11.08	(17) CSRRRRProof [EQUIVALENT, 35 ms]
22.66/11.08	(18) CSR
22.66/11.08	(19) CSRRRRProof [EQUIVALENT, 30 ms]
22.66/11.08	(20) CSR
22.66/11.08	(21) CSRRRRProof [EQUIVALENT, 31 ms]
22.66/11.08	(22) CSR
22.66/11.08	(23) CSRRRRProof [EQUIVALENT, 24 ms]
22.66/11.08	(24) CSR
22.66/11.08	(25) CSRRRRProof [EQUIVALENT, 12 ms]
22.66/11.08	(26) CSR
22.66/11.08	(27) CSRRRRProof [EQUIVALENT, 0 ms]
22.66/11.08	(28) CSR
22.66/11.08	(29) CSRRRRProof [EQUIVALENT, 0 ms]
22.66/11.08	(30) CSR
22.66/11.08	(31) CSRRRRProof [EQUIVALENT, 17 ms]
22.66/11.08	(32) CSR
22.66/11.08	(33) CSRRRRProof [EQUIVALENT, 0 ms]
22.66/11.08	(34) CSR
22.66/11.08	(35) CSRRRRProof [EQUIVALENT, 18 ms]
22.66/11.08	(36) CSR
22.66/11.08	(37) CSRRRRProof [EQUIVALENT, 13 ms]
22.66/11.08	(38) CSR
22.66/11.08	(39) CSRRRRProof [EQUIVALENT, 14 ms]
22.66/11.08	(40) CSR
22.66/11.08	(41) CSRRRRProof [EQUIVALENT, 14 ms]
22.66/11.08	(42) CSR
22.66/11.08	(43) CSRRRRProof [EQUIVALENT, 0 ms]
22.66/11.08	(44) CSR
22.66/11.08	(45) CSRRRRProof [EQUIVALENT, 0 ms]
22.66/11.08	(46) CSR
22.66/11.08	(47) CSRRRRProof [EQUIVALENT, 10 ms]
22.66/11.08	(48) CSR
22.66/11.08	(49) CSRRRRProof [EQUIVALENT, 10 ms]
22.66/11.08	(50) CSR
22.66/11.08	(51) CSRRRRProof [EQUIVALENT, 0 ms]
22.66/11.08	(52) CSR
22.66/11.08	(53) CSRRRRProof [EQUIVALENT, 0 ms]
22.66/11.08	(54) CSR
22.66/11.08	(55) CSRRRRProof [EQUIVALENT, 7 ms]
22.66/11.08	(56) CSR
22.66/11.08	(57) CSRRRRProof [EQUIVALENT, 0 ms]
22.66/11.08	(58) CSR
22.66/11.08	(59) CSRRRRProof [EQUIVALENT, 0 ms]
22.66/11.08	(60) CSR
22.66/11.08	(61) CSRRRRProof [EQUIVALENT, 0 ms]
22.66/11.08	(62) CSR
22.66/11.08	(63) RisEmptyProof [EQUIVALENT, 0 ms]
22.66/11.08	(64) YES
22.66/11.08	
22.66/11.08	
22.66/11.08	----------------------------------------
22.66/11.08	
22.66/11.08	(0)
22.66/11.08	Obligation:
22.66/11.08	Context-sensitive rewrite system:
22.66/11.08	The TRS R consists of the following rules:
22.66/11.08	
22.66/11.08	   *top*_2(a_31) -> *top*_1(f_34(a_31))
22.66/11.08	   *top*_1(f_34(a_31)) -> *top*_3(f_33(f_34(a_31)))
22.66/11.08	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.66/11.08	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.66/11.08	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.66/11.08	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.66/11.08	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.66/11.08	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.66/11.08	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.66/11.08	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.66/11.08	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.66/11.08	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.66/11.08	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.66/11.08	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.66/11.08	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.66/11.08	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.66/11.08	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.66/11.08	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.66/11.08	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.66/11.08	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.66/11.08	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.66/11.08	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.66/11.08	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.66/11.08	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.66/11.08	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.66/11.08	   *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))) -> *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))
22.66/11.08	   *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))) -> *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))
22.66/11.08	   *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))) -> *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))))
22.66/11.08	   *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))) -> *top*_30(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))))
22.66/11.08	   f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))) -> f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))))
22.66/11.08	   *top*_30(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	
22.66/11.08	The replacement map contains the following entries:
22.66/11.08	
22.66/11.08	*top*_2: {1}
22.66/11.08	a_31: empty set
22.66/11.08	*top*_1: {1}
22.66/11.08	f_34: {1}
22.66/11.08	*top*_3: {1}
22.66/11.08	f_33: {1}
22.66/11.08	*top*_4: {1}
22.66/11.08	f_35: {1}
22.66/11.08	*top*_5: {1}
22.66/11.08	f_36: {1}
22.66/11.08	*top*_6: {1}
22.66/11.08	f_37: {1}
22.66/11.08	*top*_7: {1}
22.66/11.08	f_38: {1}
22.66/11.08	*top*_8: {1}
22.66/11.08	f_39: {1}
22.66/11.08	*top*_9: {1}
22.66/11.08	f_40: {1}
22.66/11.08	*top*_10: {1}
22.66/11.08	f_41: {1}
22.66/11.08	*top*_11: {1}
22.66/11.08	f_42: {1}
22.66/11.08	*top*_12: {1}
22.66/11.08	f_43: {1}
22.66/11.08	*top*_13: {1}
22.66/11.08	f_44: {1}
22.66/11.08	*top*_14: {1}
22.66/11.08	f_45: {1}
22.66/11.08	*top*_15: {1}
22.66/11.08	f_46: {1}
22.66/11.08	*top*_16: {1}
22.66/11.08	f_47: {1}
22.66/11.08	*top*_17: {1}
22.66/11.08	f_48: {1}
22.66/11.08	*top*_18: {1}
22.66/11.08	f_49: {1}
22.66/11.08	*top*_19: {1}
22.66/11.08	f_50: {1}
22.66/11.08	*top*_20: {1}
22.66/11.08	f_51: {1}
22.66/11.08	*top*_21: {1}
22.66/11.08	f_52: {1}
22.66/11.08	*top*_22: {1}
22.66/11.08	f_53: {1}
22.66/11.08	*top*_23: {1}
22.66/11.08	f_54: {1}
22.66/11.08	*top*_24: {1}
22.66/11.08	f_55: {1}
22.66/11.08	*top*_25: {1}
22.66/11.08	f_56: {1}
22.66/11.08	*top*_26: {1}
22.66/11.08	f_57: {1}
22.66/11.08	*top*_27: {1}
22.66/11.08	f_58: {1}
22.66/11.08	*top*_28: {1}
22.66/11.08	f_59: {1}
22.66/11.08	*top*_29: {1}
22.66/11.08	f_60: {1}
22.66/11.08	*top*_30: {1}
22.66/11.08	f_61: {1}
22.66/11.08	f_62: empty set
22.66/11.08	c_32: empty set
22.66/11.08	
22.66/11.08	----------------------------------------
22.66/11.08	
22.66/11.08	(1) CSRRRRProof (EQUIVALENT)
22.66/11.08	The following CSR is given: Context-sensitive rewrite system:
22.66/11.08	The TRS R consists of the following rules:
22.66/11.08	
22.66/11.08	   *top*_2(a_31) -> *top*_1(f_34(a_31))
22.66/11.08	   *top*_1(f_34(a_31)) -> *top*_3(f_33(f_34(a_31)))
22.66/11.08	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.66/11.08	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.66/11.08	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.66/11.08	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.66/11.08	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.66/11.08	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.66/11.08	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.66/11.08	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.66/11.08	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.66/11.08	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.66/11.08	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.66/11.08	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.66/11.08	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.66/11.08	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.66/11.08	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.66/11.08	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.66/11.08	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.66/11.08	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.66/11.08	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.66/11.08	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.66/11.08	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.66/11.08	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.66/11.08	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.66/11.08	   *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))) -> *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))
22.66/11.08	   *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))) -> *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))
22.66/11.08	   *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))) -> *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))))
22.66/11.08	   *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))) -> *top*_30(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))))
22.66/11.08	   f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))) -> f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))))
22.66/11.08	   *top*_30(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	
22.66/11.08	The replacement map contains the following entries:
22.66/11.08	
22.66/11.08	*top*_2: {1}
22.66/11.08	a_31: empty set
22.66/11.08	*top*_1: {1}
22.66/11.08	f_34: {1}
22.66/11.08	*top*_3: {1}
22.66/11.08	f_33: {1}
22.66/11.08	*top*_4: {1}
22.66/11.08	f_35: {1}
22.66/11.08	*top*_5: {1}
22.66/11.08	f_36: {1}
22.66/11.08	*top*_6: {1}
22.66/11.08	f_37: {1}
22.66/11.08	*top*_7: {1}
22.66/11.08	f_38: {1}
22.66/11.08	*top*_8: {1}
22.66/11.08	f_39: {1}
22.66/11.08	*top*_9: {1}
22.66/11.08	f_40: {1}
22.66/11.08	*top*_10: {1}
22.66/11.08	f_41: {1}
22.66/11.08	*top*_11: {1}
22.66/11.08	f_42: {1}
22.66/11.08	*top*_12: {1}
22.66/11.08	f_43: {1}
22.66/11.08	*top*_13: {1}
22.66/11.08	f_44: {1}
22.66/11.08	*top*_14: {1}
22.66/11.08	f_45: {1}
22.66/11.08	*top*_15: {1}
22.66/11.08	f_46: {1}
22.66/11.08	*top*_16: {1}
22.66/11.08	f_47: {1}
22.66/11.08	*top*_17: {1}
22.66/11.08	f_48: {1}
22.66/11.08	*top*_18: {1}
22.66/11.08	f_49: {1}
22.66/11.08	*top*_19: {1}
22.66/11.08	f_50: {1}
22.66/11.08	*top*_20: {1}
22.66/11.08	f_51: {1}
22.66/11.08	*top*_21: {1}
22.66/11.08	f_52: {1}
22.66/11.08	*top*_22: {1}
22.66/11.08	f_53: {1}
22.66/11.08	*top*_23: {1}
22.66/11.08	f_54: {1}
22.66/11.08	*top*_24: {1}
22.66/11.08	f_55: {1}
22.66/11.08	*top*_25: {1}
22.66/11.08	f_56: {1}
22.66/11.08	*top*_26: {1}
22.66/11.08	f_57: {1}
22.66/11.08	*top*_27: {1}
22.66/11.08	f_58: {1}
22.66/11.08	*top*_28: {1}
22.66/11.08	f_59: {1}
22.66/11.08	*top*_29: {1}
22.66/11.08	f_60: {1}
22.66/11.08	*top*_30: {1}
22.66/11.08	f_61: {1}
22.66/11.08	f_62: empty set
22.66/11.08	c_32: empty set
22.66/11.08	Used ordering:
22.66/11.08	Polynomial interpretation [POLO]:
22.66/11.08	
22.66/11.08	   POL(*top*_1(x_1)) = x_1
22.66/11.08	   POL(*top*_10(x_1)) = x_1
22.66/11.08	   POL(*top*_11(x_1)) = x_1
22.66/11.08	   POL(*top*_12(x_1)) = x_1
22.66/11.08	   POL(*top*_13(x_1)) = x_1
22.66/11.08	   POL(*top*_14(x_1)) = x_1
22.66/11.08	   POL(*top*_15(x_1)) = x_1
22.66/11.08	   POL(*top*_16(x_1)) = x_1
22.66/11.08	   POL(*top*_17(x_1)) = x_1
22.66/11.08	   POL(*top*_18(x_1)) = x_1
22.66/11.08	   POL(*top*_19(x_1)) = x_1
22.66/11.08	   POL(*top*_2(x_1)) = x_1
22.66/11.08	   POL(*top*_20(x_1)) = x_1
22.66/11.08	   POL(*top*_21(x_1)) = x_1
22.66/11.08	   POL(*top*_22(x_1)) = x_1
22.66/11.08	   POL(*top*_23(x_1)) = x_1
22.66/11.08	   POL(*top*_24(x_1)) = x_1
22.66/11.08	   POL(*top*_25(x_1)) = x_1
22.66/11.08	   POL(*top*_26(x_1)) = x_1
22.66/11.08	   POL(*top*_27(x_1)) = x_1
22.66/11.08	   POL(*top*_28(x_1)) = x_1
22.66/11.08	   POL(*top*_29(x_1)) = x_1
22.66/11.08	   POL(*top*_3(x_1)) = x_1
22.66/11.08	   POL(*top*_30(x_1)) = x_1
22.66/11.08	   POL(*top*_4(x_1)) = x_1
22.66/11.08	   POL(*top*_5(x_1)) = x_1
22.66/11.08	   POL(*top*_6(x_1)) = x_1
22.66/11.08	   POL(*top*_7(x_1)) = x_1
22.66/11.08	   POL(*top*_8(x_1)) = x_1
22.66/11.08	   POL(*top*_9(x_1)) = x_1
22.66/11.08	   POL(a_31) = 1
22.66/11.08	   POL(c_32) = 0
22.66/11.08	   POL(f_33(x_1)) = x_1
22.66/11.08	   POL(f_34(x_1)) = x_1
22.66/11.08	   POL(f_35(x_1)) = x_1
22.66/11.08	   POL(f_36(x_1)) = x_1
22.66/11.08	   POL(f_37(x_1)) = x_1
22.66/11.08	   POL(f_38(x_1)) = x_1
22.66/11.08	   POL(f_39(x_1)) = x_1
22.66/11.08	   POL(f_40(x_1)) = x_1
22.66/11.08	   POL(f_41(x_1)) = x_1
22.66/11.08	   POL(f_42(x_1)) = x_1
22.66/11.08	   POL(f_43(x_1)) = x_1
22.66/11.08	   POL(f_44(x_1)) = x_1
22.66/11.08	   POL(f_45(x_1)) = x_1
22.66/11.08	   POL(f_46(x_1)) = x_1
22.66/11.08	   POL(f_47(x_1)) = x_1
22.66/11.08	   POL(f_48(x_1)) = x_1
22.66/11.08	   POL(f_49(x_1)) = x_1
22.66/11.08	   POL(f_50(x_1)) = x_1
22.66/11.08	   POL(f_51(x_1)) = x_1
22.66/11.08	   POL(f_52(x_1)) = x_1
22.66/11.08	   POL(f_53(x_1)) = x_1
22.66/11.08	   POL(f_54(x_1)) = x_1
22.66/11.08	   POL(f_55(x_1)) = x_1
22.66/11.08	   POL(f_56(x_1)) = x_1
22.66/11.08	   POL(f_57(x_1)) = x_1
22.66/11.08	   POL(f_58(x_1)) = x_1
22.66/11.08	   POL(f_59(x_1)) = x_1
22.66/11.08	   POL(f_60(x_1)) = x_1
22.66/11.08	   POL(f_61(x_1)) = x_1
22.66/11.08	   POL(f_62(x_1)) = 0
22.66/11.08	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
22.66/11.08	
22.66/11.08	   f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))) -> f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))))
22.66/11.08	
22.66/11.08	
22.66/11.08	
22.66/11.08	
22.66/11.08	----------------------------------------
22.66/11.08	
22.66/11.08	(2)
22.66/11.08	Obligation:
22.66/11.08	Context-sensitive rewrite system:
22.66/11.08	The TRS R consists of the following rules:
22.66/11.08	
22.66/11.08	   *top*_2(a_31) -> *top*_1(f_34(a_31))
22.66/11.08	   *top*_1(f_34(a_31)) -> *top*_3(f_33(f_34(a_31)))
22.66/11.08	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.66/11.08	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.66/11.08	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.66/11.08	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.66/11.08	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.66/11.08	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.66/11.08	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.66/11.08	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.66/11.08	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.66/11.08	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.66/11.08	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.66/11.08	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.66/11.08	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.66/11.08	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.66/11.08	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.66/11.08	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.66/11.08	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.66/11.08	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.66/11.08	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.66/11.08	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.66/11.08	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.66/11.08	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.66/11.08	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.66/11.08	   *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))) -> *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))
22.66/11.08	   *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))) -> *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))
22.66/11.08	   *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))) -> *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))))
22.66/11.08	   *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))) -> *top*_30(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))))
22.66/11.08	   *top*_30(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	
22.66/11.08	The replacement map contains the following entries:
22.66/11.08	
22.66/11.08	*top*_2: {1}
22.66/11.08	a_31: empty set
22.66/11.08	*top*_1: {1}
22.66/11.08	f_34: {1}
22.66/11.08	*top*_3: {1}
22.66/11.08	f_33: {1}
22.66/11.08	*top*_4: {1}
22.66/11.08	f_35: {1}
22.66/11.08	*top*_5: {1}
22.66/11.08	f_36: {1}
22.66/11.08	*top*_6: {1}
22.66/11.08	f_37: {1}
22.66/11.08	*top*_7: {1}
22.66/11.08	f_38: {1}
22.66/11.08	*top*_8: {1}
22.66/11.08	f_39: {1}
22.66/11.08	*top*_9: {1}
22.66/11.08	f_40: {1}
22.66/11.08	*top*_10: {1}
22.66/11.08	f_41: {1}
22.66/11.08	*top*_11: {1}
22.66/11.08	f_42: {1}
22.66/11.08	*top*_12: {1}
22.66/11.08	f_43: {1}
22.66/11.08	*top*_13: {1}
22.66/11.08	f_44: {1}
22.66/11.08	*top*_14: {1}
22.66/11.08	f_45: {1}
22.66/11.08	*top*_15: {1}
22.66/11.08	f_46: {1}
22.66/11.08	*top*_16: {1}
22.66/11.08	f_47: {1}
22.66/11.08	*top*_17: {1}
22.66/11.08	f_48: {1}
22.66/11.08	*top*_18: {1}
22.66/11.08	f_49: {1}
22.66/11.08	*top*_19: {1}
22.66/11.08	f_50: {1}
22.66/11.08	*top*_20: {1}
22.66/11.08	f_51: {1}
22.66/11.08	*top*_21: {1}
22.66/11.08	f_52: {1}
22.66/11.08	*top*_22: {1}
22.66/11.08	f_53: {1}
22.66/11.08	*top*_23: {1}
22.66/11.08	f_54: {1}
22.66/11.08	*top*_24: {1}
22.66/11.08	f_55: {1}
22.66/11.08	*top*_25: {1}
22.66/11.08	f_56: {1}
22.66/11.08	*top*_26: {1}
22.66/11.08	f_57: {1}
22.66/11.08	*top*_27: {1}
22.66/11.08	f_58: {1}
22.66/11.08	*top*_28: {1}
22.66/11.08	f_59: {1}
22.66/11.08	*top*_29: {1}
22.66/11.08	f_60: {1}
22.66/11.08	*top*_30: {1}
22.66/11.08	f_61: {1}
22.66/11.08	f_62: empty set
22.66/11.08	c_32: empty set
22.66/11.08	
22.66/11.08	----------------------------------------
22.66/11.08	
22.66/11.08	(3) CSRRRRProof (EQUIVALENT)
22.66/11.08	The following CSR is given: Context-sensitive rewrite system:
22.66/11.08	The TRS R consists of the following rules:
22.66/11.08	
22.66/11.08	   *top*_2(a_31) -> *top*_1(f_34(a_31))
22.66/11.08	   *top*_1(f_34(a_31)) -> *top*_3(f_33(f_34(a_31)))
22.66/11.08	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.66/11.08	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.66/11.08	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.66/11.08	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.66/11.08	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.66/11.08	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.66/11.08	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.66/11.08	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.66/11.08	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.66/11.08	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.66/11.08	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.66/11.08	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.66/11.08	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.66/11.08	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.66/11.08	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.66/11.08	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.66/11.08	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.66/11.08	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.66/11.08	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.66/11.08	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.66/11.08	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.66/11.08	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.66/11.08	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.66/11.08	   *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))) -> *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))
22.66/11.08	   *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))) -> *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))
22.66/11.08	   *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))) -> *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))))
22.66/11.08	   *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))) -> *top*_30(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))))
22.66/11.08	   *top*_30(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	
22.66/11.08	The replacement map contains the following entries:
22.66/11.08	
22.66/11.08	*top*_2: {1}
22.66/11.08	a_31: empty set
22.66/11.08	*top*_1: {1}
22.66/11.08	f_34: {1}
22.66/11.08	*top*_3: {1}
22.66/11.08	f_33: {1}
22.66/11.08	*top*_4: {1}
22.66/11.08	f_35: {1}
22.66/11.08	*top*_5: {1}
22.66/11.08	f_36: {1}
22.66/11.08	*top*_6: {1}
22.66/11.08	f_37: {1}
22.66/11.08	*top*_7: {1}
22.66/11.08	f_38: {1}
22.66/11.08	*top*_8: {1}
22.66/11.08	f_39: {1}
22.66/11.08	*top*_9: {1}
22.66/11.08	f_40: {1}
22.66/11.08	*top*_10: {1}
22.66/11.08	f_41: {1}
22.66/11.08	*top*_11: {1}
22.66/11.08	f_42: {1}
22.66/11.08	*top*_12: {1}
22.66/11.08	f_43: {1}
22.66/11.08	*top*_13: {1}
22.66/11.08	f_44: {1}
22.66/11.08	*top*_14: {1}
22.66/11.08	f_45: {1}
22.66/11.08	*top*_15: {1}
22.66/11.08	f_46: {1}
22.66/11.08	*top*_16: {1}
22.66/11.08	f_47: {1}
22.66/11.08	*top*_17: {1}
22.66/11.08	f_48: {1}
22.66/11.08	*top*_18: {1}
22.66/11.08	f_49: {1}
22.66/11.08	*top*_19: {1}
22.66/11.08	f_50: {1}
22.66/11.08	*top*_20: {1}
22.66/11.08	f_51: {1}
22.66/11.08	*top*_21: {1}
22.66/11.08	f_52: {1}
22.66/11.08	*top*_22: {1}
22.66/11.08	f_53: {1}
22.66/11.08	*top*_23: {1}
22.66/11.08	f_54: {1}
22.66/11.08	*top*_24: {1}
22.66/11.08	f_55: {1}
22.66/11.08	*top*_25: {1}
22.66/11.08	f_56: {1}
22.66/11.08	*top*_26: {1}
22.66/11.08	f_57: {1}
22.66/11.08	*top*_27: {1}
22.66/11.08	f_58: {1}
22.66/11.08	*top*_28: {1}
22.66/11.08	f_59: {1}
22.66/11.08	*top*_29: {1}
22.66/11.08	f_60: {1}
22.66/11.08	*top*_30: {1}
22.66/11.08	f_61: {1}
22.66/11.08	f_62: empty set
22.66/11.08	c_32: empty set
22.66/11.08	Used ordering:
22.66/11.08	Polynomial interpretation [POLO]:
22.66/11.08	
22.66/11.08	   POL(*top*_1(x_1)) = 1 + x_1
22.66/11.08	   POL(*top*_10(x_1)) = x_1
22.66/11.08	   POL(*top*_11(x_1)) = x_1
22.66/11.08	   POL(*top*_12(x_1)) = x_1
22.66/11.08	   POL(*top*_13(x_1)) = x_1
22.66/11.08	   POL(*top*_14(x_1)) = x_1
22.66/11.08	   POL(*top*_15(x_1)) = x_1
22.66/11.08	   POL(*top*_16(x_1)) = x_1
22.66/11.08	   POL(*top*_17(x_1)) = x_1
22.66/11.08	   POL(*top*_18(x_1)) = x_1
22.66/11.08	   POL(*top*_19(x_1)) = x_1
22.66/11.08	   POL(*top*_2(x_1)) = 1 + x_1
22.66/11.08	   POL(*top*_20(x_1)) = x_1
22.66/11.08	   POL(*top*_21(x_1)) = x_1
22.66/11.08	   POL(*top*_22(x_1)) = x_1
22.66/11.08	   POL(*top*_23(x_1)) = x_1
22.66/11.08	   POL(*top*_24(x_1)) = x_1
22.66/11.08	   POL(*top*_25(x_1)) = x_1
22.66/11.08	   POL(*top*_26(x_1)) = x_1
22.66/11.08	   POL(*top*_27(x_1)) = x_1
22.66/11.08	   POL(*top*_28(x_1)) = x_1
22.66/11.08	   POL(*top*_29(x_1)) = x_1
22.66/11.08	   POL(*top*_3(x_1)) = x_1
22.66/11.08	   POL(*top*_30(x_1)) = x_1
22.66/11.08	   POL(*top*_4(x_1)) = x_1
22.66/11.08	   POL(*top*_5(x_1)) = x_1
22.66/11.08	   POL(*top*_6(x_1)) = x_1
22.66/11.08	   POL(*top*_7(x_1)) = x_1
22.66/11.08	   POL(*top*_8(x_1)) = x_1
22.66/11.08	   POL(*top*_9(x_1)) = x_1
22.66/11.08	   POL(a_31) = 0
22.66/11.08	   POL(c_32) = 0
22.66/11.08	   POL(f_33(x_1)) = x_1
22.66/11.08	   POL(f_34(x_1)) = x_1
22.66/11.08	   POL(f_35(x_1)) = x_1
22.66/11.08	   POL(f_36(x_1)) = x_1
22.66/11.08	   POL(f_37(x_1)) = x_1
22.66/11.08	   POL(f_38(x_1)) = x_1
22.66/11.08	   POL(f_39(x_1)) = x_1
22.66/11.08	   POL(f_40(x_1)) = x_1
22.66/11.08	   POL(f_41(x_1)) = x_1
22.66/11.08	   POL(f_42(x_1)) = x_1
22.66/11.08	   POL(f_43(x_1)) = x_1
22.66/11.08	   POL(f_44(x_1)) = x_1
22.66/11.08	   POL(f_45(x_1)) = x_1
22.66/11.08	   POL(f_46(x_1)) = x_1
22.66/11.08	   POL(f_47(x_1)) = x_1
22.66/11.08	   POL(f_48(x_1)) = x_1
22.66/11.08	   POL(f_49(x_1)) = x_1
22.66/11.08	   POL(f_50(x_1)) = x_1
22.66/11.08	   POL(f_51(x_1)) = x_1
22.66/11.08	   POL(f_52(x_1)) = x_1
22.66/11.08	   POL(f_53(x_1)) = x_1
22.66/11.08	   POL(f_54(x_1)) = x_1
22.66/11.08	   POL(f_55(x_1)) = x_1
22.66/11.08	   POL(f_56(x_1)) = x_1
22.66/11.08	   POL(f_57(x_1)) = x_1
22.66/11.08	   POL(f_58(x_1)) = x_1
22.66/11.08	   POL(f_59(x_1)) = x_1
22.66/11.08	   POL(f_60(x_1)) = x_1
22.66/11.08	   POL(f_61(x_1)) = x_1
22.66/11.08	   POL(f_62(x_1)) = 1 + x_1
22.66/11.08	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
22.66/11.08	
22.66/11.08	   *top*_1(f_34(a_31)) -> *top*_3(f_33(f_34(a_31)))
22.66/11.08	   *top*_30(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(f_56(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(f_57(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(f_58(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(f_59(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(f_60(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_61(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	   *top*_30(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(f_62(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	
22.66/11.08	
22.66/11.08	
22.66/11.08	
22.66/11.08	----------------------------------------
22.66/11.08	
22.66/11.08	(4)
22.66/11.08	Obligation:
22.66/11.08	Context-sensitive rewrite system:
22.66/11.08	The TRS R consists of the following rules:
22.66/11.08	
22.66/11.08	   *top*_2(a_31) -> *top*_1(f_34(a_31))
22.66/11.08	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.66/11.08	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.66/11.08	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.66/11.08	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.66/11.08	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.66/11.08	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.66/11.08	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.66/11.08	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.66/11.08	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.66/11.08	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.66/11.08	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.66/11.08	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.66/11.08	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.66/11.08	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.66/11.08	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.66/11.08	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.66/11.08	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.66/11.08	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.66/11.08	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.66/11.08	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.66/11.08	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.66/11.08	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.66/11.08	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.66/11.08	   *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))) -> *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))
22.66/11.08	   *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))) -> *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))
22.66/11.08	   *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))) -> *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))))
22.66/11.08	   *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))) -> *top*_30(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))))
22.66/11.08	   *top*_30(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.66/11.08	
22.66/11.08	The replacement map contains the following entries:
22.66/11.08	
22.66/11.08	*top*_2: {1}
22.66/11.08	a_31: empty set
22.66/11.08	*top*_1: {1}
22.66/11.08	f_34: {1}
22.66/11.08	*top*_3: {1}
22.66/11.08	f_33: {1}
22.66/11.08	*top*_4: {1}
22.66/11.08	f_35: {1}
22.66/11.08	*top*_5: {1}
22.66/11.08	f_36: {1}
22.66/11.08	*top*_6: {1}
22.66/11.08	f_37: {1}
22.66/11.08	*top*_7: {1}
22.66/11.08	f_38: {1}
22.66/11.08	*top*_8: {1}
22.66/11.08	f_39: {1}
22.66/11.08	*top*_9: {1}
22.66/11.08	f_40: {1}
22.66/11.08	*top*_10: {1}
22.66/11.08	f_41: {1}
22.66/11.08	*top*_11: {1}
22.66/11.08	f_42: {1}
22.66/11.08	*top*_12: {1}
22.66/11.08	f_43: {1}
22.66/11.08	*top*_13: {1}
22.66/11.08	f_44: {1}
22.66/11.08	*top*_14: {1}
22.66/11.08	f_45: {1}
22.66/11.08	*top*_15: {1}
22.66/11.08	f_46: {1}
22.66/11.08	*top*_16: {1}
22.66/11.08	f_47: {1}
22.66/11.08	*top*_17: {1}
22.66/11.08	f_48: {1}
22.66/11.08	*top*_18: {1}
22.66/11.08	f_49: {1}
22.66/11.08	*top*_19: {1}
22.66/11.08	f_50: {1}
22.66/11.08	*top*_20: {1}
22.66/11.08	f_51: {1}
22.66/11.08	*top*_21: {1}
22.66/11.08	f_52: {1}
22.66/11.08	*top*_22: {1}
22.66/11.08	f_53: {1}
22.66/11.08	*top*_23: {1}
22.66/11.08	f_54: {1}
22.66/11.08	*top*_24: {1}
22.66/11.08	f_55: {1}
22.66/11.08	*top*_25: {1}
22.66/11.08	f_56: {1}
22.66/11.08	*top*_26: {1}
22.66/11.08	f_57: {1}
22.66/11.08	*top*_27: {1}
22.66/11.08	f_58: {1}
22.66/11.08	*top*_28: {1}
22.66/11.08	f_59: {1}
22.66/11.08	*top*_29: {1}
22.66/11.08	f_60: {1}
22.66/11.08	*top*_30: {1}
22.66/11.08	f_61: {1}
22.66/11.08	f_62: empty set
22.66/11.08	c_32: empty set
22.66/11.08	
22.66/11.08	----------------------------------------
22.66/11.08	
22.66/11.08	(5) CSRRRRProof (EQUIVALENT)
22.66/11.08	The following CSR is given: Context-sensitive rewrite system:
22.66/11.08	The TRS R consists of the following rules:
22.66/11.08	
22.66/11.08	   *top*_2(a_31) -> *top*_1(f_34(a_31))
22.66/11.08	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.66/11.08	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.66/11.08	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.66/11.08	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.09	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.09	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.09	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.09	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.09	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.09	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.09	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.09	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.09	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.09	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.09	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.09	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.09	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.09	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.09	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.09	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.09	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.97/11.09	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.97/11.09	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.97/11.09	   *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))) -> *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))
22.97/11.09	   *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))) -> *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))
22.97/11.09	   *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))) -> *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))))
22.97/11.09	   *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))) -> *top*_30(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))))
22.97/11.09	   *top*_30(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.97/11.09	
22.97/11.09	The replacement map contains the following entries:
22.97/11.09	
22.97/11.09	*top*_2: {1}
22.97/11.09	a_31: empty set
22.97/11.09	*top*_1: {1}
22.97/11.09	f_34: {1}
22.97/11.09	*top*_3: {1}
22.97/11.09	f_33: {1}
22.97/11.09	*top*_4: {1}
22.97/11.09	f_35: {1}
22.97/11.09	*top*_5: {1}
22.97/11.09	f_36: {1}
22.97/11.09	*top*_6: {1}
22.97/11.09	f_37: {1}
22.97/11.09	*top*_7: {1}
22.97/11.09	f_38: {1}
22.97/11.09	*top*_8: {1}
22.97/11.09	f_39: {1}
22.97/11.09	*top*_9: {1}
22.97/11.09	f_40: {1}
22.97/11.09	*top*_10: {1}
22.97/11.09	f_41: {1}
22.97/11.09	*top*_11: {1}
22.97/11.09	f_42: {1}
22.97/11.09	*top*_12: {1}
22.97/11.09	f_43: {1}
22.97/11.09	*top*_13: {1}
22.97/11.09	f_44: {1}
22.97/11.09	*top*_14: {1}
22.97/11.09	f_45: {1}
22.97/11.09	*top*_15: {1}
22.97/11.09	f_46: {1}
22.97/11.09	*top*_16: {1}
22.97/11.09	f_47: {1}
22.97/11.09	*top*_17: {1}
22.97/11.09	f_48: {1}
22.97/11.09	*top*_18: {1}
22.97/11.09	f_49: {1}
22.97/11.09	*top*_19: {1}
22.97/11.09	f_50: {1}
22.97/11.09	*top*_20: {1}
22.97/11.09	f_51: {1}
22.97/11.09	*top*_21: {1}
22.97/11.09	f_52: {1}
22.97/11.09	*top*_22: {1}
22.97/11.09	f_53: {1}
22.97/11.09	*top*_23: {1}
22.97/11.09	f_54: {1}
22.97/11.09	*top*_24: {1}
22.97/11.09	f_55: {1}
22.97/11.09	*top*_25: {1}
22.97/11.09	f_56: {1}
22.97/11.09	*top*_26: {1}
22.97/11.09	f_57: {1}
22.97/11.09	*top*_27: {1}
22.97/11.09	f_58: {1}
22.97/11.09	*top*_28: {1}
22.97/11.09	f_59: {1}
22.97/11.09	*top*_29: {1}
22.97/11.09	f_60: {1}
22.97/11.09	*top*_30: {1}
22.97/11.09	f_61: {1}
22.97/11.09	f_62: empty set
22.97/11.09	c_32: empty set
22.97/11.09	Used ordering:
22.97/11.09	Polynomial interpretation [POLO]:
22.97/11.09	
22.97/11.09	   POL(*top*_1(x_1)) = x_1
22.97/11.09	   POL(*top*_10(x_1)) = x_1
22.97/11.09	   POL(*top*_11(x_1)) = x_1
22.97/11.09	   POL(*top*_12(x_1)) = x_1
22.97/11.09	   POL(*top*_13(x_1)) = x_1
22.97/11.09	   POL(*top*_14(x_1)) = x_1
22.97/11.09	   POL(*top*_15(x_1)) = x_1
22.97/11.09	   POL(*top*_16(x_1)) = x_1
22.97/11.09	   POL(*top*_17(x_1)) = x_1
22.97/11.09	   POL(*top*_18(x_1)) = x_1
22.97/11.09	   POL(*top*_19(x_1)) = x_1
22.97/11.09	   POL(*top*_2(x_1)) = x_1
22.97/11.09	   POL(*top*_20(x_1)) = x_1
22.97/11.09	   POL(*top*_21(x_1)) = x_1
22.97/11.09	   POL(*top*_22(x_1)) = x_1
22.97/11.09	   POL(*top*_23(x_1)) = x_1
22.97/11.09	   POL(*top*_24(x_1)) = x_1
22.97/11.09	   POL(*top*_25(x_1)) = x_1
22.97/11.09	   POL(*top*_26(x_1)) = x_1
22.97/11.09	   POL(*top*_27(x_1)) = x_1
22.97/11.09	   POL(*top*_28(x_1)) = x_1
22.97/11.09	   POL(*top*_29(x_1)) = x_1
22.97/11.09	   POL(*top*_3(x_1)) = x_1
22.97/11.09	   POL(*top*_30(x_1)) = x_1
22.97/11.09	   POL(*top*_4(x_1)) = x_1
22.97/11.09	   POL(*top*_5(x_1)) = x_1
22.97/11.09	   POL(*top*_6(x_1)) = x_1
22.97/11.09	   POL(*top*_7(x_1)) = x_1
22.97/11.09	   POL(*top*_8(x_1)) = x_1
22.97/11.09	   POL(*top*_9(x_1)) = x_1
22.97/11.09	   POL(a_31) = 0
22.97/11.09	   POL(c_32) = 0
22.97/11.09	   POL(f_33(x_1)) = 1 + x_1
22.97/11.09	   POL(f_34(x_1)) = x_1
22.97/11.09	   POL(f_35(x_1)) = x_1
22.97/11.09	   POL(f_36(x_1)) = x_1
22.97/11.09	   POL(f_37(x_1)) = x_1
22.97/11.09	   POL(f_38(x_1)) = x_1
22.97/11.09	   POL(f_39(x_1)) = x_1
22.97/11.09	   POL(f_40(x_1)) = x_1
22.97/11.09	   POL(f_41(x_1)) = x_1
22.97/11.09	   POL(f_42(x_1)) = x_1
22.97/11.09	   POL(f_43(x_1)) = x_1
22.97/11.09	   POL(f_44(x_1)) = x_1
22.97/11.09	   POL(f_45(x_1)) = x_1
22.97/11.09	   POL(f_46(x_1)) = x_1
22.97/11.09	   POL(f_47(x_1)) = x_1
22.97/11.09	   POL(f_48(x_1)) = x_1
22.97/11.09	   POL(f_49(x_1)) = x_1
22.97/11.09	   POL(f_50(x_1)) = x_1
22.97/11.09	   POL(f_51(x_1)) = x_1
22.97/11.09	   POL(f_52(x_1)) = x_1
22.97/11.09	   POL(f_53(x_1)) = x_1
22.97/11.09	   POL(f_54(x_1)) = x_1
22.97/11.09	   POL(f_55(x_1)) = x_1
22.97/11.09	   POL(f_56(x_1)) = x_1
22.97/11.09	   POL(f_57(x_1)) = x_1
22.97/11.09	   POL(f_58(x_1)) = x_1
22.97/11.09	   POL(f_59(x_1)) = x_1
22.97/11.09	   POL(f_60(x_1)) = x_1
22.97/11.09	   POL(f_61(x_1)) = x_1
22.97/11.09	   POL(f_62(x_1)) = x_1
22.97/11.09	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
22.97/11.09	
22.97/11.09	   *top*_30(f_62(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(x))))))))))))))))))))))))))))))) -> *top*_2(c_32)
22.97/11.09	
22.97/11.09	
22.97/11.09	
22.97/11.09	
22.97/11.09	----------------------------------------
22.97/11.09	
22.97/11.09	(6)
22.97/11.09	Obligation:
22.97/11.09	Context-sensitive rewrite system:
22.97/11.09	The TRS R consists of the following rules:
22.97/11.09	
22.97/11.09	   *top*_2(a_31) -> *top*_1(f_34(a_31))
22.97/11.09	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.09	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.09	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.09	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.09	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.09	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.09	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.09	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.09	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.09	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.09	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.09	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.09	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.09	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.09	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.09	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.09	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.09	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.09	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.09	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.09	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.97/11.09	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.97/11.09	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.97/11.09	   *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))) -> *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))
22.97/11.09	   *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))) -> *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))
22.97/11.09	   *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))) -> *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))))
22.97/11.09	   *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))) -> *top*_30(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))))
22.97/11.09	
22.97/11.09	The replacement map contains the following entries:
22.97/11.09	
22.97/11.09	*top*_2: {1}
22.97/11.09	a_31: empty set
22.97/11.09	*top*_1: {1}
22.97/11.09	f_34: {1}
22.97/11.09	*top*_3: {1}
22.97/11.09	f_33: {1}
22.97/11.09	*top*_4: {1}
22.97/11.09	f_35: {1}
22.97/11.09	*top*_5: {1}
22.97/11.09	f_36: {1}
22.97/11.09	*top*_6: {1}
22.97/11.09	f_37: {1}
22.97/11.09	*top*_7: {1}
22.97/11.09	f_38: {1}
22.97/11.09	*top*_8: {1}
22.97/11.09	f_39: {1}
22.97/11.09	*top*_9: {1}
22.97/11.09	f_40: {1}
22.97/11.09	*top*_10: {1}
22.97/11.09	f_41: {1}
22.97/11.09	*top*_11: {1}
22.97/11.09	f_42: {1}
22.97/11.09	*top*_12: {1}
22.97/11.09	f_43: {1}
22.97/11.09	*top*_13: {1}
22.97/11.09	f_44: {1}
22.97/11.09	*top*_14: {1}
22.97/11.09	f_45: {1}
22.97/11.09	*top*_15: {1}
22.97/11.09	f_46: {1}
22.97/11.09	*top*_16: {1}
22.97/11.09	f_47: {1}
22.97/11.09	*top*_17: {1}
22.97/11.09	f_48: {1}
22.97/11.09	*top*_18: {1}
22.97/11.09	f_49: {1}
22.97/11.09	*top*_19: {1}
22.97/11.09	f_50: {1}
22.97/11.09	*top*_20: {1}
22.97/11.09	f_51: {1}
22.97/11.09	*top*_21: {1}
22.97/11.09	f_52: {1}
22.97/11.09	*top*_22: {1}
22.97/11.09	f_53: {1}
22.97/11.09	*top*_23: {1}
22.97/11.09	f_54: {1}
22.97/11.09	*top*_24: {1}
22.97/11.09	f_55: {1}
22.97/11.09	*top*_25: {1}
22.97/11.09	f_56: {1}
22.97/11.09	*top*_26: {1}
22.97/11.09	f_57: {1}
22.97/11.09	*top*_27: {1}
22.97/11.09	f_58: {1}
22.97/11.09	*top*_28: {1}
22.97/11.09	f_59: {1}
22.97/11.09	*top*_29: {1}
22.97/11.09	f_60: {1}
22.97/11.09	*top*_30: {1}
22.97/11.09	f_61: {1}
22.97/11.09	
22.97/11.09	----------------------------------------
22.97/11.09	
22.97/11.09	(7) CSRRRRProof (EQUIVALENT)
22.97/11.09	The following CSR is given: Context-sensitive rewrite system:
22.97/11.09	The TRS R consists of the following rules:
22.97/11.09	
22.97/11.09	   *top*_2(a_31) -> *top*_1(f_34(a_31))
22.97/11.09	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.09	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.09	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.09	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.09	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.09	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.09	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.09	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.09	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.09	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.09	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.09	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.09	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.09	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.09	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.09	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.09	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.09	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.09	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.09	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.09	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.97/11.09	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.97/11.09	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.97/11.09	   *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))) -> *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))
22.97/11.09	   *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))) -> *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))
22.97/11.09	   *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))) -> *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))))
22.97/11.09	   *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))) -> *top*_30(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))))
22.97/11.09	
22.97/11.09	The replacement map contains the following entries:
22.97/11.09	
22.97/11.09	*top*_2: {1}
22.97/11.09	a_31: empty set
22.97/11.09	*top*_1: {1}
22.97/11.09	f_34: {1}
22.97/11.09	*top*_3: {1}
22.97/11.09	f_33: {1}
22.97/11.09	*top*_4: {1}
22.97/11.09	f_35: {1}
22.97/11.09	*top*_5: {1}
22.97/11.09	f_36: {1}
22.97/11.09	*top*_6: {1}
22.97/11.09	f_37: {1}
22.97/11.09	*top*_7: {1}
22.97/11.09	f_38: {1}
22.97/11.09	*top*_8: {1}
22.97/11.09	f_39: {1}
22.97/11.09	*top*_9: {1}
22.97/11.09	f_40: {1}
22.97/11.09	*top*_10: {1}
22.97/11.09	f_41: {1}
22.97/11.09	*top*_11: {1}
22.97/11.09	f_42: {1}
22.97/11.09	*top*_12: {1}
22.97/11.09	f_43: {1}
22.97/11.09	*top*_13: {1}
22.97/11.09	f_44: {1}
22.97/11.09	*top*_14: {1}
22.97/11.09	f_45: {1}
22.97/11.09	*top*_15: {1}
22.97/11.09	f_46: {1}
22.97/11.09	*top*_16: {1}
22.97/11.09	f_47: {1}
22.97/11.09	*top*_17: {1}
22.97/11.09	f_48: {1}
22.97/11.09	*top*_18: {1}
22.97/11.09	f_49: {1}
22.97/11.09	*top*_19: {1}
22.97/11.09	f_50: {1}
22.97/11.09	*top*_20: {1}
22.97/11.09	f_51: {1}
22.97/11.09	*top*_21: {1}
22.97/11.09	f_52: {1}
22.97/11.09	*top*_22: {1}
22.97/11.09	f_53: {1}
22.97/11.09	*top*_23: {1}
22.97/11.09	f_54: {1}
22.97/11.09	*top*_24: {1}
22.97/11.09	f_55: {1}
22.97/11.09	*top*_25: {1}
22.97/11.09	f_56: {1}
22.97/11.09	*top*_26: {1}
22.97/11.09	f_57: {1}
22.97/11.09	*top*_27: {1}
22.97/11.09	f_58: {1}
22.97/11.09	*top*_28: {1}
22.97/11.09	f_59: {1}
22.97/11.09	*top*_29: {1}
22.97/11.09	f_60: {1}
22.97/11.09	*top*_30: {1}
22.97/11.09	f_61: {1}
22.97/11.09	Used ordering:
22.97/11.09	Polynomial interpretation [POLO]:
22.97/11.09	
22.97/11.09	   POL(*top*_1(x_1)) = x_1
22.97/11.09	   POL(*top*_10(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_11(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_12(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_13(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_14(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_15(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_16(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_17(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_18(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_19(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_2(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_20(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_21(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_22(x_1)) = x_1
22.97/11.09	   POL(*top*_23(x_1)) = x_1
22.97/11.09	   POL(*top*_24(x_1)) = x_1
22.97/11.09	   POL(*top*_25(x_1)) = x_1
22.97/11.09	   POL(*top*_26(x_1)) = x_1
22.97/11.09	   POL(*top*_27(x_1)) = x_1
22.97/11.09	   POL(*top*_28(x_1)) = x_1
22.97/11.09	   POL(*top*_29(x_1)) = x_1
22.97/11.09	   POL(*top*_3(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_30(x_1)) = x_1
22.97/11.09	   POL(*top*_4(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_5(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_6(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_7(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_8(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_9(x_1)) = 1 + x_1
22.97/11.09	   POL(a_31) = 0
22.97/11.09	   POL(f_33(x_1)) = x_1
22.97/11.09	   POL(f_34(x_1)) = x_1
22.97/11.09	   POL(f_35(x_1)) = x_1
22.97/11.09	   POL(f_36(x_1)) = x_1
22.97/11.09	   POL(f_37(x_1)) = x_1
22.97/11.09	   POL(f_38(x_1)) = x_1
22.97/11.09	   POL(f_39(x_1)) = x_1
22.97/11.09	   POL(f_40(x_1)) = x_1
22.97/11.09	   POL(f_41(x_1)) = x_1
22.97/11.09	   POL(f_42(x_1)) = x_1
22.97/11.09	   POL(f_43(x_1)) = x_1
22.97/11.09	   POL(f_44(x_1)) = x_1
22.97/11.09	   POL(f_45(x_1)) = x_1
22.97/11.09	   POL(f_46(x_1)) = x_1
22.97/11.09	   POL(f_47(x_1)) = x_1
22.97/11.09	   POL(f_48(x_1)) = x_1
22.97/11.09	   POL(f_49(x_1)) = x_1
22.97/11.09	   POL(f_50(x_1)) = x_1
22.97/11.09	   POL(f_51(x_1)) = x_1
22.97/11.09	   POL(f_52(x_1)) = x_1
22.97/11.09	   POL(f_53(x_1)) = 1 + x_1
22.97/11.09	   POL(f_54(x_1)) = x_1
22.97/11.09	   POL(f_55(x_1)) = x_1
22.97/11.09	   POL(f_56(x_1)) = x_1
22.97/11.09	   POL(f_57(x_1)) = x_1
22.97/11.09	   POL(f_58(x_1)) = x_1
22.97/11.09	   POL(f_59(x_1)) = x_1
22.97/11.09	   POL(f_60(x_1)) = x_1
22.97/11.09	   POL(f_61(x_1)) = x_1
22.97/11.09	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
22.97/11.09	
22.97/11.09	   *top*_2(a_31) -> *top*_1(f_34(a_31))
22.97/11.09	
22.97/11.09	
22.97/11.09	
22.97/11.09	
22.97/11.09	----------------------------------------
22.97/11.09	
22.97/11.09	(8)
22.97/11.09	Obligation:
22.97/11.09	Context-sensitive rewrite system:
22.97/11.09	The TRS R consists of the following rules:
22.97/11.09	
22.97/11.09	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.09	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.09	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.09	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.09	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.09	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.09	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.09	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.09	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.09	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.09	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.09	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.09	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.09	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.09	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.09	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.09	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.09	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.09	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.09	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.09	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.97/11.09	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.97/11.09	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.97/11.09	   *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))) -> *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))
22.97/11.09	   *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))) -> *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))
22.97/11.09	   *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))) -> *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))))
22.97/11.09	   *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))) -> *top*_30(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))))
22.97/11.09	
22.97/11.09	The replacement map contains the following entries:
22.97/11.09	
22.97/11.09	a_31: empty set
22.97/11.09	f_34: {1}
22.97/11.09	*top*_3: {1}
22.97/11.09	f_33: {1}
22.97/11.09	*top*_4: {1}
22.97/11.09	f_35: {1}
22.97/11.09	*top*_5: {1}
22.97/11.09	f_36: {1}
22.97/11.09	*top*_6: {1}
22.97/11.09	f_37: {1}
22.97/11.09	*top*_7: {1}
22.97/11.09	f_38: {1}
22.97/11.09	*top*_8: {1}
22.97/11.09	f_39: {1}
22.97/11.09	*top*_9: {1}
22.97/11.09	f_40: {1}
22.97/11.09	*top*_10: {1}
22.97/11.09	f_41: {1}
22.97/11.09	*top*_11: {1}
22.97/11.09	f_42: {1}
22.97/11.09	*top*_12: {1}
22.97/11.09	f_43: {1}
22.97/11.09	*top*_13: {1}
22.97/11.09	f_44: {1}
22.97/11.09	*top*_14: {1}
22.97/11.09	f_45: {1}
22.97/11.09	*top*_15: {1}
22.97/11.09	f_46: {1}
22.97/11.09	*top*_16: {1}
22.97/11.09	f_47: {1}
22.97/11.09	*top*_17: {1}
22.97/11.09	f_48: {1}
22.97/11.09	*top*_18: {1}
22.97/11.09	f_49: {1}
22.97/11.09	*top*_19: {1}
22.97/11.09	f_50: {1}
22.97/11.09	*top*_20: {1}
22.97/11.09	f_51: {1}
22.97/11.09	*top*_21: {1}
22.97/11.09	f_52: {1}
22.97/11.09	*top*_22: {1}
22.97/11.09	f_53: {1}
22.97/11.09	*top*_23: {1}
22.97/11.09	f_54: {1}
22.97/11.09	*top*_24: {1}
22.97/11.09	f_55: {1}
22.97/11.09	*top*_25: {1}
22.97/11.09	f_56: {1}
22.97/11.09	*top*_26: {1}
22.97/11.09	f_57: {1}
22.97/11.09	*top*_27: {1}
22.97/11.09	f_58: {1}
22.97/11.09	*top*_28: {1}
22.97/11.09	f_59: {1}
22.97/11.09	*top*_29: {1}
22.97/11.09	f_60: {1}
22.97/11.09	*top*_30: {1}
22.97/11.09	f_61: {1}
22.97/11.09	
22.97/11.09	----------------------------------------
22.97/11.09	
22.97/11.09	(9) CSRRRRProof (EQUIVALENT)
22.97/11.09	The following CSR is given: Context-sensitive rewrite system:
22.97/11.09	The TRS R consists of the following rules:
22.97/11.09	
22.97/11.09	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.09	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.09	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.09	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.09	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.09	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.09	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.09	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.09	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.09	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.09	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.09	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.09	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.09	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.09	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.09	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.09	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.09	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.09	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.09	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.09	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.97/11.09	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.97/11.09	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.97/11.09	   *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))) -> *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))
22.97/11.09	   *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))) -> *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))
22.97/11.09	   *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))) -> *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))))
22.97/11.09	   *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))) -> *top*_30(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))))
22.97/11.09	
22.97/11.09	The replacement map contains the following entries:
22.97/11.09	
22.97/11.09	a_31: empty set
22.97/11.09	f_34: {1}
22.97/11.09	*top*_3: {1}
22.97/11.09	f_33: {1}
22.97/11.09	*top*_4: {1}
22.97/11.09	f_35: {1}
22.97/11.09	*top*_5: {1}
22.97/11.09	f_36: {1}
22.97/11.09	*top*_6: {1}
22.97/11.09	f_37: {1}
22.97/11.09	*top*_7: {1}
22.97/11.09	f_38: {1}
22.97/11.09	*top*_8: {1}
22.97/11.09	f_39: {1}
22.97/11.09	*top*_9: {1}
22.97/11.09	f_40: {1}
22.97/11.09	*top*_10: {1}
22.97/11.09	f_41: {1}
22.97/11.09	*top*_11: {1}
22.97/11.09	f_42: {1}
22.97/11.09	*top*_12: {1}
22.97/11.09	f_43: {1}
22.97/11.09	*top*_13: {1}
22.97/11.09	f_44: {1}
22.97/11.09	*top*_14: {1}
22.97/11.09	f_45: {1}
22.97/11.09	*top*_15: {1}
22.97/11.09	f_46: {1}
22.97/11.09	*top*_16: {1}
22.97/11.09	f_47: {1}
22.97/11.09	*top*_17: {1}
22.97/11.09	f_48: {1}
22.97/11.09	*top*_18: {1}
22.97/11.09	f_49: {1}
22.97/11.09	*top*_19: {1}
22.97/11.09	f_50: {1}
22.97/11.09	*top*_20: {1}
22.97/11.09	f_51: {1}
22.97/11.09	*top*_21: {1}
22.97/11.09	f_52: {1}
22.97/11.09	*top*_22: {1}
22.97/11.09	f_53: {1}
22.97/11.09	*top*_23: {1}
22.97/11.09	f_54: {1}
22.97/11.09	*top*_24: {1}
22.97/11.09	f_55: {1}
22.97/11.09	*top*_25: {1}
22.97/11.09	f_56: {1}
22.97/11.09	*top*_26: {1}
22.97/11.09	f_57: {1}
22.97/11.09	*top*_27: {1}
22.97/11.09	f_58: {1}
22.97/11.09	*top*_28: {1}
22.97/11.09	f_59: {1}
22.97/11.09	*top*_29: {1}
22.97/11.09	f_60: {1}
22.97/11.09	*top*_30: {1}
22.97/11.09	f_61: {1}
22.97/11.09	Used ordering:
22.97/11.09	Polynomial interpretation [POLO]:
22.97/11.09	
22.97/11.09	   POL(*top*_10(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_11(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_12(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_13(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_14(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_15(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_16(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_17(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_18(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_19(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_20(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_21(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_22(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_23(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_24(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_25(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_26(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_27(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_28(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_29(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_3(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_30(x_1)) = x_1
22.97/11.09	   POL(*top*_4(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_5(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_6(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_7(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_8(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_9(x_1)) = 1 + x_1
22.97/11.09	   POL(a_31) = 0
22.97/11.09	   POL(f_33(x_1)) = x_1
22.97/11.09	   POL(f_34(x_1)) = x_1
22.97/11.09	   POL(f_35(x_1)) = x_1
22.97/11.09	   POL(f_36(x_1)) = x_1
22.97/11.09	   POL(f_37(x_1)) = x_1
22.97/11.09	   POL(f_38(x_1)) = x_1
22.97/11.09	   POL(f_39(x_1)) = x_1
22.97/11.09	   POL(f_40(x_1)) = x_1
22.97/11.09	   POL(f_41(x_1)) = x_1
22.97/11.09	   POL(f_42(x_1)) = x_1
22.97/11.09	   POL(f_43(x_1)) = x_1
22.97/11.09	   POL(f_44(x_1)) = x_1
22.97/11.09	   POL(f_45(x_1)) = x_1
22.97/11.09	   POL(f_46(x_1)) = x_1
22.97/11.09	   POL(f_47(x_1)) = x_1
22.97/11.09	   POL(f_48(x_1)) = x_1
22.97/11.09	   POL(f_49(x_1)) = x_1
22.97/11.09	   POL(f_50(x_1)) = x_1
22.97/11.09	   POL(f_51(x_1)) = x_1
22.97/11.09	   POL(f_52(x_1)) = x_1
22.97/11.09	   POL(f_53(x_1)) = x_1
22.97/11.09	   POL(f_54(x_1)) = x_1
22.97/11.09	   POL(f_55(x_1)) = x_1
22.97/11.09	   POL(f_56(x_1)) = x_1
22.97/11.09	   POL(f_57(x_1)) = x_1
22.97/11.09	   POL(f_58(x_1)) = x_1
22.97/11.09	   POL(f_59(x_1)) = x_1
22.97/11.09	   POL(f_60(x_1)) = x_1
22.97/11.09	   POL(f_61(x_1)) = x_1
22.97/11.09	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
22.97/11.09	
22.97/11.09	   *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))) -> *top*_30(f_61(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))))
22.97/11.09	
22.97/11.09	
22.97/11.09	
22.97/11.09	
22.97/11.09	----------------------------------------
22.97/11.09	
22.97/11.09	(10)
22.97/11.09	Obligation:
22.97/11.09	Context-sensitive rewrite system:
22.97/11.09	The TRS R consists of the following rules:
22.97/11.09	
22.97/11.09	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.09	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.09	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.09	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.09	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.09	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.09	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.09	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.09	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.09	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.09	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.09	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.09	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.09	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.09	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.09	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.09	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.09	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.09	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.09	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.09	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.97/11.09	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.97/11.09	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.97/11.09	   *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))) -> *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))
22.97/11.09	   *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))) -> *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))
22.97/11.09	   *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))) -> *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))))
22.97/11.09	
22.97/11.09	The replacement map contains the following entries:
22.97/11.09	
22.97/11.09	a_31: empty set
22.97/11.09	f_34: {1}
22.97/11.09	*top*_3: {1}
22.97/11.09	f_33: {1}
22.97/11.09	*top*_4: {1}
22.97/11.09	f_35: {1}
22.97/11.09	*top*_5: {1}
22.97/11.09	f_36: {1}
22.97/11.09	*top*_6: {1}
22.97/11.09	f_37: {1}
22.97/11.09	*top*_7: {1}
22.97/11.09	f_38: {1}
22.97/11.09	*top*_8: {1}
22.97/11.09	f_39: {1}
22.97/11.09	*top*_9: {1}
22.97/11.09	f_40: {1}
22.97/11.09	*top*_10: {1}
22.97/11.09	f_41: {1}
22.97/11.09	*top*_11: {1}
22.97/11.09	f_42: {1}
22.97/11.09	*top*_12: {1}
22.97/11.09	f_43: {1}
22.97/11.09	*top*_13: {1}
22.97/11.09	f_44: {1}
22.97/11.09	*top*_14: {1}
22.97/11.09	f_45: {1}
22.97/11.09	*top*_15: {1}
22.97/11.09	f_46: {1}
22.97/11.09	*top*_16: {1}
22.97/11.09	f_47: {1}
22.97/11.09	*top*_17: {1}
22.97/11.09	f_48: {1}
22.97/11.09	*top*_18: {1}
22.97/11.09	f_49: {1}
22.97/11.09	*top*_19: {1}
22.97/11.09	f_50: {1}
22.97/11.09	*top*_20: {1}
22.97/11.09	f_51: {1}
22.97/11.09	*top*_21: {1}
22.97/11.09	f_52: {1}
22.97/11.09	*top*_22: {1}
22.97/11.09	f_53: {1}
22.97/11.09	*top*_23: {1}
22.97/11.09	f_54: {1}
22.97/11.09	*top*_24: {1}
22.97/11.09	f_55: {1}
22.97/11.09	*top*_25: {1}
22.97/11.09	f_56: {1}
22.97/11.09	*top*_26: {1}
22.97/11.09	f_57: {1}
22.97/11.09	*top*_27: {1}
22.97/11.09	f_58: {1}
22.97/11.09	*top*_28: {1}
22.97/11.09	f_59: {1}
22.97/11.09	*top*_29: {1}
22.97/11.09	f_60: {1}
22.97/11.09	
22.97/11.09	----------------------------------------
22.97/11.09	
22.97/11.09	(11) CSRRRRProof (EQUIVALENT)
22.97/11.09	The following CSR is given: Context-sensitive rewrite system:
22.97/11.09	The TRS R consists of the following rules:
22.97/11.09	
22.97/11.09	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.09	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.09	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.09	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.09	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.09	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.09	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.09	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.09	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.09	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.09	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.09	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.09	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.09	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.09	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.09	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.09	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.09	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.09	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.09	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.09	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.97/11.09	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.97/11.09	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.97/11.09	   *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))) -> *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))
22.97/11.09	   *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))) -> *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))
22.97/11.09	   *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))) -> *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))))
22.97/11.09	
22.97/11.09	The replacement map contains the following entries:
22.97/11.09	
22.97/11.09	a_31: empty set
22.97/11.09	f_34: {1}
22.97/11.09	*top*_3: {1}
22.97/11.09	f_33: {1}
22.97/11.09	*top*_4: {1}
22.97/11.09	f_35: {1}
22.97/11.09	*top*_5: {1}
22.97/11.09	f_36: {1}
22.97/11.09	*top*_6: {1}
22.97/11.09	f_37: {1}
22.97/11.09	*top*_7: {1}
22.97/11.09	f_38: {1}
22.97/11.09	*top*_8: {1}
22.97/11.09	f_39: {1}
22.97/11.09	*top*_9: {1}
22.97/11.09	f_40: {1}
22.97/11.09	*top*_10: {1}
22.97/11.09	f_41: {1}
22.97/11.09	*top*_11: {1}
22.97/11.09	f_42: {1}
22.97/11.09	*top*_12: {1}
22.97/11.09	f_43: {1}
22.97/11.09	*top*_13: {1}
22.97/11.09	f_44: {1}
22.97/11.09	*top*_14: {1}
22.97/11.09	f_45: {1}
22.97/11.09	*top*_15: {1}
22.97/11.09	f_46: {1}
22.97/11.09	*top*_16: {1}
22.97/11.09	f_47: {1}
22.97/11.09	*top*_17: {1}
22.97/11.09	f_48: {1}
22.97/11.09	*top*_18: {1}
22.97/11.09	f_49: {1}
22.97/11.09	*top*_19: {1}
22.97/11.09	f_50: {1}
22.97/11.09	*top*_20: {1}
22.97/11.09	f_51: {1}
22.97/11.09	*top*_21: {1}
22.97/11.09	f_52: {1}
22.97/11.09	*top*_22: {1}
22.97/11.09	f_53: {1}
22.97/11.09	*top*_23: {1}
22.97/11.09	f_54: {1}
22.97/11.09	*top*_24: {1}
22.97/11.09	f_55: {1}
22.97/11.09	*top*_25: {1}
22.97/11.09	f_56: {1}
22.97/11.09	*top*_26: {1}
22.97/11.09	f_57: {1}
22.97/11.09	*top*_27: {1}
22.97/11.09	f_58: {1}
22.97/11.09	*top*_28: {1}
22.97/11.09	f_59: {1}
22.97/11.09	*top*_29: {1}
22.97/11.09	f_60: {1}
22.97/11.09	Used ordering:
22.97/11.09	Polynomial interpretation [POLO]:
22.97/11.09	
22.97/11.09	   POL(*top*_10(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_11(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_12(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_13(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_14(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_15(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_16(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_17(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_18(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_19(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_20(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_21(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_22(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_23(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_24(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_25(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_26(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_27(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_28(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_29(x_1)) = x_1
22.97/11.09	   POL(*top*_3(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_4(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_5(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_6(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_7(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_8(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_9(x_1)) = 1 + x_1
22.97/11.09	   POL(a_31) = 0
22.97/11.09	   POL(f_33(x_1)) = x_1
22.97/11.09	   POL(f_34(x_1)) = x_1
22.97/11.09	   POL(f_35(x_1)) = x_1
22.97/11.09	   POL(f_36(x_1)) = x_1
22.97/11.09	   POL(f_37(x_1)) = x_1
22.97/11.09	   POL(f_38(x_1)) = x_1
22.97/11.09	   POL(f_39(x_1)) = x_1
22.97/11.09	   POL(f_40(x_1)) = x_1
22.97/11.09	   POL(f_41(x_1)) = x_1
22.97/11.09	   POL(f_42(x_1)) = x_1
22.97/11.09	   POL(f_43(x_1)) = x_1
22.97/11.09	   POL(f_44(x_1)) = x_1
22.97/11.09	   POL(f_45(x_1)) = x_1
22.97/11.09	   POL(f_46(x_1)) = x_1
22.97/11.09	   POL(f_47(x_1)) = x_1
22.97/11.09	   POL(f_48(x_1)) = x_1
22.97/11.09	   POL(f_49(x_1)) = x_1
22.97/11.09	   POL(f_50(x_1)) = x_1
22.97/11.09	   POL(f_51(x_1)) = x_1
22.97/11.09	   POL(f_52(x_1)) = x_1
22.97/11.09	   POL(f_53(x_1)) = x_1
22.97/11.09	   POL(f_54(x_1)) = x_1
22.97/11.09	   POL(f_55(x_1)) = x_1
22.97/11.09	   POL(f_56(x_1)) = x_1
22.97/11.09	   POL(f_57(x_1)) = x_1
22.97/11.09	   POL(f_58(x_1)) = x_1
22.97/11.09	   POL(f_59(x_1)) = x_1
22.97/11.09	   POL(f_60(x_1)) = x_1
22.97/11.09	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
22.97/11.09	
22.97/11.09	   *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))) -> *top*_29(f_60(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))))
22.97/11.09	
22.97/11.09	
22.97/11.09	
22.97/11.09	
22.97/11.09	----------------------------------------
22.97/11.09	
22.97/11.09	(12)
22.97/11.09	Obligation:
22.97/11.09	Context-sensitive rewrite system:
22.97/11.09	The TRS R consists of the following rules:
22.97/11.09	
22.97/11.09	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.09	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.09	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.09	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.09	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.09	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.09	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.09	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.09	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.09	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.09	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.09	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.09	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.09	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.09	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.09	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.09	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.09	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.09	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.09	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.09	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.97/11.09	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.97/11.09	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.97/11.09	   *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))) -> *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))
22.97/11.09	   *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))) -> *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))
22.97/11.09	
22.97/11.09	The replacement map contains the following entries:
22.97/11.09	
22.97/11.09	a_31: empty set
22.97/11.09	f_34: {1}
22.97/11.09	*top*_3: {1}
22.97/11.09	f_33: {1}
22.97/11.09	*top*_4: {1}
22.97/11.09	f_35: {1}
22.97/11.09	*top*_5: {1}
22.97/11.09	f_36: {1}
22.97/11.09	*top*_6: {1}
22.97/11.09	f_37: {1}
22.97/11.09	*top*_7: {1}
22.97/11.09	f_38: {1}
22.97/11.09	*top*_8: {1}
22.97/11.09	f_39: {1}
22.97/11.09	*top*_9: {1}
22.97/11.09	f_40: {1}
22.97/11.09	*top*_10: {1}
22.97/11.09	f_41: {1}
22.97/11.09	*top*_11: {1}
22.97/11.09	f_42: {1}
22.97/11.09	*top*_12: {1}
22.97/11.09	f_43: {1}
22.97/11.09	*top*_13: {1}
22.97/11.09	f_44: {1}
22.97/11.09	*top*_14: {1}
22.97/11.09	f_45: {1}
22.97/11.09	*top*_15: {1}
22.97/11.09	f_46: {1}
22.97/11.09	*top*_16: {1}
22.97/11.09	f_47: {1}
22.97/11.09	*top*_17: {1}
22.97/11.09	f_48: {1}
22.97/11.09	*top*_18: {1}
22.97/11.09	f_49: {1}
22.97/11.09	*top*_19: {1}
22.97/11.09	f_50: {1}
22.97/11.09	*top*_20: {1}
22.97/11.09	f_51: {1}
22.97/11.09	*top*_21: {1}
22.97/11.09	f_52: {1}
22.97/11.09	*top*_22: {1}
22.97/11.09	f_53: {1}
22.97/11.09	*top*_23: {1}
22.97/11.09	f_54: {1}
22.97/11.09	*top*_24: {1}
22.97/11.09	f_55: {1}
22.97/11.09	*top*_25: {1}
22.97/11.09	f_56: {1}
22.97/11.09	*top*_26: {1}
22.97/11.09	f_57: {1}
22.97/11.09	*top*_27: {1}
22.97/11.09	f_58: {1}
22.97/11.09	*top*_28: {1}
22.97/11.09	f_59: {1}
22.97/11.09	
22.97/11.09	----------------------------------------
22.97/11.09	
22.97/11.09	(13) CSRRRRProof (EQUIVALENT)
22.97/11.09	The following CSR is given: Context-sensitive rewrite system:
22.97/11.09	The TRS R consists of the following rules:
22.97/11.09	
22.97/11.09	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.09	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.09	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.09	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.09	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.09	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.09	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.09	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.09	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.09	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.09	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.09	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.09	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.09	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.09	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.09	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.09	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.09	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.09	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.09	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.09	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.97/11.09	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.97/11.09	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.97/11.09	   *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))) -> *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))
22.97/11.09	   *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))) -> *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))
22.97/11.09	
22.97/11.09	The replacement map contains the following entries:
22.97/11.09	
22.97/11.09	a_31: empty set
22.97/11.09	f_34: {1}
22.97/11.09	*top*_3: {1}
22.97/11.09	f_33: {1}
22.97/11.09	*top*_4: {1}
22.97/11.09	f_35: {1}
22.97/11.09	*top*_5: {1}
22.97/11.09	f_36: {1}
22.97/11.09	*top*_6: {1}
22.97/11.09	f_37: {1}
22.97/11.09	*top*_7: {1}
22.97/11.09	f_38: {1}
22.97/11.09	*top*_8: {1}
22.97/11.09	f_39: {1}
22.97/11.09	*top*_9: {1}
22.97/11.09	f_40: {1}
22.97/11.09	*top*_10: {1}
22.97/11.09	f_41: {1}
22.97/11.09	*top*_11: {1}
22.97/11.09	f_42: {1}
22.97/11.09	*top*_12: {1}
22.97/11.09	f_43: {1}
22.97/11.09	*top*_13: {1}
22.97/11.09	f_44: {1}
22.97/11.09	*top*_14: {1}
22.97/11.09	f_45: {1}
22.97/11.09	*top*_15: {1}
22.97/11.09	f_46: {1}
22.97/11.09	*top*_16: {1}
22.97/11.09	f_47: {1}
22.97/11.09	*top*_17: {1}
22.97/11.09	f_48: {1}
22.97/11.09	*top*_18: {1}
22.97/11.09	f_49: {1}
22.97/11.09	*top*_19: {1}
22.97/11.09	f_50: {1}
22.97/11.09	*top*_20: {1}
22.97/11.09	f_51: {1}
22.97/11.09	*top*_21: {1}
22.97/11.09	f_52: {1}
22.97/11.09	*top*_22: {1}
22.97/11.09	f_53: {1}
22.97/11.09	*top*_23: {1}
22.97/11.09	f_54: {1}
22.97/11.09	*top*_24: {1}
22.97/11.09	f_55: {1}
22.97/11.09	*top*_25: {1}
22.97/11.09	f_56: {1}
22.97/11.09	*top*_26: {1}
22.97/11.09	f_57: {1}
22.97/11.09	*top*_27: {1}
22.97/11.09	f_58: {1}
22.97/11.09	*top*_28: {1}
22.97/11.09	f_59: {1}
22.97/11.09	Used ordering:
22.97/11.09	Polynomial interpretation [POLO]:
22.97/11.09	
22.97/11.09	   POL(*top*_10(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_11(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_12(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_13(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_14(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_15(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_16(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_17(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_18(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_19(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_20(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_21(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_22(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_23(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_24(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_25(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_26(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_27(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_28(x_1)) = x_1
22.97/11.09	   POL(*top*_3(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_4(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_5(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_6(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_7(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_8(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_9(x_1)) = 1 + x_1
22.97/11.09	   POL(a_31) = 0
22.97/11.09	   POL(f_33(x_1)) = x_1
22.97/11.09	   POL(f_34(x_1)) = x_1
22.97/11.09	   POL(f_35(x_1)) = x_1
22.97/11.09	   POL(f_36(x_1)) = x_1
22.97/11.09	   POL(f_37(x_1)) = x_1
22.97/11.09	   POL(f_38(x_1)) = x_1
22.97/11.09	   POL(f_39(x_1)) = x_1
22.97/11.09	   POL(f_40(x_1)) = x_1
22.97/11.09	   POL(f_41(x_1)) = x_1
22.97/11.09	   POL(f_42(x_1)) = x_1
22.97/11.09	   POL(f_43(x_1)) = x_1
22.97/11.09	   POL(f_44(x_1)) = x_1
22.97/11.09	   POL(f_45(x_1)) = x_1
22.97/11.09	   POL(f_46(x_1)) = x_1
22.97/11.09	   POL(f_47(x_1)) = x_1
22.97/11.09	   POL(f_48(x_1)) = x_1
22.97/11.09	   POL(f_49(x_1)) = x_1
22.97/11.09	   POL(f_50(x_1)) = x_1
22.97/11.09	   POL(f_51(x_1)) = x_1
22.97/11.09	   POL(f_52(x_1)) = x_1
22.97/11.09	   POL(f_53(x_1)) = x_1
22.97/11.09	   POL(f_54(x_1)) = x_1
22.97/11.09	   POL(f_55(x_1)) = x_1
22.97/11.09	   POL(f_56(x_1)) = x_1
22.97/11.09	   POL(f_57(x_1)) = x_1
22.97/11.09	   POL(f_58(x_1)) = x_1
22.97/11.09	   POL(f_59(x_1)) = x_1
22.97/11.09	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
22.97/11.09	
22.97/11.09	   *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))) -> *top*_28(f_59(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))))
22.97/11.09	
22.97/11.09	
22.97/11.09	
22.97/11.09	
22.97/11.09	----------------------------------------
22.97/11.09	
22.97/11.09	(14)
22.97/11.09	Obligation:
22.97/11.09	Context-sensitive rewrite system:
22.97/11.09	The TRS R consists of the following rules:
22.97/11.09	
22.97/11.09	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.09	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.09	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.09	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.09	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.09	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.09	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.09	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.09	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.09	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.09	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.09	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.09	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.09	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.09	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.09	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.09	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.09	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.09	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.09	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.09	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.97/11.09	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.97/11.09	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.97/11.09	   *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))) -> *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))
22.97/11.09	
22.97/11.09	The replacement map contains the following entries:
22.97/11.09	
22.97/11.09	a_31: empty set
22.97/11.09	f_34: {1}
22.97/11.09	*top*_3: {1}
22.97/11.09	f_33: {1}
22.97/11.09	*top*_4: {1}
22.97/11.09	f_35: {1}
22.97/11.09	*top*_5: {1}
22.97/11.09	f_36: {1}
22.97/11.09	*top*_6: {1}
22.97/11.09	f_37: {1}
22.97/11.09	*top*_7: {1}
22.97/11.09	f_38: {1}
22.97/11.09	*top*_8: {1}
22.97/11.09	f_39: {1}
22.97/11.09	*top*_9: {1}
22.97/11.09	f_40: {1}
22.97/11.09	*top*_10: {1}
22.97/11.09	f_41: {1}
22.97/11.09	*top*_11: {1}
22.97/11.09	f_42: {1}
22.97/11.09	*top*_12: {1}
22.97/11.09	f_43: {1}
22.97/11.09	*top*_13: {1}
22.97/11.09	f_44: {1}
22.97/11.09	*top*_14: {1}
22.97/11.09	f_45: {1}
22.97/11.09	*top*_15: {1}
22.97/11.09	f_46: {1}
22.97/11.09	*top*_16: {1}
22.97/11.09	f_47: {1}
22.97/11.09	*top*_17: {1}
22.97/11.09	f_48: {1}
22.97/11.09	*top*_18: {1}
22.97/11.09	f_49: {1}
22.97/11.09	*top*_19: {1}
22.97/11.09	f_50: {1}
22.97/11.09	*top*_20: {1}
22.97/11.09	f_51: {1}
22.97/11.09	*top*_21: {1}
22.97/11.09	f_52: {1}
22.97/11.09	*top*_22: {1}
22.97/11.09	f_53: {1}
22.97/11.09	*top*_23: {1}
22.97/11.09	f_54: {1}
22.97/11.09	*top*_24: {1}
22.97/11.09	f_55: {1}
22.97/11.09	*top*_25: {1}
22.97/11.09	f_56: {1}
22.97/11.09	*top*_26: {1}
22.97/11.09	f_57: {1}
22.97/11.09	*top*_27: {1}
22.97/11.09	f_58: {1}
22.97/11.09	
22.97/11.09	----------------------------------------
22.97/11.09	
22.97/11.09	(15) CSRRRRProof (EQUIVALENT)
22.97/11.09	The following CSR is given: Context-sensitive rewrite system:
22.97/11.09	The TRS R consists of the following rules:
22.97/11.09	
22.97/11.09	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.09	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.09	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.09	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.09	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.09	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.09	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.09	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.09	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.09	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.09	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.09	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.09	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.09	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.09	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.09	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.09	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.09	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.09	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.09	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.09	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.97/11.09	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.97/11.09	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.97/11.09	   *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))) -> *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))
22.97/11.09	
22.97/11.09	The replacement map contains the following entries:
22.97/11.09	
22.97/11.09	a_31: empty set
22.97/11.09	f_34: {1}
22.97/11.09	*top*_3: {1}
22.97/11.09	f_33: {1}
22.97/11.09	*top*_4: {1}
22.97/11.09	f_35: {1}
22.97/11.09	*top*_5: {1}
22.97/11.09	f_36: {1}
22.97/11.09	*top*_6: {1}
22.97/11.09	f_37: {1}
22.97/11.09	*top*_7: {1}
22.97/11.09	f_38: {1}
22.97/11.09	*top*_8: {1}
22.97/11.09	f_39: {1}
22.97/11.09	*top*_9: {1}
22.97/11.09	f_40: {1}
22.97/11.09	*top*_10: {1}
22.97/11.09	f_41: {1}
22.97/11.09	*top*_11: {1}
22.97/11.09	f_42: {1}
22.97/11.09	*top*_12: {1}
22.97/11.09	f_43: {1}
22.97/11.09	*top*_13: {1}
22.97/11.09	f_44: {1}
22.97/11.09	*top*_14: {1}
22.97/11.09	f_45: {1}
22.97/11.09	*top*_15: {1}
22.97/11.09	f_46: {1}
22.97/11.09	*top*_16: {1}
22.97/11.09	f_47: {1}
22.97/11.09	*top*_17: {1}
22.97/11.09	f_48: {1}
22.97/11.09	*top*_18: {1}
22.97/11.09	f_49: {1}
22.97/11.09	*top*_19: {1}
22.97/11.09	f_50: {1}
22.97/11.09	*top*_20: {1}
22.97/11.09	f_51: {1}
22.97/11.09	*top*_21: {1}
22.97/11.09	f_52: {1}
22.97/11.09	*top*_22: {1}
22.97/11.09	f_53: {1}
22.97/11.09	*top*_23: {1}
22.97/11.09	f_54: {1}
22.97/11.09	*top*_24: {1}
22.97/11.09	f_55: {1}
22.97/11.09	*top*_25: {1}
22.97/11.09	f_56: {1}
22.97/11.09	*top*_26: {1}
22.97/11.09	f_57: {1}
22.97/11.09	*top*_27: {1}
22.97/11.09	f_58: {1}
22.97/11.09	Used ordering:
22.97/11.09	Polynomial interpretation [POLO]:
22.97/11.09	
22.97/11.09	   POL(*top*_10(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_11(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_12(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_13(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_14(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_15(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_16(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_17(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_18(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_19(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_20(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_21(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_22(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_23(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_24(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_25(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_26(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_27(x_1)) = x_1
22.97/11.09	   POL(*top*_3(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_4(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_5(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_6(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_7(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_8(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_9(x_1)) = 1 + x_1
22.97/11.09	   POL(a_31) = 0
22.97/11.09	   POL(f_33(x_1)) = x_1
22.97/11.09	   POL(f_34(x_1)) = x_1
22.97/11.09	   POL(f_35(x_1)) = x_1
22.97/11.09	   POL(f_36(x_1)) = x_1
22.97/11.09	   POL(f_37(x_1)) = x_1
22.97/11.09	   POL(f_38(x_1)) = x_1
22.97/11.09	   POL(f_39(x_1)) = x_1
22.97/11.09	   POL(f_40(x_1)) = x_1
22.97/11.09	   POL(f_41(x_1)) = x_1
22.97/11.09	   POL(f_42(x_1)) = x_1
22.97/11.09	   POL(f_43(x_1)) = x_1
22.97/11.09	   POL(f_44(x_1)) = x_1
22.97/11.09	   POL(f_45(x_1)) = x_1
22.97/11.09	   POL(f_46(x_1)) = x_1
22.97/11.09	   POL(f_47(x_1)) = x_1
22.97/11.09	   POL(f_48(x_1)) = x_1
22.97/11.09	   POL(f_49(x_1)) = x_1
22.97/11.09	   POL(f_50(x_1)) = x_1
22.97/11.09	   POL(f_51(x_1)) = x_1
22.97/11.09	   POL(f_52(x_1)) = x_1
22.97/11.09	   POL(f_53(x_1)) = x_1
22.97/11.09	   POL(f_54(x_1)) = x_1
22.97/11.09	   POL(f_55(x_1)) = x_1
22.97/11.09	   POL(f_56(x_1)) = x_1
22.97/11.09	   POL(f_57(x_1)) = x_1
22.97/11.09	   POL(f_58(x_1)) = x_1
22.97/11.09	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
22.97/11.09	
22.97/11.09	   *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))) -> *top*_27(f_58(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))))
22.97/11.09	
22.97/11.09	
22.97/11.09	
22.97/11.09	
22.97/11.09	----------------------------------------
22.97/11.09	
22.97/11.09	(16)
22.97/11.09	Obligation:
22.97/11.09	Context-sensitive rewrite system:
22.97/11.09	The TRS R consists of the following rules:
22.97/11.09	
22.97/11.09	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.09	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.09	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.09	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.09	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.09	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.09	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.09	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.09	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.09	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.09	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.09	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.09	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.09	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.09	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.09	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.09	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.09	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.09	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.09	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.09	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.97/11.09	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.97/11.09	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.97/11.09	
22.97/11.09	The replacement map contains the following entries:
22.97/11.09	
22.97/11.09	a_31: empty set
22.97/11.09	f_34: {1}
22.97/11.09	*top*_3: {1}
22.97/11.09	f_33: {1}
22.97/11.09	*top*_4: {1}
22.97/11.09	f_35: {1}
22.97/11.09	*top*_5: {1}
22.97/11.09	f_36: {1}
22.97/11.09	*top*_6: {1}
22.97/11.09	f_37: {1}
22.97/11.09	*top*_7: {1}
22.97/11.09	f_38: {1}
22.97/11.09	*top*_8: {1}
22.97/11.09	f_39: {1}
22.97/11.09	*top*_9: {1}
22.97/11.09	f_40: {1}
22.97/11.09	*top*_10: {1}
22.97/11.09	f_41: {1}
22.97/11.09	*top*_11: {1}
22.97/11.09	f_42: {1}
22.97/11.09	*top*_12: {1}
22.97/11.09	f_43: {1}
22.97/11.09	*top*_13: {1}
22.97/11.09	f_44: {1}
22.97/11.09	*top*_14: {1}
22.97/11.09	f_45: {1}
22.97/11.09	*top*_15: {1}
22.97/11.09	f_46: {1}
22.97/11.09	*top*_16: {1}
22.97/11.09	f_47: {1}
22.97/11.09	*top*_17: {1}
22.97/11.09	f_48: {1}
22.97/11.09	*top*_18: {1}
22.97/11.09	f_49: {1}
22.97/11.09	*top*_19: {1}
22.97/11.09	f_50: {1}
22.97/11.09	*top*_20: {1}
22.97/11.09	f_51: {1}
22.97/11.09	*top*_21: {1}
22.97/11.09	f_52: {1}
22.97/11.09	*top*_22: {1}
22.97/11.09	f_53: {1}
22.97/11.09	*top*_23: {1}
22.97/11.09	f_54: {1}
22.97/11.09	*top*_24: {1}
22.97/11.09	f_55: {1}
22.97/11.09	*top*_25: {1}
22.97/11.09	f_56: {1}
22.97/11.09	*top*_26: {1}
22.97/11.09	f_57: {1}
22.97/11.09	
22.97/11.09	----------------------------------------
22.97/11.09	
22.97/11.09	(17) CSRRRRProof (EQUIVALENT)
22.97/11.09	The following CSR is given: Context-sensitive rewrite system:
22.97/11.09	The TRS R consists of the following rules:
22.97/11.09	
22.97/11.09	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.09	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.09	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.09	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.09	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.09	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.09	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.09	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.09	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.09	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.09	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.09	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.09	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.09	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.09	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.09	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.09	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.09	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.09	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.09	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.09	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.97/11.09	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.97/11.09	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.97/11.09	
22.97/11.09	The replacement map contains the following entries:
22.97/11.09	
22.97/11.09	a_31: empty set
22.97/11.09	f_34: {1}
22.97/11.09	*top*_3: {1}
22.97/11.09	f_33: {1}
22.97/11.09	*top*_4: {1}
22.97/11.09	f_35: {1}
22.97/11.09	*top*_5: {1}
22.97/11.09	f_36: {1}
22.97/11.09	*top*_6: {1}
22.97/11.09	f_37: {1}
22.97/11.09	*top*_7: {1}
22.97/11.09	f_38: {1}
22.97/11.09	*top*_8: {1}
22.97/11.09	f_39: {1}
22.97/11.09	*top*_9: {1}
22.97/11.09	f_40: {1}
22.97/11.09	*top*_10: {1}
22.97/11.09	f_41: {1}
22.97/11.09	*top*_11: {1}
22.97/11.09	f_42: {1}
22.97/11.09	*top*_12: {1}
22.97/11.09	f_43: {1}
22.97/11.09	*top*_13: {1}
22.97/11.09	f_44: {1}
22.97/11.09	*top*_14: {1}
22.97/11.09	f_45: {1}
22.97/11.09	*top*_15: {1}
22.97/11.09	f_46: {1}
22.97/11.09	*top*_16: {1}
22.97/11.09	f_47: {1}
22.97/11.09	*top*_17: {1}
22.97/11.09	f_48: {1}
22.97/11.09	*top*_18: {1}
22.97/11.09	f_49: {1}
22.97/11.09	*top*_19: {1}
22.97/11.09	f_50: {1}
22.97/11.09	*top*_20: {1}
22.97/11.09	f_51: {1}
22.97/11.09	*top*_21: {1}
22.97/11.09	f_52: {1}
22.97/11.09	*top*_22: {1}
22.97/11.09	f_53: {1}
22.97/11.09	*top*_23: {1}
22.97/11.09	f_54: {1}
22.97/11.09	*top*_24: {1}
22.97/11.09	f_55: {1}
22.97/11.09	*top*_25: {1}
22.97/11.09	f_56: {1}
22.97/11.09	*top*_26: {1}
22.97/11.09	f_57: {1}
22.97/11.09	Used ordering:
22.97/11.09	Polynomial interpretation [POLO]:
22.97/11.09	
22.97/11.09	   POL(*top*_10(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_11(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_12(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_13(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_14(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_15(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_16(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_17(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_18(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_19(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_20(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_21(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_22(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_23(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_24(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_25(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_26(x_1)) = x_1
22.97/11.09	   POL(*top*_3(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_4(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_5(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_6(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_7(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_8(x_1)) = 1 + x_1
22.97/11.09	   POL(*top*_9(x_1)) = 1 + x_1
22.97/11.09	   POL(a_31) = 0
22.97/11.09	   POL(f_33(x_1)) = x_1
22.97/11.09	   POL(f_34(x_1)) = x_1
22.97/11.09	   POL(f_35(x_1)) = x_1
22.97/11.09	   POL(f_36(x_1)) = x_1
22.97/11.09	   POL(f_37(x_1)) = x_1
22.97/11.09	   POL(f_38(x_1)) = x_1
22.97/11.09	   POL(f_39(x_1)) = x_1
22.97/11.09	   POL(f_40(x_1)) = x_1
22.97/11.09	   POL(f_41(x_1)) = x_1
22.97/11.09	   POL(f_42(x_1)) = x_1
22.97/11.09	   POL(f_43(x_1)) = x_1
22.97/11.09	   POL(f_44(x_1)) = x_1
22.97/11.09	   POL(f_45(x_1)) = x_1
22.97/11.09	   POL(f_46(x_1)) = x_1
22.97/11.09	   POL(f_47(x_1)) = x_1
22.97/11.09	   POL(f_48(x_1)) = x_1
22.97/11.09	   POL(f_49(x_1)) = x_1
22.97/11.09	   POL(f_50(x_1)) = x_1
22.97/11.09	   POL(f_51(x_1)) = x_1
22.97/11.09	   POL(f_52(x_1)) = x_1
22.97/11.09	   POL(f_53(x_1)) = x_1
22.97/11.09	   POL(f_54(x_1)) = x_1
22.97/11.09	   POL(f_55(x_1)) = x_1
22.97/11.09	   POL(f_56(x_1)) = x_1
22.97/11.09	   POL(f_57(x_1)) = x_1
22.97/11.09	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
22.97/11.09	
22.97/11.09	   *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))) -> *top*_26(f_57(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))))
22.97/11.09	
22.97/11.09	
22.97/11.09	
22.97/11.09	
22.97/11.09	----------------------------------------
22.97/11.09	
22.97/11.09	(18)
22.97/11.09	Obligation:
22.97/11.09	Context-sensitive rewrite system:
22.97/11.09	The TRS R consists of the following rules:
22.97/11.09	
22.97/11.09	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.09	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.09	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.09	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.09	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.09	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.09	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.09	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.09	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.09	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.09	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.09	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.09	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.09	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.09	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.09	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.09	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.09	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.09	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.09	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.09	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.97/11.09	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.97/11.09	
22.97/11.09	The replacement map contains the following entries:
22.97/11.09	
22.97/11.09	a_31: empty set
22.97/11.09	f_34: {1}
22.97/11.09	*top*_3: {1}
22.97/11.09	f_33: {1}
22.97/11.09	*top*_4: {1}
22.97/11.09	f_35: {1}
22.97/11.09	*top*_5: {1}
22.97/11.09	f_36: {1}
22.97/11.09	*top*_6: {1}
22.97/11.09	f_37: {1}
22.97/11.09	*top*_7: {1}
22.97/11.09	f_38: {1}
22.97/11.09	*top*_8: {1}
22.97/11.09	f_39: {1}
22.97/11.09	*top*_9: {1}
22.97/11.09	f_40: {1}
22.97/11.09	*top*_10: {1}
22.97/11.09	f_41: {1}
22.97/11.09	*top*_11: {1}
22.97/11.09	f_42: {1}
22.97/11.09	*top*_12: {1}
22.97/11.09	f_43: {1}
22.97/11.09	*top*_13: {1}
22.97/11.09	f_44: {1}
22.97/11.09	*top*_14: {1}
22.97/11.09	f_45: {1}
22.97/11.09	*top*_15: {1}
22.97/11.09	f_46: {1}
22.97/11.09	*top*_16: {1}
22.97/11.09	f_47: {1}
22.97/11.09	*top*_17: {1}
22.97/11.09	f_48: {1}
22.97/11.09	*top*_18: {1}
22.97/11.09	f_49: {1}
22.97/11.09	*top*_19: {1}
22.97/11.09	f_50: {1}
22.97/11.09	*top*_20: {1}
22.97/11.09	f_51: {1}
22.97/11.09	*top*_21: {1}
22.97/11.09	f_52: {1}
22.97/11.09	*top*_22: {1}
22.97/11.09	f_53: {1}
22.97/11.09	*top*_23: {1}
22.97/11.09	f_54: {1}
22.97/11.09	*top*_24: {1}
22.97/11.09	f_55: {1}
22.97/11.09	*top*_25: {1}
22.97/11.09	f_56: {1}
22.97/11.09	
22.97/11.09	----------------------------------------
22.97/11.09	
22.97/11.09	(19) CSRRRRProof (EQUIVALENT)
22.97/11.09	The following CSR is given: Context-sensitive rewrite system:
22.97/11.09	The TRS R consists of the following rules:
22.97/11.09	
22.97/11.09	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.09	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.09	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.09	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.09	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.09	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.09	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.09	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.09	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.09	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.09	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.09	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.09	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.09	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.09	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.09	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.09	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.09	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.09	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.09	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.09	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.97/11.10	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.97/11.10	
22.97/11.10	The replacement map contains the following entries:
22.97/11.10	
22.97/11.10	a_31: empty set
22.97/11.10	f_34: {1}
22.97/11.10	*top*_3: {1}
22.97/11.10	f_33: {1}
22.97/11.10	*top*_4: {1}
22.97/11.10	f_35: {1}
22.97/11.10	*top*_5: {1}
22.97/11.10	f_36: {1}
22.97/11.10	*top*_6: {1}
22.97/11.10	f_37: {1}
22.97/11.10	*top*_7: {1}
22.97/11.10	f_38: {1}
22.97/11.10	*top*_8: {1}
22.97/11.10	f_39: {1}
22.97/11.10	*top*_9: {1}
22.97/11.10	f_40: {1}
22.97/11.10	*top*_10: {1}
22.97/11.10	f_41: {1}
22.97/11.10	*top*_11: {1}
22.97/11.10	f_42: {1}
22.97/11.10	*top*_12: {1}
22.97/11.10	f_43: {1}
22.97/11.10	*top*_13: {1}
22.97/11.10	f_44: {1}
22.97/11.10	*top*_14: {1}
22.97/11.10	f_45: {1}
22.97/11.10	*top*_15: {1}
22.97/11.10	f_46: {1}
22.97/11.10	*top*_16: {1}
22.97/11.10	f_47: {1}
22.97/11.10	*top*_17: {1}
22.97/11.10	f_48: {1}
22.97/11.10	*top*_18: {1}
22.97/11.10	f_49: {1}
22.97/11.10	*top*_19: {1}
22.97/11.10	f_50: {1}
22.97/11.10	*top*_20: {1}
22.97/11.10	f_51: {1}
22.97/11.10	*top*_21: {1}
22.97/11.10	f_52: {1}
22.97/11.10	*top*_22: {1}
22.97/11.10	f_53: {1}
22.97/11.10	*top*_23: {1}
22.97/11.10	f_54: {1}
22.97/11.10	*top*_24: {1}
22.97/11.10	f_55: {1}
22.97/11.10	*top*_25: {1}
22.97/11.10	f_56: {1}
22.97/11.10	Used ordering:
22.97/11.10	Polynomial interpretation [POLO]:
22.97/11.10	
22.97/11.10	   POL(*top*_10(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_11(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_12(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_13(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_14(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_15(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_16(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_17(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_18(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_19(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_20(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_21(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_22(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_23(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_24(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_25(x_1)) = x_1
22.97/11.10	   POL(*top*_3(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_4(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_5(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_6(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_7(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_8(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_9(x_1)) = 1 + x_1
22.97/11.10	   POL(a_31) = 0
22.97/11.10	   POL(f_33(x_1)) = x_1
22.97/11.10	   POL(f_34(x_1)) = x_1
22.97/11.10	   POL(f_35(x_1)) = x_1
22.97/11.10	   POL(f_36(x_1)) = x_1
22.97/11.10	   POL(f_37(x_1)) = x_1
22.97/11.10	   POL(f_38(x_1)) = x_1
22.97/11.10	   POL(f_39(x_1)) = x_1
22.97/11.10	   POL(f_40(x_1)) = x_1
22.97/11.10	   POL(f_41(x_1)) = x_1
22.97/11.10	   POL(f_42(x_1)) = x_1
22.97/11.10	   POL(f_43(x_1)) = x_1
22.97/11.10	   POL(f_44(x_1)) = x_1
22.97/11.10	   POL(f_45(x_1)) = x_1
22.97/11.10	   POL(f_46(x_1)) = x_1
22.97/11.10	   POL(f_47(x_1)) = x_1
22.97/11.10	   POL(f_48(x_1)) = x_1
22.97/11.10	   POL(f_49(x_1)) = x_1
22.97/11.10	   POL(f_50(x_1)) = x_1
22.97/11.10	   POL(f_51(x_1)) = x_1
22.97/11.10	   POL(f_52(x_1)) = x_1
22.97/11.10	   POL(f_53(x_1)) = x_1
22.97/11.10	   POL(f_54(x_1)) = x_1
22.97/11.10	   POL(f_55(x_1)) = x_1
22.97/11.10	   POL(f_56(x_1)) = x_1
22.97/11.10	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
22.97/11.10	
22.97/11.10	   *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))) -> *top*_25(f_56(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))))
22.97/11.10	
22.97/11.10	
22.97/11.10	
22.97/11.10	
22.97/11.10	----------------------------------------
22.97/11.10	
22.97/11.10	(20)
22.97/11.10	Obligation:
22.97/11.10	Context-sensitive rewrite system:
22.97/11.10	The TRS R consists of the following rules:
22.97/11.10	
22.97/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.10	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.10	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.10	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.10	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.10	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.10	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.10	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.10	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.97/11.10	
22.97/11.10	The replacement map contains the following entries:
22.97/11.10	
22.97/11.10	a_31: empty set
22.97/11.10	f_34: {1}
22.97/11.10	*top*_3: {1}
22.97/11.10	f_33: {1}
22.97/11.10	*top*_4: {1}
22.97/11.10	f_35: {1}
22.97/11.10	*top*_5: {1}
22.97/11.10	f_36: {1}
22.97/11.10	*top*_6: {1}
22.97/11.10	f_37: {1}
22.97/11.10	*top*_7: {1}
22.97/11.10	f_38: {1}
22.97/11.10	*top*_8: {1}
22.97/11.10	f_39: {1}
22.97/11.10	*top*_9: {1}
22.97/11.10	f_40: {1}
22.97/11.10	*top*_10: {1}
22.97/11.10	f_41: {1}
22.97/11.10	*top*_11: {1}
22.97/11.10	f_42: {1}
22.97/11.10	*top*_12: {1}
22.97/11.10	f_43: {1}
22.97/11.10	*top*_13: {1}
22.97/11.10	f_44: {1}
22.97/11.10	*top*_14: {1}
22.97/11.10	f_45: {1}
22.97/11.10	*top*_15: {1}
22.97/11.10	f_46: {1}
22.97/11.10	*top*_16: {1}
22.97/11.10	f_47: {1}
22.97/11.10	*top*_17: {1}
22.97/11.10	f_48: {1}
22.97/11.10	*top*_18: {1}
22.97/11.10	f_49: {1}
22.97/11.10	*top*_19: {1}
22.97/11.10	f_50: {1}
22.97/11.10	*top*_20: {1}
22.97/11.10	f_51: {1}
22.97/11.10	*top*_21: {1}
22.97/11.10	f_52: {1}
22.97/11.10	*top*_22: {1}
22.97/11.10	f_53: {1}
22.97/11.10	*top*_23: {1}
22.97/11.10	f_54: {1}
22.97/11.10	*top*_24: {1}
22.97/11.10	f_55: {1}
22.97/11.10	
22.97/11.10	----------------------------------------
22.97/11.10	
22.97/11.10	(21) CSRRRRProof (EQUIVALENT)
22.97/11.10	The following CSR is given: Context-sensitive rewrite system:
22.97/11.10	The TRS R consists of the following rules:
22.97/11.10	
22.97/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.10	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.10	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.10	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.10	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.10	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.10	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.10	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.10	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.97/11.10	
22.97/11.10	The replacement map contains the following entries:
22.97/11.10	
22.97/11.10	a_31: empty set
22.97/11.10	f_34: {1}
22.97/11.10	*top*_3: {1}
22.97/11.10	f_33: {1}
22.97/11.10	*top*_4: {1}
22.97/11.10	f_35: {1}
22.97/11.10	*top*_5: {1}
22.97/11.10	f_36: {1}
22.97/11.10	*top*_6: {1}
22.97/11.10	f_37: {1}
22.97/11.10	*top*_7: {1}
22.97/11.10	f_38: {1}
22.97/11.10	*top*_8: {1}
22.97/11.10	f_39: {1}
22.97/11.10	*top*_9: {1}
22.97/11.10	f_40: {1}
22.97/11.10	*top*_10: {1}
22.97/11.10	f_41: {1}
22.97/11.10	*top*_11: {1}
22.97/11.10	f_42: {1}
22.97/11.10	*top*_12: {1}
22.97/11.10	f_43: {1}
22.97/11.10	*top*_13: {1}
22.97/11.10	f_44: {1}
22.97/11.10	*top*_14: {1}
22.97/11.10	f_45: {1}
22.97/11.10	*top*_15: {1}
22.97/11.10	f_46: {1}
22.97/11.10	*top*_16: {1}
22.97/11.10	f_47: {1}
22.97/11.10	*top*_17: {1}
22.97/11.10	f_48: {1}
22.97/11.10	*top*_18: {1}
22.97/11.10	f_49: {1}
22.97/11.10	*top*_19: {1}
22.97/11.10	f_50: {1}
22.97/11.10	*top*_20: {1}
22.97/11.10	f_51: {1}
22.97/11.10	*top*_21: {1}
22.97/11.10	f_52: {1}
22.97/11.10	*top*_22: {1}
22.97/11.10	f_53: {1}
22.97/11.10	*top*_23: {1}
22.97/11.10	f_54: {1}
22.97/11.10	*top*_24: {1}
22.97/11.10	f_55: {1}
22.97/11.10	Used ordering:
22.97/11.10	Polynomial interpretation [POLO]:
22.97/11.10	
22.97/11.10	   POL(*top*_10(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_11(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_12(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_13(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_14(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_15(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_16(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_17(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_18(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_19(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_20(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_21(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_22(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_23(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_24(x_1)) = x_1
22.97/11.10	   POL(*top*_3(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_4(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_5(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_6(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_7(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_8(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_9(x_1)) = 1 + x_1
22.97/11.10	   POL(a_31) = 0
22.97/11.10	   POL(f_33(x_1)) = x_1
22.97/11.10	   POL(f_34(x_1)) = x_1
22.97/11.10	   POL(f_35(x_1)) = x_1
22.97/11.10	   POL(f_36(x_1)) = x_1
22.97/11.10	   POL(f_37(x_1)) = x_1
22.97/11.10	   POL(f_38(x_1)) = x_1
22.97/11.10	   POL(f_39(x_1)) = x_1
22.97/11.10	   POL(f_40(x_1)) = x_1
22.97/11.10	   POL(f_41(x_1)) = x_1
22.97/11.10	   POL(f_42(x_1)) = x_1
22.97/11.10	   POL(f_43(x_1)) = x_1
22.97/11.10	   POL(f_44(x_1)) = x_1
22.97/11.10	   POL(f_45(x_1)) = x_1
22.97/11.10	   POL(f_46(x_1)) = x_1
22.97/11.10	   POL(f_47(x_1)) = x_1
22.97/11.10	   POL(f_48(x_1)) = x_1
22.97/11.10	   POL(f_49(x_1)) = x_1
22.97/11.10	   POL(f_50(x_1)) = x_1
22.97/11.10	   POL(f_51(x_1)) = x_1
22.97/11.10	   POL(f_52(x_1)) = x_1
22.97/11.10	   POL(f_53(x_1)) = x_1
22.97/11.10	   POL(f_54(x_1)) = x_1
22.97/11.10	   POL(f_55(x_1)) = x_1
22.97/11.10	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
22.97/11.10	
22.97/11.10	   *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))) -> *top*_24(f_55(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))))
22.97/11.10	
22.97/11.10	
22.97/11.10	
22.97/11.10	
22.97/11.10	----------------------------------------
22.97/11.10	
22.97/11.10	(22)
22.97/11.10	Obligation:
22.97/11.10	Context-sensitive rewrite system:
22.97/11.10	The TRS R consists of the following rules:
22.97/11.10	
22.97/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.10	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.10	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.10	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.10	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.10	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.10	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.10	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.10	
22.97/11.10	The replacement map contains the following entries:
22.97/11.10	
22.97/11.10	a_31: empty set
22.97/11.10	f_34: {1}
22.97/11.10	*top*_3: {1}
22.97/11.10	f_33: {1}
22.97/11.10	*top*_4: {1}
22.97/11.10	f_35: {1}
22.97/11.10	*top*_5: {1}
22.97/11.10	f_36: {1}
22.97/11.10	*top*_6: {1}
22.97/11.10	f_37: {1}
22.97/11.10	*top*_7: {1}
22.97/11.10	f_38: {1}
22.97/11.10	*top*_8: {1}
22.97/11.10	f_39: {1}
22.97/11.10	*top*_9: {1}
22.97/11.10	f_40: {1}
22.97/11.10	*top*_10: {1}
22.97/11.10	f_41: {1}
22.97/11.10	*top*_11: {1}
22.97/11.10	f_42: {1}
22.97/11.10	*top*_12: {1}
22.97/11.10	f_43: {1}
22.97/11.10	*top*_13: {1}
22.97/11.10	f_44: {1}
22.97/11.10	*top*_14: {1}
22.97/11.10	f_45: {1}
22.97/11.10	*top*_15: {1}
22.97/11.10	f_46: {1}
22.97/11.10	*top*_16: {1}
22.97/11.10	f_47: {1}
22.97/11.10	*top*_17: {1}
22.97/11.10	f_48: {1}
22.97/11.10	*top*_18: {1}
22.97/11.10	f_49: {1}
22.97/11.10	*top*_19: {1}
22.97/11.10	f_50: {1}
22.97/11.10	*top*_20: {1}
22.97/11.10	f_51: {1}
22.97/11.10	*top*_21: {1}
22.97/11.10	f_52: {1}
22.97/11.10	*top*_22: {1}
22.97/11.10	f_53: {1}
22.97/11.10	*top*_23: {1}
22.97/11.10	f_54: {1}
22.97/11.10	
22.97/11.10	----------------------------------------
22.97/11.10	
22.97/11.10	(23) CSRRRRProof (EQUIVALENT)
22.97/11.10	The following CSR is given: Context-sensitive rewrite system:
22.97/11.10	The TRS R consists of the following rules:
22.97/11.10	
22.97/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.10	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.10	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.10	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.10	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.10	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.10	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.10	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.10	
22.97/11.10	The replacement map contains the following entries:
22.97/11.10	
22.97/11.10	a_31: empty set
22.97/11.10	f_34: {1}
22.97/11.10	*top*_3: {1}
22.97/11.10	f_33: {1}
22.97/11.10	*top*_4: {1}
22.97/11.10	f_35: {1}
22.97/11.10	*top*_5: {1}
22.97/11.10	f_36: {1}
22.97/11.10	*top*_6: {1}
22.97/11.10	f_37: {1}
22.97/11.10	*top*_7: {1}
22.97/11.10	f_38: {1}
22.97/11.10	*top*_8: {1}
22.97/11.10	f_39: {1}
22.97/11.10	*top*_9: {1}
22.97/11.10	f_40: {1}
22.97/11.10	*top*_10: {1}
22.97/11.10	f_41: {1}
22.97/11.10	*top*_11: {1}
22.97/11.10	f_42: {1}
22.97/11.10	*top*_12: {1}
22.97/11.10	f_43: {1}
22.97/11.10	*top*_13: {1}
22.97/11.10	f_44: {1}
22.97/11.10	*top*_14: {1}
22.97/11.10	f_45: {1}
22.97/11.10	*top*_15: {1}
22.97/11.10	f_46: {1}
22.97/11.10	*top*_16: {1}
22.97/11.10	f_47: {1}
22.97/11.10	*top*_17: {1}
22.97/11.10	f_48: {1}
22.97/11.10	*top*_18: {1}
22.97/11.10	f_49: {1}
22.97/11.10	*top*_19: {1}
22.97/11.10	f_50: {1}
22.97/11.10	*top*_20: {1}
22.97/11.10	f_51: {1}
22.97/11.10	*top*_21: {1}
22.97/11.10	f_52: {1}
22.97/11.10	*top*_22: {1}
22.97/11.10	f_53: {1}
22.97/11.10	*top*_23: {1}
22.97/11.10	f_54: {1}
22.97/11.10	Used ordering:
22.97/11.10	Polynomial interpretation [POLO]:
22.97/11.10	
22.97/11.10	   POL(*top*_10(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_11(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_12(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_13(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_14(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_15(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_16(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_17(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_18(x_1)) = x_1
22.97/11.10	   POL(*top*_19(x_1)) = x_1
22.97/11.10	   POL(*top*_20(x_1)) = x_1
22.97/11.10	   POL(*top*_21(x_1)) = x_1
22.97/11.10	   POL(*top*_22(x_1)) = x_1
22.97/11.10	   POL(*top*_23(x_1)) = x_1
22.97/11.10	   POL(*top*_3(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_4(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_5(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_6(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_7(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_8(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_9(x_1)) = 1 + x_1
22.97/11.10	   POL(a_31) = 0
22.97/11.10	   POL(f_33(x_1)) = x_1
22.97/11.10	   POL(f_34(x_1)) = x_1
22.97/11.10	   POL(f_35(x_1)) = x_1
22.97/11.10	   POL(f_36(x_1)) = x_1
22.97/11.10	   POL(f_37(x_1)) = x_1
22.97/11.10	   POL(f_38(x_1)) = x_1
22.97/11.10	   POL(f_39(x_1)) = x_1
22.97/11.10	   POL(f_40(x_1)) = x_1
22.97/11.10	   POL(f_41(x_1)) = x_1
22.97/11.10	   POL(f_42(x_1)) = x_1
22.97/11.10	   POL(f_43(x_1)) = x_1
22.97/11.10	   POL(f_44(x_1)) = x_1
22.97/11.10	   POL(f_45(x_1)) = x_1
22.97/11.10	   POL(f_46(x_1)) = x_1
22.97/11.10	   POL(f_47(x_1)) = x_1
22.97/11.10	   POL(f_48(x_1)) = x_1
22.97/11.10	   POL(f_49(x_1)) = x_1
22.97/11.10	   POL(f_50(x_1)) = x_1
22.97/11.10	   POL(f_51(x_1)) = x_1
22.97/11.10	   POL(f_52(x_1)) = x_1
22.97/11.10	   POL(f_53(x_1)) = x_1
22.97/11.10	   POL(f_54(x_1)) = x_1
22.97/11.10	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
22.97/11.10	
22.97/11.10	   *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))) -> *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))
22.97/11.10	
22.97/11.10	
22.97/11.10	
22.97/11.10	
22.97/11.10	----------------------------------------
22.97/11.10	
22.97/11.10	(24)
22.97/11.10	Obligation:
22.97/11.10	Context-sensitive rewrite system:
22.97/11.10	The TRS R consists of the following rules:
22.97/11.10	
22.97/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.10	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.10	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.10	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.10	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.10	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.10	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.10	
22.97/11.10	The replacement map contains the following entries:
22.97/11.10	
22.97/11.10	a_31: empty set
22.97/11.10	f_34: {1}
22.97/11.10	*top*_3: {1}
22.97/11.10	f_33: {1}
22.97/11.10	*top*_4: {1}
22.97/11.10	f_35: {1}
22.97/11.10	*top*_5: {1}
22.97/11.10	f_36: {1}
22.97/11.10	*top*_6: {1}
22.97/11.10	f_37: {1}
22.97/11.10	*top*_7: {1}
22.97/11.10	f_38: {1}
22.97/11.10	*top*_8: {1}
22.97/11.10	f_39: {1}
22.97/11.10	*top*_9: {1}
22.97/11.10	f_40: {1}
22.97/11.10	*top*_10: {1}
22.97/11.10	f_41: {1}
22.97/11.10	*top*_11: {1}
22.97/11.10	f_42: {1}
22.97/11.10	*top*_12: {1}
22.97/11.10	f_43: {1}
22.97/11.10	*top*_13: {1}
22.97/11.10	f_44: {1}
22.97/11.10	*top*_14: {1}
22.97/11.10	f_45: {1}
22.97/11.10	*top*_15: {1}
22.97/11.10	f_46: {1}
22.97/11.10	*top*_16: {1}
22.97/11.10	f_47: {1}
22.97/11.10	*top*_17: {1}
22.97/11.10	f_48: {1}
22.97/11.10	*top*_18: {1}
22.97/11.10	f_49: {1}
22.97/11.10	*top*_19: {1}
22.97/11.10	f_50: {1}
22.97/11.10	*top*_20: {1}
22.97/11.10	f_51: {1}
22.97/11.10	*top*_21: {1}
22.97/11.10	f_52: {1}
22.97/11.10	*top*_22: {1}
22.97/11.10	f_53: {1}
22.97/11.10	*top*_23: {1}
22.97/11.10	f_54: {1}
22.97/11.10	
22.97/11.10	----------------------------------------
22.97/11.10	
22.97/11.10	(25) CSRRRRProof (EQUIVALENT)
22.97/11.10	The following CSR is given: Context-sensitive rewrite system:
22.97/11.10	The TRS R consists of the following rules:
22.97/11.10	
22.97/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.10	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.10	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.10	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.10	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.10	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.10	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.10	
22.97/11.10	The replacement map contains the following entries:
22.97/11.10	
22.97/11.10	a_31: empty set
22.97/11.10	f_34: {1}
22.97/11.10	*top*_3: {1}
22.97/11.10	f_33: {1}
22.97/11.10	*top*_4: {1}
22.97/11.10	f_35: {1}
22.97/11.10	*top*_5: {1}
22.97/11.10	f_36: {1}
22.97/11.10	*top*_6: {1}
22.97/11.10	f_37: {1}
22.97/11.10	*top*_7: {1}
22.97/11.10	f_38: {1}
22.97/11.10	*top*_8: {1}
22.97/11.10	f_39: {1}
22.97/11.10	*top*_9: {1}
22.97/11.10	f_40: {1}
22.97/11.10	*top*_10: {1}
22.97/11.10	f_41: {1}
22.97/11.10	*top*_11: {1}
22.97/11.10	f_42: {1}
22.97/11.10	*top*_12: {1}
22.97/11.10	f_43: {1}
22.97/11.10	*top*_13: {1}
22.97/11.10	f_44: {1}
22.97/11.10	*top*_14: {1}
22.97/11.10	f_45: {1}
22.97/11.10	*top*_15: {1}
22.97/11.10	f_46: {1}
22.97/11.10	*top*_16: {1}
22.97/11.10	f_47: {1}
22.97/11.10	*top*_17: {1}
22.97/11.10	f_48: {1}
22.97/11.10	*top*_18: {1}
22.97/11.10	f_49: {1}
22.97/11.10	*top*_19: {1}
22.97/11.10	f_50: {1}
22.97/11.10	*top*_20: {1}
22.97/11.10	f_51: {1}
22.97/11.10	*top*_21: {1}
22.97/11.10	f_52: {1}
22.97/11.10	*top*_22: {1}
22.97/11.10	f_53: {1}
22.97/11.10	*top*_23: {1}
22.97/11.10	f_54: {1}
22.97/11.10	Used ordering:
22.97/11.10	Polynomial interpretation [POLO]:
22.97/11.10	
22.97/11.10	   POL(*top*_10(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_11(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_12(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_13(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_14(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_15(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_16(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_17(x_1)) = x_1
22.97/11.10	   POL(*top*_18(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_19(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_20(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_21(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_22(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_23(x_1)) = x_1
22.97/11.10	   POL(*top*_3(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_4(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_5(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_6(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_7(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_8(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_9(x_1)) = 1 + x_1
22.97/11.10	   POL(a_31) = 0
22.97/11.10	   POL(f_33(x_1)) = x_1
22.97/11.10	   POL(f_34(x_1)) = x_1
22.97/11.10	   POL(f_35(x_1)) = x_1
22.97/11.10	   POL(f_36(x_1)) = x_1
22.97/11.10	   POL(f_37(x_1)) = x_1
22.97/11.10	   POL(f_38(x_1)) = x_1
22.97/11.10	   POL(f_39(x_1)) = x_1
22.97/11.10	   POL(f_40(x_1)) = x_1
22.97/11.10	   POL(f_41(x_1)) = x_1
22.97/11.10	   POL(f_42(x_1)) = x_1
22.97/11.10	   POL(f_43(x_1)) = x_1
22.97/11.10	   POL(f_44(x_1)) = x_1
22.97/11.10	   POL(f_45(x_1)) = x_1
22.97/11.10	   POL(f_46(x_1)) = x_1
22.97/11.10	   POL(f_47(x_1)) = x_1
22.97/11.10	   POL(f_48(x_1)) = x_1
22.97/11.10	   POL(f_49(x_1)) = x_1
22.97/11.10	   POL(f_50(x_1)) = x_1
22.97/11.10	   POL(f_51(x_1)) = x_1
22.97/11.10	   POL(f_52(x_1)) = x_1
22.97/11.10	   POL(f_53(x_1)) = x_1
22.97/11.10	   POL(f_54(x_1)) = 1 + x_1
22.97/11.10	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
22.97/11.10	
22.97/11.10	   *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))) -> *top*_17(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))
22.97/11.10	
22.97/11.10	
22.97/11.10	
22.97/11.10	
22.97/11.10	----------------------------------------
22.97/11.10	
22.97/11.10	(26)
22.97/11.10	Obligation:
22.97/11.10	Context-sensitive rewrite system:
22.97/11.10	The TRS R consists of the following rules:
22.97/11.10	
22.97/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.10	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.10	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.10	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.10	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.10	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.10	
22.97/11.10	The replacement map contains the following entries:
22.97/11.10	
22.97/11.10	a_31: empty set
22.97/11.10	f_34: {1}
22.97/11.10	*top*_3: {1}
22.97/11.10	f_33: {1}
22.97/11.10	*top*_4: {1}
22.97/11.10	f_35: {1}
22.97/11.10	*top*_5: {1}
22.97/11.10	f_36: {1}
22.97/11.10	*top*_6: {1}
22.97/11.10	f_37: {1}
22.97/11.10	*top*_7: {1}
22.97/11.10	f_38: {1}
22.97/11.10	*top*_8: {1}
22.97/11.10	f_39: {1}
22.97/11.10	*top*_9: {1}
22.97/11.10	f_40: {1}
22.97/11.10	*top*_10: {1}
22.97/11.10	f_41: {1}
22.97/11.10	*top*_11: {1}
22.97/11.10	f_42: {1}
22.97/11.10	*top*_12: {1}
22.97/11.10	f_43: {1}
22.97/11.10	*top*_13: {1}
22.97/11.10	f_44: {1}
22.97/11.10	*top*_14: {1}
22.97/11.10	f_45: {1}
22.97/11.10	*top*_15: {1}
22.97/11.10	f_46: {1}
22.97/11.10	*top*_16: {1}
22.97/11.10	f_47: {1}
22.97/11.10	f_48: {1}
22.97/11.10	*top*_18: {1}
22.97/11.10	f_49: {1}
22.97/11.10	*top*_19: {1}
22.97/11.10	f_50: {1}
22.97/11.10	*top*_20: {1}
22.97/11.10	f_51: {1}
22.97/11.10	*top*_21: {1}
22.97/11.10	f_52: {1}
22.97/11.10	*top*_22: {1}
22.97/11.10	f_53: {1}
22.97/11.10	*top*_23: {1}
22.97/11.10	f_54: {1}
22.97/11.10	
22.97/11.10	----------------------------------------
22.97/11.10	
22.97/11.10	(27) CSRRRRProof (EQUIVALENT)
22.97/11.10	The following CSR is given: Context-sensitive rewrite system:
22.97/11.10	The TRS R consists of the following rules:
22.97/11.10	
22.97/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.10	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.10	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.10	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.10	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.10	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.10	
22.97/11.10	The replacement map contains the following entries:
22.97/11.10	
22.97/11.10	a_31: empty set
22.97/11.10	f_34: {1}
22.97/11.10	*top*_3: {1}
22.97/11.10	f_33: {1}
22.97/11.10	*top*_4: {1}
22.97/11.10	f_35: {1}
22.97/11.10	*top*_5: {1}
22.97/11.10	f_36: {1}
22.97/11.10	*top*_6: {1}
22.97/11.10	f_37: {1}
22.97/11.10	*top*_7: {1}
22.97/11.10	f_38: {1}
22.97/11.10	*top*_8: {1}
22.97/11.10	f_39: {1}
22.97/11.10	*top*_9: {1}
22.97/11.10	f_40: {1}
22.97/11.10	*top*_10: {1}
22.97/11.10	f_41: {1}
22.97/11.10	*top*_11: {1}
22.97/11.10	f_42: {1}
22.97/11.10	*top*_12: {1}
22.97/11.10	f_43: {1}
22.97/11.10	*top*_13: {1}
22.97/11.10	f_44: {1}
22.97/11.10	*top*_14: {1}
22.97/11.10	f_45: {1}
22.97/11.10	*top*_15: {1}
22.97/11.10	f_46: {1}
22.97/11.10	*top*_16: {1}
22.97/11.10	f_47: {1}
22.97/11.10	f_48: {1}
22.97/11.10	*top*_18: {1}
22.97/11.10	f_49: {1}
22.97/11.10	*top*_19: {1}
22.97/11.10	f_50: {1}
22.97/11.10	*top*_20: {1}
22.97/11.10	f_51: {1}
22.97/11.10	*top*_21: {1}
22.97/11.10	f_52: {1}
22.97/11.10	*top*_22: {1}
22.97/11.10	f_53: {1}
22.97/11.10	*top*_23: {1}
22.97/11.10	f_54: {1}
22.97/11.10	Used ordering:
22.97/11.10	Polynomial interpretation [POLO]:
22.97/11.10	
22.97/11.10	   POL(*top*_10(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_11(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_12(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_13(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_14(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_15(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_16(x_1)) = x_1
22.97/11.10	   POL(*top*_18(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_19(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_20(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_21(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_22(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_23(x_1)) = x_1
22.97/11.10	   POL(*top*_3(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_4(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_5(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_6(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_7(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_8(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_9(x_1)) = 1 + x_1
22.97/11.10	   POL(a_31) = 0
22.97/11.10	   POL(f_33(x_1)) = x_1
22.97/11.10	   POL(f_34(x_1)) = x_1
22.97/11.10	   POL(f_35(x_1)) = x_1
22.97/11.10	   POL(f_36(x_1)) = x_1
22.97/11.10	   POL(f_37(x_1)) = x_1
22.97/11.10	   POL(f_38(x_1)) = x_1
22.97/11.10	   POL(f_39(x_1)) = x_1
22.97/11.10	   POL(f_40(x_1)) = x_1
22.97/11.10	   POL(f_41(x_1)) = x_1
22.97/11.10	   POL(f_42(x_1)) = x_1
22.97/11.10	   POL(f_43(x_1)) = x_1
22.97/11.10	   POL(f_44(x_1)) = x_1
22.97/11.10	   POL(f_45(x_1)) = x_1
22.97/11.10	   POL(f_46(x_1)) = x_1
22.97/11.10	   POL(f_47(x_1)) = x_1
22.97/11.10	   POL(f_48(x_1)) = x_1
22.97/11.10	   POL(f_49(x_1)) = x_1
22.97/11.10	   POL(f_50(x_1)) = x_1
22.97/11.10	   POL(f_51(x_1)) = x_1
22.97/11.10	   POL(f_52(x_1)) = x_1
22.97/11.10	   POL(f_53(x_1)) = x_1
22.97/11.10	   POL(f_54(x_1)) = 1 + x_1
22.97/11.10	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
22.97/11.10	
22.97/11.10	   *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))) -> *top*_16(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))
22.97/11.10	
22.97/11.10	
22.97/11.10	
22.97/11.10	
22.97/11.10	----------------------------------------
22.97/11.10	
22.97/11.10	(28)
22.97/11.10	Obligation:
22.97/11.10	Context-sensitive rewrite system:
22.97/11.10	The TRS R consists of the following rules:
22.97/11.10	
22.97/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.10	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.10	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.10	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.10	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.10	
22.97/11.10	The replacement map contains the following entries:
22.97/11.10	
22.97/11.10	a_31: empty set
22.97/11.10	f_34: {1}
22.97/11.10	*top*_3: {1}
22.97/11.10	f_33: {1}
22.97/11.10	*top*_4: {1}
22.97/11.10	f_35: {1}
22.97/11.10	*top*_5: {1}
22.97/11.10	f_36: {1}
22.97/11.10	*top*_6: {1}
22.97/11.10	f_37: {1}
22.97/11.10	*top*_7: {1}
22.97/11.10	f_38: {1}
22.97/11.10	*top*_8: {1}
22.97/11.10	f_39: {1}
22.97/11.10	*top*_9: {1}
22.97/11.10	f_40: {1}
22.97/11.10	*top*_10: {1}
22.97/11.10	f_41: {1}
22.97/11.10	*top*_11: {1}
22.97/11.10	f_42: {1}
22.97/11.10	*top*_12: {1}
22.97/11.10	f_43: {1}
22.97/11.10	*top*_13: {1}
22.97/11.10	f_44: {1}
22.97/11.10	*top*_14: {1}
22.97/11.10	f_45: {1}
22.97/11.10	*top*_15: {1}
22.97/11.10	f_46: {1}
22.97/11.10	f_47: {1}
22.97/11.10	f_48: {1}
22.97/11.10	*top*_18: {1}
22.97/11.10	f_49: {1}
22.97/11.10	*top*_19: {1}
22.97/11.10	f_50: {1}
22.97/11.10	*top*_20: {1}
22.97/11.10	f_51: {1}
22.97/11.10	*top*_21: {1}
22.97/11.10	f_52: {1}
22.97/11.10	*top*_22: {1}
22.97/11.10	f_53: {1}
22.97/11.10	*top*_23: {1}
22.97/11.10	f_54: {1}
22.97/11.10	
22.97/11.10	----------------------------------------
22.97/11.10	
22.97/11.10	(29) CSRRRRProof (EQUIVALENT)
22.97/11.10	The following CSR is given: Context-sensitive rewrite system:
22.97/11.10	The TRS R consists of the following rules:
22.97/11.10	
22.97/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
22.97/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
22.97/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
22.97/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
22.97/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
22.97/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
22.97/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
22.97/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
22.97/11.10	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
22.97/11.10	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
22.97/11.10	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
22.97/11.10	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
22.97/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
22.97/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
22.97/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
22.97/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
22.97/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
22.97/11.10	
22.97/11.10	The replacement map contains the following entries:
22.97/11.10	
22.97/11.10	a_31: empty set
22.97/11.10	f_34: {1}
22.97/11.10	*top*_3: {1}
22.97/11.10	f_33: {1}
22.97/11.10	*top*_4: {1}
22.97/11.10	f_35: {1}
22.97/11.10	*top*_5: {1}
22.97/11.10	f_36: {1}
22.97/11.10	*top*_6: {1}
22.97/11.10	f_37: {1}
22.97/11.10	*top*_7: {1}
22.97/11.10	f_38: {1}
22.97/11.10	*top*_8: {1}
22.97/11.10	f_39: {1}
22.97/11.10	*top*_9: {1}
22.97/11.10	f_40: {1}
22.97/11.10	*top*_10: {1}
22.97/11.10	f_41: {1}
22.97/11.10	*top*_11: {1}
22.97/11.10	f_42: {1}
22.97/11.10	*top*_12: {1}
22.97/11.10	f_43: {1}
22.97/11.10	*top*_13: {1}
22.97/11.10	f_44: {1}
22.97/11.10	*top*_14: {1}
22.97/11.10	f_45: {1}
22.97/11.10	*top*_15: {1}
22.97/11.10	f_46: {1}
22.97/11.10	f_47: {1}
22.97/11.10	f_48: {1}
22.97/11.10	*top*_18: {1}
22.97/11.10	f_49: {1}
22.97/11.10	*top*_19: {1}
22.97/11.10	f_50: {1}
22.97/11.10	*top*_20: {1}
22.97/11.10	f_51: {1}
22.97/11.10	*top*_21: {1}
22.97/11.10	f_52: {1}
22.97/11.10	*top*_22: {1}
22.97/11.10	f_53: {1}
22.97/11.10	*top*_23: {1}
22.97/11.10	f_54: {1}
22.97/11.10	Used ordering:
22.97/11.10	Polynomial interpretation [POLO]:
22.97/11.10	
22.97/11.10	   POL(*top*_10(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_11(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_12(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_13(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_14(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_15(x_1)) = x_1
22.97/11.10	   POL(*top*_18(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_19(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_20(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_21(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_22(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_23(x_1)) = x_1
22.97/11.10	   POL(*top*_3(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_4(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_5(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_6(x_1)) = 1 + x_1
22.97/11.10	   POL(*top*_7(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_8(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_9(x_1)) = 1 + x_1
23.01/11.10	   POL(a_31) = 0
23.01/11.10	   POL(f_33(x_1)) = x_1
23.01/11.10	   POL(f_34(x_1)) = x_1
23.01/11.10	   POL(f_35(x_1)) = x_1
23.01/11.10	   POL(f_36(x_1)) = x_1
23.01/11.10	   POL(f_37(x_1)) = x_1
23.01/11.10	   POL(f_38(x_1)) = x_1
23.01/11.10	   POL(f_39(x_1)) = x_1
23.01/11.10	   POL(f_40(x_1)) = x_1
23.01/11.10	   POL(f_41(x_1)) = x_1
23.01/11.10	   POL(f_42(x_1)) = x_1
23.01/11.10	   POL(f_43(x_1)) = x_1
23.01/11.10	   POL(f_44(x_1)) = x_1
23.01/11.10	   POL(f_45(x_1)) = x_1
23.01/11.10	   POL(f_46(x_1)) = x_1
23.01/11.10	   POL(f_47(x_1)) = x_1
23.01/11.10	   POL(f_48(x_1)) = x_1
23.01/11.10	   POL(f_49(x_1)) = x_1
23.01/11.10	   POL(f_50(x_1)) = x_1
23.01/11.10	   POL(f_51(x_1)) = x_1
23.01/11.10	   POL(f_52(x_1)) = x_1
23.01/11.10	   POL(f_53(x_1)) = x_1
23.01/11.10	   POL(f_54(x_1)) = 1 + x_1
23.01/11.10	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
23.01/11.10	
23.01/11.10	   *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))) -> *top*_15(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))
23.01/11.10	
23.01/11.10	
23.01/11.10	
23.01/11.10	
23.01/11.10	----------------------------------------
23.01/11.10	
23.01/11.10	(30)
23.01/11.10	Obligation:
23.01/11.10	Context-sensitive rewrite system:
23.01/11.10	The TRS R consists of the following rules:
23.01/11.10	
23.01/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
23.01/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
23.01/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
23.01/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
23.01/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
23.01/11.10	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
23.01/11.10	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
23.01/11.10	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
23.01/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.10	
23.01/11.10	The replacement map contains the following entries:
23.01/11.10	
23.01/11.10	a_31: empty set
23.01/11.10	f_34: {1}
23.01/11.10	*top*_3: {1}
23.01/11.10	f_33: {1}
23.01/11.10	*top*_4: {1}
23.01/11.10	f_35: {1}
23.01/11.10	*top*_5: {1}
23.01/11.10	f_36: {1}
23.01/11.10	*top*_6: {1}
23.01/11.10	f_37: {1}
23.01/11.10	*top*_7: {1}
23.01/11.10	f_38: {1}
23.01/11.10	*top*_8: {1}
23.01/11.10	f_39: {1}
23.01/11.10	*top*_9: {1}
23.01/11.10	f_40: {1}
23.01/11.10	*top*_10: {1}
23.01/11.10	f_41: {1}
23.01/11.10	*top*_11: {1}
23.01/11.10	f_42: {1}
23.01/11.10	*top*_12: {1}
23.01/11.10	f_43: {1}
23.01/11.10	*top*_13: {1}
23.01/11.10	f_44: {1}
23.01/11.10	*top*_14: {1}
23.01/11.10	f_45: {1}
23.01/11.10	f_46: {1}
23.01/11.10	f_47: {1}
23.01/11.10	f_48: {1}
23.01/11.10	*top*_18: {1}
23.01/11.10	f_49: {1}
23.01/11.10	*top*_19: {1}
23.01/11.10	f_50: {1}
23.01/11.10	*top*_20: {1}
23.01/11.10	f_51: {1}
23.01/11.10	*top*_21: {1}
23.01/11.10	f_52: {1}
23.01/11.10	*top*_22: {1}
23.01/11.10	f_53: {1}
23.01/11.10	*top*_23: {1}
23.01/11.10	f_54: {1}
23.01/11.10	
23.01/11.10	----------------------------------------
23.01/11.10	
23.01/11.10	(31) CSRRRRProof (EQUIVALENT)
23.01/11.10	The following CSR is given: Context-sensitive rewrite system:
23.01/11.10	The TRS R consists of the following rules:
23.01/11.10	
23.01/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
23.01/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
23.01/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
23.01/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
23.01/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
23.01/11.10	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
23.01/11.10	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
23.01/11.10	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
23.01/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.10	
23.01/11.10	The replacement map contains the following entries:
23.01/11.10	
23.01/11.10	a_31: empty set
23.01/11.10	f_34: {1}
23.01/11.10	*top*_3: {1}
23.01/11.10	f_33: {1}
23.01/11.10	*top*_4: {1}
23.01/11.10	f_35: {1}
23.01/11.10	*top*_5: {1}
23.01/11.10	f_36: {1}
23.01/11.10	*top*_6: {1}
23.01/11.10	f_37: {1}
23.01/11.10	*top*_7: {1}
23.01/11.10	f_38: {1}
23.01/11.10	*top*_8: {1}
23.01/11.10	f_39: {1}
23.01/11.10	*top*_9: {1}
23.01/11.10	f_40: {1}
23.01/11.10	*top*_10: {1}
23.01/11.10	f_41: {1}
23.01/11.10	*top*_11: {1}
23.01/11.10	f_42: {1}
23.01/11.10	*top*_12: {1}
23.01/11.10	f_43: {1}
23.01/11.10	*top*_13: {1}
23.01/11.10	f_44: {1}
23.01/11.10	*top*_14: {1}
23.01/11.10	f_45: {1}
23.01/11.10	f_46: {1}
23.01/11.10	f_47: {1}
23.01/11.10	f_48: {1}
23.01/11.10	*top*_18: {1}
23.01/11.10	f_49: {1}
23.01/11.10	*top*_19: {1}
23.01/11.10	f_50: {1}
23.01/11.10	*top*_20: {1}
23.01/11.10	f_51: {1}
23.01/11.10	*top*_21: {1}
23.01/11.10	f_52: {1}
23.01/11.10	*top*_22: {1}
23.01/11.10	f_53: {1}
23.01/11.10	*top*_23: {1}
23.01/11.10	f_54: {1}
23.01/11.10	Used ordering:
23.01/11.10	Polynomial interpretation [POLO]:
23.01/11.10	
23.01/11.10	   POL(*top*_10(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_11(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_12(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_13(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_14(x_1)) = x_1
23.01/11.10	   POL(*top*_18(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_19(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_20(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_21(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_22(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_23(x_1)) = x_1
23.01/11.10	   POL(*top*_3(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_4(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_5(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_6(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_7(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_8(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_9(x_1)) = 1 + x_1
23.01/11.10	   POL(a_31) = 0
23.01/11.10	   POL(f_33(x_1)) = x_1
23.01/11.10	   POL(f_34(x_1)) = x_1
23.01/11.10	   POL(f_35(x_1)) = x_1
23.01/11.10	   POL(f_36(x_1)) = x_1
23.01/11.10	   POL(f_37(x_1)) = x_1
23.01/11.10	   POL(f_38(x_1)) = x_1
23.01/11.10	   POL(f_39(x_1)) = x_1
23.01/11.10	   POL(f_40(x_1)) = x_1
23.01/11.10	   POL(f_41(x_1)) = x_1
23.01/11.10	   POL(f_42(x_1)) = x_1
23.01/11.10	   POL(f_43(x_1)) = x_1
23.01/11.10	   POL(f_44(x_1)) = x_1
23.01/11.10	   POL(f_45(x_1)) = x_1
23.01/11.10	   POL(f_46(x_1)) = x_1
23.01/11.10	   POL(f_47(x_1)) = x_1
23.01/11.10	   POL(f_48(x_1)) = x_1
23.01/11.10	   POL(f_49(x_1)) = x_1
23.01/11.10	   POL(f_50(x_1)) = x_1
23.01/11.10	   POL(f_51(x_1)) = x_1
23.01/11.10	   POL(f_52(x_1)) = x_1
23.01/11.10	   POL(f_53(x_1)) = x_1
23.01/11.10	   POL(f_54(x_1)) = 1 + x_1
23.01/11.10	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
23.01/11.10	
23.01/11.10	   *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))) -> *top*_14(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))
23.01/11.10	
23.01/11.10	
23.01/11.10	
23.01/11.10	
23.01/11.10	----------------------------------------
23.01/11.10	
23.01/11.10	(32)
23.01/11.10	Obligation:
23.01/11.10	Context-sensitive rewrite system:
23.01/11.10	The TRS R consists of the following rules:
23.01/11.10	
23.01/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
23.01/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
23.01/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
23.01/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
23.01/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
23.01/11.10	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
23.01/11.10	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
23.01/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.10	
23.01/11.10	The replacement map contains the following entries:
23.01/11.10	
23.01/11.10	a_31: empty set
23.01/11.10	f_34: {1}
23.01/11.10	*top*_3: {1}
23.01/11.10	f_33: {1}
23.01/11.10	*top*_4: {1}
23.01/11.10	f_35: {1}
23.01/11.10	*top*_5: {1}
23.01/11.10	f_36: {1}
23.01/11.10	*top*_6: {1}
23.01/11.10	f_37: {1}
23.01/11.10	*top*_7: {1}
23.01/11.10	f_38: {1}
23.01/11.10	*top*_8: {1}
23.01/11.10	f_39: {1}
23.01/11.10	*top*_9: {1}
23.01/11.10	f_40: {1}
23.01/11.10	*top*_10: {1}
23.01/11.10	f_41: {1}
23.01/11.10	*top*_11: {1}
23.01/11.10	f_42: {1}
23.01/11.10	*top*_12: {1}
23.01/11.10	f_43: {1}
23.01/11.10	*top*_13: {1}
23.01/11.10	f_44: {1}
23.01/11.10	f_45: {1}
23.01/11.10	f_46: {1}
23.01/11.10	f_47: {1}
23.01/11.10	f_48: {1}
23.01/11.10	*top*_18: {1}
23.01/11.10	f_49: {1}
23.01/11.10	*top*_19: {1}
23.01/11.10	f_50: {1}
23.01/11.10	*top*_20: {1}
23.01/11.10	f_51: {1}
23.01/11.10	*top*_21: {1}
23.01/11.10	f_52: {1}
23.01/11.10	*top*_22: {1}
23.01/11.10	f_53: {1}
23.01/11.10	*top*_23: {1}
23.01/11.10	f_54: {1}
23.01/11.10	
23.01/11.10	----------------------------------------
23.01/11.10	
23.01/11.10	(33) CSRRRRProof (EQUIVALENT)
23.01/11.10	The following CSR is given: Context-sensitive rewrite system:
23.01/11.10	The TRS R consists of the following rules:
23.01/11.10	
23.01/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
23.01/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
23.01/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
23.01/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
23.01/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
23.01/11.10	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
23.01/11.10	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
23.01/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.10	
23.01/11.10	The replacement map contains the following entries:
23.01/11.10	
23.01/11.10	a_31: empty set
23.01/11.10	f_34: {1}
23.01/11.10	*top*_3: {1}
23.01/11.10	f_33: {1}
23.01/11.10	*top*_4: {1}
23.01/11.10	f_35: {1}
23.01/11.10	*top*_5: {1}
23.01/11.10	f_36: {1}
23.01/11.10	*top*_6: {1}
23.01/11.10	f_37: {1}
23.01/11.10	*top*_7: {1}
23.01/11.10	f_38: {1}
23.01/11.10	*top*_8: {1}
23.01/11.10	f_39: {1}
23.01/11.10	*top*_9: {1}
23.01/11.10	f_40: {1}
23.01/11.10	*top*_10: {1}
23.01/11.10	f_41: {1}
23.01/11.10	*top*_11: {1}
23.01/11.10	f_42: {1}
23.01/11.10	*top*_12: {1}
23.01/11.10	f_43: {1}
23.01/11.10	*top*_13: {1}
23.01/11.10	f_44: {1}
23.01/11.10	f_45: {1}
23.01/11.10	f_46: {1}
23.01/11.10	f_47: {1}
23.01/11.10	f_48: {1}
23.01/11.10	*top*_18: {1}
23.01/11.10	f_49: {1}
23.01/11.10	*top*_19: {1}
23.01/11.10	f_50: {1}
23.01/11.10	*top*_20: {1}
23.01/11.10	f_51: {1}
23.01/11.10	*top*_21: {1}
23.01/11.10	f_52: {1}
23.01/11.10	*top*_22: {1}
23.01/11.10	f_53: {1}
23.01/11.10	*top*_23: {1}
23.01/11.10	f_54: {1}
23.01/11.10	Used ordering:
23.01/11.10	Polynomial interpretation [POLO]:
23.01/11.10	
23.01/11.10	   POL(*top*_10(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_11(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_12(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_13(x_1)) = x_1
23.01/11.10	   POL(*top*_18(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_19(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_20(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_21(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_22(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_23(x_1)) = x_1
23.01/11.10	   POL(*top*_3(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_4(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_5(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_6(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_7(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_8(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_9(x_1)) = 1 + x_1
23.01/11.10	   POL(a_31) = 0
23.01/11.10	   POL(f_33(x_1)) = x_1
23.01/11.10	   POL(f_34(x_1)) = x_1
23.01/11.10	   POL(f_35(x_1)) = x_1
23.01/11.10	   POL(f_36(x_1)) = x_1
23.01/11.10	   POL(f_37(x_1)) = x_1
23.01/11.10	   POL(f_38(x_1)) = x_1
23.01/11.10	   POL(f_39(x_1)) = x_1
23.01/11.10	   POL(f_40(x_1)) = x_1
23.01/11.10	   POL(f_41(x_1)) = x_1
23.01/11.10	   POL(f_42(x_1)) = x_1
23.01/11.10	   POL(f_43(x_1)) = x_1
23.01/11.10	   POL(f_44(x_1)) = x_1
23.01/11.10	   POL(f_45(x_1)) = x_1
23.01/11.10	   POL(f_46(x_1)) = x_1
23.01/11.10	   POL(f_47(x_1)) = x_1
23.01/11.10	   POL(f_48(x_1)) = x_1
23.01/11.10	   POL(f_49(x_1)) = x_1
23.01/11.10	   POL(f_50(x_1)) = x_1
23.01/11.10	   POL(f_51(x_1)) = x_1
23.01/11.10	   POL(f_52(x_1)) = x_1
23.01/11.10	   POL(f_53(x_1)) = x_1
23.01/11.10	   POL(f_54(x_1)) = 1 + x_1
23.01/11.10	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
23.01/11.10	
23.01/11.10	   *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))) -> *top*_13(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))
23.01/11.10	
23.01/11.10	
23.01/11.10	
23.01/11.10	
23.01/11.10	----------------------------------------
23.01/11.10	
23.01/11.10	(34)
23.01/11.10	Obligation:
23.01/11.10	Context-sensitive rewrite system:
23.01/11.10	The TRS R consists of the following rules:
23.01/11.10	
23.01/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
23.01/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
23.01/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
23.01/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
23.01/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
23.01/11.10	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
23.01/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.10	
23.01/11.10	The replacement map contains the following entries:
23.01/11.10	
23.01/11.10	a_31: empty set
23.01/11.10	f_34: {1}
23.01/11.10	*top*_3: {1}
23.01/11.10	f_33: {1}
23.01/11.10	*top*_4: {1}
23.01/11.10	f_35: {1}
23.01/11.10	*top*_5: {1}
23.01/11.10	f_36: {1}
23.01/11.10	*top*_6: {1}
23.01/11.10	f_37: {1}
23.01/11.10	*top*_7: {1}
23.01/11.10	f_38: {1}
23.01/11.10	*top*_8: {1}
23.01/11.10	f_39: {1}
23.01/11.10	*top*_9: {1}
23.01/11.10	f_40: {1}
23.01/11.10	*top*_10: {1}
23.01/11.10	f_41: {1}
23.01/11.10	*top*_11: {1}
23.01/11.10	f_42: {1}
23.01/11.10	*top*_12: {1}
23.01/11.10	f_43: {1}
23.01/11.10	f_44: {1}
23.01/11.10	f_45: {1}
23.01/11.10	f_46: {1}
23.01/11.10	f_47: {1}
23.01/11.10	f_48: {1}
23.01/11.10	*top*_18: {1}
23.01/11.10	f_49: {1}
23.01/11.10	*top*_19: {1}
23.01/11.10	f_50: {1}
23.01/11.10	*top*_20: {1}
23.01/11.10	f_51: {1}
23.01/11.10	*top*_21: {1}
23.01/11.10	f_52: {1}
23.01/11.10	*top*_22: {1}
23.01/11.10	f_53: {1}
23.01/11.10	*top*_23: {1}
23.01/11.10	f_54: {1}
23.01/11.10	
23.01/11.10	----------------------------------------
23.01/11.10	
23.01/11.10	(35) CSRRRRProof (EQUIVALENT)
23.01/11.10	The following CSR is given: Context-sensitive rewrite system:
23.01/11.10	The TRS R consists of the following rules:
23.01/11.10	
23.01/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
23.01/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
23.01/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
23.01/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
23.01/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
23.01/11.10	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
23.01/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.10	
23.01/11.10	The replacement map contains the following entries:
23.01/11.10	
23.01/11.10	a_31: empty set
23.01/11.10	f_34: {1}
23.01/11.10	*top*_3: {1}
23.01/11.10	f_33: {1}
23.01/11.10	*top*_4: {1}
23.01/11.10	f_35: {1}
23.01/11.10	*top*_5: {1}
23.01/11.10	f_36: {1}
23.01/11.10	*top*_6: {1}
23.01/11.10	f_37: {1}
23.01/11.10	*top*_7: {1}
23.01/11.10	f_38: {1}
23.01/11.10	*top*_8: {1}
23.01/11.10	f_39: {1}
23.01/11.10	*top*_9: {1}
23.01/11.10	f_40: {1}
23.01/11.10	*top*_10: {1}
23.01/11.10	f_41: {1}
23.01/11.10	*top*_11: {1}
23.01/11.10	f_42: {1}
23.01/11.10	*top*_12: {1}
23.01/11.10	f_43: {1}
23.01/11.10	f_44: {1}
23.01/11.10	f_45: {1}
23.01/11.10	f_46: {1}
23.01/11.10	f_47: {1}
23.01/11.10	f_48: {1}
23.01/11.10	*top*_18: {1}
23.01/11.10	f_49: {1}
23.01/11.10	*top*_19: {1}
23.01/11.10	f_50: {1}
23.01/11.10	*top*_20: {1}
23.01/11.10	f_51: {1}
23.01/11.10	*top*_21: {1}
23.01/11.10	f_52: {1}
23.01/11.10	*top*_22: {1}
23.01/11.10	f_53: {1}
23.01/11.10	*top*_23: {1}
23.01/11.10	f_54: {1}
23.01/11.10	Used ordering:
23.01/11.10	Polynomial interpretation [POLO]:
23.01/11.10	
23.01/11.10	   POL(*top*_10(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_11(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_12(x_1)) = x_1
23.01/11.10	   POL(*top*_18(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_19(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_20(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_21(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_22(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_23(x_1)) = x_1
23.01/11.10	   POL(*top*_3(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_4(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_5(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_6(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_7(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_8(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_9(x_1)) = 1 + x_1
23.01/11.10	   POL(a_31) = 0
23.01/11.10	   POL(f_33(x_1)) = x_1
23.01/11.10	   POL(f_34(x_1)) = x_1
23.01/11.10	   POL(f_35(x_1)) = x_1
23.01/11.10	   POL(f_36(x_1)) = x_1
23.01/11.10	   POL(f_37(x_1)) = x_1
23.01/11.10	   POL(f_38(x_1)) = x_1
23.01/11.10	   POL(f_39(x_1)) = x_1
23.01/11.10	   POL(f_40(x_1)) = x_1
23.01/11.10	   POL(f_41(x_1)) = x_1
23.01/11.10	   POL(f_42(x_1)) = x_1
23.01/11.10	   POL(f_43(x_1)) = x_1
23.01/11.10	   POL(f_44(x_1)) = x_1
23.01/11.10	   POL(f_45(x_1)) = x_1
23.01/11.10	   POL(f_46(x_1)) = x_1
23.01/11.10	   POL(f_47(x_1)) = x_1
23.01/11.10	   POL(f_48(x_1)) = x_1
23.01/11.10	   POL(f_49(x_1)) = x_1
23.01/11.10	   POL(f_50(x_1)) = x_1
23.01/11.10	   POL(f_51(x_1)) = x_1
23.01/11.10	   POL(f_52(x_1)) = x_1
23.01/11.10	   POL(f_53(x_1)) = x_1
23.01/11.10	   POL(f_54(x_1)) = 1 + x_1
23.01/11.10	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
23.01/11.10	
23.01/11.10	   *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))) -> *top*_12(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))
23.01/11.10	
23.01/11.10	
23.01/11.10	
23.01/11.10	
23.01/11.10	----------------------------------------
23.01/11.10	
23.01/11.10	(36)
23.01/11.10	Obligation:
23.01/11.10	Context-sensitive rewrite system:
23.01/11.10	The TRS R consists of the following rules:
23.01/11.10	
23.01/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
23.01/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
23.01/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
23.01/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
23.01/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
23.01/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.10	
23.01/11.10	The replacement map contains the following entries:
23.01/11.10	
23.01/11.10	a_31: empty set
23.01/11.10	f_34: {1}
23.01/11.10	*top*_3: {1}
23.01/11.10	f_33: {1}
23.01/11.10	*top*_4: {1}
23.01/11.10	f_35: {1}
23.01/11.10	*top*_5: {1}
23.01/11.10	f_36: {1}
23.01/11.10	*top*_6: {1}
23.01/11.10	f_37: {1}
23.01/11.10	*top*_7: {1}
23.01/11.10	f_38: {1}
23.01/11.10	*top*_8: {1}
23.01/11.10	f_39: {1}
23.01/11.10	*top*_9: {1}
23.01/11.10	f_40: {1}
23.01/11.10	*top*_10: {1}
23.01/11.10	f_41: {1}
23.01/11.10	*top*_11: {1}
23.01/11.10	f_42: {1}
23.01/11.10	f_43: {1}
23.01/11.10	f_44: {1}
23.01/11.10	f_45: {1}
23.01/11.10	f_46: {1}
23.01/11.10	f_47: {1}
23.01/11.10	f_48: {1}
23.01/11.10	*top*_18: {1}
23.01/11.10	f_49: {1}
23.01/11.10	*top*_19: {1}
23.01/11.10	f_50: {1}
23.01/11.10	*top*_20: {1}
23.01/11.10	f_51: {1}
23.01/11.10	*top*_21: {1}
23.01/11.10	f_52: {1}
23.01/11.10	*top*_22: {1}
23.01/11.10	f_53: {1}
23.01/11.10	*top*_23: {1}
23.01/11.10	f_54: {1}
23.01/11.10	
23.01/11.10	----------------------------------------
23.01/11.10	
23.01/11.10	(37) CSRRRRProof (EQUIVALENT)
23.01/11.10	The following CSR is given: Context-sensitive rewrite system:
23.01/11.10	The TRS R consists of the following rules:
23.01/11.10	
23.01/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
23.01/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
23.01/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
23.01/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
23.01/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
23.01/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.10	
23.01/11.10	The replacement map contains the following entries:
23.01/11.10	
23.01/11.10	a_31: empty set
23.01/11.10	f_34: {1}
23.01/11.10	*top*_3: {1}
23.01/11.10	f_33: {1}
23.01/11.10	*top*_4: {1}
23.01/11.10	f_35: {1}
23.01/11.10	*top*_5: {1}
23.01/11.10	f_36: {1}
23.01/11.10	*top*_6: {1}
23.01/11.10	f_37: {1}
23.01/11.10	*top*_7: {1}
23.01/11.10	f_38: {1}
23.01/11.10	*top*_8: {1}
23.01/11.10	f_39: {1}
23.01/11.10	*top*_9: {1}
23.01/11.10	f_40: {1}
23.01/11.10	*top*_10: {1}
23.01/11.10	f_41: {1}
23.01/11.10	*top*_11: {1}
23.01/11.10	f_42: {1}
23.01/11.10	f_43: {1}
23.01/11.10	f_44: {1}
23.01/11.10	f_45: {1}
23.01/11.10	f_46: {1}
23.01/11.10	f_47: {1}
23.01/11.10	f_48: {1}
23.01/11.10	*top*_18: {1}
23.01/11.10	f_49: {1}
23.01/11.10	*top*_19: {1}
23.01/11.10	f_50: {1}
23.01/11.10	*top*_20: {1}
23.01/11.10	f_51: {1}
23.01/11.10	*top*_21: {1}
23.01/11.10	f_52: {1}
23.01/11.10	*top*_22: {1}
23.01/11.10	f_53: {1}
23.01/11.10	*top*_23: {1}
23.01/11.10	f_54: {1}
23.01/11.10	Used ordering:
23.01/11.10	Polynomial interpretation [POLO]:
23.01/11.10	
23.01/11.10	   POL(*top*_10(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_11(x_1)) = x_1
23.01/11.10	   POL(*top*_18(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_19(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_20(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_21(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_22(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_23(x_1)) = x_1
23.01/11.10	   POL(*top*_3(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_4(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_5(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_6(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_7(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_8(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_9(x_1)) = 1 + x_1
23.01/11.10	   POL(a_31) = 0
23.01/11.10	   POL(f_33(x_1)) = x_1
23.01/11.10	   POL(f_34(x_1)) = x_1
23.01/11.10	   POL(f_35(x_1)) = x_1
23.01/11.10	   POL(f_36(x_1)) = x_1
23.01/11.10	   POL(f_37(x_1)) = x_1
23.01/11.10	   POL(f_38(x_1)) = x_1
23.01/11.10	   POL(f_39(x_1)) = x_1
23.01/11.10	   POL(f_40(x_1)) = x_1
23.01/11.10	   POL(f_41(x_1)) = x_1
23.01/11.10	   POL(f_42(x_1)) = x_1
23.01/11.10	   POL(f_43(x_1)) = x_1
23.01/11.10	   POL(f_44(x_1)) = x_1
23.01/11.10	   POL(f_45(x_1)) = x_1
23.01/11.10	   POL(f_46(x_1)) = x_1
23.01/11.10	   POL(f_47(x_1)) = x_1
23.01/11.10	   POL(f_48(x_1)) = x_1
23.01/11.10	   POL(f_49(x_1)) = x_1
23.01/11.10	   POL(f_50(x_1)) = x_1
23.01/11.10	   POL(f_51(x_1)) = x_1
23.01/11.10	   POL(f_52(x_1)) = x_1
23.01/11.10	   POL(f_53(x_1)) = x_1
23.01/11.10	   POL(f_54(x_1)) = 1 + x_1
23.01/11.10	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
23.01/11.10	
23.01/11.10	   *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))) -> *top*_11(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))
23.01/11.10	
23.01/11.10	
23.01/11.10	
23.01/11.10	
23.01/11.10	----------------------------------------
23.01/11.10	
23.01/11.10	(38)
23.01/11.10	Obligation:
23.01/11.10	Context-sensitive rewrite system:
23.01/11.10	The TRS R consists of the following rules:
23.01/11.10	
23.01/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
23.01/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
23.01/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
23.01/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
23.01/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.10	
23.01/11.10	The replacement map contains the following entries:
23.01/11.10	
23.01/11.10	a_31: empty set
23.01/11.10	f_34: {1}
23.01/11.10	*top*_3: {1}
23.01/11.10	f_33: {1}
23.01/11.10	*top*_4: {1}
23.01/11.10	f_35: {1}
23.01/11.10	*top*_5: {1}
23.01/11.10	f_36: {1}
23.01/11.10	*top*_6: {1}
23.01/11.10	f_37: {1}
23.01/11.10	*top*_7: {1}
23.01/11.10	f_38: {1}
23.01/11.10	*top*_8: {1}
23.01/11.10	f_39: {1}
23.01/11.10	*top*_9: {1}
23.01/11.10	f_40: {1}
23.01/11.10	*top*_10: {1}
23.01/11.10	f_41: {1}
23.01/11.10	f_42: {1}
23.01/11.10	f_43: {1}
23.01/11.10	f_44: {1}
23.01/11.10	f_45: {1}
23.01/11.10	f_46: {1}
23.01/11.10	f_47: {1}
23.01/11.10	f_48: {1}
23.01/11.10	*top*_18: {1}
23.01/11.10	f_49: {1}
23.01/11.10	*top*_19: {1}
23.01/11.10	f_50: {1}
23.01/11.10	*top*_20: {1}
23.01/11.10	f_51: {1}
23.01/11.10	*top*_21: {1}
23.01/11.10	f_52: {1}
23.01/11.10	*top*_22: {1}
23.01/11.10	f_53: {1}
23.01/11.10	*top*_23: {1}
23.01/11.10	f_54: {1}
23.01/11.10	
23.01/11.10	----------------------------------------
23.01/11.10	
23.01/11.10	(39) CSRRRRProof (EQUIVALENT)
23.01/11.10	The following CSR is given: Context-sensitive rewrite system:
23.01/11.10	The TRS R consists of the following rules:
23.01/11.10	
23.01/11.10	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.10	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.10	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.10	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
23.01/11.10	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
23.01/11.10	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
23.01/11.10	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
23.01/11.10	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.10	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.10	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.10	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.10	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.10	
23.01/11.10	The replacement map contains the following entries:
23.01/11.10	
23.01/11.10	a_31: empty set
23.01/11.10	f_34: {1}
23.01/11.10	*top*_3: {1}
23.01/11.10	f_33: {1}
23.01/11.10	*top*_4: {1}
23.01/11.10	f_35: {1}
23.01/11.10	*top*_5: {1}
23.01/11.10	f_36: {1}
23.01/11.10	*top*_6: {1}
23.01/11.10	f_37: {1}
23.01/11.10	*top*_7: {1}
23.01/11.10	f_38: {1}
23.01/11.10	*top*_8: {1}
23.01/11.10	f_39: {1}
23.01/11.10	*top*_9: {1}
23.01/11.10	f_40: {1}
23.01/11.10	*top*_10: {1}
23.01/11.10	f_41: {1}
23.01/11.10	f_42: {1}
23.01/11.10	f_43: {1}
23.01/11.10	f_44: {1}
23.01/11.10	f_45: {1}
23.01/11.10	f_46: {1}
23.01/11.10	f_47: {1}
23.01/11.10	f_48: {1}
23.01/11.10	*top*_18: {1}
23.01/11.10	f_49: {1}
23.01/11.10	*top*_19: {1}
23.01/11.10	f_50: {1}
23.01/11.10	*top*_20: {1}
23.01/11.10	f_51: {1}
23.01/11.10	*top*_21: {1}
23.01/11.10	f_52: {1}
23.01/11.10	*top*_22: {1}
23.01/11.10	f_53: {1}
23.01/11.10	*top*_23: {1}
23.01/11.10	f_54: {1}
23.01/11.10	Used ordering:
23.01/11.10	Polynomial interpretation [POLO]:
23.01/11.10	
23.01/11.10	   POL(*top*_10(x_1)) = x_1
23.01/11.10	   POL(*top*_18(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_19(x_1)) = x_1
23.01/11.10	   POL(*top*_20(x_1)) = x_1
23.01/11.10	   POL(*top*_21(x_1)) = x_1
23.01/11.10	   POL(*top*_22(x_1)) = x_1
23.01/11.10	   POL(*top*_23(x_1)) = x_1
23.01/11.10	   POL(*top*_3(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_4(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_5(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_6(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_7(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_8(x_1)) = 1 + x_1
23.01/11.10	   POL(*top*_9(x_1)) = 1 + x_1
23.01/11.10	   POL(a_31) = 0
23.01/11.10	   POL(f_33(x_1)) = x_1
23.01/11.10	   POL(f_34(x_1)) = x_1
23.01/11.10	   POL(f_35(x_1)) = x_1
23.01/11.10	   POL(f_36(x_1)) = x_1
23.01/11.10	   POL(f_37(x_1)) = x_1
23.01/11.10	   POL(f_38(x_1)) = x_1
23.01/11.10	   POL(f_39(x_1)) = x_1
23.01/11.10	   POL(f_40(x_1)) = x_1
23.01/11.10	   POL(f_41(x_1)) = x_1
23.01/11.10	   POL(f_42(x_1)) = x_1
23.01/11.10	   POL(f_43(x_1)) = x_1
23.01/11.10	   POL(f_44(x_1)) = x_1
23.01/11.10	   POL(f_45(x_1)) = x_1
23.01/11.10	   POL(f_46(x_1)) = x_1
23.01/11.10	   POL(f_47(x_1)) = x_1
23.01/11.10	   POL(f_48(x_1)) = x_1
23.01/11.10	   POL(f_49(x_1)) = x_1
23.01/11.11	   POL(f_50(x_1)) = 1 + x_1
23.01/11.11	   POL(f_51(x_1)) = x_1
23.01/11.11	   POL(f_52(x_1)) = x_1
23.01/11.11	   POL(f_53(x_1)) = x_1
23.01/11.11	   POL(f_54(x_1)) = x_1
23.01/11.11	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
23.01/11.11	
23.01/11.11	   *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))) -> *top*_10(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(40)
23.01/11.11	Obligation:
23.01/11.11	Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.11	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.11	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.11	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
23.01/11.11	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
23.01/11.11	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.11	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	*top*_3: {1}
23.01/11.11	f_33: {1}
23.01/11.11	*top*_4: {1}
23.01/11.11	f_35: {1}
23.01/11.11	*top*_5: {1}
23.01/11.11	f_36: {1}
23.01/11.11	*top*_6: {1}
23.01/11.11	f_37: {1}
23.01/11.11	*top*_7: {1}
23.01/11.11	f_38: {1}
23.01/11.11	*top*_8: {1}
23.01/11.11	f_39: {1}
23.01/11.11	*top*_9: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	*top*_21: {1}
23.01/11.11	f_52: {1}
23.01/11.11	*top*_22: {1}
23.01/11.11	f_53: {1}
23.01/11.11	*top*_23: {1}
23.01/11.11	f_54: {1}
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(41) CSRRRRProof (EQUIVALENT)
23.01/11.11	The following CSR is given: Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.11	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.11	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.11	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
23.01/11.11	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
23.01/11.11	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.11	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	*top*_3: {1}
23.01/11.11	f_33: {1}
23.01/11.11	*top*_4: {1}
23.01/11.11	f_35: {1}
23.01/11.11	*top*_5: {1}
23.01/11.11	f_36: {1}
23.01/11.11	*top*_6: {1}
23.01/11.11	f_37: {1}
23.01/11.11	*top*_7: {1}
23.01/11.11	f_38: {1}
23.01/11.11	*top*_8: {1}
23.01/11.11	f_39: {1}
23.01/11.11	*top*_9: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	*top*_21: {1}
23.01/11.11	f_52: {1}
23.01/11.11	*top*_22: {1}
23.01/11.11	f_53: {1}
23.01/11.11	*top*_23: {1}
23.01/11.11	f_54: {1}
23.01/11.11	Used ordering:
23.01/11.11	Polynomial interpretation [POLO]:
23.01/11.11	
23.01/11.11	   POL(*top*_18(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_19(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_20(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_21(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_22(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_23(x_1)) = x_1
23.01/11.11	   POL(*top*_3(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_4(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_5(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_6(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_7(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_8(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_9(x_1)) = x_1
23.01/11.11	   POL(a_31) = 0
23.01/11.11	   POL(f_33(x_1)) = x_1
23.01/11.11	   POL(f_34(x_1)) = x_1
23.01/11.11	   POL(f_35(x_1)) = x_1
23.01/11.11	   POL(f_36(x_1)) = x_1
23.01/11.11	   POL(f_37(x_1)) = x_1
23.01/11.11	   POL(f_38(x_1)) = x_1
23.01/11.11	   POL(f_39(x_1)) = x_1
23.01/11.11	   POL(f_40(x_1)) = x_1
23.01/11.11	   POL(f_41(x_1)) = x_1
23.01/11.11	   POL(f_42(x_1)) = x_1
23.01/11.11	   POL(f_43(x_1)) = x_1
23.01/11.11	   POL(f_44(x_1)) = x_1
23.01/11.11	   POL(f_45(x_1)) = x_1
23.01/11.11	   POL(f_46(x_1)) = x_1
23.01/11.11	   POL(f_47(x_1)) = x_1
23.01/11.11	   POL(f_48(x_1)) = x_1
23.01/11.11	   POL(f_49(x_1)) = x_1
23.01/11.11	   POL(f_50(x_1)) = x_1
23.01/11.11	   POL(f_51(x_1)) = x_1
23.01/11.11	   POL(f_52(x_1)) = x_1
23.01/11.11	   POL(f_53(x_1)) = x_1
23.01/11.11	   POL(f_54(x_1)) = 1 + x_1
23.01/11.11	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
23.01/11.11	
23.01/11.11	   *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))) -> *top*_9(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(42)
23.01/11.11	Obligation:
23.01/11.11	Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.11	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.11	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.11	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
23.01/11.11	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.11	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	*top*_3: {1}
23.01/11.11	f_33: {1}
23.01/11.11	*top*_4: {1}
23.01/11.11	f_35: {1}
23.01/11.11	*top*_5: {1}
23.01/11.11	f_36: {1}
23.01/11.11	*top*_6: {1}
23.01/11.11	f_37: {1}
23.01/11.11	*top*_7: {1}
23.01/11.11	f_38: {1}
23.01/11.11	*top*_8: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	*top*_21: {1}
23.01/11.11	f_52: {1}
23.01/11.11	*top*_22: {1}
23.01/11.11	f_53: {1}
23.01/11.11	*top*_23: {1}
23.01/11.11	f_54: {1}
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(43) CSRRRRProof (EQUIVALENT)
23.01/11.11	The following CSR is given: Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.11	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.11	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.11	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
23.01/11.11	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.11	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	*top*_3: {1}
23.01/11.11	f_33: {1}
23.01/11.11	*top*_4: {1}
23.01/11.11	f_35: {1}
23.01/11.11	*top*_5: {1}
23.01/11.11	f_36: {1}
23.01/11.11	*top*_6: {1}
23.01/11.11	f_37: {1}
23.01/11.11	*top*_7: {1}
23.01/11.11	f_38: {1}
23.01/11.11	*top*_8: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	*top*_21: {1}
23.01/11.11	f_52: {1}
23.01/11.11	*top*_22: {1}
23.01/11.11	f_53: {1}
23.01/11.11	*top*_23: {1}
23.01/11.11	f_54: {1}
23.01/11.11	Used ordering:
23.01/11.11	Polynomial interpretation [POLO]:
23.01/11.11	
23.01/11.11	   POL(*top*_18(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_19(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_20(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_21(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_22(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_23(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_3(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_4(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_5(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_6(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_7(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_8(x_1)) = x_1
23.01/11.11	   POL(a_31) = 0
23.01/11.11	   POL(f_33(x_1)) = x_1
23.01/11.11	   POL(f_34(x_1)) = x_1
23.01/11.11	   POL(f_35(x_1)) = x_1
23.01/11.11	   POL(f_36(x_1)) = x_1
23.01/11.11	   POL(f_37(x_1)) = x_1
23.01/11.11	   POL(f_38(x_1)) = x_1
23.01/11.11	   POL(f_39(x_1)) = x_1
23.01/11.11	   POL(f_40(x_1)) = x_1
23.01/11.11	   POL(f_41(x_1)) = x_1
23.01/11.11	   POL(f_42(x_1)) = x_1
23.01/11.11	   POL(f_43(x_1)) = x_1
23.01/11.11	   POL(f_44(x_1)) = x_1
23.01/11.11	   POL(f_45(x_1)) = x_1
23.01/11.11	   POL(f_46(x_1)) = x_1
23.01/11.11	   POL(f_47(x_1)) = x_1
23.01/11.11	   POL(f_48(x_1)) = x_1
23.01/11.11	   POL(f_49(x_1)) = x_1
23.01/11.11	   POL(f_50(x_1)) = x_1
23.01/11.11	   POL(f_51(x_1)) = x_1
23.01/11.11	   POL(f_52(x_1)) = x_1
23.01/11.11	   POL(f_53(x_1)) = x_1
23.01/11.11	   POL(f_54(x_1)) = x_1
23.01/11.11	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
23.01/11.11	
23.01/11.11	   *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))) -> *top*_8(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(44)
23.01/11.11	Obligation:
23.01/11.11	Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.11	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.11	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.11	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.11	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	*top*_3: {1}
23.01/11.11	f_33: {1}
23.01/11.11	*top*_4: {1}
23.01/11.11	f_35: {1}
23.01/11.11	*top*_5: {1}
23.01/11.11	f_36: {1}
23.01/11.11	*top*_6: {1}
23.01/11.11	f_37: {1}
23.01/11.11	*top*_7: {1}
23.01/11.11	f_38: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	*top*_21: {1}
23.01/11.11	f_52: {1}
23.01/11.11	*top*_22: {1}
23.01/11.11	f_53: {1}
23.01/11.11	*top*_23: {1}
23.01/11.11	f_54: {1}
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(45) CSRRRRProof (EQUIVALENT)
23.01/11.11	The following CSR is given: Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.11	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.11	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.11	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.11	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	*top*_3: {1}
23.01/11.11	f_33: {1}
23.01/11.11	*top*_4: {1}
23.01/11.11	f_35: {1}
23.01/11.11	*top*_5: {1}
23.01/11.11	f_36: {1}
23.01/11.11	*top*_6: {1}
23.01/11.11	f_37: {1}
23.01/11.11	*top*_7: {1}
23.01/11.11	f_38: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	*top*_21: {1}
23.01/11.11	f_52: {1}
23.01/11.11	*top*_22: {1}
23.01/11.11	f_53: {1}
23.01/11.11	*top*_23: {1}
23.01/11.11	f_54: {1}
23.01/11.11	Used ordering:
23.01/11.11	Polynomial interpretation [POLO]:
23.01/11.11	
23.01/11.11	   POL(*top*_18(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_19(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_20(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_21(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_22(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_23(x_1)) = x_1
23.01/11.11	   POL(*top*_3(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_4(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_5(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_6(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_7(x_1)) = x_1
23.01/11.11	   POL(a_31) = 0
23.01/11.11	   POL(f_33(x_1)) = x_1
23.01/11.11	   POL(f_34(x_1)) = x_1
23.01/11.11	   POL(f_35(x_1)) = x_1
23.01/11.11	   POL(f_36(x_1)) = x_1
23.01/11.11	   POL(f_37(x_1)) = x_1
23.01/11.11	   POL(f_38(x_1)) = x_1
23.01/11.11	   POL(f_39(x_1)) = x_1
23.01/11.11	   POL(f_40(x_1)) = x_1
23.01/11.11	   POL(f_41(x_1)) = x_1
23.01/11.11	   POL(f_42(x_1)) = x_1
23.01/11.11	   POL(f_43(x_1)) = x_1
23.01/11.11	   POL(f_44(x_1)) = x_1
23.01/11.11	   POL(f_45(x_1)) = x_1
23.01/11.11	   POL(f_46(x_1)) = x_1
23.01/11.11	   POL(f_47(x_1)) = x_1
23.01/11.11	   POL(f_48(x_1)) = x_1
23.01/11.11	   POL(f_49(x_1)) = x_1
23.01/11.11	   POL(f_50(x_1)) = x_1
23.01/11.11	   POL(f_51(x_1)) = x_1
23.01/11.11	   POL(f_52(x_1)) = x_1
23.01/11.11	   POL(f_53(x_1)) = x_1
23.01/11.11	   POL(f_54(x_1)) = 1 + x_1
23.01/11.11	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
23.01/11.11	
23.01/11.11	   *top*_6(f_37(f_36(f_35(f_33(f_34(a_31)))))) -> *top*_7(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(46)
23.01/11.11	Obligation:
23.01/11.11	Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.11	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.11	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.11	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	*top*_3: {1}
23.01/11.11	f_33: {1}
23.01/11.11	*top*_4: {1}
23.01/11.11	f_35: {1}
23.01/11.11	*top*_5: {1}
23.01/11.11	f_36: {1}
23.01/11.11	*top*_6: {1}
23.01/11.11	f_37: {1}
23.01/11.11	f_38: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	*top*_21: {1}
23.01/11.11	f_52: {1}
23.01/11.11	*top*_22: {1}
23.01/11.11	f_53: {1}
23.01/11.11	*top*_23: {1}
23.01/11.11	f_54: {1}
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(47) CSRRRRProof (EQUIVALENT)
23.01/11.11	The following CSR is given: Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.11	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.11	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.11	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	*top*_3: {1}
23.01/11.11	f_33: {1}
23.01/11.11	*top*_4: {1}
23.01/11.11	f_35: {1}
23.01/11.11	*top*_5: {1}
23.01/11.11	f_36: {1}
23.01/11.11	*top*_6: {1}
23.01/11.11	f_37: {1}
23.01/11.11	f_38: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	*top*_21: {1}
23.01/11.11	f_52: {1}
23.01/11.11	*top*_22: {1}
23.01/11.11	f_53: {1}
23.01/11.11	*top*_23: {1}
23.01/11.11	f_54: {1}
23.01/11.11	Used ordering:
23.01/11.11	Polynomial interpretation [POLO]:
23.01/11.11	
23.01/11.11	   POL(*top*_18(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_19(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_20(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_21(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_22(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_23(x_1)) = x_1
23.01/11.11	   POL(*top*_3(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_4(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_5(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_6(x_1)) = x_1
23.01/11.11	   POL(a_31) = 0
23.01/11.11	   POL(f_33(x_1)) = x_1
23.01/11.11	   POL(f_34(x_1)) = x_1
23.01/11.11	   POL(f_35(x_1)) = x_1
23.01/11.11	   POL(f_36(x_1)) = x_1
23.01/11.11	   POL(f_37(x_1)) = 1 + x_1
23.01/11.11	   POL(f_38(x_1)) = x_1
23.01/11.11	   POL(f_39(x_1)) = x_1
23.01/11.11	   POL(f_40(x_1)) = x_1
23.01/11.11	   POL(f_41(x_1)) = x_1
23.01/11.11	   POL(f_42(x_1)) = x_1
23.01/11.11	   POL(f_43(x_1)) = x_1
23.01/11.11	   POL(f_44(x_1)) = x_1
23.01/11.11	   POL(f_45(x_1)) = x_1
23.01/11.11	   POL(f_46(x_1)) = x_1
23.01/11.11	   POL(f_47(x_1)) = x_1
23.01/11.11	   POL(f_48(x_1)) = x_1
23.01/11.11	   POL(f_49(x_1)) = x_1
23.01/11.11	   POL(f_50(x_1)) = x_1
23.01/11.11	   POL(f_51(x_1)) = x_1
23.01/11.11	   POL(f_52(x_1)) = x_1
23.01/11.11	   POL(f_53(x_1)) = x_1
23.01/11.11	   POL(f_54(x_1)) = x_1
23.01/11.11	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
23.01/11.11	
23.01/11.11	   *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))) -> *top*_23(f_54(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))))
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(48)
23.01/11.11	Obligation:
23.01/11.11	Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.11	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.11	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	*top*_3: {1}
23.01/11.11	f_33: {1}
23.01/11.11	*top*_4: {1}
23.01/11.11	f_35: {1}
23.01/11.11	*top*_5: {1}
23.01/11.11	f_36: {1}
23.01/11.11	*top*_6: {1}
23.01/11.11	f_37: {1}
23.01/11.11	f_38: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	*top*_21: {1}
23.01/11.11	f_52: {1}
23.01/11.11	*top*_22: {1}
23.01/11.11	f_53: {1}
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(49) CSRRRRProof (EQUIVALENT)
23.01/11.11	The following CSR is given: Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.11	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.11	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	*top*_3: {1}
23.01/11.11	f_33: {1}
23.01/11.11	*top*_4: {1}
23.01/11.11	f_35: {1}
23.01/11.11	*top*_5: {1}
23.01/11.11	f_36: {1}
23.01/11.11	*top*_6: {1}
23.01/11.11	f_37: {1}
23.01/11.11	f_38: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	*top*_21: {1}
23.01/11.11	f_52: {1}
23.01/11.11	*top*_22: {1}
23.01/11.11	f_53: {1}
23.01/11.11	Used ordering:
23.01/11.11	Polynomial interpretation [POLO]:
23.01/11.11	
23.01/11.11	   POL(*top*_18(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_19(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_20(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_21(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_22(x_1)) = x_1
23.01/11.11	   POL(*top*_3(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_4(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_5(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_6(x_1)) = x_1
23.01/11.11	   POL(a_31) = 0
23.01/11.11	   POL(f_33(x_1)) = x_1
23.01/11.11	   POL(f_34(x_1)) = x_1
23.01/11.11	   POL(f_35(x_1)) = x_1
23.01/11.11	   POL(f_36(x_1)) = x_1
23.01/11.11	   POL(f_37(x_1)) = 1 + x_1
23.01/11.11	   POL(f_38(x_1)) = x_1
23.01/11.11	   POL(f_39(x_1)) = x_1
23.01/11.11	   POL(f_40(x_1)) = x_1
23.01/11.11	   POL(f_41(x_1)) = x_1
23.01/11.11	   POL(f_42(x_1)) = x_1
23.01/11.11	   POL(f_43(x_1)) = x_1
23.01/11.11	   POL(f_44(x_1)) = x_1
23.01/11.11	   POL(f_45(x_1)) = x_1
23.01/11.11	   POL(f_46(x_1)) = x_1
23.01/11.11	   POL(f_47(x_1)) = x_1
23.01/11.11	   POL(f_48(x_1)) = x_1
23.01/11.11	   POL(f_49(x_1)) = x_1
23.01/11.11	   POL(f_50(x_1)) = x_1
23.01/11.11	   POL(f_51(x_1)) = x_1
23.01/11.11	   POL(f_52(x_1)) = x_1
23.01/11.11	   POL(f_53(x_1)) = x_1
23.01/11.11	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
23.01/11.11	
23.01/11.11	   *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))) -> *top*_22(f_53(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))))
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(50)
23.01/11.11	Obligation:
23.01/11.11	Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.11	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.11	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	*top*_3: {1}
23.01/11.11	f_33: {1}
23.01/11.11	*top*_4: {1}
23.01/11.11	f_35: {1}
23.01/11.11	*top*_5: {1}
23.01/11.11	f_36: {1}
23.01/11.11	*top*_6: {1}
23.01/11.11	f_37: {1}
23.01/11.11	f_38: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	*top*_21: {1}
23.01/11.11	f_52: {1}
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(51) CSRRRRProof (EQUIVALENT)
23.01/11.11	The following CSR is given: Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.11	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.11	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	*top*_3: {1}
23.01/11.11	f_33: {1}
23.01/11.11	*top*_4: {1}
23.01/11.11	f_35: {1}
23.01/11.11	*top*_5: {1}
23.01/11.11	f_36: {1}
23.01/11.11	*top*_6: {1}
23.01/11.11	f_37: {1}
23.01/11.11	f_38: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	*top*_21: {1}
23.01/11.11	f_52: {1}
23.01/11.11	Used ordering:
23.01/11.11	Polynomial interpretation [POLO]:
23.01/11.11	
23.01/11.11	   POL(*top*_18(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_19(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_20(x_1)) = x_1
23.01/11.11	   POL(*top*_21(x_1)) = x_1
23.01/11.11	   POL(*top*_3(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_4(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_5(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_6(x_1)) = x_1
23.01/11.11	   POL(a_31) = 0
23.01/11.11	   POL(f_33(x_1)) = x_1
23.01/11.11	   POL(f_34(x_1)) = x_1
23.01/11.11	   POL(f_35(x_1)) = x_1
23.01/11.11	   POL(f_36(x_1)) = x_1
23.01/11.11	   POL(f_37(x_1)) = x_1
23.01/11.11	   POL(f_38(x_1)) = x_1
23.01/11.11	   POL(f_39(x_1)) = x_1
23.01/11.11	   POL(f_40(x_1)) = x_1
23.01/11.11	   POL(f_41(x_1)) = x_1
23.01/11.11	   POL(f_42(x_1)) = x_1
23.01/11.11	   POL(f_43(x_1)) = x_1
23.01/11.11	   POL(f_44(x_1)) = x_1
23.01/11.11	   POL(f_45(x_1)) = x_1
23.01/11.11	   POL(f_46(x_1)) = x_1
23.01/11.11	   POL(f_47(x_1)) = x_1
23.01/11.11	   POL(f_48(x_1)) = x_1
23.01/11.11	   POL(f_49(x_1)) = x_1
23.01/11.11	   POL(f_50(x_1)) = x_1
23.01/11.11	   POL(f_51(x_1)) = 1 + x_1
23.01/11.11	   POL(f_52(x_1)) = x_1
23.01/11.11	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
23.01/11.11	
23.01/11.11	   *top*_5(f_36(f_35(f_33(f_34(a_31))))) -> *top*_6(f_37(f_36(f_35(f_33(f_34(a_31))))))
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(52)
23.01/11.11	Obligation:
23.01/11.11	Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.11	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	*top*_3: {1}
23.01/11.11	f_33: {1}
23.01/11.11	*top*_4: {1}
23.01/11.11	f_35: {1}
23.01/11.11	*top*_5: {1}
23.01/11.11	f_36: {1}
23.01/11.11	f_37: {1}
23.01/11.11	f_38: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	*top*_21: {1}
23.01/11.11	f_52: {1}
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(53) CSRRRRProof (EQUIVALENT)
23.01/11.11	The following CSR is given: Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.11	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	*top*_3: {1}
23.01/11.11	f_33: {1}
23.01/11.11	*top*_4: {1}
23.01/11.11	f_35: {1}
23.01/11.11	*top*_5: {1}
23.01/11.11	f_36: {1}
23.01/11.11	f_37: {1}
23.01/11.11	f_38: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	*top*_21: {1}
23.01/11.11	f_52: {1}
23.01/11.11	Used ordering:
23.01/11.11	Polynomial interpretation [POLO]:
23.01/11.11	
23.01/11.11	   POL(*top*_18(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_19(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_20(x_1)) = x_1
23.01/11.11	   POL(*top*_21(x_1)) = x_1
23.01/11.11	   POL(*top*_3(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_4(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_5(x_1)) = x_1
23.01/11.11	   POL(a_31) = 0
23.01/11.11	   POL(f_33(x_1)) = x_1
23.01/11.11	   POL(f_34(x_1)) = x_1
23.01/11.11	   POL(f_35(x_1)) = x_1
23.01/11.11	   POL(f_36(x_1)) = x_1
23.01/11.11	   POL(f_37(x_1)) = x_1
23.01/11.11	   POL(f_38(x_1)) = x_1
23.01/11.11	   POL(f_39(x_1)) = x_1
23.01/11.11	   POL(f_40(x_1)) = x_1
23.01/11.11	   POL(f_41(x_1)) = x_1
23.01/11.11	   POL(f_42(x_1)) = x_1
23.01/11.11	   POL(f_43(x_1)) = x_1
23.01/11.11	   POL(f_44(x_1)) = x_1
23.01/11.11	   POL(f_45(x_1)) = x_1
23.01/11.11	   POL(f_46(x_1)) = x_1
23.01/11.11	   POL(f_47(x_1)) = x_1
23.01/11.11	   POL(f_48(x_1)) = x_1
23.01/11.11	   POL(f_49(x_1)) = x_1
23.01/11.11	   POL(f_50(x_1)) = x_1
23.01/11.11	   POL(f_51(x_1)) = 1 + x_1
23.01/11.11	   POL(f_52(x_1)) = x_1
23.01/11.11	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
23.01/11.11	
23.01/11.11	   *top*_4(f_35(f_33(f_34(a_31)))) -> *top*_5(f_36(f_35(f_33(f_34(a_31)))))
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(54)
23.01/11.11	Obligation:
23.01/11.11	Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	*top*_3: {1}
23.01/11.11	f_33: {1}
23.01/11.11	*top*_4: {1}
23.01/11.11	f_35: {1}
23.01/11.11	f_36: {1}
23.01/11.11	f_37: {1}
23.01/11.11	f_38: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	*top*_21: {1}
23.01/11.11	f_52: {1}
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(55) CSRRRRProof (EQUIVALENT)
23.01/11.11	The following CSR is given: Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	*top*_3: {1}
23.01/11.11	f_33: {1}
23.01/11.11	*top*_4: {1}
23.01/11.11	f_35: {1}
23.01/11.11	f_36: {1}
23.01/11.11	f_37: {1}
23.01/11.11	f_38: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	*top*_21: {1}
23.01/11.11	f_52: {1}
23.01/11.11	Used ordering:
23.01/11.11	Polynomial interpretation [POLO]:
23.01/11.11	
23.01/11.11	   POL(*top*_18(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_19(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_20(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_21(x_1)) = x_1
23.01/11.11	   POL(*top*_3(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_4(x_1)) = x_1
23.01/11.11	   POL(a_31) = 0
23.01/11.11	   POL(f_33(x_1)) = x_1
23.01/11.11	   POL(f_34(x_1)) = x_1
23.01/11.11	   POL(f_35(x_1)) = x_1
23.01/11.11	   POL(f_36(x_1)) = x_1
23.01/11.11	   POL(f_37(x_1)) = x_1
23.01/11.11	   POL(f_38(x_1)) = x_1
23.01/11.11	   POL(f_39(x_1)) = x_1
23.01/11.11	   POL(f_40(x_1)) = x_1
23.01/11.11	   POL(f_41(x_1)) = x_1
23.01/11.11	   POL(f_42(x_1)) = x_1
23.01/11.11	   POL(f_43(x_1)) = x_1
23.01/11.11	   POL(f_44(x_1)) = x_1
23.01/11.11	   POL(f_45(x_1)) = x_1
23.01/11.11	   POL(f_46(x_1)) = x_1
23.01/11.11	   POL(f_47(x_1)) = x_1
23.01/11.11	   POL(f_48(x_1)) = x_1
23.01/11.11	   POL(f_49(x_1)) = x_1
23.01/11.11	   POL(f_50(x_1)) = x_1
23.01/11.11	   POL(f_51(x_1)) = x_1
23.01/11.11	   POL(f_52(x_1)) = 1 + x_1
23.01/11.11	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
23.01/11.11	
23.01/11.11	   *top*_3(f_33(f_34(a_31))) -> *top*_4(f_35(f_33(f_34(a_31))))
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(56)
23.01/11.11	Obligation:
23.01/11.11	Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	f_33: {1}
23.01/11.11	f_35: {1}
23.01/11.11	f_36: {1}
23.01/11.11	f_37: {1}
23.01/11.11	f_38: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	*top*_21: {1}
23.01/11.11	f_52: {1}
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(57) CSRRRRProof (EQUIVALENT)
23.01/11.11	The following CSR is given: Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	f_33: {1}
23.01/11.11	f_35: {1}
23.01/11.11	f_36: {1}
23.01/11.11	f_37: {1}
23.01/11.11	f_38: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	*top*_21: {1}
23.01/11.11	f_52: {1}
23.01/11.11	Used ordering:
23.01/11.11	Polynomial interpretation [POLO]:
23.01/11.11	
23.01/11.11	   POL(*top*_18(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_19(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_20(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_21(x_1)) = x_1
23.01/11.11	   POL(a_31) = 0
23.01/11.11	   POL(f_33(x_1)) = x_1
23.01/11.11	   POL(f_34(x_1)) = x_1
23.01/11.11	   POL(f_35(x_1)) = x_1
23.01/11.11	   POL(f_36(x_1)) = x_1
23.01/11.11	   POL(f_37(x_1)) = x_1
23.01/11.11	   POL(f_38(x_1)) = x_1
23.01/11.11	   POL(f_39(x_1)) = x_1
23.01/11.11	   POL(f_40(x_1)) = x_1
23.01/11.11	   POL(f_41(x_1)) = x_1
23.01/11.11	   POL(f_42(x_1)) = x_1
23.01/11.11	   POL(f_43(x_1)) = x_1
23.01/11.11	   POL(f_44(x_1)) = x_1
23.01/11.11	   POL(f_45(x_1)) = x_1
23.01/11.11	   POL(f_46(x_1)) = x_1
23.01/11.11	   POL(f_47(x_1)) = x_1
23.01/11.11	   POL(f_48(x_1)) = x_1
23.01/11.11	   POL(f_49(x_1)) = x_1
23.01/11.11	   POL(f_50(x_1)) = x_1
23.01/11.11	   POL(f_51(x_1)) = x_1
23.01/11.11	   POL(f_52(x_1)) = x_1
23.01/11.11	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
23.01/11.11	
23.01/11.11	   *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))) -> *top*_21(f_52(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))))
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(58)
23.01/11.11	Obligation:
23.01/11.11	Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	f_33: {1}
23.01/11.11	f_35: {1}
23.01/11.11	f_36: {1}
23.01/11.11	f_37: {1}
23.01/11.11	f_38: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(59) CSRRRRProof (EQUIVALENT)
23.01/11.11	The following CSR is given: Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	f_33: {1}
23.01/11.11	f_35: {1}
23.01/11.11	f_36: {1}
23.01/11.11	f_37: {1}
23.01/11.11	f_38: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	*top*_20: {1}
23.01/11.11	f_51: {1}
23.01/11.11	Used ordering:
23.01/11.11	Polynomial interpretation [POLO]:
23.01/11.11	
23.01/11.11	   POL(*top*_18(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_19(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_20(x_1)) = x_1
23.01/11.11	   POL(a_31) = 0
23.01/11.11	   POL(f_33(x_1)) = x_1
23.01/11.11	   POL(f_34(x_1)) = x_1
23.01/11.11	   POL(f_35(x_1)) = x_1
23.01/11.11	   POL(f_36(x_1)) = x_1
23.01/11.11	   POL(f_37(x_1)) = x_1
23.01/11.11	   POL(f_38(x_1)) = x_1
23.01/11.11	   POL(f_39(x_1)) = x_1
23.01/11.11	   POL(f_40(x_1)) = x_1
23.01/11.11	   POL(f_41(x_1)) = x_1
23.01/11.11	   POL(f_42(x_1)) = x_1
23.01/11.11	   POL(f_43(x_1)) = x_1
23.01/11.11	   POL(f_44(x_1)) = x_1
23.01/11.11	   POL(f_45(x_1)) = x_1
23.01/11.11	   POL(f_46(x_1)) = x_1
23.01/11.11	   POL(f_47(x_1)) = x_1
23.01/11.11	   POL(f_48(x_1)) = x_1
23.01/11.11	   POL(f_49(x_1)) = x_1
23.01/11.11	   POL(f_50(x_1)) = x_1
23.01/11.11	   POL(f_51(x_1)) = x_1
23.01/11.11	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
23.01/11.11	
23.01/11.11	   *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))) -> *top*_20(f_51(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31))))))))))))))))))))
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(60)
23.01/11.11	Obligation:
23.01/11.11	Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	f_33: {1}
23.01/11.11	f_35: {1}
23.01/11.11	f_36: {1}
23.01/11.11	f_37: {1}
23.01/11.11	f_38: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(61) CSRRRRProof (EQUIVALENT)
23.01/11.11	The following CSR is given: Context-sensitive rewrite system:
23.01/11.11	The TRS R consists of the following rules:
23.01/11.11	
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	
23.01/11.11	The replacement map contains the following entries:
23.01/11.11	
23.01/11.11	a_31: empty set
23.01/11.11	f_34: {1}
23.01/11.11	f_33: {1}
23.01/11.11	f_35: {1}
23.01/11.11	f_36: {1}
23.01/11.11	f_37: {1}
23.01/11.11	f_38: {1}
23.01/11.11	f_39: {1}
23.01/11.11	f_40: {1}
23.01/11.11	f_41: {1}
23.01/11.11	f_42: {1}
23.01/11.11	f_43: {1}
23.01/11.11	f_44: {1}
23.01/11.11	f_45: {1}
23.01/11.11	f_46: {1}
23.01/11.11	f_47: {1}
23.01/11.11	f_48: {1}
23.01/11.11	*top*_18: {1}
23.01/11.11	f_49: {1}
23.01/11.11	*top*_19: {1}
23.01/11.11	f_50: {1}
23.01/11.11	Used ordering:
23.01/11.11	Polynomial interpretation [POLO]:
23.01/11.11	
23.01/11.11	   POL(*top*_18(x_1)) = 1 + x_1
23.01/11.11	   POL(*top*_19(x_1)) = x_1
23.01/11.11	   POL(a_31) = 0
23.01/11.11	   POL(f_33(x_1)) = x_1
23.01/11.11	   POL(f_34(x_1)) = x_1
23.01/11.11	   POL(f_35(x_1)) = x_1
23.01/11.11	   POL(f_36(x_1)) = x_1
23.01/11.11	   POL(f_37(x_1)) = x_1
23.01/11.11	   POL(f_38(x_1)) = x_1
23.01/11.11	   POL(f_39(x_1)) = x_1
23.01/11.11	   POL(f_40(x_1)) = x_1
23.01/11.11	   POL(f_41(x_1)) = x_1
23.01/11.11	   POL(f_42(x_1)) = x_1
23.01/11.11	   POL(f_43(x_1)) = x_1
23.01/11.11	   POL(f_44(x_1)) = x_1
23.01/11.11	   POL(f_45(x_1)) = x_1
23.01/11.11	   POL(f_46(x_1)) = x_1
23.01/11.11	   POL(f_47(x_1)) = x_1
23.01/11.11	   POL(f_48(x_1)) = x_1
23.01/11.11	   POL(f_49(x_1)) = x_1
23.01/11.11	   POL(f_50(x_1)) = x_1
23.01/11.11	With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
23.01/11.11	
23.01/11.11	   *top*_18(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))) -> *top*_19(f_50(f_49(f_48(f_47(f_46(f_45(f_44(f_43(f_42(f_41(f_40(f_39(f_38(f_37(f_36(f_35(f_33(f_34(a_31)))))))))))))))))))
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(62)
23.01/11.11	Obligation:
23.01/11.11	Context-sensitive rewrite system:
23.01/11.11	R is empty.
23.01/11.11	
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(63) RisEmptyProof (EQUIVALENT)
23.01/11.11	The CSR R is empty. Hence, termination is trivially proven.
23.01/11.11	----------------------------------------
23.01/11.11	
23.01/11.11	(64)
23.01/11.11	YES
23.05/11.18	EOF