392.57/193.62 MAYBE 392.57/193.64 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 392.57/193.64 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 392.57/193.64 392.57/193.64 392.57/193.64 Outermost Termination of the given OTRS could not be shown: 392.57/193.64 392.57/193.64 (0) OTRS 392.57/193.64 (1) Thiemann-SpecialC-Transformation [EQUIVALENT, 0 ms] 392.57/193.64 (2) QTRS 392.57/193.64 (3) DependencyPairsProof [EQUIVALENT, 0 ms] 392.57/193.64 (4) QDP 392.57/193.64 (5) DependencyGraphProof [EQUIVALENT, 0 ms] 392.57/193.64 (6) AND 392.57/193.64 (7) QDP 392.57/193.64 (8) UsableRulesProof [EQUIVALENT, 0 ms] 392.57/193.64 (9) QDP 392.57/193.64 (10) QReductionProof [EQUIVALENT, 0 ms] 392.57/193.64 (11) QDP 392.57/193.64 (12) MRRProof [EQUIVALENT, 24 ms] 392.57/193.64 (13) QDP 392.57/193.64 (14) MRRProof [EQUIVALENT, 14 ms] 392.57/193.64 (15) QDP 392.57/193.64 (16) MRRProof [EQUIVALENT, 23 ms] 392.57/193.64 (17) QDP 392.57/193.64 (18) UsableRulesReductionPairsProof [EQUIVALENT, 7 ms] 392.57/193.64 (19) QDP 392.57/193.64 (20) DependencyGraphProof [EQUIVALENT, 0 ms] 392.57/193.64 (21) TRUE 392.57/193.64 (22) QDP 392.57/193.64 (23) UsableRulesProof [EQUIVALENT, 0 ms] 392.57/193.64 (24) QDP 392.57/193.65 (25) QReductionProof [EQUIVALENT, 0 ms] 392.57/193.65 (26) QDP 392.57/193.65 (27) TransformationProof [EQUIVALENT, 0 ms] 392.57/193.65 (28) QDP 392.57/193.65 (29) UsableRulesProof [EQUIVALENT, 0 ms] 392.57/193.65 (30) QDP 392.57/193.65 (31) QReductionProof [EQUIVALENT, 0 ms] 392.57/193.65 (32) QDP 392.57/193.65 (33) Trivial-Transformation [SOUND, 0 ms] 392.57/193.65 (34) QTRS 392.57/193.65 (35) DependencyPairsProof [EQUIVALENT, 0 ms] 392.57/193.65 (36) QDP 392.57/193.65 (37) DependencyGraphProof [EQUIVALENT, 0 ms] 392.57/193.65 (38) QDP 392.57/193.65 (39) TransformationProof [EQUIVALENT, 2 ms] 392.57/193.65 (40) QDP 392.57/193.65 (41) NonTerminationLoopProof [COMPLETE, 0 ms] 392.57/193.65 (42) NO 392.57/193.65 (43) Raffelsieper-Zantema-Transformation [SOUND, 127.6 s] 392.57/193.65 (44) QTRS 392.57/193.65 (45) DependencyPairsProof [EQUIVALENT, 1546 ms] 392.57/193.65 (46) QDP 392.57/193.65 (47) DependencyGraphProof [EQUIVALENT, 7 ms] 392.57/193.65 (48) AND 392.57/193.65 (49) QDP 392.57/193.65 (50) UsableRulesProof [EQUIVALENT, 535 ms] 392.57/193.65 (51) QDP 392.57/193.65 (52) QDPOrderProof [EQUIVALENT, 373 ms] 392.57/193.65 (53) QDP 392.57/193.65 (54) DependencyGraphProof [EQUIVALENT, 0 ms] 392.57/193.65 (55) QDP 392.57/193.65 (56) QDPSizeChangeProof [EQUIVALENT, 0 ms] 392.57/193.65 (57) YES 392.57/193.65 (58) QDP 392.57/193.65 392.57/193.65 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (0) 392.57/193.65 Obligation: 392.57/193.65 Term rewrite system R: 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 app(app(f, 0), n) -> app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n) 392.57/193.65 app(app(map, f), nil) -> nil 392.57/193.65 app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) 392.57/193.65 392.57/193.65 392.57/193.65 392.57/193.65 Outermost Strategy. 392.57/193.65 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (1) Thiemann-SpecialC-Transformation (EQUIVALENT) 392.57/193.65 We applied the Thiemann-SpecialC transformation to transform the outermost TRS to an innermost TRS. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (2) 392.57/193.65 Obligation: 392.57/193.65 Q restricted rewrite system: 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 top(go_up(x)) -> top(reduce(x)) 392.57/193.65 reduce(app(x_1, x_2)) -> check_app(redex_app(x_1, x_2)) 392.57/193.65 redex_app(app(f, 0), n) -> result_app(app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)) 392.57/193.65 redex_app(app(map, f), nil) -> result_app(nil) 392.57/193.65 redex_app(app(map, f), app(app(cons, x), xs)) -> result_app(app(app(cons, app(f, x)), app(app(map, f), xs))) 392.57/193.65 check_app(result_app(x)) -> go_up(x) 392.57/193.65 check_app(redex_app(x_1, x_2)) -> in_app_1(reduce(x_1), x_2) 392.57/193.65 check_app(redex_app(x_1, x_2)) -> in_app_2(x_1, reduce(x_2)) 392.57/193.65 in_app_1(go_up(x_1), x_2) -> go_up(app(x_1, x_2)) 392.57/193.65 in_app_2(x_1, go_up(x_2)) -> go_up(app(x_1, x_2)) 392.57/193.65 392.57/193.65 The set Q consists of the following terms: 392.57/193.65 392.57/193.65 top(go_up(x0)) 392.57/193.65 reduce(app(x0, x1)) 392.57/193.65 redex_app(app(x0, 0), x1) 392.57/193.65 redex_app(app(map, x0), nil) 392.57/193.65 redex_app(app(map, x0), app(app(cons, x1), x2)) 392.57/193.65 check_app(result_app(x0)) 392.57/193.65 check_app(redex_app(x0, x1)) 392.57/193.65 in_app_1(go_up(x0), x1) 392.57/193.65 in_app_2(x0, go_up(x1)) 392.57/193.65 392.57/193.65 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (3) DependencyPairsProof (EQUIVALENT) 392.57/193.65 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (4) 392.57/193.65 Obligation: 392.57/193.65 Q DP problem: 392.57/193.65 The TRS P consists of the following rules: 392.57/193.65 392.57/193.65 TOP(go_up(x)) -> TOP(reduce(x)) 392.57/193.65 TOP(go_up(x)) -> REDUCE(x) 392.57/193.65 REDUCE(app(x_1, x_2)) -> CHECK_APP(redex_app(x_1, x_2)) 392.57/193.65 REDUCE(app(x_1, x_2)) -> REDEX_APP(x_1, x_2) 392.57/193.65 CHECK_APP(redex_app(x_1, x_2)) -> IN_APP_1(reduce(x_1), x_2) 392.57/193.65 CHECK_APP(redex_app(x_1, x_2)) -> REDUCE(x_1) 392.57/193.65 CHECK_APP(redex_app(x_1, x_2)) -> IN_APP_2(x_1, reduce(x_2)) 392.57/193.65 CHECK_APP(redex_app(x_1, x_2)) -> REDUCE(x_2) 392.57/193.65 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 top(go_up(x)) -> top(reduce(x)) 392.57/193.65 reduce(app(x_1, x_2)) -> check_app(redex_app(x_1, x_2)) 392.57/193.65 redex_app(app(f, 0), n) -> result_app(app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)) 392.57/193.65 redex_app(app(map, f), nil) -> result_app(nil) 392.57/193.65 redex_app(app(map, f), app(app(cons, x), xs)) -> result_app(app(app(cons, app(f, x)), app(app(map, f), xs))) 392.57/193.65 check_app(result_app(x)) -> go_up(x) 392.57/193.65 check_app(redex_app(x_1, x_2)) -> in_app_1(reduce(x_1), x_2) 392.57/193.65 check_app(redex_app(x_1, x_2)) -> in_app_2(x_1, reduce(x_2)) 392.57/193.65 in_app_1(go_up(x_1), x_2) -> go_up(app(x_1, x_2)) 392.57/193.65 in_app_2(x_1, go_up(x_2)) -> go_up(app(x_1, x_2)) 392.57/193.65 392.57/193.65 The set Q consists of the following terms: 392.57/193.65 392.57/193.65 top(go_up(x0)) 392.57/193.65 reduce(app(x0, x1)) 392.57/193.65 redex_app(app(x0, 0), x1) 392.57/193.65 redex_app(app(map, x0), nil) 392.57/193.65 redex_app(app(map, x0), app(app(cons, x1), x2)) 392.57/193.65 check_app(result_app(x0)) 392.57/193.65 check_app(redex_app(x0, x1)) 392.57/193.65 in_app_1(go_up(x0), x1) 392.57/193.65 in_app_2(x0, go_up(x1)) 392.57/193.65 392.57/193.65 We have to consider all minimal (P,Q,R)-chains. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (5) DependencyGraphProof (EQUIVALENT) 392.57/193.65 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 4 less nodes. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (6) 392.57/193.65 Complex Obligation (AND) 392.57/193.65 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (7) 392.57/193.65 Obligation: 392.57/193.65 Q DP problem: 392.57/193.65 The TRS P consists of the following rules: 392.57/193.65 392.57/193.65 CHECK_APP(redex_app(x_1, x_2)) -> REDUCE(x_1) 392.57/193.65 REDUCE(app(x_1, x_2)) -> CHECK_APP(redex_app(x_1, x_2)) 392.57/193.65 CHECK_APP(redex_app(x_1, x_2)) -> REDUCE(x_2) 392.57/193.65 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 top(go_up(x)) -> top(reduce(x)) 392.57/193.65 reduce(app(x_1, x_2)) -> check_app(redex_app(x_1, x_2)) 392.57/193.65 redex_app(app(f, 0), n) -> result_app(app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)) 392.57/193.65 redex_app(app(map, f), nil) -> result_app(nil) 392.57/193.65 redex_app(app(map, f), app(app(cons, x), xs)) -> result_app(app(app(cons, app(f, x)), app(app(map, f), xs))) 392.57/193.65 check_app(result_app(x)) -> go_up(x) 392.57/193.65 check_app(redex_app(x_1, x_2)) -> in_app_1(reduce(x_1), x_2) 392.57/193.65 check_app(redex_app(x_1, x_2)) -> in_app_2(x_1, reduce(x_2)) 392.57/193.65 in_app_1(go_up(x_1), x_2) -> go_up(app(x_1, x_2)) 392.57/193.65 in_app_2(x_1, go_up(x_2)) -> go_up(app(x_1, x_2)) 392.57/193.65 392.57/193.65 The set Q consists of the following terms: 392.57/193.65 392.57/193.65 top(go_up(x0)) 392.57/193.65 reduce(app(x0, x1)) 392.57/193.65 redex_app(app(x0, 0), x1) 392.57/193.65 redex_app(app(map, x0), nil) 392.57/193.65 redex_app(app(map, x0), app(app(cons, x1), x2)) 392.57/193.65 check_app(result_app(x0)) 392.57/193.65 check_app(redex_app(x0, x1)) 392.57/193.65 in_app_1(go_up(x0), x1) 392.57/193.65 in_app_2(x0, go_up(x1)) 392.57/193.65 392.57/193.65 We have to consider all minimal (P,Q,R)-chains. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (8) UsableRulesProof (EQUIVALENT) 392.57/193.65 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (9) 392.57/193.65 Obligation: 392.57/193.65 Q DP problem: 392.57/193.65 The TRS P consists of the following rules: 392.57/193.65 392.57/193.65 CHECK_APP(redex_app(x_1, x_2)) -> REDUCE(x_1) 392.57/193.65 REDUCE(app(x_1, x_2)) -> CHECK_APP(redex_app(x_1, x_2)) 392.57/193.65 CHECK_APP(redex_app(x_1, x_2)) -> REDUCE(x_2) 392.57/193.65 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 redex_app(app(f, 0), n) -> result_app(app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)) 392.57/193.65 redex_app(app(map, f), nil) -> result_app(nil) 392.57/193.65 redex_app(app(map, f), app(app(cons, x), xs)) -> result_app(app(app(cons, app(f, x)), app(app(map, f), xs))) 392.57/193.65 392.57/193.65 The set Q consists of the following terms: 392.57/193.65 392.57/193.65 top(go_up(x0)) 392.57/193.65 reduce(app(x0, x1)) 392.57/193.65 redex_app(app(x0, 0), x1) 392.57/193.65 redex_app(app(map, x0), nil) 392.57/193.65 redex_app(app(map, x0), app(app(cons, x1), x2)) 392.57/193.65 check_app(result_app(x0)) 392.57/193.65 check_app(redex_app(x0, x1)) 392.57/193.65 in_app_1(go_up(x0), x1) 392.57/193.65 in_app_2(x0, go_up(x1)) 392.57/193.65 392.57/193.65 We have to consider all minimal (P,Q,R)-chains. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (10) QReductionProof (EQUIVALENT) 392.57/193.65 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 392.57/193.65 392.57/193.65 top(go_up(x0)) 392.57/193.65 reduce(app(x0, x1)) 392.57/193.65 check_app(result_app(x0)) 392.57/193.65 check_app(redex_app(x0, x1)) 392.57/193.65 in_app_1(go_up(x0), x1) 392.57/193.65 in_app_2(x0, go_up(x1)) 392.57/193.65 392.57/193.65 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (11) 392.57/193.65 Obligation: 392.57/193.65 Q DP problem: 392.57/193.65 The TRS P consists of the following rules: 392.57/193.65 392.57/193.65 CHECK_APP(redex_app(x_1, x_2)) -> REDUCE(x_1) 392.57/193.65 REDUCE(app(x_1, x_2)) -> CHECK_APP(redex_app(x_1, x_2)) 392.57/193.65 CHECK_APP(redex_app(x_1, x_2)) -> REDUCE(x_2) 392.57/193.65 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 redex_app(app(f, 0), n) -> result_app(app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)) 392.57/193.65 redex_app(app(map, f), nil) -> result_app(nil) 392.57/193.65 redex_app(app(map, f), app(app(cons, x), xs)) -> result_app(app(app(cons, app(f, x)), app(app(map, f), xs))) 392.57/193.65 392.57/193.65 The set Q consists of the following terms: 392.57/193.65 392.57/193.65 redex_app(app(x0, 0), x1) 392.57/193.65 redex_app(app(map, x0), nil) 392.57/193.65 redex_app(app(map, x0), app(app(cons, x1), x2)) 392.57/193.65 392.57/193.65 We have to consider all minimal (P,Q,R)-chains. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (12) MRRProof (EQUIVALENT) 392.57/193.65 By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. 392.57/193.65 392.57/193.65 392.57/193.65 Strictly oriented rules of the TRS R: 392.57/193.65 392.57/193.65 redex_app(app(map, f), nil) -> result_app(nil) 392.57/193.65 392.57/193.65 Used ordering: Polynomial interpretation [POLO]: 392.57/193.65 392.57/193.65 POL(0) = 1 392.57/193.65 POL(CHECK_APP(x_1)) = x_1 392.57/193.65 POL(REDUCE(x_1)) = 2*x_1 392.57/193.65 POL(app(x_1, x_2)) = x_1 + x_2 392.57/193.65 POL(cons) = 0 392.57/193.65 POL(hd) = 0 392.57/193.65 POL(map) = 0 392.57/193.65 POL(nil) = 1 392.57/193.65 POL(redex_app(x_1, x_2)) = 2*x_1 + 2*x_2 392.57/193.65 POL(result_app(x_1)) = x_1 392.57/193.65 392.57/193.65 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (13) 392.57/193.65 Obligation: 392.57/193.65 Q DP problem: 392.57/193.65 The TRS P consists of the following rules: 392.57/193.65 392.57/193.65 CHECK_APP(redex_app(x_1, x_2)) -> REDUCE(x_1) 392.57/193.65 REDUCE(app(x_1, x_2)) -> CHECK_APP(redex_app(x_1, x_2)) 392.57/193.65 CHECK_APP(redex_app(x_1, x_2)) -> REDUCE(x_2) 392.57/193.65 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 redex_app(app(f, 0), n) -> result_app(app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)) 392.57/193.65 redex_app(app(map, f), app(app(cons, x), xs)) -> result_app(app(app(cons, app(f, x)), app(app(map, f), xs))) 392.57/193.65 392.57/193.65 The set Q consists of the following terms: 392.57/193.65 392.57/193.65 redex_app(app(x0, 0), x1) 392.57/193.65 redex_app(app(map, x0), nil) 392.57/193.65 redex_app(app(map, x0), app(app(cons, x1), x2)) 392.57/193.65 392.57/193.65 We have to consider all minimal (P,Q,R)-chains. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (14) MRRProof (EQUIVALENT) 392.57/193.65 By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. 392.57/193.65 392.57/193.65 392.57/193.65 Strictly oriented rules of the TRS R: 392.57/193.65 392.57/193.65 redex_app(app(map, f), app(app(cons, x), xs)) -> result_app(app(app(cons, app(f, x)), app(app(map, f), xs))) 392.57/193.65 392.57/193.65 Used ordering: Polynomial interpretation [POLO]: 392.57/193.65 392.57/193.65 POL(0) = 0 392.57/193.65 POL(CHECK_APP(x_1)) = x_1 392.57/193.65 POL(REDUCE(x_1)) = 1 + 2*x_1 392.57/193.65 POL(app(x_1, x_2)) = x_1 + x_2 392.57/193.65 POL(cons) = 0 392.57/193.65 POL(hd) = 0 392.57/193.65 POL(map) = 0 392.57/193.65 POL(nil) = 1 392.57/193.65 POL(redex_app(x_1, x_2)) = 1 + 2*x_1 + 2*x_2 392.57/193.65 POL(result_app(x_1)) = x_1 392.57/193.65 392.57/193.65 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (15) 392.57/193.65 Obligation: 392.57/193.65 Q DP problem: 392.57/193.65 The TRS P consists of the following rules: 392.57/193.65 392.57/193.65 CHECK_APP(redex_app(x_1, x_2)) -> REDUCE(x_1) 392.57/193.65 REDUCE(app(x_1, x_2)) -> CHECK_APP(redex_app(x_1, x_2)) 392.57/193.65 CHECK_APP(redex_app(x_1, x_2)) -> REDUCE(x_2) 392.57/193.65 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 redex_app(app(f, 0), n) -> result_app(app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)) 392.57/193.65 392.57/193.65 The set Q consists of the following terms: 392.57/193.65 392.57/193.65 redex_app(app(x0, 0), x1) 392.57/193.65 redex_app(app(map, x0), nil) 392.57/193.65 redex_app(app(map, x0), app(app(cons, x1), x2)) 392.57/193.65 392.57/193.65 We have to consider all minimal (P,Q,R)-chains. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (16) MRRProof (EQUIVALENT) 392.57/193.65 By using the rule removal processor [LPAR04] with the following ordering, at least one Dependency Pair or term rewrite system rule of this QDP problem can be strictly oriented. 392.57/193.65 392.57/193.65 392.57/193.65 Strictly oriented rules of the TRS R: 392.57/193.65 392.57/193.65 redex_app(app(f, 0), n) -> result_app(app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)) 392.57/193.65 392.57/193.65 Used ordering: Polynomial interpretation [POLO]: 392.57/193.65 392.57/193.65 POL(0) = 0 392.57/193.65 POL(CHECK_APP(x_1)) = x_1 392.57/193.65 POL(REDUCE(x_1)) = 1 + x_1 392.57/193.65 POL(app(x_1, x_2)) = 2*x_1 + x_2 392.57/193.65 POL(cons) = 0 392.57/193.65 POL(hd) = 0 392.57/193.65 POL(map) = 0 392.57/193.65 POL(nil) = 0 392.57/193.65 POL(redex_app(x_1, x_2)) = 1 + 2*x_1 + x_2 392.57/193.65 POL(result_app(x_1)) = x_1 392.57/193.65 392.57/193.65 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (17) 392.57/193.65 Obligation: 392.57/193.65 Q DP problem: 392.57/193.65 The TRS P consists of the following rules: 392.57/193.65 392.57/193.65 CHECK_APP(redex_app(x_1, x_2)) -> REDUCE(x_1) 392.57/193.65 REDUCE(app(x_1, x_2)) -> CHECK_APP(redex_app(x_1, x_2)) 392.57/193.65 CHECK_APP(redex_app(x_1, x_2)) -> REDUCE(x_2) 392.57/193.65 392.57/193.65 R is empty. 392.57/193.65 The set Q consists of the following terms: 392.57/193.65 392.57/193.65 redex_app(app(x0, 0), x1) 392.57/193.65 redex_app(app(map, x0), nil) 392.57/193.65 redex_app(app(map, x0), app(app(cons, x1), x2)) 392.57/193.65 392.57/193.65 We have to consider all minimal (P,Q,R)-chains. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (18) UsableRulesReductionPairsProof (EQUIVALENT) 392.57/193.65 By using the usable rules with reduction pair processor [LPAR04] with a polynomial ordering [POLO], all dependency pairs and the corresponding usable rules [FROCOS05] can be oriented non-strictly. All non-usable rules are removed, and those dependency pairs and usable rules that have been oriented strictly or contain non-usable symbols in their left-hand side are removed as well. 392.57/193.65 392.57/193.65 The following dependency pairs can be deleted: 392.57/193.65 392.57/193.65 REDUCE(app(x_1, x_2)) -> CHECK_APP(redex_app(x_1, x_2)) 392.57/193.65 No rules are removed from R. 392.57/193.65 392.57/193.65 Used ordering: POLO with Polynomial interpretation [POLO]: 392.57/193.65 392.57/193.65 POL(CHECK_APP(x_1)) = 2*x_1 392.57/193.65 POL(REDUCE(x_1)) = 2*x_1 392.57/193.65 POL(app(x_1, x_2)) = 2*x_1 + 2*x_2 392.57/193.65 POL(redex_app(x_1, x_2)) = 2*x_1 + x_2 392.57/193.65 392.57/193.65 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (19) 392.57/193.65 Obligation: 392.57/193.65 Q DP problem: 392.57/193.65 The TRS P consists of the following rules: 392.57/193.65 392.57/193.65 CHECK_APP(redex_app(x_1, x_2)) -> REDUCE(x_1) 392.57/193.65 CHECK_APP(redex_app(x_1, x_2)) -> REDUCE(x_2) 392.57/193.65 392.57/193.65 R is empty. 392.57/193.65 The set Q consists of the following terms: 392.57/193.65 392.57/193.65 redex_app(app(x0, 0), x1) 392.57/193.65 redex_app(app(map, x0), nil) 392.57/193.65 redex_app(app(map, x0), app(app(cons, x1), x2)) 392.57/193.65 392.57/193.65 We have to consider all minimal (P,Q,R)-chains. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (20) DependencyGraphProof (EQUIVALENT) 392.57/193.65 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 0 SCCs with 2 less nodes. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (21) 392.57/193.65 TRUE 392.57/193.65 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (22) 392.57/193.65 Obligation: 392.57/193.65 Q DP problem: 392.57/193.65 The TRS P consists of the following rules: 392.57/193.65 392.57/193.65 TOP(go_up(x)) -> TOP(reduce(x)) 392.57/193.65 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 top(go_up(x)) -> top(reduce(x)) 392.57/193.65 reduce(app(x_1, x_2)) -> check_app(redex_app(x_1, x_2)) 392.57/193.65 redex_app(app(f, 0), n) -> result_app(app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)) 392.57/193.65 redex_app(app(map, f), nil) -> result_app(nil) 392.57/193.65 redex_app(app(map, f), app(app(cons, x), xs)) -> result_app(app(app(cons, app(f, x)), app(app(map, f), xs))) 392.57/193.65 check_app(result_app(x)) -> go_up(x) 392.57/193.65 check_app(redex_app(x_1, x_2)) -> in_app_1(reduce(x_1), x_2) 392.57/193.65 check_app(redex_app(x_1, x_2)) -> in_app_2(x_1, reduce(x_2)) 392.57/193.65 in_app_1(go_up(x_1), x_2) -> go_up(app(x_1, x_2)) 392.57/193.65 in_app_2(x_1, go_up(x_2)) -> go_up(app(x_1, x_2)) 392.57/193.65 392.57/193.65 The set Q consists of the following terms: 392.57/193.65 392.57/193.65 top(go_up(x0)) 392.57/193.65 reduce(app(x0, x1)) 392.57/193.65 redex_app(app(x0, 0), x1) 392.57/193.65 redex_app(app(map, x0), nil) 392.57/193.65 redex_app(app(map, x0), app(app(cons, x1), x2)) 392.57/193.65 check_app(result_app(x0)) 392.57/193.65 check_app(redex_app(x0, x1)) 392.57/193.65 in_app_1(go_up(x0), x1) 392.57/193.65 in_app_2(x0, go_up(x1)) 392.57/193.65 392.57/193.65 We have to consider all minimal (P,Q,R)-chains. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (23) UsableRulesProof (EQUIVALENT) 392.57/193.65 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (24) 392.57/193.65 Obligation: 392.57/193.65 Q DP problem: 392.57/193.65 The TRS P consists of the following rules: 392.57/193.65 392.57/193.65 TOP(go_up(x)) -> TOP(reduce(x)) 392.57/193.65 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 reduce(app(x_1, x_2)) -> check_app(redex_app(x_1, x_2)) 392.57/193.65 redex_app(app(f, 0), n) -> result_app(app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)) 392.57/193.65 redex_app(app(map, f), nil) -> result_app(nil) 392.57/193.65 redex_app(app(map, f), app(app(cons, x), xs)) -> result_app(app(app(cons, app(f, x)), app(app(map, f), xs))) 392.57/193.65 check_app(result_app(x)) -> go_up(x) 392.57/193.65 check_app(redex_app(x_1, x_2)) -> in_app_1(reduce(x_1), x_2) 392.57/193.65 check_app(redex_app(x_1, x_2)) -> in_app_2(x_1, reduce(x_2)) 392.57/193.65 in_app_2(x_1, go_up(x_2)) -> go_up(app(x_1, x_2)) 392.57/193.65 in_app_1(go_up(x_1), x_2) -> go_up(app(x_1, x_2)) 392.57/193.65 392.57/193.65 The set Q consists of the following terms: 392.57/193.65 392.57/193.65 top(go_up(x0)) 392.57/193.65 reduce(app(x0, x1)) 392.57/193.65 redex_app(app(x0, 0), x1) 392.57/193.65 redex_app(app(map, x0), nil) 392.57/193.65 redex_app(app(map, x0), app(app(cons, x1), x2)) 392.57/193.65 check_app(result_app(x0)) 392.57/193.65 check_app(redex_app(x0, x1)) 392.57/193.65 in_app_1(go_up(x0), x1) 392.57/193.65 in_app_2(x0, go_up(x1)) 392.57/193.65 392.57/193.65 We have to consider all minimal (P,Q,R)-chains. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (25) QReductionProof (EQUIVALENT) 392.57/193.65 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 392.57/193.65 392.57/193.65 top(go_up(x0)) 392.57/193.65 392.57/193.65 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (26) 392.57/193.65 Obligation: 392.57/193.65 Q DP problem: 392.57/193.65 The TRS P consists of the following rules: 392.57/193.65 392.57/193.65 TOP(go_up(x)) -> TOP(reduce(x)) 392.57/193.65 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 reduce(app(x_1, x_2)) -> check_app(redex_app(x_1, x_2)) 392.57/193.65 redex_app(app(f, 0), n) -> result_app(app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)) 392.57/193.65 redex_app(app(map, f), nil) -> result_app(nil) 392.57/193.65 redex_app(app(map, f), app(app(cons, x), xs)) -> result_app(app(app(cons, app(f, x)), app(app(map, f), xs))) 392.57/193.65 check_app(result_app(x)) -> go_up(x) 392.57/193.65 check_app(redex_app(x_1, x_2)) -> in_app_1(reduce(x_1), x_2) 392.57/193.65 check_app(redex_app(x_1, x_2)) -> in_app_2(x_1, reduce(x_2)) 392.57/193.65 in_app_2(x_1, go_up(x_2)) -> go_up(app(x_1, x_2)) 392.57/193.65 in_app_1(go_up(x_1), x_2) -> go_up(app(x_1, x_2)) 392.57/193.65 392.57/193.65 The set Q consists of the following terms: 392.57/193.65 392.57/193.65 reduce(app(x0, x1)) 392.57/193.65 redex_app(app(x0, 0), x1) 392.57/193.65 redex_app(app(map, x0), nil) 392.57/193.65 redex_app(app(map, x0), app(app(cons, x1), x2)) 392.57/193.65 check_app(result_app(x0)) 392.57/193.65 check_app(redex_app(x0, x1)) 392.57/193.65 in_app_1(go_up(x0), x1) 392.57/193.65 in_app_2(x0, go_up(x1)) 392.57/193.65 392.57/193.65 We have to consider all minimal (P,Q,R)-chains. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (27) TransformationProof (EQUIVALENT) 392.57/193.65 By narrowing [LPAR04] the rule TOP(go_up(x)) -> TOP(reduce(x)) at position [0] we obtained the following new rules [LPAR04]: 392.57/193.65 392.57/193.65 (TOP(go_up(app(x0, x1))) -> TOP(check_app(redex_app(x0, x1))),TOP(go_up(app(x0, x1))) -> TOP(check_app(redex_app(x0, x1)))) 392.57/193.65 392.57/193.65 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (28) 392.57/193.65 Obligation: 392.57/193.65 Q DP problem: 392.57/193.65 The TRS P consists of the following rules: 392.57/193.65 392.57/193.65 TOP(go_up(app(x0, x1))) -> TOP(check_app(redex_app(x0, x1))) 392.57/193.65 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 reduce(app(x_1, x_2)) -> check_app(redex_app(x_1, x_2)) 392.57/193.65 redex_app(app(f, 0), n) -> result_app(app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)) 392.57/193.65 redex_app(app(map, f), nil) -> result_app(nil) 392.57/193.65 redex_app(app(map, f), app(app(cons, x), xs)) -> result_app(app(app(cons, app(f, x)), app(app(map, f), xs))) 392.57/193.65 check_app(result_app(x)) -> go_up(x) 392.57/193.65 check_app(redex_app(x_1, x_2)) -> in_app_1(reduce(x_1), x_2) 392.57/193.65 check_app(redex_app(x_1, x_2)) -> in_app_2(x_1, reduce(x_2)) 392.57/193.65 in_app_2(x_1, go_up(x_2)) -> go_up(app(x_1, x_2)) 392.57/193.65 in_app_1(go_up(x_1), x_2) -> go_up(app(x_1, x_2)) 392.57/193.65 392.57/193.65 The set Q consists of the following terms: 392.57/193.65 392.57/193.65 reduce(app(x0, x1)) 392.57/193.65 redex_app(app(x0, 0), x1) 392.57/193.65 redex_app(app(map, x0), nil) 392.57/193.65 redex_app(app(map, x0), app(app(cons, x1), x2)) 392.57/193.65 check_app(result_app(x0)) 392.57/193.65 check_app(redex_app(x0, x1)) 392.57/193.65 in_app_1(go_up(x0), x1) 392.57/193.65 in_app_2(x0, go_up(x1)) 392.57/193.65 392.57/193.65 We have to consider all minimal (P,Q,R)-chains. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (29) UsableRulesProof (EQUIVALENT) 392.57/193.65 As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (30) 392.57/193.65 Obligation: 392.57/193.65 Q DP problem: 392.57/193.65 The TRS P consists of the following rules: 392.57/193.65 392.57/193.65 TOP(go_up(x)) -> TOP(reduce(x)) 392.57/193.65 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 reduce(app(x_1, x_2)) -> check_app(redex_app(x_1, x_2)) 392.57/193.65 redex_app(app(f, 0), n) -> result_app(app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)) 392.57/193.65 redex_app(app(map, f), nil) -> result_app(nil) 392.57/193.65 redex_app(app(map, f), app(app(cons, x), xs)) -> result_app(app(app(cons, app(f, x)), app(app(map, f), xs))) 392.57/193.65 check_app(result_app(x)) -> go_up(x) 392.57/193.65 check_app(redex_app(x_1, x_2)) -> in_app_1(reduce(x_1), x_2) 392.57/193.65 check_app(redex_app(x_1, x_2)) -> in_app_2(x_1, reduce(x_2)) 392.57/193.65 in_app_2(x_1, go_up(x_2)) -> go_up(app(x_1, x_2)) 392.57/193.65 in_app_1(go_up(x_1), x_2) -> go_up(app(x_1, x_2)) 392.57/193.65 392.57/193.65 The set Q consists of the following terms: 392.57/193.65 392.57/193.65 top(go_up(x0)) 392.57/193.65 reduce(app(x0, x1)) 392.57/193.65 redex_app(app(x0, 0), x1) 392.57/193.65 redex_app(app(map, x0), nil) 392.57/193.65 redex_app(app(map, x0), app(app(cons, x1), x2)) 392.57/193.65 check_app(result_app(x0)) 392.57/193.65 check_app(redex_app(x0, x1)) 392.57/193.65 in_app_1(go_up(x0), x1) 392.57/193.65 in_app_2(x0, go_up(x1)) 392.57/193.65 392.57/193.65 We have to consider all minimal (P,Q,R)-chains. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (31) QReductionProof (EQUIVALENT) 392.57/193.65 We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. 392.57/193.65 392.57/193.65 top(go_up(x0)) 392.57/193.65 392.57/193.65 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (32) 392.57/193.65 Obligation: 392.57/193.65 Q DP problem: 392.57/193.65 The TRS P consists of the following rules: 392.57/193.65 392.57/193.65 TOP(go_up(x)) -> TOP(reduce(x)) 392.57/193.65 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 reduce(app(x_1, x_2)) -> check_app(redex_app(x_1, x_2)) 392.57/193.65 redex_app(app(f, 0), n) -> result_app(app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)) 392.57/193.65 redex_app(app(map, f), nil) -> result_app(nil) 392.57/193.65 redex_app(app(map, f), app(app(cons, x), xs)) -> result_app(app(app(cons, app(f, x)), app(app(map, f), xs))) 392.57/193.65 check_app(result_app(x)) -> go_up(x) 392.57/193.65 check_app(redex_app(x_1, x_2)) -> in_app_1(reduce(x_1), x_2) 392.57/193.65 check_app(redex_app(x_1, x_2)) -> in_app_2(x_1, reduce(x_2)) 392.57/193.65 in_app_2(x_1, go_up(x_2)) -> go_up(app(x_1, x_2)) 392.57/193.65 in_app_1(go_up(x_1), x_2) -> go_up(app(x_1, x_2)) 392.57/193.65 392.57/193.65 The set Q consists of the following terms: 392.57/193.65 392.57/193.65 reduce(app(x0, x1)) 392.57/193.65 redex_app(app(x0, 0), x1) 392.57/193.65 redex_app(app(map, x0), nil) 392.57/193.65 redex_app(app(map, x0), app(app(cons, x1), x2)) 392.57/193.65 check_app(result_app(x0)) 392.57/193.65 check_app(redex_app(x0, x1)) 392.57/193.65 in_app_1(go_up(x0), x1) 392.57/193.65 in_app_2(x0, go_up(x1)) 392.57/193.65 392.57/193.65 We have to consider all minimal (P,Q,R)-chains. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (33) Trivial-Transformation (SOUND) 392.57/193.65 We applied the Trivial transformation to transform the outermost TRS to a standard TRS. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (34) 392.57/193.65 Obligation: 392.57/193.65 Q restricted rewrite system: 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 app(app(f, 0), n) -> app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n) 392.57/193.65 app(app(map, f), nil) -> nil 392.57/193.65 app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) 392.57/193.65 392.57/193.65 Q is empty. 392.57/193.65 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (35) DependencyPairsProof (EQUIVALENT) 392.57/193.65 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (36) 392.57/193.65 Obligation: 392.57/193.65 Q DP problem: 392.57/193.65 The TRS P consists of the following rules: 392.57/193.65 392.57/193.65 APP(app(f, 0), n) -> APP(app(hd, app(app(map, f), app(app(cons, 0), nil))), n) 392.57/193.65 APP(app(f, 0), n) -> APP(hd, app(app(map, f), app(app(cons, 0), nil))) 392.57/193.65 APP(app(f, 0), n) -> APP(app(map, f), app(app(cons, 0), nil)) 392.57/193.65 APP(app(f, 0), n) -> APP(map, f) 392.57/193.65 APP(app(f, 0), n) -> APP(app(cons, 0), nil) 392.57/193.65 APP(app(f, 0), n) -> APP(cons, 0) 392.57/193.65 APP(app(map, f), app(app(cons, x), xs)) -> APP(app(cons, app(f, x)), app(app(map, f), xs)) 392.57/193.65 APP(app(map, f), app(app(cons, x), xs)) -> APP(cons, app(f, x)) 392.57/193.65 APP(app(map, f), app(app(cons, x), xs)) -> APP(f, x) 392.57/193.65 APP(app(map, f), app(app(cons, x), xs)) -> APP(app(map, f), xs) 392.57/193.65 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 app(app(f, 0), n) -> app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n) 392.57/193.65 app(app(map, f), nil) -> nil 392.57/193.65 app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) 392.57/193.65 392.57/193.65 Q is empty. 392.57/193.65 We have to consider all minimal (P,Q,R)-chains. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (37) DependencyGraphProof (EQUIVALENT) 392.57/193.65 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 4 less nodes. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (38) 392.57/193.65 Obligation: 392.57/193.65 Q DP problem: 392.57/193.65 The TRS P consists of the following rules: 392.57/193.65 392.57/193.65 APP(app(f, 0), n) -> APP(app(map, f), app(app(cons, 0), nil)) 392.57/193.65 APP(app(f, 0), n) -> APP(app(hd, app(app(map, f), app(app(cons, 0), nil))), n) 392.57/193.65 APP(app(f, 0), n) -> APP(app(cons, 0), nil) 392.57/193.65 APP(app(map, f), app(app(cons, x), xs)) -> APP(app(cons, app(f, x)), app(app(map, f), xs)) 392.57/193.65 APP(app(map, f), app(app(cons, x), xs)) -> APP(f, x) 392.57/193.65 APP(app(map, f), app(app(cons, x), xs)) -> APP(app(map, f), xs) 392.57/193.65 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 app(app(f, 0), n) -> app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n) 392.57/193.65 app(app(map, f), nil) -> nil 392.57/193.65 app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) 392.57/193.65 392.57/193.65 Q is empty. 392.57/193.65 We have to consider all minimal (P,Q,R)-chains. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (39) TransformationProof (EQUIVALENT) 392.57/193.65 By narrowing [LPAR04] the rule APP(app(f, 0), n) -> APP(app(hd, app(app(map, f), app(app(cons, 0), nil))), n) at position [0,1] we obtained the following new rules [LPAR04]: 392.57/193.65 392.57/193.65 (APP(app(0, 0), y1) -> APP(app(hd, app(app(hd, app(app(map, map), app(app(cons, 0), nil))), app(app(cons, 0), nil))), y1),APP(app(0, 0), y1) -> APP(app(hd, app(app(hd, app(app(map, map), app(app(cons, 0), nil))), app(app(cons, 0), nil))), y1)) 392.57/193.65 (APP(app(x0, 0), y1) -> APP(app(hd, app(app(cons, app(x0, 0)), app(app(map, x0), nil))), y1),APP(app(x0, 0), y1) -> APP(app(hd, app(app(cons, app(x0, 0)), app(app(map, x0), nil))), y1)) 392.57/193.65 (APP(app(y0, 0), y1) -> APP(app(hd, app(app(map, y0), app(app(hd, app(app(map, cons), app(app(cons, 0), nil))), nil))), y1),APP(app(y0, 0), y1) -> APP(app(hd, app(app(map, y0), app(app(hd, app(app(map, cons), app(app(cons, 0), nil))), nil))), y1)) 392.57/193.65 392.57/193.65 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (40) 392.57/193.65 Obligation: 392.57/193.65 Q DP problem: 392.57/193.65 The TRS P consists of the following rules: 392.57/193.65 392.57/193.65 APP(app(f, 0), n) -> APP(app(map, f), app(app(cons, 0), nil)) 392.57/193.65 APP(app(f, 0), n) -> APP(app(cons, 0), nil) 392.57/193.65 APP(app(map, f), app(app(cons, x), xs)) -> APP(app(cons, app(f, x)), app(app(map, f), xs)) 392.57/193.65 APP(app(map, f), app(app(cons, x), xs)) -> APP(f, x) 392.57/193.65 APP(app(map, f), app(app(cons, x), xs)) -> APP(app(map, f), xs) 392.57/193.65 APP(app(0, 0), y1) -> APP(app(hd, app(app(hd, app(app(map, map), app(app(cons, 0), nil))), app(app(cons, 0), nil))), y1) 392.57/193.65 APP(app(x0, 0), y1) -> APP(app(hd, app(app(cons, app(x0, 0)), app(app(map, x0), nil))), y1) 392.57/193.65 APP(app(y0, 0), y1) -> APP(app(hd, app(app(map, y0), app(app(hd, app(app(map, cons), app(app(cons, 0), nil))), nil))), y1) 392.57/193.65 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 app(app(f, 0), n) -> app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n) 392.57/193.65 app(app(map, f), nil) -> nil 392.57/193.65 app(app(map, f), app(app(cons, x), xs)) -> app(app(cons, app(f, x)), app(app(map, f), xs)) 392.57/193.65 392.57/193.65 Q is empty. 392.57/193.65 We have to consider all minimal (P,Q,R)-chains. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (41) NonTerminationLoopProof (COMPLETE) 392.57/193.65 We used the non-termination processor [FROCOS05] to show that the DP problem is infinite. 392.57/193.65 Found a loop by semiunifying a rule from P directly. 392.57/193.65 392.57/193.65 s = APP(app(f, 0), n) evaluates to t =APP(app(cons, 0), nil) 392.57/193.65 392.57/193.65 Thus s starts an infinite chain as s semiunifies with t with the following substitutions: 392.57/193.65 * Matcher: [f / cons, n / nil] 392.57/193.65 * Semiunifier: [ ] 392.57/193.65 392.57/193.65 -------------------------------------------------------------------------------- 392.57/193.65 Rewriting sequence 392.57/193.65 392.57/193.65 The DP semiunifies directly so there is only one rewrite step from APP(app(f, 0), n) to APP(app(cons, 0), nil). 392.57/193.65 392.57/193.65 392.57/193.65 392.57/193.65 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (42) 392.57/193.65 NO 392.57/193.65 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (43) Raffelsieper-Zantema-Transformation (SOUND) 392.57/193.65 We applied the Raffelsieper-Zantema transformation to transform the outermost TRS to a standard TRS. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (44) 392.57/193.65 Obligation: 392.57/193.65 Q restricted rewrite system: 392.57/193.65 The TRS R consists of the following rules: 392.57/193.65 392.57/193.65 down(app(app(f, 0), n)) -> up(app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)) 392.57/193.65 down(app(app(map, f), nil)) -> up(nil) 392.57/193.65 down(app(app(map, f), app(app(cons, x), xs))) -> up(app(app(cons, app(f, x)), app(app(map, f), xs))) 392.57/193.65 top(up(x)) -> top(down(x)) 392.57/193.65 down(app(0, y7)) -> app_flat(down(0), block(y7)) 392.57/193.65 down(app(0, y7)) -> app_flat(block(0), down(y7)) 392.57/193.65 down(app(hd, y8)) -> app_flat(down(hd), block(y8)) 392.57/193.65 down(app(hd, y8)) -> app_flat(block(hd), down(y8)) 392.57/193.65 down(app(map, y9)) -> app_flat(down(map), block(y9)) 392.57/193.65 down(app(map, y9)) -> app_flat(block(map), down(y9)) 392.57/193.65 down(app(cons, y10)) -> app_flat(down(cons), block(y10)) 392.57/193.65 down(app(cons, y10)) -> app_flat(block(cons), down(y10)) 392.57/193.65 down(app(nil, y11)) -> app_flat(down(nil), block(y11)) 392.57/193.65 down(app(nil, y11)) -> app_flat(block(nil), down(y11)) 392.57/193.65 down(app(fresh_constant, y12)) -> app_flat(down(fresh_constant), block(y12)) 392.57/193.65 down(app(fresh_constant, y12)) -> app_flat(block(fresh_constant), down(y12)) 392.57/193.65 down(app(app(app(y64, y65), app(y66, y67)), y6)) -> app_flat(down(app(app(y64, y65), app(y66, y67))), block(y6)) 392.57/193.65 down(app(app(app(y64, y65), app(y66, y67)), y6)) -> app_flat(block(app(app(y64, y65), app(y66, y67))), down(y6)) 392.57/193.65 down(app(app(0, app(y68, y69)), y6)) -> app_flat(down(app(0, app(y68, y69))), block(y6)) 392.57/193.65 down(app(app(0, app(y68, y69)), y6)) -> app_flat(block(app(0, app(y68, y69))), down(y6)) 392.57/193.65 down(app(app(hd, app(y70, y71)), y6)) -> app_flat(down(app(hd, app(y70, y71))), block(y6)) 392.57/193.65 down(app(app(hd, app(y70, y71)), y6)) -> app_flat(block(app(hd, app(y70, y71))), down(y6)) 392.57/193.65 down(app(app(cons, app(y74, y75)), y6)) -> app_flat(down(app(cons, app(y74, y75))), block(y6)) 392.57/193.65 down(app(app(cons, app(y74, y75)), y6)) -> app_flat(block(app(cons, app(y74, y75))), down(y6)) 392.57/193.65 down(app(app(nil, app(y76, y77)), y6)) -> app_flat(down(app(nil, app(y76, y77))), block(y6)) 392.57/193.65 down(app(app(nil, app(y76, y77)), y6)) -> app_flat(block(app(nil, app(y76, y77))), down(y6)) 392.57/193.65 down(app(app(fresh_constant, app(y78, y79)), y6)) -> app_flat(down(app(fresh_constant, app(y78, y79))), block(y6)) 392.57/193.65 down(app(app(fresh_constant, app(y78, y79)), y6)) -> app_flat(block(app(fresh_constant, app(y78, y79))), down(y6)) 392.57/193.65 down(app(app(app(y84, y85), hd), y6)) -> app_flat(down(app(app(y84, y85), hd)), block(y6)) 392.57/193.65 down(app(app(app(y84, y85), hd), y6)) -> app_flat(block(app(app(y84, y85), hd)), down(y6)) 392.57/193.65 down(app(app(0, hd), y6)) -> app_flat(down(app(0, hd)), block(y6)) 392.57/193.65 down(app(app(0, hd), y6)) -> app_flat(block(app(0, hd)), down(y6)) 392.57/193.65 down(app(app(hd, hd), y6)) -> app_flat(down(app(hd, hd)), block(y6)) 392.57/193.65 down(app(app(hd, hd), y6)) -> app_flat(block(app(hd, hd)), down(y6)) 392.57/193.65 down(app(app(cons, hd), y6)) -> app_flat(down(app(cons, hd)), block(y6)) 392.57/193.65 down(app(app(cons, hd), y6)) -> app_flat(block(app(cons, hd)), down(y6)) 392.57/193.65 down(app(app(nil, hd), y6)) -> app_flat(down(app(nil, hd)), block(y6)) 392.57/193.65 down(app(app(nil, hd), y6)) -> app_flat(block(app(nil, hd)), down(y6)) 392.57/193.65 down(app(app(fresh_constant, hd), y6)) -> app_flat(down(app(fresh_constant, hd)), block(y6)) 392.57/193.65 down(app(app(fresh_constant, hd), y6)) -> app_flat(block(app(fresh_constant, hd)), down(y6)) 392.57/193.65 down(app(app(app(y87, y88), map), y6)) -> app_flat(down(app(app(y87, y88), map)), block(y6)) 392.57/193.65 down(app(app(app(y87, y88), map), y6)) -> app_flat(block(app(app(y87, y88), map)), down(y6)) 392.57/193.65 down(app(app(0, map), y6)) -> app_flat(down(app(0, map)), block(y6)) 392.57/193.65 down(app(app(0, map), y6)) -> app_flat(block(app(0, map)), down(y6)) 392.57/193.65 down(app(app(hd, map), y6)) -> app_flat(down(app(hd, map)), block(y6)) 392.57/193.65 down(app(app(hd, map), y6)) -> app_flat(block(app(hd, map)), down(y6)) 392.57/193.65 down(app(app(cons, map), y6)) -> app_flat(down(app(cons, map)), block(y6)) 392.57/193.65 down(app(app(cons, map), y6)) -> app_flat(block(app(cons, map)), down(y6)) 392.57/193.65 down(app(app(nil, map), y6)) -> app_flat(down(app(nil, map)), block(y6)) 392.57/193.65 down(app(app(nil, map), y6)) -> app_flat(block(app(nil, map)), down(y6)) 392.57/193.65 down(app(app(fresh_constant, map), y6)) -> app_flat(down(app(fresh_constant, map)), block(y6)) 392.57/193.65 down(app(app(fresh_constant, map), y6)) -> app_flat(block(app(fresh_constant, map)), down(y6)) 392.57/193.65 down(app(app(app(y90, y91), cons), y6)) -> app_flat(down(app(app(y90, y91), cons)), block(y6)) 392.57/193.65 down(app(app(app(y90, y91), cons), y6)) -> app_flat(block(app(app(y90, y91), cons)), down(y6)) 392.57/193.65 down(app(app(0, cons), y6)) -> app_flat(down(app(0, cons)), block(y6)) 392.57/193.65 down(app(app(0, cons), y6)) -> app_flat(block(app(0, cons)), down(y6)) 392.57/193.65 down(app(app(hd, cons), y6)) -> app_flat(down(app(hd, cons)), block(y6)) 392.57/193.65 down(app(app(hd, cons), y6)) -> app_flat(block(app(hd, cons)), down(y6)) 392.57/193.65 down(app(app(cons, cons), y6)) -> app_flat(down(app(cons, cons)), block(y6)) 392.57/193.65 down(app(app(cons, cons), y6)) -> app_flat(block(app(cons, cons)), down(y6)) 392.57/193.65 down(app(app(nil, cons), y6)) -> app_flat(down(app(nil, cons)), block(y6)) 392.57/193.65 down(app(app(nil, cons), y6)) -> app_flat(block(app(nil, cons)), down(y6)) 392.57/193.65 down(app(app(fresh_constant, cons), y6)) -> app_flat(down(app(fresh_constant, cons)), block(y6)) 392.57/193.65 down(app(app(fresh_constant, cons), y6)) -> app_flat(block(app(fresh_constant, cons)), down(y6)) 392.57/193.65 down(app(app(app(y93, y94), nil), y6)) -> app_flat(down(app(app(y93, y94), nil)), block(y6)) 392.57/193.65 down(app(app(app(y93, y94), nil), y6)) -> app_flat(block(app(app(y93, y94), nil)), down(y6)) 392.57/193.65 down(app(app(0, nil), y6)) -> app_flat(down(app(0, nil)), block(y6)) 392.57/193.65 down(app(app(0, nil), y6)) -> app_flat(block(app(0, nil)), down(y6)) 392.57/193.65 down(app(app(hd, nil), y6)) -> app_flat(down(app(hd, nil)), block(y6)) 392.57/193.65 down(app(app(hd, nil), y6)) -> app_flat(block(app(hd, nil)), down(y6)) 392.57/193.65 down(app(app(cons, nil), y6)) -> app_flat(down(app(cons, nil)), block(y6)) 392.57/193.65 down(app(app(cons, nil), y6)) -> app_flat(block(app(cons, nil)), down(y6)) 392.57/193.65 down(app(app(nil, nil), y6)) -> app_flat(down(app(nil, nil)), block(y6)) 392.57/193.65 down(app(app(nil, nil), y6)) -> app_flat(block(app(nil, nil)), down(y6)) 392.57/193.65 down(app(app(fresh_constant, nil), y6)) -> app_flat(down(app(fresh_constant, nil)), block(y6)) 392.57/193.65 down(app(app(fresh_constant, nil), y6)) -> app_flat(block(app(fresh_constant, nil)), down(y6)) 392.57/193.65 down(app(app(app(y96, y97), fresh_constant), y6)) -> app_flat(down(app(app(y96, y97), fresh_constant)), block(y6)) 392.57/193.65 down(app(app(app(y96, y97), fresh_constant), y6)) -> app_flat(block(app(app(y96, y97), fresh_constant)), down(y6)) 392.57/193.65 down(app(app(0, fresh_constant), y6)) -> app_flat(down(app(0, fresh_constant)), block(y6)) 392.57/193.65 down(app(app(0, fresh_constant), y6)) -> app_flat(block(app(0, fresh_constant)), down(y6)) 392.57/193.65 down(app(app(hd, fresh_constant), y6)) -> app_flat(down(app(hd, fresh_constant)), block(y6)) 392.57/193.65 down(app(app(hd, fresh_constant), y6)) -> app_flat(block(app(hd, fresh_constant)), down(y6)) 392.57/193.65 down(app(app(cons, fresh_constant), y6)) -> app_flat(down(app(cons, fresh_constant)), block(y6)) 392.57/193.65 down(app(app(cons, fresh_constant), y6)) -> app_flat(block(app(cons, fresh_constant)), down(y6)) 392.57/193.65 down(app(app(nil, fresh_constant), y6)) -> app_flat(down(app(nil, fresh_constant)), block(y6)) 392.57/193.65 down(app(app(nil, fresh_constant), y6)) -> app_flat(block(app(nil, fresh_constant)), down(y6)) 392.57/193.65 down(app(app(fresh_constant, fresh_constant), y6)) -> app_flat(down(app(fresh_constant, fresh_constant)), block(y6)) 392.57/193.65 down(app(app(fresh_constant, fresh_constant), y6)) -> app_flat(block(app(fresh_constant, fresh_constant)), down(y6)) 392.57/193.65 down(app(app(y581, app(y582, y583)), app(0, y584))) -> app_flat(down(app(y581, app(y582, y583))), block(app(0, y584))) 392.57/193.65 down(app(app(y581, app(y582, y583)), app(0, y584))) -> app_flat(block(app(y581, app(y582, y583))), down(app(0, y584))) 392.57/193.65 down(app(app(y619, hd), app(0, y620))) -> app_flat(down(app(y619, hd)), block(app(0, y620))) 392.57/193.65 down(app(app(y619, hd), app(0, y620))) -> app_flat(block(app(y619, hd)), down(app(0, y620))) 392.57/193.65 down(app(app(y630, map), app(0, y631))) -> app_flat(down(app(y630, map)), block(app(0, y631))) 392.57/193.65 down(app(app(y630, map), app(0, y631))) -> app_flat(block(app(y630, map)), down(app(0, y631))) 392.57/193.65 down(app(app(y641, cons), app(0, y642))) -> app_flat(down(app(y641, cons)), block(app(0, y642))) 392.57/193.65 down(app(app(y641, cons), app(0, y642))) -> app_flat(block(app(y641, cons)), down(app(0, y642))) 392.57/193.65 down(app(app(y652, nil), app(0, y653))) -> app_flat(down(app(y652, nil)), block(app(0, y653))) 392.57/193.65 down(app(app(y652, nil), app(0, y653))) -> app_flat(block(app(y652, nil)), down(app(0, y653))) 392.57/193.65 down(app(app(y663, fresh_constant), app(0, y664))) -> app_flat(down(app(y663, fresh_constant)), block(app(0, y664))) 392.57/193.65 down(app(app(y663, fresh_constant), app(0, y664))) -> app_flat(block(app(y663, fresh_constant)), down(app(0, y664))) 392.57/193.65 down(app(app(y693, app(y694, y695)), app(hd, y696))) -> app_flat(down(app(y693, app(y694, y695))), block(app(hd, y696))) 392.57/193.65 down(app(app(y693, app(y694, y695)), app(hd, y696))) -> app_flat(block(app(y693, app(y694, y695))), down(app(hd, y696))) 392.57/193.65 down(app(app(y731, hd), app(hd, y732))) -> app_flat(down(app(y731, hd)), block(app(hd, y732))) 392.57/193.65 down(app(app(y731, hd), app(hd, y732))) -> app_flat(block(app(y731, hd)), down(app(hd, y732))) 392.57/193.65 down(app(app(y742, map), app(hd, y743))) -> app_flat(down(app(y742, map)), block(app(hd, y743))) 392.57/193.65 down(app(app(y742, map), app(hd, y743))) -> app_flat(block(app(y742, map)), down(app(hd, y743))) 392.57/193.65 down(app(app(y753, cons), app(hd, y754))) -> app_flat(down(app(y753, cons)), block(app(hd, y754))) 392.57/193.65 down(app(app(y753, cons), app(hd, y754))) -> app_flat(block(app(y753, cons)), down(app(hd, y754))) 392.57/193.65 down(app(app(y764, nil), app(hd, y765))) -> app_flat(down(app(y764, nil)), block(app(hd, y765))) 392.57/193.65 down(app(app(y764, nil), app(hd, y765))) -> app_flat(block(app(y764, nil)), down(app(hd, y765))) 392.57/193.65 down(app(app(y775, fresh_constant), app(hd, y776))) -> app_flat(down(app(y775, fresh_constant)), block(app(hd, y776))) 392.57/193.65 down(app(app(y775, fresh_constant), app(hd, y776))) -> app_flat(block(app(y775, fresh_constant)), down(app(hd, y776))) 392.57/193.65 down(app(app(y805, app(y806, y807)), app(map, y808))) -> app_flat(down(app(y805, app(y806, y807))), block(app(map, y808))) 392.57/193.65 down(app(app(y805, app(y806, y807)), app(map, y808))) -> app_flat(block(app(y805, app(y806, y807))), down(app(map, y808))) 392.57/193.65 down(app(app(y843, hd), app(map, y844))) -> app_flat(down(app(y843, hd)), block(app(map, y844))) 392.57/193.65 down(app(app(y843, hd), app(map, y844))) -> app_flat(block(app(y843, hd)), down(app(map, y844))) 392.57/193.65 down(app(app(y854, map), app(map, y855))) -> app_flat(down(app(y854, map)), block(app(map, y855))) 392.57/193.65 down(app(app(y854, map), app(map, y855))) -> app_flat(block(app(y854, map)), down(app(map, y855))) 392.57/193.65 down(app(app(y865, cons), app(map, y866))) -> app_flat(down(app(y865, cons)), block(app(map, y866))) 392.57/193.65 down(app(app(y865, cons), app(map, y866))) -> app_flat(block(app(y865, cons)), down(app(map, y866))) 392.57/193.65 down(app(app(y876, nil), app(map, y877))) -> app_flat(down(app(y876, nil)), block(app(map, y877))) 392.57/193.65 down(app(app(y876, nil), app(map, y877))) -> app_flat(block(app(y876, nil)), down(app(map, y877))) 392.57/193.65 down(app(app(y887, fresh_constant), app(map, y888))) -> app_flat(down(app(y887, fresh_constant)), block(app(map, y888))) 392.57/193.65 down(app(app(y887, fresh_constant), app(map, y888))) -> app_flat(block(app(y887, fresh_constant)), down(app(map, y888))) 392.57/193.65 down(app(app(y917, app(y918, y919)), app(cons, y920))) -> app_flat(down(app(y917, app(y918, y919))), block(app(cons, y920))) 392.57/193.65 down(app(app(y917, app(y918, y919)), app(cons, y920))) -> app_flat(block(app(y917, app(y918, y919))), down(app(cons, y920))) 392.57/193.65 down(app(app(y955, hd), app(cons, y956))) -> app_flat(down(app(y955, hd)), block(app(cons, y956))) 392.57/193.65 down(app(app(y955, hd), app(cons, y956))) -> app_flat(block(app(y955, hd)), down(app(cons, y956))) 392.57/193.65 down(app(app(y966, map), app(cons, y967))) -> app_flat(down(app(y966, map)), block(app(cons, y967))) 392.57/193.65 down(app(app(y966, map), app(cons, y967))) -> app_flat(block(app(y966, map)), down(app(cons, y967))) 392.57/193.65 down(app(app(y977, cons), app(cons, y978))) -> app_flat(down(app(y977, cons)), block(app(cons, y978))) 392.57/193.65 down(app(app(y977, cons), app(cons, y978))) -> app_flat(block(app(y977, cons)), down(app(cons, y978))) 392.57/193.65 down(app(app(y988, nil), app(cons, y989))) -> app_flat(down(app(y988, nil)), block(app(cons, y989))) 392.57/193.65 down(app(app(y988, nil), app(cons, y989))) -> app_flat(block(app(y988, nil)), down(app(cons, y989))) 392.57/193.65 down(app(app(y999, fresh_constant), app(cons, y1000))) -> app_flat(down(app(y999, fresh_constant)), block(app(cons, y1000))) 392.57/193.65 down(app(app(y999, fresh_constant), app(cons, y1000))) -> app_flat(block(app(y999, fresh_constant)), down(app(cons, y1000))) 392.57/193.65 down(app(app(y1029, app(y1030, y1031)), app(nil, y1032))) -> app_flat(down(app(y1029, app(y1030, y1031))), block(app(nil, y1032))) 392.57/193.65 down(app(app(y1029, app(y1030, y1031)), app(nil, y1032))) -> app_flat(block(app(y1029, app(y1030, y1031))), down(app(nil, y1032))) 392.57/193.65 down(app(app(y1067, hd), app(nil, y1068))) -> app_flat(down(app(y1067, hd)), block(app(nil, y1068))) 392.57/193.65 down(app(app(y1067, hd), app(nil, y1068))) -> app_flat(block(app(y1067, hd)), down(app(nil, y1068))) 392.57/193.65 down(app(app(y1078, map), app(nil, y1079))) -> app_flat(down(app(y1078, map)), block(app(nil, y1079))) 392.57/193.65 down(app(app(y1078, map), app(nil, y1079))) -> app_flat(block(app(y1078, map)), down(app(nil, y1079))) 392.57/193.65 down(app(app(y1089, cons), app(nil, y1090))) -> app_flat(down(app(y1089, cons)), block(app(nil, y1090))) 392.57/193.65 down(app(app(y1089, cons), app(nil, y1090))) -> app_flat(block(app(y1089, cons)), down(app(nil, y1090))) 392.57/193.65 down(app(app(y1100, nil), app(nil, y1101))) -> app_flat(down(app(y1100, nil)), block(app(nil, y1101))) 392.57/193.65 down(app(app(y1100, nil), app(nil, y1101))) -> app_flat(block(app(y1100, nil)), down(app(nil, y1101))) 392.57/193.65 down(app(app(y1111, fresh_constant), app(nil, y1112))) -> app_flat(down(app(y1111, fresh_constant)), block(app(nil, y1112))) 392.57/193.65 down(app(app(y1111, fresh_constant), app(nil, y1112))) -> app_flat(block(app(y1111, fresh_constant)), down(app(nil, y1112))) 392.57/193.65 down(app(app(y1141, app(y1142, y1143)), app(fresh_constant, y1144))) -> app_flat(down(app(y1141, app(y1142, y1143))), block(app(fresh_constant, y1144))) 392.57/193.65 down(app(app(y1141, app(y1142, y1143)), app(fresh_constant, y1144))) -> app_flat(block(app(y1141, app(y1142, y1143))), down(app(fresh_constant, y1144))) 392.57/193.65 down(app(app(y1179, hd), app(fresh_constant, y1180))) -> app_flat(down(app(y1179, hd)), block(app(fresh_constant, y1180))) 392.57/193.65 down(app(app(y1179, hd), app(fresh_constant, y1180))) -> app_flat(block(app(y1179, hd)), down(app(fresh_constant, y1180))) 392.57/193.65 down(app(app(y1190, map), app(fresh_constant, y1191))) -> app_flat(down(app(y1190, map)), block(app(fresh_constant, y1191))) 392.57/193.65 down(app(app(y1190, map), app(fresh_constant, y1191))) -> app_flat(block(app(y1190, map)), down(app(fresh_constant, y1191))) 392.57/193.65 down(app(app(y1201, cons), app(fresh_constant, y1202))) -> app_flat(down(app(y1201, cons)), block(app(fresh_constant, y1202))) 392.57/193.65 down(app(app(y1201, cons), app(fresh_constant, y1202))) -> app_flat(block(app(y1201, cons)), down(app(fresh_constant, y1202))) 392.57/193.65 down(app(app(y1212, nil), app(fresh_constant, y1213))) -> app_flat(down(app(y1212, nil)), block(app(fresh_constant, y1213))) 392.57/193.65 down(app(app(y1212, nil), app(fresh_constant, y1213))) -> app_flat(block(app(y1212, nil)), down(app(fresh_constant, y1213))) 392.57/193.65 down(app(app(y1223, fresh_constant), app(fresh_constant, y1224))) -> app_flat(down(app(y1223, fresh_constant)), block(app(fresh_constant, y1224))) 392.57/193.65 down(app(app(y1223, fresh_constant), app(fresh_constant, y1224))) -> app_flat(block(app(y1223, fresh_constant)), down(app(fresh_constant, y1224))) 392.57/193.65 down(app(app(y6301, app(y6302, y6303)), 0)) -> app_flat(down(app(y6301, app(y6302, y6303))), block(0)) 392.57/193.65 down(app(app(y6301, app(y6302, y6303)), 0)) -> app_flat(block(app(y6301, app(y6302, y6303))), down(0)) 392.57/193.65 down(app(app(y6323, hd), 0)) -> app_flat(down(app(y6323, hd)), block(0)) 392.57/193.65 down(app(app(y6323, hd), 0)) -> app_flat(block(app(y6323, hd)), down(0)) 392.57/193.65 down(app(app(y6326, map), 0)) -> app_flat(down(app(y6326, map)), block(0)) 392.57/193.65 down(app(app(y6326, map), 0)) -> app_flat(block(app(y6326, map)), down(0)) 392.57/193.65 down(app(app(y6329, cons), 0)) -> app_flat(down(app(y6329, cons)), block(0)) 392.57/193.65 down(app(app(y6329, cons), 0)) -> app_flat(block(app(y6329, cons)), down(0)) 392.57/193.65 down(app(app(y6332, nil), 0)) -> app_flat(down(app(y6332, nil)), block(0)) 392.57/193.65 down(app(app(y6332, nil), 0)) -> app_flat(block(app(y6332, nil)), down(0)) 392.57/193.65 down(app(app(y6335, fresh_constant), 0)) -> app_flat(down(app(y6335, fresh_constant)), block(0)) 392.57/193.65 down(app(app(y6335, fresh_constant), 0)) -> app_flat(block(app(y6335, fresh_constant)), down(0)) 392.57/193.65 down(app(app(y6349, app(y6350, y6351)), hd)) -> app_flat(down(app(y6349, app(y6350, y6351))), block(hd)) 392.57/193.65 down(app(app(y6349, app(y6350, y6351)), hd)) -> app_flat(block(app(y6349, app(y6350, y6351))), down(hd)) 392.57/193.65 down(app(app(y6371, hd), hd)) -> app_flat(down(app(y6371, hd)), block(hd)) 392.57/193.65 down(app(app(y6371, hd), hd)) -> app_flat(block(app(y6371, hd)), down(hd)) 392.57/193.65 down(app(app(y6374, map), hd)) -> app_flat(down(app(y6374, map)), block(hd)) 392.57/193.65 down(app(app(y6374, map), hd)) -> app_flat(block(app(y6374, map)), down(hd)) 392.57/193.65 down(app(app(y6377, cons), hd)) -> app_flat(down(app(y6377, cons)), block(hd)) 392.57/193.65 down(app(app(y6377, cons), hd)) -> app_flat(block(app(y6377, cons)), down(hd)) 392.57/193.65 down(app(app(y6380, nil), hd)) -> app_flat(down(app(y6380, nil)), block(hd)) 392.57/193.65 down(app(app(y6380, nil), hd)) -> app_flat(block(app(y6380, nil)), down(hd)) 392.57/193.65 down(app(app(y6383, fresh_constant), hd)) -> app_flat(down(app(y6383, fresh_constant)), block(hd)) 392.57/193.65 down(app(app(y6383, fresh_constant), hd)) -> app_flat(block(app(y6383, fresh_constant)), down(hd)) 392.57/193.65 down(app(app(y6397, app(y6398, y6399)), map)) -> app_flat(down(app(y6397, app(y6398, y6399))), block(map)) 392.57/193.65 down(app(app(y6397, app(y6398, y6399)), map)) -> app_flat(block(app(y6397, app(y6398, y6399))), down(map)) 392.57/193.65 down(app(app(y6419, hd), map)) -> app_flat(down(app(y6419, hd)), block(map)) 392.57/193.65 down(app(app(y6419, hd), map)) -> app_flat(block(app(y6419, hd)), down(map)) 392.57/193.65 down(app(app(y6422, map), map)) -> app_flat(down(app(y6422, map)), block(map)) 392.57/193.65 down(app(app(y6422, map), map)) -> app_flat(block(app(y6422, map)), down(map)) 392.57/193.65 down(app(app(y6425, cons), map)) -> app_flat(down(app(y6425, cons)), block(map)) 392.57/193.65 down(app(app(y6425, cons), map)) -> app_flat(block(app(y6425, cons)), down(map)) 392.57/193.65 down(app(app(y6428, nil), map)) -> app_flat(down(app(y6428, nil)), block(map)) 392.57/193.65 down(app(app(y6428, nil), map)) -> app_flat(block(app(y6428, nil)), down(map)) 392.57/193.65 down(app(app(y6431, fresh_constant), map)) -> app_flat(down(app(y6431, fresh_constant)), block(map)) 392.57/193.65 down(app(app(y6431, fresh_constant), map)) -> app_flat(block(app(y6431, fresh_constant)), down(map)) 392.57/193.65 down(app(app(y6445, app(y6446, y6447)), cons)) -> app_flat(down(app(y6445, app(y6446, y6447))), block(cons)) 392.57/193.65 down(app(app(y6445, app(y6446, y6447)), cons)) -> app_flat(block(app(y6445, app(y6446, y6447))), down(cons)) 392.57/193.65 down(app(app(y6467, hd), cons)) -> app_flat(down(app(y6467, hd)), block(cons)) 392.57/193.65 down(app(app(y6467, hd), cons)) -> app_flat(block(app(y6467, hd)), down(cons)) 392.57/193.65 down(app(app(y6470, map), cons)) -> app_flat(down(app(y6470, map)), block(cons)) 392.57/193.65 down(app(app(y6470, map), cons)) -> app_flat(block(app(y6470, map)), down(cons)) 392.57/193.65 down(app(app(y6473, cons), cons)) -> app_flat(down(app(y6473, cons)), block(cons)) 392.57/193.65 down(app(app(y6473, cons), cons)) -> app_flat(block(app(y6473, cons)), down(cons)) 392.57/193.65 down(app(app(y6476, nil), cons)) -> app_flat(down(app(y6476, nil)), block(cons)) 392.57/193.65 down(app(app(y6476, nil), cons)) -> app_flat(block(app(y6476, nil)), down(cons)) 392.57/193.65 down(app(app(y6479, fresh_constant), cons)) -> app_flat(down(app(y6479, fresh_constant)), block(cons)) 392.57/193.65 down(app(app(y6479, fresh_constant), cons)) -> app_flat(block(app(y6479, fresh_constant)), down(cons)) 392.57/193.65 down(app(app(y6541, app(y6542, y6543)), fresh_constant)) -> app_flat(down(app(y6541, app(y6542, y6543))), block(fresh_constant)) 392.57/193.65 down(app(app(y6541, app(y6542, y6543)), fresh_constant)) -> app_flat(block(app(y6541, app(y6542, y6543))), down(fresh_constant)) 392.57/193.65 down(app(app(y6563, hd), fresh_constant)) -> app_flat(down(app(y6563, hd)), block(fresh_constant)) 392.57/193.65 down(app(app(y6563, hd), fresh_constant)) -> app_flat(block(app(y6563, hd)), down(fresh_constant)) 392.57/193.65 down(app(app(y6566, map), fresh_constant)) -> app_flat(down(app(y6566, map)), block(fresh_constant)) 392.57/193.65 down(app(app(y6566, map), fresh_constant)) -> app_flat(block(app(y6566, map)), down(fresh_constant)) 392.57/193.65 down(app(app(y6569, cons), fresh_constant)) -> app_flat(down(app(y6569, cons)), block(fresh_constant)) 392.57/193.65 down(app(app(y6569, cons), fresh_constant)) -> app_flat(block(app(y6569, cons)), down(fresh_constant)) 392.57/193.65 down(app(app(y6572, nil), fresh_constant)) -> app_flat(down(app(y6572, nil)), block(fresh_constant)) 392.57/193.65 down(app(app(y6572, nil), fresh_constant)) -> app_flat(block(app(y6572, nil)), down(fresh_constant)) 392.57/193.65 down(app(app(y6575, fresh_constant), fresh_constant)) -> app_flat(down(app(y6575, fresh_constant)), block(fresh_constant)) 392.57/193.65 down(app(app(y6575, fresh_constant), fresh_constant)) -> app_flat(block(app(y6575, fresh_constant)), down(fresh_constant)) 392.57/193.65 down(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> app_flat(down(app(y357, app(y20338, y20339))), block(app(app(app(y20340, y20341), y20342), y362))) 392.57/193.65 down(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> app_flat(block(app(y357, app(y20338, y20339))), down(app(app(app(y20340, y20341), y20342), y362))) 392.57/193.65 down(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> app_flat(down(app(y357, app(y20578, y20579))), block(app(app(0, y20580), y362))) 392.57/193.65 down(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> app_flat(block(app(y357, app(y20578, y20579))), down(app(app(0, y20580), y362))) 392.57/193.65 down(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> app_flat(down(app(y357, app(y20690, y20691))), block(app(app(hd, y20692), y362))) 392.57/193.65 down(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> app_flat(block(app(y357, app(y20690, y20691))), down(app(app(hd, y20692), y362))) 392.57/193.65 down(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> app_flat(down(app(y357, app(y20802, y20803))), block(app(app(map, y20804), y362))) 392.57/193.65 down(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> app_flat(block(app(y357, app(y20802, y20803))), down(app(app(map, y20804), y362))) 392.57/193.65 down(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> app_flat(down(app(y357, app(y21026, y21027))), block(app(app(nil, y21028), y362))) 392.57/193.65 down(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> app_flat(block(app(y357, app(y21026, y21027))), down(app(app(nil, y21028), y362))) 392.57/193.65 down(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> app_flat(down(app(y357, app(y21138, y21139))), block(app(app(fresh_constant, y21140), y362))) 392.57/193.65 down(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> app_flat(block(app(y357, app(y21138, y21139))), down(app(app(fresh_constant, y21140), y362))) 392.57/193.65 down(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> app_flat(down(app(y427, hd)), block(app(app(app(y32452, y32453), y32454), y430))) 392.57/193.65 down(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> app_flat(block(app(y427, hd)), down(app(app(app(y32452, y32453), y32454), y430))) 392.57/193.65 down(app(app(y427, hd), app(app(0, y32455), y430))) -> app_flat(down(app(y427, hd)), block(app(app(0, y32455), y430))) 392.57/193.65 down(app(app(y427, hd), app(app(0, y32455), y430))) -> app_flat(block(app(y427, hd)), down(app(app(0, y32455), y430))) 392.57/193.65 down(app(app(y427, hd), app(app(hd, y32456), y430))) -> app_flat(down(app(y427, hd)), block(app(app(hd, y32456), y430))) 392.57/193.65 down(app(app(y427, hd), app(app(hd, y32456), y430))) -> app_flat(block(app(y427, hd)), down(app(app(hd, y32456), y430))) 392.57/193.65 down(app(app(y427, hd), app(app(map, y32457), y430))) -> app_flat(down(app(y427, hd)), block(app(app(map, y32457), y430))) 392.57/193.65 down(app(app(y427, hd), app(app(map, y32457), y430))) -> app_flat(block(app(y427, hd)), down(app(app(map, y32457), y430))) 392.57/193.65 down(app(app(y427, hd), app(app(nil, y32459), y430))) -> app_flat(down(app(y427, hd)), block(app(app(nil, y32459), y430))) 392.57/193.65 down(app(app(y427, hd), app(app(nil, y32459), y430))) -> app_flat(block(app(y427, hd)), down(app(app(nil, y32459), y430))) 392.57/193.65 down(app(app(y427, hd), app(app(fresh_constant, y32460), y430))) -> app_flat(down(app(y427, hd)), block(app(app(fresh_constant, y32460), y430))) 392.57/193.65 down(app(app(y427, hd), app(app(fresh_constant, y32460), y430))) -> app_flat(block(app(y427, hd)), down(app(app(fresh_constant, y32460), y430))) 392.57/193.65 down(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> app_flat(down(app(y454, map)), block(app(app(app(y32548, y32549), y32550), y457))) 392.57/193.65 down(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> app_flat(block(app(y454, map)), down(app(app(app(y32548, y32549), y32550), y457))) 392.57/193.65 down(app(app(y454, map), app(app(0, y32551), y457))) -> app_flat(down(app(y454, map)), block(app(app(0, y32551), y457))) 392.57/193.65 down(app(app(y454, map), app(app(0, y32551), y457))) -> app_flat(block(app(y454, map)), down(app(app(0, y32551), y457))) 392.57/193.65 down(app(app(y454, map), app(app(hd, y32552), y457))) -> app_flat(down(app(y454, map)), block(app(app(hd, y32552), y457))) 392.57/193.65 down(app(app(y454, map), app(app(hd, y32552), y457))) -> app_flat(block(app(y454, map)), down(app(app(hd, y32552), y457))) 392.57/193.65 down(app(app(y454, map), app(app(map, y32553), y457))) -> app_flat(down(app(y454, map)), block(app(app(map, y32553), y457))) 392.57/193.65 down(app(app(y454, map), app(app(map, y32553), y457))) -> app_flat(block(app(y454, map)), down(app(app(map, y32553), y457))) 392.57/193.65 down(app(app(y454, map), app(app(nil, y32555), y457))) -> app_flat(down(app(y454, map)), block(app(app(nil, y32555), y457))) 392.57/193.65 down(app(app(y454, map), app(app(nil, y32555), y457))) -> app_flat(block(app(y454, map)), down(app(app(nil, y32555), y457))) 392.57/193.65 down(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> app_flat(down(app(y454, map)), block(app(app(fresh_constant, y32556), y457))) 392.57/193.65 down(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> app_flat(block(app(y454, map)), down(app(app(fresh_constant, y32556), y457))) 392.57/193.65 down(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> app_flat(down(app(y481, cons)), block(app(app(app(y32644, y32645), y32646), y484))) 392.57/193.65 down(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> app_flat(block(app(y481, cons)), down(app(app(app(y32644, y32645), y32646), y484))) 392.57/193.65 down(app(app(y481, cons), app(app(0, y32647), y484))) -> app_flat(down(app(y481, cons)), block(app(app(0, y32647), y484))) 392.57/193.65 down(app(app(y481, cons), app(app(0, y32647), y484))) -> app_flat(block(app(y481, cons)), down(app(app(0, y32647), y484))) 392.57/193.65 down(app(app(y481, cons), app(app(hd, y32648), y484))) -> app_flat(down(app(y481, cons)), block(app(app(hd, y32648), y484))) 392.57/193.65 down(app(app(y481, cons), app(app(hd, y32648), y484))) -> app_flat(block(app(y481, cons)), down(app(app(hd, y32648), y484))) 392.57/193.65 down(app(app(y481, cons), app(app(map, y32649), y484))) -> app_flat(down(app(y481, cons)), block(app(app(map, y32649), y484))) 392.57/193.65 down(app(app(y481, cons), app(app(map, y32649), y484))) -> app_flat(block(app(y481, cons)), down(app(app(map, y32649), y484))) 392.57/193.65 down(app(app(y481, cons), app(app(nil, y32651), y484))) -> app_flat(down(app(y481, cons)), block(app(app(nil, y32651), y484))) 392.57/193.65 down(app(app(y481, cons), app(app(nil, y32651), y484))) -> app_flat(block(app(y481, cons)), down(app(app(nil, y32651), y484))) 392.57/193.65 down(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> app_flat(down(app(y481, cons)), block(app(app(fresh_constant, y32652), y484))) 392.57/193.65 down(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> app_flat(block(app(y481, cons)), down(app(app(fresh_constant, y32652), y484))) 392.57/193.65 down(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> app_flat(down(app(y508, nil)), block(app(app(app(y32740, y32741), y32742), y511))) 392.57/193.65 down(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> app_flat(block(app(y508, nil)), down(app(app(app(y32740, y32741), y32742), y511))) 392.57/193.65 down(app(app(y508, nil), app(app(0, y32743), y511))) -> app_flat(down(app(y508, nil)), block(app(app(0, y32743), y511))) 392.57/193.65 down(app(app(y508, nil), app(app(0, y32743), y511))) -> app_flat(block(app(y508, nil)), down(app(app(0, y32743), y511))) 392.57/193.65 down(app(app(y508, nil), app(app(hd, y32744), y511))) -> app_flat(down(app(y508, nil)), block(app(app(hd, y32744), y511))) 392.57/193.65 down(app(app(y508, nil), app(app(hd, y32744), y511))) -> app_flat(block(app(y508, nil)), down(app(app(hd, y32744), y511))) 392.57/193.65 down(app(app(y508, nil), app(app(map, y32745), y511))) -> app_flat(down(app(y508, nil)), block(app(app(map, y32745), y511))) 392.57/193.65 down(app(app(y508, nil), app(app(map, y32745), y511))) -> app_flat(block(app(y508, nil)), down(app(app(map, y32745), y511))) 392.57/193.65 down(app(app(y508, nil), app(app(nil, y32747), y511))) -> app_flat(down(app(y508, nil)), block(app(app(nil, y32747), y511))) 392.57/193.65 down(app(app(y508, nil), app(app(nil, y32747), y511))) -> app_flat(block(app(y508, nil)), down(app(app(nil, y32747), y511))) 392.57/193.65 down(app(app(y508, nil), app(app(fresh_constant, y32748), y511))) -> app_flat(down(app(y508, nil)), block(app(app(fresh_constant, y32748), y511))) 392.57/193.65 down(app(app(y508, nil), app(app(fresh_constant, y32748), y511))) -> app_flat(block(app(y508, nil)), down(app(app(fresh_constant, y32748), y511))) 392.57/193.65 down(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(app(y32836, y32837), y32838), y538))) 392.57/193.65 down(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(app(y32836, y32837), y32838), y538))) 392.57/193.65 down(app(app(y535, fresh_constant), app(app(0, y32839), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(0, y32839), y538))) 392.57/193.65 down(app(app(y535, fresh_constant), app(app(0, y32839), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(0, y32839), y538))) 392.57/193.65 down(app(app(y535, fresh_constant), app(app(hd, y32840), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(hd, y32840), y538))) 392.57/193.65 down(app(app(y535, fresh_constant), app(app(hd, y32840), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(hd, y32840), y538))) 392.57/193.65 down(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(map, y32841), y538))) 392.57/193.65 down(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(map, y32841), y538))) 392.57/193.65 down(app(app(y535, fresh_constant), app(app(nil, y32843), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(nil, y32843), y538))) 392.57/193.65 down(app(app(y535, fresh_constant), app(app(nil, y32843), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(nil, y32843), y538))) 392.57/193.65 down(app(app(y535, fresh_constant), app(app(fresh_constant, y32844), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(fresh_constant, y32844), y538))) 392.57/193.65 down(app(app(y535, fresh_constant), app(app(fresh_constant, y32844), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(fresh_constant, y32844), y538))) 392.57/193.65 app_flat(up(x_1), block(x_2)) -> up(app(x_1, x_2)) 392.57/193.65 app_flat(block(x_1), up(x_2)) -> up(app(x_1, x_2)) 392.57/193.65 392.57/193.65 Q is empty. 392.57/193.65 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (45) DependencyPairsProof (EQUIVALENT) 392.57/193.65 Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. 392.57/193.65 ---------------------------------------- 392.57/193.65 392.57/193.65 (46) 392.57/193.65 Obligation: 392.57/193.65 Q DP problem: 392.57/193.65 The TRS P consists of the following rules: 392.57/193.65 392.57/193.65 TOP(up(x)) -> TOP(down(x)) 392.57/193.65 TOP(up(x)) -> DOWN(x) 392.57/193.65 DOWN(app(0, y7)) -> APP_FLAT(down(0), block(y7)) 392.57/193.65 DOWN(app(0, y7)) -> DOWN(0) 392.57/193.65 DOWN(app(0, y7)) -> APP_FLAT(block(0), down(y7)) 392.57/193.65 DOWN(app(0, y7)) -> DOWN(y7) 392.57/193.65 DOWN(app(hd, y8)) -> APP_FLAT(down(hd), block(y8)) 392.57/193.65 DOWN(app(hd, y8)) -> DOWN(hd) 392.57/193.65 DOWN(app(hd, y8)) -> APP_FLAT(block(hd), down(y8)) 392.57/193.65 DOWN(app(hd, y8)) -> DOWN(y8) 392.57/193.65 DOWN(app(map, y9)) -> APP_FLAT(down(map), block(y9)) 392.57/193.65 DOWN(app(map, y9)) -> DOWN(map) 392.57/193.65 DOWN(app(map, y9)) -> APP_FLAT(block(map), down(y9)) 392.57/193.65 DOWN(app(map, y9)) -> DOWN(y9) 392.57/193.65 DOWN(app(cons, y10)) -> APP_FLAT(down(cons), block(y10)) 392.57/193.65 DOWN(app(cons, y10)) -> DOWN(cons) 392.57/193.65 DOWN(app(cons, y10)) -> APP_FLAT(block(cons), down(y10)) 392.57/193.65 DOWN(app(cons, y10)) -> DOWN(y10) 392.57/193.65 DOWN(app(nil, y11)) -> APP_FLAT(down(nil), block(y11)) 392.57/193.65 DOWN(app(nil, y11)) -> DOWN(nil) 392.57/193.65 DOWN(app(nil, y11)) -> APP_FLAT(block(nil), down(y11)) 392.57/193.65 DOWN(app(nil, y11)) -> DOWN(y11) 392.57/193.65 DOWN(app(fresh_constant, y12)) -> APP_FLAT(down(fresh_constant), block(y12)) 392.57/193.65 DOWN(app(fresh_constant, y12)) -> DOWN(fresh_constant) 392.57/193.65 DOWN(app(fresh_constant, y12)) -> APP_FLAT(block(fresh_constant), down(y12)) 392.57/193.65 DOWN(app(fresh_constant, y12)) -> DOWN(y12) 392.57/193.65 DOWN(app(app(app(y64, y65), app(y66, y67)), y6)) -> APP_FLAT(down(app(app(y64, y65), app(y66, y67))), block(y6)) 392.57/193.65 DOWN(app(app(app(y64, y65), app(y66, y67)), y6)) -> DOWN(app(app(y64, y65), app(y66, y67))) 392.57/193.65 DOWN(app(app(app(y64, y65), app(y66, y67)), y6)) -> APP_FLAT(block(app(app(y64, y65), app(y66, y67))), down(y6)) 392.57/193.65 DOWN(app(app(app(y64, y65), app(y66, y67)), y6)) -> DOWN(y6) 392.57/193.65 DOWN(app(app(0, app(y68, y69)), y6)) -> APP_FLAT(down(app(0, app(y68, y69))), block(y6)) 392.57/193.65 DOWN(app(app(0, app(y68, y69)), y6)) -> DOWN(app(0, app(y68, y69))) 392.57/193.65 DOWN(app(app(0, app(y68, y69)), y6)) -> APP_FLAT(block(app(0, app(y68, y69))), down(y6)) 392.57/193.65 DOWN(app(app(0, app(y68, y69)), y6)) -> DOWN(y6) 392.57/193.65 DOWN(app(app(hd, app(y70, y71)), y6)) -> APP_FLAT(down(app(hd, app(y70, y71))), block(y6)) 392.57/193.65 DOWN(app(app(hd, app(y70, y71)), y6)) -> DOWN(app(hd, app(y70, y71))) 392.57/193.65 DOWN(app(app(hd, app(y70, y71)), y6)) -> APP_FLAT(block(app(hd, app(y70, y71))), down(y6)) 392.57/193.65 DOWN(app(app(hd, app(y70, y71)), y6)) -> DOWN(y6) 392.57/193.65 DOWN(app(app(cons, app(y74, y75)), y6)) -> APP_FLAT(down(app(cons, app(y74, y75))), block(y6)) 392.57/193.65 DOWN(app(app(cons, app(y74, y75)), y6)) -> DOWN(app(cons, app(y74, y75))) 392.57/193.65 DOWN(app(app(cons, app(y74, y75)), y6)) -> APP_FLAT(block(app(cons, app(y74, y75))), down(y6)) 392.57/193.65 DOWN(app(app(cons, app(y74, y75)), y6)) -> DOWN(y6) 392.57/193.65 DOWN(app(app(nil, app(y76, y77)), y6)) -> APP_FLAT(down(app(nil, app(y76, y77))), block(y6)) 392.57/193.65 DOWN(app(app(nil, app(y76, y77)), y6)) -> DOWN(app(nil, app(y76, y77))) 392.57/193.65 DOWN(app(app(nil, app(y76, y77)), y6)) -> APP_FLAT(block(app(nil, app(y76, y77))), down(y6)) 392.57/193.65 DOWN(app(app(nil, app(y76, y77)), y6)) -> DOWN(y6) 392.57/193.65 DOWN(app(app(fresh_constant, app(y78, y79)), y6)) -> APP_FLAT(down(app(fresh_constant, app(y78, y79))), block(y6)) 392.57/193.65 DOWN(app(app(fresh_constant, app(y78, y79)), y6)) -> DOWN(app(fresh_constant, app(y78, y79))) 392.57/193.65 DOWN(app(app(fresh_constant, app(y78, y79)), y6)) -> APP_FLAT(block(app(fresh_constant, app(y78, y79))), down(y6)) 392.57/193.65 DOWN(app(app(fresh_constant, app(y78, y79)), y6)) -> DOWN(y6) 392.57/193.65 DOWN(app(app(app(y84, y85), hd), y6)) -> APP_FLAT(down(app(app(y84, y85), hd)), block(y6)) 392.57/193.65 DOWN(app(app(app(y84, y85), hd), y6)) -> DOWN(app(app(y84, y85), hd)) 392.57/193.65 DOWN(app(app(app(y84, y85), hd), y6)) -> APP_FLAT(block(app(app(y84, y85), hd)), down(y6)) 392.57/193.65 DOWN(app(app(app(y84, y85), hd), y6)) -> DOWN(y6) 392.57/193.65 DOWN(app(app(0, hd), y6)) -> APP_FLAT(down(app(0, hd)), block(y6)) 392.57/193.65 DOWN(app(app(0, hd), y6)) -> DOWN(app(0, hd)) 392.57/193.65 DOWN(app(app(0, hd), y6)) -> APP_FLAT(block(app(0, hd)), down(y6)) 392.57/193.65 DOWN(app(app(0, hd), y6)) -> DOWN(y6) 392.57/193.65 DOWN(app(app(hd, hd), y6)) -> APP_FLAT(down(app(hd, hd)), block(y6)) 392.57/193.65 DOWN(app(app(hd, hd), y6)) -> DOWN(app(hd, hd)) 392.57/193.65 DOWN(app(app(hd, hd), y6)) -> APP_FLAT(block(app(hd, hd)), down(y6)) 392.57/193.65 DOWN(app(app(hd, hd), y6)) -> DOWN(y6) 392.57/193.65 DOWN(app(app(cons, hd), y6)) -> APP_FLAT(down(app(cons, hd)), block(y6)) 392.57/193.65 DOWN(app(app(cons, hd), y6)) -> DOWN(app(cons, hd)) 392.57/193.65 DOWN(app(app(cons, hd), y6)) -> APP_FLAT(block(app(cons, hd)), down(y6)) 392.57/193.65 DOWN(app(app(cons, hd), y6)) -> DOWN(y6) 392.57/193.65 DOWN(app(app(nil, hd), y6)) -> APP_FLAT(down(app(nil, hd)), block(y6)) 392.57/193.65 DOWN(app(app(nil, hd), y6)) -> DOWN(app(nil, hd)) 392.57/193.65 DOWN(app(app(nil, hd), y6)) -> APP_FLAT(block(app(nil, hd)), down(y6)) 392.57/193.65 DOWN(app(app(nil, hd), y6)) -> DOWN(y6) 392.57/193.65 DOWN(app(app(fresh_constant, hd), y6)) -> APP_FLAT(down(app(fresh_constant, hd)), block(y6)) 392.66/193.65 DOWN(app(app(fresh_constant, hd), y6)) -> DOWN(app(fresh_constant, hd)) 392.66/193.65 DOWN(app(app(fresh_constant, hd), y6)) -> APP_FLAT(block(app(fresh_constant, hd)), down(y6)) 392.66/193.65 DOWN(app(app(fresh_constant, hd), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(app(y87, y88), map), y6)) -> APP_FLAT(down(app(app(y87, y88), map)), block(y6)) 392.66/193.65 DOWN(app(app(app(y87, y88), map), y6)) -> DOWN(app(app(y87, y88), map)) 392.66/193.65 DOWN(app(app(app(y87, y88), map), y6)) -> APP_FLAT(block(app(app(y87, y88), map)), down(y6)) 392.66/193.65 DOWN(app(app(app(y87, y88), map), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(0, map), y6)) -> APP_FLAT(down(app(0, map)), block(y6)) 392.66/193.65 DOWN(app(app(0, map), y6)) -> DOWN(app(0, map)) 392.66/193.65 DOWN(app(app(0, map), y6)) -> APP_FLAT(block(app(0, map)), down(y6)) 392.66/193.65 DOWN(app(app(0, map), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(hd, map), y6)) -> APP_FLAT(down(app(hd, map)), block(y6)) 392.66/193.65 DOWN(app(app(hd, map), y6)) -> DOWN(app(hd, map)) 392.66/193.65 DOWN(app(app(hd, map), y6)) -> APP_FLAT(block(app(hd, map)), down(y6)) 392.66/193.65 DOWN(app(app(hd, map), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(cons, map), y6)) -> APP_FLAT(down(app(cons, map)), block(y6)) 392.66/193.65 DOWN(app(app(cons, map), y6)) -> DOWN(app(cons, map)) 392.66/193.65 DOWN(app(app(cons, map), y6)) -> APP_FLAT(block(app(cons, map)), down(y6)) 392.66/193.65 DOWN(app(app(cons, map), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(nil, map), y6)) -> APP_FLAT(down(app(nil, map)), block(y6)) 392.66/193.65 DOWN(app(app(nil, map), y6)) -> DOWN(app(nil, map)) 392.66/193.65 DOWN(app(app(nil, map), y6)) -> APP_FLAT(block(app(nil, map)), down(y6)) 392.66/193.65 DOWN(app(app(nil, map), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(fresh_constant, map), y6)) -> APP_FLAT(down(app(fresh_constant, map)), block(y6)) 392.66/193.65 DOWN(app(app(fresh_constant, map), y6)) -> DOWN(app(fresh_constant, map)) 392.66/193.65 DOWN(app(app(fresh_constant, map), y6)) -> APP_FLAT(block(app(fresh_constant, map)), down(y6)) 392.66/193.65 DOWN(app(app(fresh_constant, map), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(app(y90, y91), cons), y6)) -> APP_FLAT(down(app(app(y90, y91), cons)), block(y6)) 392.66/193.65 DOWN(app(app(app(y90, y91), cons), y6)) -> DOWN(app(app(y90, y91), cons)) 392.66/193.65 DOWN(app(app(app(y90, y91), cons), y6)) -> APP_FLAT(block(app(app(y90, y91), cons)), down(y6)) 392.66/193.65 DOWN(app(app(app(y90, y91), cons), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(0, cons), y6)) -> APP_FLAT(down(app(0, cons)), block(y6)) 392.66/193.65 DOWN(app(app(0, cons), y6)) -> DOWN(app(0, cons)) 392.66/193.65 DOWN(app(app(0, cons), y6)) -> APP_FLAT(block(app(0, cons)), down(y6)) 392.66/193.65 DOWN(app(app(0, cons), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(hd, cons), y6)) -> APP_FLAT(down(app(hd, cons)), block(y6)) 392.66/193.65 DOWN(app(app(hd, cons), y6)) -> DOWN(app(hd, cons)) 392.66/193.65 DOWN(app(app(hd, cons), y6)) -> APP_FLAT(block(app(hd, cons)), down(y6)) 392.66/193.65 DOWN(app(app(hd, cons), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(cons, cons), y6)) -> APP_FLAT(down(app(cons, cons)), block(y6)) 392.66/193.65 DOWN(app(app(cons, cons), y6)) -> DOWN(app(cons, cons)) 392.66/193.65 DOWN(app(app(cons, cons), y6)) -> APP_FLAT(block(app(cons, cons)), down(y6)) 392.66/193.65 DOWN(app(app(cons, cons), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(nil, cons), y6)) -> APP_FLAT(down(app(nil, cons)), block(y6)) 392.66/193.65 DOWN(app(app(nil, cons), y6)) -> DOWN(app(nil, cons)) 392.66/193.65 DOWN(app(app(nil, cons), y6)) -> APP_FLAT(block(app(nil, cons)), down(y6)) 392.66/193.65 DOWN(app(app(nil, cons), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(fresh_constant, cons), y6)) -> APP_FLAT(down(app(fresh_constant, cons)), block(y6)) 392.66/193.65 DOWN(app(app(fresh_constant, cons), y6)) -> DOWN(app(fresh_constant, cons)) 392.66/193.65 DOWN(app(app(fresh_constant, cons), y6)) -> APP_FLAT(block(app(fresh_constant, cons)), down(y6)) 392.66/193.65 DOWN(app(app(fresh_constant, cons), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(app(y93, y94), nil), y6)) -> APP_FLAT(down(app(app(y93, y94), nil)), block(y6)) 392.66/193.65 DOWN(app(app(app(y93, y94), nil), y6)) -> DOWN(app(app(y93, y94), nil)) 392.66/193.65 DOWN(app(app(app(y93, y94), nil), y6)) -> APP_FLAT(block(app(app(y93, y94), nil)), down(y6)) 392.66/193.65 DOWN(app(app(app(y93, y94), nil), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(0, nil), y6)) -> APP_FLAT(down(app(0, nil)), block(y6)) 392.66/193.65 DOWN(app(app(0, nil), y6)) -> DOWN(app(0, nil)) 392.66/193.65 DOWN(app(app(0, nil), y6)) -> APP_FLAT(block(app(0, nil)), down(y6)) 392.66/193.65 DOWN(app(app(0, nil), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(hd, nil), y6)) -> APP_FLAT(down(app(hd, nil)), block(y6)) 392.66/193.65 DOWN(app(app(hd, nil), y6)) -> DOWN(app(hd, nil)) 392.66/193.65 DOWN(app(app(hd, nil), y6)) -> APP_FLAT(block(app(hd, nil)), down(y6)) 392.66/193.65 DOWN(app(app(hd, nil), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(cons, nil), y6)) -> APP_FLAT(down(app(cons, nil)), block(y6)) 392.66/193.65 DOWN(app(app(cons, nil), y6)) -> DOWN(app(cons, nil)) 392.66/193.65 DOWN(app(app(cons, nil), y6)) -> APP_FLAT(block(app(cons, nil)), down(y6)) 392.66/193.65 DOWN(app(app(cons, nil), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(nil, nil), y6)) -> APP_FLAT(down(app(nil, nil)), block(y6)) 392.66/193.65 DOWN(app(app(nil, nil), y6)) -> DOWN(app(nil, nil)) 392.66/193.65 DOWN(app(app(nil, nil), y6)) -> APP_FLAT(block(app(nil, nil)), down(y6)) 392.66/193.65 DOWN(app(app(nil, nil), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(fresh_constant, nil), y6)) -> APP_FLAT(down(app(fresh_constant, nil)), block(y6)) 392.66/193.65 DOWN(app(app(fresh_constant, nil), y6)) -> DOWN(app(fresh_constant, nil)) 392.66/193.65 DOWN(app(app(fresh_constant, nil), y6)) -> APP_FLAT(block(app(fresh_constant, nil)), down(y6)) 392.66/193.65 DOWN(app(app(fresh_constant, nil), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(app(y96, y97), fresh_constant), y6)) -> APP_FLAT(down(app(app(y96, y97), fresh_constant)), block(y6)) 392.66/193.65 DOWN(app(app(app(y96, y97), fresh_constant), y6)) -> DOWN(app(app(y96, y97), fresh_constant)) 392.66/193.65 DOWN(app(app(app(y96, y97), fresh_constant), y6)) -> APP_FLAT(block(app(app(y96, y97), fresh_constant)), down(y6)) 392.66/193.65 DOWN(app(app(app(y96, y97), fresh_constant), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(0, fresh_constant), y6)) -> APP_FLAT(down(app(0, fresh_constant)), block(y6)) 392.66/193.65 DOWN(app(app(0, fresh_constant), y6)) -> DOWN(app(0, fresh_constant)) 392.66/193.65 DOWN(app(app(0, fresh_constant), y6)) -> APP_FLAT(block(app(0, fresh_constant)), down(y6)) 392.66/193.65 DOWN(app(app(0, fresh_constant), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(hd, fresh_constant), y6)) -> APP_FLAT(down(app(hd, fresh_constant)), block(y6)) 392.66/193.65 DOWN(app(app(hd, fresh_constant), y6)) -> DOWN(app(hd, fresh_constant)) 392.66/193.65 DOWN(app(app(hd, fresh_constant), y6)) -> APP_FLAT(block(app(hd, fresh_constant)), down(y6)) 392.66/193.65 DOWN(app(app(hd, fresh_constant), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(cons, fresh_constant), y6)) -> APP_FLAT(down(app(cons, fresh_constant)), block(y6)) 392.66/193.65 DOWN(app(app(cons, fresh_constant), y6)) -> DOWN(app(cons, fresh_constant)) 392.66/193.65 DOWN(app(app(cons, fresh_constant), y6)) -> APP_FLAT(block(app(cons, fresh_constant)), down(y6)) 392.66/193.65 DOWN(app(app(cons, fresh_constant), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(nil, fresh_constant), y6)) -> APP_FLAT(down(app(nil, fresh_constant)), block(y6)) 392.66/193.65 DOWN(app(app(nil, fresh_constant), y6)) -> DOWN(app(nil, fresh_constant)) 392.66/193.65 DOWN(app(app(nil, fresh_constant), y6)) -> APP_FLAT(block(app(nil, fresh_constant)), down(y6)) 392.66/193.65 DOWN(app(app(nil, fresh_constant), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(fresh_constant, fresh_constant), y6)) -> APP_FLAT(down(app(fresh_constant, fresh_constant)), block(y6)) 392.66/193.65 DOWN(app(app(fresh_constant, fresh_constant), y6)) -> DOWN(app(fresh_constant, fresh_constant)) 392.66/193.65 DOWN(app(app(fresh_constant, fresh_constant), y6)) -> APP_FLAT(block(app(fresh_constant, fresh_constant)), down(y6)) 392.66/193.65 DOWN(app(app(fresh_constant, fresh_constant), y6)) -> DOWN(y6) 392.66/193.65 DOWN(app(app(y581, app(y582, y583)), app(0, y584))) -> APP_FLAT(down(app(y581, app(y582, y583))), block(app(0, y584))) 392.66/193.65 DOWN(app(app(y581, app(y582, y583)), app(0, y584))) -> DOWN(app(y581, app(y582, y583))) 392.66/193.65 DOWN(app(app(y581, app(y582, y583)), app(0, y584))) -> APP_FLAT(block(app(y581, app(y582, y583))), down(app(0, y584))) 392.66/193.65 DOWN(app(app(y581, app(y582, y583)), app(0, y584))) -> DOWN(app(0, y584)) 392.66/193.65 DOWN(app(app(y619, hd), app(0, y620))) -> APP_FLAT(down(app(y619, hd)), block(app(0, y620))) 392.66/193.65 DOWN(app(app(y619, hd), app(0, y620))) -> DOWN(app(y619, hd)) 392.66/193.65 DOWN(app(app(y619, hd), app(0, y620))) -> APP_FLAT(block(app(y619, hd)), down(app(0, y620))) 392.66/193.65 DOWN(app(app(y619, hd), app(0, y620))) -> DOWN(app(0, y620)) 392.66/193.65 DOWN(app(app(y630, map), app(0, y631))) -> APP_FLAT(down(app(y630, map)), block(app(0, y631))) 392.66/193.65 DOWN(app(app(y630, map), app(0, y631))) -> DOWN(app(y630, map)) 392.66/193.65 DOWN(app(app(y630, map), app(0, y631))) -> APP_FLAT(block(app(y630, map)), down(app(0, y631))) 392.66/193.65 DOWN(app(app(y630, map), app(0, y631))) -> DOWN(app(0, y631)) 392.66/193.65 DOWN(app(app(y641, cons), app(0, y642))) -> APP_FLAT(down(app(y641, cons)), block(app(0, y642))) 392.66/193.65 DOWN(app(app(y641, cons), app(0, y642))) -> DOWN(app(y641, cons)) 392.66/193.65 DOWN(app(app(y641, cons), app(0, y642))) -> APP_FLAT(block(app(y641, cons)), down(app(0, y642))) 392.66/193.65 DOWN(app(app(y641, cons), app(0, y642))) -> DOWN(app(0, y642)) 392.66/193.65 DOWN(app(app(y652, nil), app(0, y653))) -> APP_FLAT(down(app(y652, nil)), block(app(0, y653))) 392.66/193.65 DOWN(app(app(y652, nil), app(0, y653))) -> DOWN(app(y652, nil)) 392.66/193.65 DOWN(app(app(y652, nil), app(0, y653))) -> APP_FLAT(block(app(y652, nil)), down(app(0, y653))) 392.66/193.65 DOWN(app(app(y652, nil), app(0, y653))) -> DOWN(app(0, y653)) 392.66/193.65 DOWN(app(app(y663, fresh_constant), app(0, y664))) -> APP_FLAT(down(app(y663, fresh_constant)), block(app(0, y664))) 392.66/193.65 DOWN(app(app(y663, fresh_constant), app(0, y664))) -> DOWN(app(y663, fresh_constant)) 392.66/193.65 DOWN(app(app(y663, fresh_constant), app(0, y664))) -> APP_FLAT(block(app(y663, fresh_constant)), down(app(0, y664))) 392.66/193.65 DOWN(app(app(y663, fresh_constant), app(0, y664))) -> DOWN(app(0, y664)) 392.66/193.65 DOWN(app(app(y693, app(y694, y695)), app(hd, y696))) -> APP_FLAT(down(app(y693, app(y694, y695))), block(app(hd, y696))) 392.66/193.65 DOWN(app(app(y693, app(y694, y695)), app(hd, y696))) -> DOWN(app(y693, app(y694, y695))) 392.66/193.65 DOWN(app(app(y693, app(y694, y695)), app(hd, y696))) -> APP_FLAT(block(app(y693, app(y694, y695))), down(app(hd, y696))) 392.66/193.65 DOWN(app(app(y693, app(y694, y695)), app(hd, y696))) -> DOWN(app(hd, y696)) 392.66/193.65 DOWN(app(app(y731, hd), app(hd, y732))) -> APP_FLAT(down(app(y731, hd)), block(app(hd, y732))) 392.66/193.65 DOWN(app(app(y731, hd), app(hd, y732))) -> DOWN(app(y731, hd)) 392.66/193.65 DOWN(app(app(y731, hd), app(hd, y732))) -> APP_FLAT(block(app(y731, hd)), down(app(hd, y732))) 392.66/193.65 DOWN(app(app(y731, hd), app(hd, y732))) -> DOWN(app(hd, y732)) 392.66/193.65 DOWN(app(app(y742, map), app(hd, y743))) -> APP_FLAT(down(app(y742, map)), block(app(hd, y743))) 392.66/193.65 DOWN(app(app(y742, map), app(hd, y743))) -> DOWN(app(y742, map)) 392.66/193.65 DOWN(app(app(y742, map), app(hd, y743))) -> APP_FLAT(block(app(y742, map)), down(app(hd, y743))) 392.66/193.65 DOWN(app(app(y742, map), app(hd, y743))) -> DOWN(app(hd, y743)) 392.66/193.65 DOWN(app(app(y753, cons), app(hd, y754))) -> APP_FLAT(down(app(y753, cons)), block(app(hd, y754))) 392.66/193.65 DOWN(app(app(y753, cons), app(hd, y754))) -> DOWN(app(y753, cons)) 392.66/193.65 DOWN(app(app(y753, cons), app(hd, y754))) -> APP_FLAT(block(app(y753, cons)), down(app(hd, y754))) 392.66/193.65 DOWN(app(app(y753, cons), app(hd, y754))) -> DOWN(app(hd, y754)) 392.66/193.65 DOWN(app(app(y764, nil), app(hd, y765))) -> APP_FLAT(down(app(y764, nil)), block(app(hd, y765))) 392.66/193.65 DOWN(app(app(y764, nil), app(hd, y765))) -> DOWN(app(y764, nil)) 392.66/193.65 DOWN(app(app(y764, nil), app(hd, y765))) -> APP_FLAT(block(app(y764, nil)), down(app(hd, y765))) 392.66/193.65 DOWN(app(app(y764, nil), app(hd, y765))) -> DOWN(app(hd, y765)) 392.66/193.65 DOWN(app(app(y775, fresh_constant), app(hd, y776))) -> APP_FLAT(down(app(y775, fresh_constant)), block(app(hd, y776))) 392.66/193.65 DOWN(app(app(y775, fresh_constant), app(hd, y776))) -> DOWN(app(y775, fresh_constant)) 392.66/193.65 DOWN(app(app(y775, fresh_constant), app(hd, y776))) -> APP_FLAT(block(app(y775, fresh_constant)), down(app(hd, y776))) 392.66/193.65 DOWN(app(app(y775, fresh_constant), app(hd, y776))) -> DOWN(app(hd, y776)) 392.66/193.65 DOWN(app(app(y805, app(y806, y807)), app(map, y808))) -> APP_FLAT(down(app(y805, app(y806, y807))), block(app(map, y808))) 392.66/193.65 DOWN(app(app(y805, app(y806, y807)), app(map, y808))) -> DOWN(app(y805, app(y806, y807))) 392.66/193.65 DOWN(app(app(y805, app(y806, y807)), app(map, y808))) -> APP_FLAT(block(app(y805, app(y806, y807))), down(app(map, y808))) 392.66/193.65 DOWN(app(app(y805, app(y806, y807)), app(map, y808))) -> DOWN(app(map, y808)) 392.66/193.65 DOWN(app(app(y843, hd), app(map, y844))) -> APP_FLAT(down(app(y843, hd)), block(app(map, y844))) 392.66/193.65 DOWN(app(app(y843, hd), app(map, y844))) -> DOWN(app(y843, hd)) 392.66/193.65 DOWN(app(app(y843, hd), app(map, y844))) -> APP_FLAT(block(app(y843, hd)), down(app(map, y844))) 392.66/193.65 DOWN(app(app(y843, hd), app(map, y844))) -> DOWN(app(map, y844)) 392.66/193.65 DOWN(app(app(y854, map), app(map, y855))) -> APP_FLAT(down(app(y854, map)), block(app(map, y855))) 392.66/193.65 DOWN(app(app(y854, map), app(map, y855))) -> DOWN(app(y854, map)) 392.66/193.65 DOWN(app(app(y854, map), app(map, y855))) -> APP_FLAT(block(app(y854, map)), down(app(map, y855))) 392.66/193.65 DOWN(app(app(y854, map), app(map, y855))) -> DOWN(app(map, y855)) 392.66/193.65 DOWN(app(app(y865, cons), app(map, y866))) -> APP_FLAT(down(app(y865, cons)), block(app(map, y866))) 392.66/193.65 DOWN(app(app(y865, cons), app(map, y866))) -> DOWN(app(y865, cons)) 392.66/193.65 DOWN(app(app(y865, cons), app(map, y866))) -> APP_FLAT(block(app(y865, cons)), down(app(map, y866))) 392.66/193.65 DOWN(app(app(y865, cons), app(map, y866))) -> DOWN(app(map, y866)) 392.66/193.65 DOWN(app(app(y876, nil), app(map, y877))) -> APP_FLAT(down(app(y876, nil)), block(app(map, y877))) 392.66/193.65 DOWN(app(app(y876, nil), app(map, y877))) -> DOWN(app(y876, nil)) 392.66/193.65 DOWN(app(app(y876, nil), app(map, y877))) -> APP_FLAT(block(app(y876, nil)), down(app(map, y877))) 392.66/193.65 DOWN(app(app(y876, nil), app(map, y877))) -> DOWN(app(map, y877)) 392.66/193.65 DOWN(app(app(y887, fresh_constant), app(map, y888))) -> APP_FLAT(down(app(y887, fresh_constant)), block(app(map, y888))) 392.66/193.65 DOWN(app(app(y887, fresh_constant), app(map, y888))) -> DOWN(app(y887, fresh_constant)) 392.66/193.65 DOWN(app(app(y887, fresh_constant), app(map, y888))) -> APP_FLAT(block(app(y887, fresh_constant)), down(app(map, y888))) 392.66/193.65 DOWN(app(app(y887, fresh_constant), app(map, y888))) -> DOWN(app(map, y888)) 392.66/193.65 DOWN(app(app(y917, app(y918, y919)), app(cons, y920))) -> APP_FLAT(down(app(y917, app(y918, y919))), block(app(cons, y920))) 392.66/193.65 DOWN(app(app(y917, app(y918, y919)), app(cons, y920))) -> DOWN(app(y917, app(y918, y919))) 392.66/193.65 DOWN(app(app(y917, app(y918, y919)), app(cons, y920))) -> APP_FLAT(block(app(y917, app(y918, y919))), down(app(cons, y920))) 392.66/193.65 DOWN(app(app(y917, app(y918, y919)), app(cons, y920))) -> DOWN(app(cons, y920)) 392.66/193.65 DOWN(app(app(y955, hd), app(cons, y956))) -> APP_FLAT(down(app(y955, hd)), block(app(cons, y956))) 392.66/193.65 DOWN(app(app(y955, hd), app(cons, y956))) -> DOWN(app(y955, hd)) 392.66/193.65 DOWN(app(app(y955, hd), app(cons, y956))) -> APP_FLAT(block(app(y955, hd)), down(app(cons, y956))) 392.66/193.65 DOWN(app(app(y955, hd), app(cons, y956))) -> DOWN(app(cons, y956)) 392.66/193.65 DOWN(app(app(y966, map), app(cons, y967))) -> APP_FLAT(down(app(y966, map)), block(app(cons, y967))) 392.66/193.65 DOWN(app(app(y966, map), app(cons, y967))) -> DOWN(app(y966, map)) 392.66/193.65 DOWN(app(app(y966, map), app(cons, y967))) -> APP_FLAT(block(app(y966, map)), down(app(cons, y967))) 392.66/193.65 DOWN(app(app(y966, map), app(cons, y967))) -> DOWN(app(cons, y967)) 392.66/193.65 DOWN(app(app(y977, cons), app(cons, y978))) -> APP_FLAT(down(app(y977, cons)), block(app(cons, y978))) 392.66/193.65 DOWN(app(app(y977, cons), app(cons, y978))) -> DOWN(app(y977, cons)) 392.66/193.65 DOWN(app(app(y977, cons), app(cons, y978))) -> APP_FLAT(block(app(y977, cons)), down(app(cons, y978))) 392.66/193.65 DOWN(app(app(y977, cons), app(cons, y978))) -> DOWN(app(cons, y978)) 392.66/193.65 DOWN(app(app(y988, nil), app(cons, y989))) -> APP_FLAT(down(app(y988, nil)), block(app(cons, y989))) 392.66/193.65 DOWN(app(app(y988, nil), app(cons, y989))) -> DOWN(app(y988, nil)) 392.66/193.65 DOWN(app(app(y988, nil), app(cons, y989))) -> APP_FLAT(block(app(y988, nil)), down(app(cons, y989))) 392.66/193.65 DOWN(app(app(y988, nil), app(cons, y989))) -> DOWN(app(cons, y989)) 392.66/193.65 DOWN(app(app(y999, fresh_constant), app(cons, y1000))) -> APP_FLAT(down(app(y999, fresh_constant)), block(app(cons, y1000))) 392.66/193.65 DOWN(app(app(y999, fresh_constant), app(cons, y1000))) -> DOWN(app(y999, fresh_constant)) 392.66/193.65 DOWN(app(app(y999, fresh_constant), app(cons, y1000))) -> APP_FLAT(block(app(y999, fresh_constant)), down(app(cons, y1000))) 392.66/193.65 DOWN(app(app(y999, fresh_constant), app(cons, y1000))) -> DOWN(app(cons, y1000)) 392.66/193.65 DOWN(app(app(y1029, app(y1030, y1031)), app(nil, y1032))) -> APP_FLAT(down(app(y1029, app(y1030, y1031))), block(app(nil, y1032))) 392.66/193.65 DOWN(app(app(y1029, app(y1030, y1031)), app(nil, y1032))) -> DOWN(app(y1029, app(y1030, y1031))) 392.66/193.65 DOWN(app(app(y1029, app(y1030, y1031)), app(nil, y1032))) -> APP_FLAT(block(app(y1029, app(y1030, y1031))), down(app(nil, y1032))) 392.66/193.65 DOWN(app(app(y1029, app(y1030, y1031)), app(nil, y1032))) -> DOWN(app(nil, y1032)) 392.66/193.65 DOWN(app(app(y1067, hd), app(nil, y1068))) -> APP_FLAT(down(app(y1067, hd)), block(app(nil, y1068))) 392.66/193.65 DOWN(app(app(y1067, hd), app(nil, y1068))) -> DOWN(app(y1067, hd)) 392.66/193.65 DOWN(app(app(y1067, hd), app(nil, y1068))) -> APP_FLAT(block(app(y1067, hd)), down(app(nil, y1068))) 392.66/193.65 DOWN(app(app(y1067, hd), app(nil, y1068))) -> DOWN(app(nil, y1068)) 392.66/193.65 DOWN(app(app(y1078, map), app(nil, y1079))) -> APP_FLAT(down(app(y1078, map)), block(app(nil, y1079))) 392.66/193.65 DOWN(app(app(y1078, map), app(nil, y1079))) -> DOWN(app(y1078, map)) 392.66/193.65 DOWN(app(app(y1078, map), app(nil, y1079))) -> APP_FLAT(block(app(y1078, map)), down(app(nil, y1079))) 392.66/193.65 DOWN(app(app(y1078, map), app(nil, y1079))) -> DOWN(app(nil, y1079)) 392.66/193.65 DOWN(app(app(y1089, cons), app(nil, y1090))) -> APP_FLAT(down(app(y1089, cons)), block(app(nil, y1090))) 392.66/193.65 DOWN(app(app(y1089, cons), app(nil, y1090))) -> DOWN(app(y1089, cons)) 392.66/193.65 DOWN(app(app(y1089, cons), app(nil, y1090))) -> APP_FLAT(block(app(y1089, cons)), down(app(nil, y1090))) 392.66/193.65 DOWN(app(app(y1089, cons), app(nil, y1090))) -> DOWN(app(nil, y1090)) 392.66/193.65 DOWN(app(app(y1100, nil), app(nil, y1101))) -> APP_FLAT(down(app(y1100, nil)), block(app(nil, y1101))) 392.66/193.65 DOWN(app(app(y1100, nil), app(nil, y1101))) -> DOWN(app(y1100, nil)) 392.66/193.65 DOWN(app(app(y1100, nil), app(nil, y1101))) -> APP_FLAT(block(app(y1100, nil)), down(app(nil, y1101))) 392.66/193.65 DOWN(app(app(y1100, nil), app(nil, y1101))) -> DOWN(app(nil, y1101)) 392.66/193.65 DOWN(app(app(y1111, fresh_constant), app(nil, y1112))) -> APP_FLAT(down(app(y1111, fresh_constant)), block(app(nil, y1112))) 392.66/193.65 DOWN(app(app(y1111, fresh_constant), app(nil, y1112))) -> DOWN(app(y1111, fresh_constant)) 392.66/193.65 DOWN(app(app(y1111, fresh_constant), app(nil, y1112))) -> APP_FLAT(block(app(y1111, fresh_constant)), down(app(nil, y1112))) 392.66/193.65 DOWN(app(app(y1111, fresh_constant), app(nil, y1112))) -> DOWN(app(nil, y1112)) 392.66/193.65 DOWN(app(app(y1141, app(y1142, y1143)), app(fresh_constant, y1144))) -> APP_FLAT(down(app(y1141, app(y1142, y1143))), block(app(fresh_constant, y1144))) 392.66/193.65 DOWN(app(app(y1141, app(y1142, y1143)), app(fresh_constant, y1144))) -> DOWN(app(y1141, app(y1142, y1143))) 392.66/193.65 DOWN(app(app(y1141, app(y1142, y1143)), app(fresh_constant, y1144))) -> APP_FLAT(block(app(y1141, app(y1142, y1143))), down(app(fresh_constant, y1144))) 392.66/193.65 DOWN(app(app(y1141, app(y1142, y1143)), app(fresh_constant, y1144))) -> DOWN(app(fresh_constant, y1144)) 392.66/193.65 DOWN(app(app(y1179, hd), app(fresh_constant, y1180))) -> APP_FLAT(down(app(y1179, hd)), block(app(fresh_constant, y1180))) 392.66/193.65 DOWN(app(app(y1179, hd), app(fresh_constant, y1180))) -> DOWN(app(y1179, hd)) 392.66/193.65 DOWN(app(app(y1179, hd), app(fresh_constant, y1180))) -> APP_FLAT(block(app(y1179, hd)), down(app(fresh_constant, y1180))) 392.66/193.65 DOWN(app(app(y1179, hd), app(fresh_constant, y1180))) -> DOWN(app(fresh_constant, y1180)) 392.66/193.65 DOWN(app(app(y1190, map), app(fresh_constant, y1191))) -> APP_FLAT(down(app(y1190, map)), block(app(fresh_constant, y1191))) 392.66/193.65 DOWN(app(app(y1190, map), app(fresh_constant, y1191))) -> DOWN(app(y1190, map)) 392.66/193.65 DOWN(app(app(y1190, map), app(fresh_constant, y1191))) -> APP_FLAT(block(app(y1190, map)), down(app(fresh_constant, y1191))) 392.66/193.65 DOWN(app(app(y1190, map), app(fresh_constant, y1191))) -> DOWN(app(fresh_constant, y1191)) 392.66/193.65 DOWN(app(app(y1201, cons), app(fresh_constant, y1202))) -> APP_FLAT(down(app(y1201, cons)), block(app(fresh_constant, y1202))) 392.66/193.65 DOWN(app(app(y1201, cons), app(fresh_constant, y1202))) -> DOWN(app(y1201, cons)) 392.66/193.65 DOWN(app(app(y1201, cons), app(fresh_constant, y1202))) -> APP_FLAT(block(app(y1201, cons)), down(app(fresh_constant, y1202))) 392.66/193.65 DOWN(app(app(y1201, cons), app(fresh_constant, y1202))) -> DOWN(app(fresh_constant, y1202)) 392.66/193.65 DOWN(app(app(y1212, nil), app(fresh_constant, y1213))) -> APP_FLAT(down(app(y1212, nil)), block(app(fresh_constant, y1213))) 392.66/193.65 DOWN(app(app(y1212, nil), app(fresh_constant, y1213))) -> DOWN(app(y1212, nil)) 392.66/193.65 DOWN(app(app(y1212, nil), app(fresh_constant, y1213))) -> APP_FLAT(block(app(y1212, nil)), down(app(fresh_constant, y1213))) 392.66/193.65 DOWN(app(app(y1212, nil), app(fresh_constant, y1213))) -> DOWN(app(fresh_constant, y1213)) 392.66/193.65 DOWN(app(app(y1223, fresh_constant), app(fresh_constant, y1224))) -> APP_FLAT(down(app(y1223, fresh_constant)), block(app(fresh_constant, y1224))) 392.66/193.65 DOWN(app(app(y1223, fresh_constant), app(fresh_constant, y1224))) -> DOWN(app(y1223, fresh_constant)) 392.66/193.65 DOWN(app(app(y1223, fresh_constant), app(fresh_constant, y1224))) -> APP_FLAT(block(app(y1223, fresh_constant)), down(app(fresh_constant, y1224))) 392.66/193.65 DOWN(app(app(y1223, fresh_constant), app(fresh_constant, y1224))) -> DOWN(app(fresh_constant, y1224)) 392.66/193.65 DOWN(app(app(y6301, app(y6302, y6303)), 0)) -> APP_FLAT(down(app(y6301, app(y6302, y6303))), block(0)) 392.66/193.65 DOWN(app(app(y6301, app(y6302, y6303)), 0)) -> DOWN(app(y6301, app(y6302, y6303))) 392.66/193.65 DOWN(app(app(y6301, app(y6302, y6303)), 0)) -> APP_FLAT(block(app(y6301, app(y6302, y6303))), down(0)) 392.66/193.65 DOWN(app(app(y6301, app(y6302, y6303)), 0)) -> DOWN(0) 392.66/193.65 DOWN(app(app(y6323, hd), 0)) -> APP_FLAT(down(app(y6323, hd)), block(0)) 392.66/193.65 DOWN(app(app(y6323, hd), 0)) -> DOWN(app(y6323, hd)) 392.66/193.65 DOWN(app(app(y6323, hd), 0)) -> APP_FLAT(block(app(y6323, hd)), down(0)) 392.66/193.65 DOWN(app(app(y6323, hd), 0)) -> DOWN(0) 392.66/193.65 DOWN(app(app(y6326, map), 0)) -> APP_FLAT(down(app(y6326, map)), block(0)) 392.66/193.65 DOWN(app(app(y6326, map), 0)) -> DOWN(app(y6326, map)) 392.66/193.65 DOWN(app(app(y6326, map), 0)) -> APP_FLAT(block(app(y6326, map)), down(0)) 392.66/193.65 DOWN(app(app(y6326, map), 0)) -> DOWN(0) 392.66/193.65 DOWN(app(app(y6329, cons), 0)) -> APP_FLAT(down(app(y6329, cons)), block(0)) 392.66/193.65 DOWN(app(app(y6329, cons), 0)) -> DOWN(app(y6329, cons)) 392.66/193.65 DOWN(app(app(y6329, cons), 0)) -> APP_FLAT(block(app(y6329, cons)), down(0)) 392.66/193.65 DOWN(app(app(y6329, cons), 0)) -> DOWN(0) 392.66/193.65 DOWN(app(app(y6332, nil), 0)) -> APP_FLAT(down(app(y6332, nil)), block(0)) 392.66/193.65 DOWN(app(app(y6332, nil), 0)) -> DOWN(app(y6332, nil)) 392.66/193.65 DOWN(app(app(y6332, nil), 0)) -> APP_FLAT(block(app(y6332, nil)), down(0)) 392.66/193.65 DOWN(app(app(y6332, nil), 0)) -> DOWN(0) 392.66/193.65 DOWN(app(app(y6335, fresh_constant), 0)) -> APP_FLAT(down(app(y6335, fresh_constant)), block(0)) 392.66/193.65 DOWN(app(app(y6335, fresh_constant), 0)) -> DOWN(app(y6335, fresh_constant)) 392.66/193.65 DOWN(app(app(y6335, fresh_constant), 0)) -> APP_FLAT(block(app(y6335, fresh_constant)), down(0)) 392.66/193.65 DOWN(app(app(y6335, fresh_constant), 0)) -> DOWN(0) 392.66/193.65 DOWN(app(app(y6349, app(y6350, y6351)), hd)) -> APP_FLAT(down(app(y6349, app(y6350, y6351))), block(hd)) 392.66/193.65 DOWN(app(app(y6349, app(y6350, y6351)), hd)) -> DOWN(app(y6349, app(y6350, y6351))) 392.66/193.65 DOWN(app(app(y6349, app(y6350, y6351)), hd)) -> APP_FLAT(block(app(y6349, app(y6350, y6351))), down(hd)) 392.66/193.65 DOWN(app(app(y6349, app(y6350, y6351)), hd)) -> DOWN(hd) 392.66/193.65 DOWN(app(app(y6371, hd), hd)) -> APP_FLAT(down(app(y6371, hd)), block(hd)) 392.66/193.65 DOWN(app(app(y6371, hd), hd)) -> DOWN(app(y6371, hd)) 392.66/193.65 DOWN(app(app(y6371, hd), hd)) -> APP_FLAT(block(app(y6371, hd)), down(hd)) 392.66/193.65 DOWN(app(app(y6371, hd), hd)) -> DOWN(hd) 392.66/193.65 DOWN(app(app(y6374, map), hd)) -> APP_FLAT(down(app(y6374, map)), block(hd)) 392.66/193.65 DOWN(app(app(y6374, map), hd)) -> DOWN(app(y6374, map)) 392.66/193.65 DOWN(app(app(y6374, map), hd)) -> APP_FLAT(block(app(y6374, map)), down(hd)) 392.66/193.65 DOWN(app(app(y6374, map), hd)) -> DOWN(hd) 392.66/193.65 DOWN(app(app(y6377, cons), hd)) -> APP_FLAT(down(app(y6377, cons)), block(hd)) 392.66/193.65 DOWN(app(app(y6377, cons), hd)) -> DOWN(app(y6377, cons)) 392.66/193.65 DOWN(app(app(y6377, cons), hd)) -> APP_FLAT(block(app(y6377, cons)), down(hd)) 392.66/193.65 DOWN(app(app(y6377, cons), hd)) -> DOWN(hd) 392.66/193.65 DOWN(app(app(y6380, nil), hd)) -> APP_FLAT(down(app(y6380, nil)), block(hd)) 392.66/193.65 DOWN(app(app(y6380, nil), hd)) -> DOWN(app(y6380, nil)) 392.66/193.65 DOWN(app(app(y6380, nil), hd)) -> APP_FLAT(block(app(y6380, nil)), down(hd)) 392.66/193.65 DOWN(app(app(y6380, nil), hd)) -> DOWN(hd) 392.66/193.65 DOWN(app(app(y6383, fresh_constant), hd)) -> APP_FLAT(down(app(y6383, fresh_constant)), block(hd)) 392.66/193.65 DOWN(app(app(y6383, fresh_constant), hd)) -> DOWN(app(y6383, fresh_constant)) 392.66/193.65 DOWN(app(app(y6383, fresh_constant), hd)) -> APP_FLAT(block(app(y6383, fresh_constant)), down(hd)) 392.66/193.65 DOWN(app(app(y6383, fresh_constant), hd)) -> DOWN(hd) 392.66/193.65 DOWN(app(app(y6397, app(y6398, y6399)), map)) -> APP_FLAT(down(app(y6397, app(y6398, y6399))), block(map)) 392.66/193.65 DOWN(app(app(y6397, app(y6398, y6399)), map)) -> DOWN(app(y6397, app(y6398, y6399))) 392.66/193.65 DOWN(app(app(y6397, app(y6398, y6399)), map)) -> APP_FLAT(block(app(y6397, app(y6398, y6399))), down(map)) 392.66/193.65 DOWN(app(app(y6397, app(y6398, y6399)), map)) -> DOWN(map) 392.66/193.65 DOWN(app(app(y6419, hd), map)) -> APP_FLAT(down(app(y6419, hd)), block(map)) 392.66/193.65 DOWN(app(app(y6419, hd), map)) -> DOWN(app(y6419, hd)) 392.66/193.65 DOWN(app(app(y6419, hd), map)) -> APP_FLAT(block(app(y6419, hd)), down(map)) 392.66/193.65 DOWN(app(app(y6419, hd), map)) -> DOWN(map) 392.66/193.65 DOWN(app(app(y6422, map), map)) -> APP_FLAT(down(app(y6422, map)), block(map)) 392.66/193.65 DOWN(app(app(y6422, map), map)) -> DOWN(app(y6422, map)) 392.66/193.65 DOWN(app(app(y6422, map), map)) -> APP_FLAT(block(app(y6422, map)), down(map)) 392.66/193.65 DOWN(app(app(y6422, map), map)) -> DOWN(map) 392.66/193.65 DOWN(app(app(y6425, cons), map)) -> APP_FLAT(down(app(y6425, cons)), block(map)) 392.66/193.65 DOWN(app(app(y6425, cons), map)) -> DOWN(app(y6425, cons)) 392.66/193.65 DOWN(app(app(y6425, cons), map)) -> APP_FLAT(block(app(y6425, cons)), down(map)) 392.66/193.65 DOWN(app(app(y6425, cons), map)) -> DOWN(map) 392.66/193.65 DOWN(app(app(y6428, nil), map)) -> APP_FLAT(down(app(y6428, nil)), block(map)) 392.66/193.65 DOWN(app(app(y6428, nil), map)) -> DOWN(app(y6428, nil)) 392.66/193.65 DOWN(app(app(y6428, nil), map)) -> APP_FLAT(block(app(y6428, nil)), down(map)) 392.66/193.65 DOWN(app(app(y6428, nil), map)) -> DOWN(map) 392.66/193.65 DOWN(app(app(y6431, fresh_constant), map)) -> APP_FLAT(down(app(y6431, fresh_constant)), block(map)) 392.66/193.65 DOWN(app(app(y6431, fresh_constant), map)) -> DOWN(app(y6431, fresh_constant)) 392.66/193.65 DOWN(app(app(y6431, fresh_constant), map)) -> APP_FLAT(block(app(y6431, fresh_constant)), down(map)) 392.66/193.65 DOWN(app(app(y6431, fresh_constant), map)) -> DOWN(map) 392.66/193.65 DOWN(app(app(y6445, app(y6446, y6447)), cons)) -> APP_FLAT(down(app(y6445, app(y6446, y6447))), block(cons)) 392.66/193.65 DOWN(app(app(y6445, app(y6446, y6447)), cons)) -> DOWN(app(y6445, app(y6446, y6447))) 392.66/193.65 DOWN(app(app(y6445, app(y6446, y6447)), cons)) -> APP_FLAT(block(app(y6445, app(y6446, y6447))), down(cons)) 392.66/193.65 DOWN(app(app(y6445, app(y6446, y6447)), cons)) -> DOWN(cons) 392.66/193.65 DOWN(app(app(y6467, hd), cons)) -> APP_FLAT(down(app(y6467, hd)), block(cons)) 392.66/193.65 DOWN(app(app(y6467, hd), cons)) -> DOWN(app(y6467, hd)) 392.66/193.65 DOWN(app(app(y6467, hd), cons)) -> APP_FLAT(block(app(y6467, hd)), down(cons)) 392.66/193.65 DOWN(app(app(y6467, hd), cons)) -> DOWN(cons) 392.66/193.65 DOWN(app(app(y6470, map), cons)) -> APP_FLAT(down(app(y6470, map)), block(cons)) 392.66/193.65 DOWN(app(app(y6470, map), cons)) -> DOWN(app(y6470, map)) 392.66/193.65 DOWN(app(app(y6470, map), cons)) -> APP_FLAT(block(app(y6470, map)), down(cons)) 392.66/193.65 DOWN(app(app(y6470, map), cons)) -> DOWN(cons) 392.66/193.65 DOWN(app(app(y6473, cons), cons)) -> APP_FLAT(down(app(y6473, cons)), block(cons)) 392.66/193.65 DOWN(app(app(y6473, cons), cons)) -> DOWN(app(y6473, cons)) 392.66/193.65 DOWN(app(app(y6473, cons), cons)) -> APP_FLAT(block(app(y6473, cons)), down(cons)) 392.66/193.65 DOWN(app(app(y6473, cons), cons)) -> DOWN(cons) 392.66/193.65 DOWN(app(app(y6476, nil), cons)) -> APP_FLAT(down(app(y6476, nil)), block(cons)) 392.66/193.65 DOWN(app(app(y6476, nil), cons)) -> DOWN(app(y6476, nil)) 392.66/193.65 DOWN(app(app(y6476, nil), cons)) -> APP_FLAT(block(app(y6476, nil)), down(cons)) 392.66/193.65 DOWN(app(app(y6476, nil), cons)) -> DOWN(cons) 392.66/193.65 DOWN(app(app(y6479, fresh_constant), cons)) -> APP_FLAT(down(app(y6479, fresh_constant)), block(cons)) 392.66/193.65 DOWN(app(app(y6479, fresh_constant), cons)) -> DOWN(app(y6479, fresh_constant)) 392.66/193.65 DOWN(app(app(y6479, fresh_constant), cons)) -> APP_FLAT(block(app(y6479, fresh_constant)), down(cons)) 392.66/193.65 DOWN(app(app(y6479, fresh_constant), cons)) -> DOWN(cons) 392.66/193.65 DOWN(app(app(y6541, app(y6542, y6543)), fresh_constant)) -> APP_FLAT(down(app(y6541, app(y6542, y6543))), block(fresh_constant)) 392.66/193.65 DOWN(app(app(y6541, app(y6542, y6543)), fresh_constant)) -> DOWN(app(y6541, app(y6542, y6543))) 392.66/193.65 DOWN(app(app(y6541, app(y6542, y6543)), fresh_constant)) -> APP_FLAT(block(app(y6541, app(y6542, y6543))), down(fresh_constant)) 392.66/193.65 DOWN(app(app(y6541, app(y6542, y6543)), fresh_constant)) -> DOWN(fresh_constant) 392.66/193.65 DOWN(app(app(y6563, hd), fresh_constant)) -> APP_FLAT(down(app(y6563, hd)), block(fresh_constant)) 392.66/193.65 DOWN(app(app(y6563, hd), fresh_constant)) -> DOWN(app(y6563, hd)) 392.66/193.65 DOWN(app(app(y6563, hd), fresh_constant)) -> APP_FLAT(block(app(y6563, hd)), down(fresh_constant)) 392.66/193.65 DOWN(app(app(y6563, hd), fresh_constant)) -> DOWN(fresh_constant) 392.66/193.65 DOWN(app(app(y6566, map), fresh_constant)) -> APP_FLAT(down(app(y6566, map)), block(fresh_constant)) 392.66/193.65 DOWN(app(app(y6566, map), fresh_constant)) -> DOWN(app(y6566, map)) 392.66/193.65 DOWN(app(app(y6566, map), fresh_constant)) -> APP_FLAT(block(app(y6566, map)), down(fresh_constant)) 392.66/193.65 DOWN(app(app(y6566, map), fresh_constant)) -> DOWN(fresh_constant) 392.66/193.65 DOWN(app(app(y6569, cons), fresh_constant)) -> APP_FLAT(down(app(y6569, cons)), block(fresh_constant)) 392.66/193.65 DOWN(app(app(y6569, cons), fresh_constant)) -> DOWN(app(y6569, cons)) 392.66/193.65 DOWN(app(app(y6569, cons), fresh_constant)) -> APP_FLAT(block(app(y6569, cons)), down(fresh_constant)) 392.66/193.65 DOWN(app(app(y6569, cons), fresh_constant)) -> DOWN(fresh_constant) 392.66/193.65 DOWN(app(app(y6572, nil), fresh_constant)) -> APP_FLAT(down(app(y6572, nil)), block(fresh_constant)) 392.66/193.65 DOWN(app(app(y6572, nil), fresh_constant)) -> DOWN(app(y6572, nil)) 392.66/193.65 DOWN(app(app(y6572, nil), fresh_constant)) -> APP_FLAT(block(app(y6572, nil)), down(fresh_constant)) 392.66/193.65 DOWN(app(app(y6572, nil), fresh_constant)) -> DOWN(fresh_constant) 392.66/193.65 DOWN(app(app(y6575, fresh_constant), fresh_constant)) -> APP_FLAT(down(app(y6575, fresh_constant)), block(fresh_constant)) 392.66/193.65 DOWN(app(app(y6575, fresh_constant), fresh_constant)) -> DOWN(app(y6575, fresh_constant)) 392.66/193.65 DOWN(app(app(y6575, fresh_constant), fresh_constant)) -> APP_FLAT(block(app(y6575, fresh_constant)), down(fresh_constant)) 392.66/193.65 DOWN(app(app(y6575, fresh_constant), fresh_constant)) -> DOWN(fresh_constant) 392.66/193.65 DOWN(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> APP_FLAT(down(app(y357, app(y20338, y20339))), block(app(app(app(y20340, y20341), y20342), y362))) 392.66/193.65 DOWN(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> DOWN(app(y357, app(y20338, y20339))) 392.66/193.65 DOWN(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> APP_FLAT(block(app(y357, app(y20338, y20339))), down(app(app(app(y20340, y20341), y20342), y362))) 392.66/193.65 DOWN(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> DOWN(app(app(app(y20340, y20341), y20342), y362)) 392.66/193.65 DOWN(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> APP_FLAT(down(app(y357, app(y20578, y20579))), block(app(app(0, y20580), y362))) 392.66/193.65 DOWN(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> DOWN(app(y357, app(y20578, y20579))) 392.66/193.65 DOWN(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> APP_FLAT(block(app(y357, app(y20578, y20579))), down(app(app(0, y20580), y362))) 392.66/193.65 DOWN(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> DOWN(app(app(0, y20580), y362)) 392.66/193.65 DOWN(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> APP_FLAT(down(app(y357, app(y20690, y20691))), block(app(app(hd, y20692), y362))) 392.66/193.65 DOWN(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> DOWN(app(y357, app(y20690, y20691))) 392.66/193.65 DOWN(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> APP_FLAT(block(app(y357, app(y20690, y20691))), down(app(app(hd, y20692), y362))) 392.66/193.65 DOWN(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> DOWN(app(app(hd, y20692), y362)) 392.66/193.65 DOWN(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> APP_FLAT(down(app(y357, app(y20802, y20803))), block(app(app(map, y20804), y362))) 392.66/193.65 DOWN(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> DOWN(app(y357, app(y20802, y20803))) 392.66/193.65 DOWN(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> APP_FLAT(block(app(y357, app(y20802, y20803))), down(app(app(map, y20804), y362))) 392.66/193.65 DOWN(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> DOWN(app(app(map, y20804), y362)) 392.66/193.65 DOWN(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> APP_FLAT(down(app(y357, app(y21026, y21027))), block(app(app(nil, y21028), y362))) 392.66/193.65 DOWN(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> DOWN(app(y357, app(y21026, y21027))) 392.66/193.65 DOWN(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> APP_FLAT(block(app(y357, app(y21026, y21027))), down(app(app(nil, y21028), y362))) 392.66/193.65 DOWN(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> DOWN(app(app(nil, y21028), y362)) 392.66/193.65 DOWN(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> APP_FLAT(down(app(y357, app(y21138, y21139))), block(app(app(fresh_constant, y21140), y362))) 392.66/193.65 DOWN(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> DOWN(app(y357, app(y21138, y21139))) 392.66/193.65 DOWN(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> APP_FLAT(block(app(y357, app(y21138, y21139))), down(app(app(fresh_constant, y21140), y362))) 392.66/193.65 DOWN(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> DOWN(app(app(fresh_constant, y21140), y362)) 392.66/193.65 DOWN(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> APP_FLAT(down(app(y427, hd)), block(app(app(app(y32452, y32453), y32454), y430))) 392.66/193.65 DOWN(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> DOWN(app(y427, hd)) 392.66/193.65 DOWN(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> APP_FLAT(block(app(y427, hd)), down(app(app(app(y32452, y32453), y32454), y430))) 392.66/193.65 DOWN(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> DOWN(app(app(app(y32452, y32453), y32454), y430)) 392.66/193.65 DOWN(app(app(y427, hd), app(app(0, y32455), y430))) -> APP_FLAT(down(app(y427, hd)), block(app(app(0, y32455), y430))) 392.66/193.65 DOWN(app(app(y427, hd), app(app(0, y32455), y430))) -> DOWN(app(y427, hd)) 392.66/193.65 DOWN(app(app(y427, hd), app(app(0, y32455), y430))) -> APP_FLAT(block(app(y427, hd)), down(app(app(0, y32455), y430))) 392.66/193.65 DOWN(app(app(y427, hd), app(app(0, y32455), y430))) -> DOWN(app(app(0, y32455), y430)) 392.66/193.65 DOWN(app(app(y427, hd), app(app(hd, y32456), y430))) -> APP_FLAT(down(app(y427, hd)), block(app(app(hd, y32456), y430))) 392.66/193.65 DOWN(app(app(y427, hd), app(app(hd, y32456), y430))) -> DOWN(app(y427, hd)) 392.66/193.65 DOWN(app(app(y427, hd), app(app(hd, y32456), y430))) -> APP_FLAT(block(app(y427, hd)), down(app(app(hd, y32456), y430))) 392.66/193.65 DOWN(app(app(y427, hd), app(app(hd, y32456), y430))) -> DOWN(app(app(hd, y32456), y430)) 392.66/193.65 DOWN(app(app(y427, hd), app(app(map, y32457), y430))) -> APP_FLAT(down(app(y427, hd)), block(app(app(map, y32457), y430))) 392.66/193.65 DOWN(app(app(y427, hd), app(app(map, y32457), y430))) -> DOWN(app(y427, hd)) 392.66/193.65 DOWN(app(app(y427, hd), app(app(map, y32457), y430))) -> APP_FLAT(block(app(y427, hd)), down(app(app(map, y32457), y430))) 392.66/193.65 DOWN(app(app(y427, hd), app(app(map, y32457), y430))) -> DOWN(app(app(map, y32457), y430)) 392.66/193.65 DOWN(app(app(y427, hd), app(app(nil, y32459), y430))) -> APP_FLAT(down(app(y427, hd)), block(app(app(nil, y32459), y430))) 392.66/193.65 DOWN(app(app(y427, hd), app(app(nil, y32459), y430))) -> DOWN(app(y427, hd)) 392.66/193.65 DOWN(app(app(y427, hd), app(app(nil, y32459), y430))) -> APP_FLAT(block(app(y427, hd)), down(app(app(nil, y32459), y430))) 392.66/193.65 DOWN(app(app(y427, hd), app(app(nil, y32459), y430))) -> DOWN(app(app(nil, y32459), y430)) 392.66/193.65 DOWN(app(app(y427, hd), app(app(fresh_constant, y32460), y430))) -> APP_FLAT(down(app(y427, hd)), block(app(app(fresh_constant, y32460), y430))) 392.66/193.65 DOWN(app(app(y427, hd), app(app(fresh_constant, y32460), y430))) -> DOWN(app(y427, hd)) 392.66/193.65 DOWN(app(app(y427, hd), app(app(fresh_constant, y32460), y430))) -> APP_FLAT(block(app(y427, hd)), down(app(app(fresh_constant, y32460), y430))) 392.66/193.65 DOWN(app(app(y427, hd), app(app(fresh_constant, y32460), y430))) -> DOWN(app(app(fresh_constant, y32460), y430)) 392.66/193.65 DOWN(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> APP_FLAT(down(app(y454, map)), block(app(app(app(y32548, y32549), y32550), y457))) 392.66/193.65 DOWN(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> DOWN(app(y454, map)) 392.66/193.65 DOWN(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> APP_FLAT(block(app(y454, map)), down(app(app(app(y32548, y32549), y32550), y457))) 392.66/193.65 DOWN(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> DOWN(app(app(app(y32548, y32549), y32550), y457)) 392.66/193.65 DOWN(app(app(y454, map), app(app(0, y32551), y457))) -> APP_FLAT(down(app(y454, map)), block(app(app(0, y32551), y457))) 392.66/193.65 DOWN(app(app(y454, map), app(app(0, y32551), y457))) -> DOWN(app(y454, map)) 392.66/193.65 DOWN(app(app(y454, map), app(app(0, y32551), y457))) -> APP_FLAT(block(app(y454, map)), down(app(app(0, y32551), y457))) 392.66/193.65 DOWN(app(app(y454, map), app(app(0, y32551), y457))) -> DOWN(app(app(0, y32551), y457)) 392.66/193.65 DOWN(app(app(y454, map), app(app(hd, y32552), y457))) -> APP_FLAT(down(app(y454, map)), block(app(app(hd, y32552), y457))) 392.66/193.65 DOWN(app(app(y454, map), app(app(hd, y32552), y457))) -> DOWN(app(y454, map)) 392.66/193.65 DOWN(app(app(y454, map), app(app(hd, y32552), y457))) -> APP_FLAT(block(app(y454, map)), down(app(app(hd, y32552), y457))) 392.66/193.65 DOWN(app(app(y454, map), app(app(hd, y32552), y457))) -> DOWN(app(app(hd, y32552), y457)) 392.66/193.65 DOWN(app(app(y454, map), app(app(map, y32553), y457))) -> APP_FLAT(down(app(y454, map)), block(app(app(map, y32553), y457))) 392.66/193.65 DOWN(app(app(y454, map), app(app(map, y32553), y457))) -> DOWN(app(y454, map)) 392.66/193.65 DOWN(app(app(y454, map), app(app(map, y32553), y457))) -> APP_FLAT(block(app(y454, map)), down(app(app(map, y32553), y457))) 392.66/193.65 DOWN(app(app(y454, map), app(app(map, y32553), y457))) -> DOWN(app(app(map, y32553), y457)) 392.66/193.65 DOWN(app(app(y454, map), app(app(nil, y32555), y457))) -> APP_FLAT(down(app(y454, map)), block(app(app(nil, y32555), y457))) 392.66/193.65 DOWN(app(app(y454, map), app(app(nil, y32555), y457))) -> DOWN(app(y454, map)) 392.66/193.65 DOWN(app(app(y454, map), app(app(nil, y32555), y457))) -> APP_FLAT(block(app(y454, map)), down(app(app(nil, y32555), y457))) 392.66/193.65 DOWN(app(app(y454, map), app(app(nil, y32555), y457))) -> DOWN(app(app(nil, y32555), y457)) 392.66/193.65 DOWN(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> APP_FLAT(down(app(y454, map)), block(app(app(fresh_constant, y32556), y457))) 392.66/193.65 DOWN(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> DOWN(app(y454, map)) 392.66/193.65 DOWN(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> APP_FLAT(block(app(y454, map)), down(app(app(fresh_constant, y32556), y457))) 392.66/193.65 DOWN(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> DOWN(app(app(fresh_constant, y32556), y457)) 392.66/193.65 DOWN(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> APP_FLAT(down(app(y481, cons)), block(app(app(app(y32644, y32645), y32646), y484))) 392.66/193.65 DOWN(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> DOWN(app(y481, cons)) 392.66/193.65 DOWN(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> APP_FLAT(block(app(y481, cons)), down(app(app(app(y32644, y32645), y32646), y484))) 392.66/193.65 DOWN(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> DOWN(app(app(app(y32644, y32645), y32646), y484)) 392.66/193.65 DOWN(app(app(y481, cons), app(app(0, y32647), y484))) -> APP_FLAT(down(app(y481, cons)), block(app(app(0, y32647), y484))) 392.66/193.65 DOWN(app(app(y481, cons), app(app(0, y32647), y484))) -> DOWN(app(y481, cons)) 392.66/193.65 DOWN(app(app(y481, cons), app(app(0, y32647), y484))) -> APP_FLAT(block(app(y481, cons)), down(app(app(0, y32647), y484))) 392.66/193.65 DOWN(app(app(y481, cons), app(app(0, y32647), y484))) -> DOWN(app(app(0, y32647), y484)) 392.66/193.65 DOWN(app(app(y481, cons), app(app(hd, y32648), y484))) -> APP_FLAT(down(app(y481, cons)), block(app(app(hd, y32648), y484))) 392.66/193.65 DOWN(app(app(y481, cons), app(app(hd, y32648), y484))) -> DOWN(app(y481, cons)) 392.66/193.65 DOWN(app(app(y481, cons), app(app(hd, y32648), y484))) -> APP_FLAT(block(app(y481, cons)), down(app(app(hd, y32648), y484))) 392.66/193.65 DOWN(app(app(y481, cons), app(app(hd, y32648), y484))) -> DOWN(app(app(hd, y32648), y484)) 392.66/193.65 DOWN(app(app(y481, cons), app(app(map, y32649), y484))) -> APP_FLAT(down(app(y481, cons)), block(app(app(map, y32649), y484))) 392.66/193.65 DOWN(app(app(y481, cons), app(app(map, y32649), y484))) -> DOWN(app(y481, cons)) 392.66/193.65 DOWN(app(app(y481, cons), app(app(map, y32649), y484))) -> APP_FLAT(block(app(y481, cons)), down(app(app(map, y32649), y484))) 392.66/193.65 DOWN(app(app(y481, cons), app(app(map, y32649), y484))) -> DOWN(app(app(map, y32649), y484)) 392.66/193.65 DOWN(app(app(y481, cons), app(app(nil, y32651), y484))) -> APP_FLAT(down(app(y481, cons)), block(app(app(nil, y32651), y484))) 392.66/193.65 DOWN(app(app(y481, cons), app(app(nil, y32651), y484))) -> DOWN(app(y481, cons)) 392.66/193.65 DOWN(app(app(y481, cons), app(app(nil, y32651), y484))) -> APP_FLAT(block(app(y481, cons)), down(app(app(nil, y32651), y484))) 392.66/193.65 DOWN(app(app(y481, cons), app(app(nil, y32651), y484))) -> DOWN(app(app(nil, y32651), y484)) 392.66/193.65 DOWN(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> APP_FLAT(down(app(y481, cons)), block(app(app(fresh_constant, y32652), y484))) 392.66/193.65 DOWN(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> DOWN(app(y481, cons)) 392.66/193.65 DOWN(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> APP_FLAT(block(app(y481, cons)), down(app(app(fresh_constant, y32652), y484))) 392.66/193.65 DOWN(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> DOWN(app(app(fresh_constant, y32652), y484)) 392.66/193.65 DOWN(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> APP_FLAT(down(app(y508, nil)), block(app(app(app(y32740, y32741), y32742), y511))) 392.66/193.65 DOWN(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> DOWN(app(y508, nil)) 392.66/193.65 DOWN(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> APP_FLAT(block(app(y508, nil)), down(app(app(app(y32740, y32741), y32742), y511))) 392.66/193.65 DOWN(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> DOWN(app(app(app(y32740, y32741), y32742), y511)) 392.66/193.65 DOWN(app(app(y508, nil), app(app(0, y32743), y511))) -> APP_FLAT(down(app(y508, nil)), block(app(app(0, y32743), y511))) 392.66/193.65 DOWN(app(app(y508, nil), app(app(0, y32743), y511))) -> DOWN(app(y508, nil)) 392.66/193.65 DOWN(app(app(y508, nil), app(app(0, y32743), y511))) -> APP_FLAT(block(app(y508, nil)), down(app(app(0, y32743), y511))) 392.66/193.65 DOWN(app(app(y508, nil), app(app(0, y32743), y511))) -> DOWN(app(app(0, y32743), y511)) 392.66/193.65 DOWN(app(app(y508, nil), app(app(hd, y32744), y511))) -> APP_FLAT(down(app(y508, nil)), block(app(app(hd, y32744), y511))) 392.66/193.65 DOWN(app(app(y508, nil), app(app(hd, y32744), y511))) -> DOWN(app(y508, nil)) 392.66/193.65 DOWN(app(app(y508, nil), app(app(hd, y32744), y511))) -> APP_FLAT(block(app(y508, nil)), down(app(app(hd, y32744), y511))) 392.66/193.65 DOWN(app(app(y508, nil), app(app(hd, y32744), y511))) -> DOWN(app(app(hd, y32744), y511)) 392.66/193.65 DOWN(app(app(y508, nil), app(app(map, y32745), y511))) -> APP_FLAT(down(app(y508, nil)), block(app(app(map, y32745), y511))) 392.66/193.65 DOWN(app(app(y508, nil), app(app(map, y32745), y511))) -> DOWN(app(y508, nil)) 392.66/193.65 DOWN(app(app(y508, nil), app(app(map, y32745), y511))) -> APP_FLAT(block(app(y508, nil)), down(app(app(map, y32745), y511))) 392.66/193.65 DOWN(app(app(y508, nil), app(app(map, y32745), y511))) -> DOWN(app(app(map, y32745), y511)) 392.66/193.65 DOWN(app(app(y508, nil), app(app(nil, y32747), y511))) -> APP_FLAT(down(app(y508, nil)), block(app(app(nil, y32747), y511))) 392.66/193.65 DOWN(app(app(y508, nil), app(app(nil, y32747), y511))) -> DOWN(app(y508, nil)) 392.66/193.65 DOWN(app(app(y508, nil), app(app(nil, y32747), y511))) -> APP_FLAT(block(app(y508, nil)), down(app(app(nil, y32747), y511))) 392.66/193.65 DOWN(app(app(y508, nil), app(app(nil, y32747), y511))) -> DOWN(app(app(nil, y32747), y511)) 392.66/193.65 DOWN(app(app(y508, nil), app(app(fresh_constant, y32748), y511))) -> APP_FLAT(down(app(y508, nil)), block(app(app(fresh_constant, y32748), y511))) 392.66/193.65 DOWN(app(app(y508, nil), app(app(fresh_constant, y32748), y511))) -> DOWN(app(y508, nil)) 392.66/193.65 DOWN(app(app(y508, nil), app(app(fresh_constant, y32748), y511))) -> APP_FLAT(block(app(y508, nil)), down(app(app(fresh_constant, y32748), y511))) 392.66/193.65 DOWN(app(app(y508, nil), app(app(fresh_constant, y32748), y511))) -> DOWN(app(app(fresh_constant, y32748), y511)) 392.66/193.65 DOWN(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> APP_FLAT(down(app(y535, fresh_constant)), block(app(app(app(y32836, y32837), y32838), y538))) 392.66/193.65 DOWN(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.65 DOWN(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> APP_FLAT(block(app(y535, fresh_constant)), down(app(app(app(y32836, y32837), y32838), y538))) 392.66/193.65 DOWN(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> DOWN(app(app(app(y32836, y32837), y32838), y538)) 392.66/193.65 DOWN(app(app(y535, fresh_constant), app(app(0, y32839), y538))) -> APP_FLAT(down(app(y535, fresh_constant)), block(app(app(0, y32839), y538))) 392.66/193.65 DOWN(app(app(y535, fresh_constant), app(app(0, y32839), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.65 DOWN(app(app(y535, fresh_constant), app(app(0, y32839), y538))) -> APP_FLAT(block(app(y535, fresh_constant)), down(app(app(0, y32839), y538))) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(0, y32839), y538))) -> DOWN(app(app(0, y32839), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(hd, y32840), y538))) -> APP_FLAT(down(app(y535, fresh_constant)), block(app(app(hd, y32840), y538))) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(hd, y32840), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(hd, y32840), y538))) -> APP_FLAT(block(app(y535, fresh_constant)), down(app(app(hd, y32840), y538))) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(hd, y32840), y538))) -> DOWN(app(app(hd, y32840), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> APP_FLAT(down(app(y535, fresh_constant)), block(app(app(map, y32841), y538))) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> APP_FLAT(block(app(y535, fresh_constant)), down(app(app(map, y32841), y538))) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> DOWN(app(app(map, y32841), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(nil, y32843), y538))) -> APP_FLAT(down(app(y535, fresh_constant)), block(app(app(nil, y32843), y538))) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(nil, y32843), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(nil, y32843), y538))) -> APP_FLAT(block(app(y535, fresh_constant)), down(app(app(nil, y32843), y538))) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(nil, y32843), y538))) -> DOWN(app(app(nil, y32843), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(fresh_constant, y32844), y538))) -> APP_FLAT(down(app(y535, fresh_constant)), block(app(app(fresh_constant, y32844), y538))) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(fresh_constant, y32844), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(fresh_constant, y32844), y538))) -> APP_FLAT(block(app(y535, fresh_constant)), down(app(app(fresh_constant, y32844), y538))) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(fresh_constant, y32844), y538))) -> DOWN(app(app(fresh_constant, y32844), y538)) 392.66/193.66 392.66/193.66 The TRS R consists of the following rules: 392.66/193.66 392.66/193.66 down(app(app(f, 0), n)) -> up(app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)) 392.66/193.66 down(app(app(map, f), nil)) -> up(nil) 392.66/193.66 down(app(app(map, f), app(app(cons, x), xs))) -> up(app(app(cons, app(f, x)), app(app(map, f), xs))) 392.66/193.66 top(up(x)) -> top(down(x)) 392.66/193.66 down(app(0, y7)) -> app_flat(down(0), block(y7)) 392.66/193.66 down(app(0, y7)) -> app_flat(block(0), down(y7)) 392.66/193.66 down(app(hd, y8)) -> app_flat(down(hd), block(y8)) 392.66/193.66 down(app(hd, y8)) -> app_flat(block(hd), down(y8)) 392.66/193.66 down(app(map, y9)) -> app_flat(down(map), block(y9)) 392.66/193.66 down(app(map, y9)) -> app_flat(block(map), down(y9)) 392.66/193.66 down(app(cons, y10)) -> app_flat(down(cons), block(y10)) 392.66/193.66 down(app(cons, y10)) -> app_flat(block(cons), down(y10)) 392.66/193.66 down(app(nil, y11)) -> app_flat(down(nil), block(y11)) 392.66/193.66 down(app(nil, y11)) -> app_flat(block(nil), down(y11)) 392.66/193.66 down(app(fresh_constant, y12)) -> app_flat(down(fresh_constant), block(y12)) 392.66/193.66 down(app(fresh_constant, y12)) -> app_flat(block(fresh_constant), down(y12)) 392.66/193.66 down(app(app(app(y64, y65), app(y66, y67)), y6)) -> app_flat(down(app(app(y64, y65), app(y66, y67))), block(y6)) 392.66/193.66 down(app(app(app(y64, y65), app(y66, y67)), y6)) -> app_flat(block(app(app(y64, y65), app(y66, y67))), down(y6)) 392.66/193.66 down(app(app(0, app(y68, y69)), y6)) -> app_flat(down(app(0, app(y68, y69))), block(y6)) 392.66/193.66 down(app(app(0, app(y68, y69)), y6)) -> app_flat(block(app(0, app(y68, y69))), down(y6)) 392.66/193.66 down(app(app(hd, app(y70, y71)), y6)) -> app_flat(down(app(hd, app(y70, y71))), block(y6)) 392.66/193.66 down(app(app(hd, app(y70, y71)), y6)) -> app_flat(block(app(hd, app(y70, y71))), down(y6)) 392.66/193.66 down(app(app(cons, app(y74, y75)), y6)) -> app_flat(down(app(cons, app(y74, y75))), block(y6)) 392.66/193.66 down(app(app(cons, app(y74, y75)), y6)) -> app_flat(block(app(cons, app(y74, y75))), down(y6)) 392.66/193.66 down(app(app(nil, app(y76, y77)), y6)) -> app_flat(down(app(nil, app(y76, y77))), block(y6)) 392.66/193.66 down(app(app(nil, app(y76, y77)), y6)) -> app_flat(block(app(nil, app(y76, y77))), down(y6)) 392.66/193.66 down(app(app(fresh_constant, app(y78, y79)), y6)) -> app_flat(down(app(fresh_constant, app(y78, y79))), block(y6)) 392.66/193.66 down(app(app(fresh_constant, app(y78, y79)), y6)) -> app_flat(block(app(fresh_constant, app(y78, y79))), down(y6)) 392.66/193.66 down(app(app(app(y84, y85), hd), y6)) -> app_flat(down(app(app(y84, y85), hd)), block(y6)) 392.66/193.66 down(app(app(app(y84, y85), hd), y6)) -> app_flat(block(app(app(y84, y85), hd)), down(y6)) 392.66/193.66 down(app(app(0, hd), y6)) -> app_flat(down(app(0, hd)), block(y6)) 392.66/193.66 down(app(app(0, hd), y6)) -> app_flat(block(app(0, hd)), down(y6)) 392.66/193.66 down(app(app(hd, hd), y6)) -> app_flat(down(app(hd, hd)), block(y6)) 392.66/193.66 down(app(app(hd, hd), y6)) -> app_flat(block(app(hd, hd)), down(y6)) 392.66/193.66 down(app(app(cons, hd), y6)) -> app_flat(down(app(cons, hd)), block(y6)) 392.66/193.66 down(app(app(cons, hd), y6)) -> app_flat(block(app(cons, hd)), down(y6)) 392.66/193.66 down(app(app(nil, hd), y6)) -> app_flat(down(app(nil, hd)), block(y6)) 392.66/193.66 down(app(app(nil, hd), y6)) -> app_flat(block(app(nil, hd)), down(y6)) 392.66/193.66 down(app(app(fresh_constant, hd), y6)) -> app_flat(down(app(fresh_constant, hd)), block(y6)) 392.66/193.66 down(app(app(fresh_constant, hd), y6)) -> app_flat(block(app(fresh_constant, hd)), down(y6)) 392.66/193.66 down(app(app(app(y87, y88), map), y6)) -> app_flat(down(app(app(y87, y88), map)), block(y6)) 392.66/193.66 down(app(app(app(y87, y88), map), y6)) -> app_flat(block(app(app(y87, y88), map)), down(y6)) 392.66/193.66 down(app(app(0, map), y6)) -> app_flat(down(app(0, map)), block(y6)) 392.66/193.66 down(app(app(0, map), y6)) -> app_flat(block(app(0, map)), down(y6)) 392.66/193.66 down(app(app(hd, map), y6)) -> app_flat(down(app(hd, map)), block(y6)) 392.66/193.66 down(app(app(hd, map), y6)) -> app_flat(block(app(hd, map)), down(y6)) 392.66/193.66 down(app(app(cons, map), y6)) -> app_flat(down(app(cons, map)), block(y6)) 392.66/193.66 down(app(app(cons, map), y6)) -> app_flat(block(app(cons, map)), down(y6)) 392.66/193.66 down(app(app(nil, map), y6)) -> app_flat(down(app(nil, map)), block(y6)) 392.66/193.66 down(app(app(nil, map), y6)) -> app_flat(block(app(nil, map)), down(y6)) 392.66/193.66 down(app(app(fresh_constant, map), y6)) -> app_flat(down(app(fresh_constant, map)), block(y6)) 392.66/193.66 down(app(app(fresh_constant, map), y6)) -> app_flat(block(app(fresh_constant, map)), down(y6)) 392.66/193.66 down(app(app(app(y90, y91), cons), y6)) -> app_flat(down(app(app(y90, y91), cons)), block(y6)) 392.66/193.66 down(app(app(app(y90, y91), cons), y6)) -> app_flat(block(app(app(y90, y91), cons)), down(y6)) 392.66/193.66 down(app(app(0, cons), y6)) -> app_flat(down(app(0, cons)), block(y6)) 392.66/193.66 down(app(app(0, cons), y6)) -> app_flat(block(app(0, cons)), down(y6)) 392.66/193.66 down(app(app(hd, cons), y6)) -> app_flat(down(app(hd, cons)), block(y6)) 392.66/193.66 down(app(app(hd, cons), y6)) -> app_flat(block(app(hd, cons)), down(y6)) 392.66/193.66 down(app(app(cons, cons), y6)) -> app_flat(down(app(cons, cons)), block(y6)) 392.66/193.66 down(app(app(cons, cons), y6)) -> app_flat(block(app(cons, cons)), down(y6)) 392.66/193.66 down(app(app(nil, cons), y6)) -> app_flat(down(app(nil, cons)), block(y6)) 392.66/193.66 down(app(app(nil, cons), y6)) -> app_flat(block(app(nil, cons)), down(y6)) 392.66/193.66 down(app(app(fresh_constant, cons), y6)) -> app_flat(down(app(fresh_constant, cons)), block(y6)) 392.66/193.66 down(app(app(fresh_constant, cons), y6)) -> app_flat(block(app(fresh_constant, cons)), down(y6)) 392.66/193.66 down(app(app(app(y93, y94), nil), y6)) -> app_flat(down(app(app(y93, y94), nil)), block(y6)) 392.66/193.66 down(app(app(app(y93, y94), nil), y6)) -> app_flat(block(app(app(y93, y94), nil)), down(y6)) 392.66/193.66 down(app(app(0, nil), y6)) -> app_flat(down(app(0, nil)), block(y6)) 392.66/193.66 down(app(app(0, nil), y6)) -> app_flat(block(app(0, nil)), down(y6)) 392.66/193.66 down(app(app(hd, nil), y6)) -> app_flat(down(app(hd, nil)), block(y6)) 392.66/193.66 down(app(app(hd, nil), y6)) -> app_flat(block(app(hd, nil)), down(y6)) 392.66/193.66 down(app(app(cons, nil), y6)) -> app_flat(down(app(cons, nil)), block(y6)) 392.66/193.66 down(app(app(cons, nil), y6)) -> app_flat(block(app(cons, nil)), down(y6)) 392.66/193.66 down(app(app(nil, nil), y6)) -> app_flat(down(app(nil, nil)), block(y6)) 392.66/193.66 down(app(app(nil, nil), y6)) -> app_flat(block(app(nil, nil)), down(y6)) 392.66/193.66 down(app(app(fresh_constant, nil), y6)) -> app_flat(down(app(fresh_constant, nil)), block(y6)) 392.66/193.66 down(app(app(fresh_constant, nil), y6)) -> app_flat(block(app(fresh_constant, nil)), down(y6)) 392.66/193.66 down(app(app(app(y96, y97), fresh_constant), y6)) -> app_flat(down(app(app(y96, y97), fresh_constant)), block(y6)) 392.66/193.66 down(app(app(app(y96, y97), fresh_constant), y6)) -> app_flat(block(app(app(y96, y97), fresh_constant)), down(y6)) 392.66/193.66 down(app(app(0, fresh_constant), y6)) -> app_flat(down(app(0, fresh_constant)), block(y6)) 392.66/193.66 down(app(app(0, fresh_constant), y6)) -> app_flat(block(app(0, fresh_constant)), down(y6)) 392.66/193.66 down(app(app(hd, fresh_constant), y6)) -> app_flat(down(app(hd, fresh_constant)), block(y6)) 392.66/193.66 down(app(app(hd, fresh_constant), y6)) -> app_flat(block(app(hd, fresh_constant)), down(y6)) 392.66/193.66 down(app(app(cons, fresh_constant), y6)) -> app_flat(down(app(cons, fresh_constant)), block(y6)) 392.66/193.66 down(app(app(cons, fresh_constant), y6)) -> app_flat(block(app(cons, fresh_constant)), down(y6)) 392.66/193.66 down(app(app(nil, fresh_constant), y6)) -> app_flat(down(app(nil, fresh_constant)), block(y6)) 392.66/193.66 down(app(app(nil, fresh_constant), y6)) -> app_flat(block(app(nil, fresh_constant)), down(y6)) 392.66/193.66 down(app(app(fresh_constant, fresh_constant), y6)) -> app_flat(down(app(fresh_constant, fresh_constant)), block(y6)) 392.66/193.66 down(app(app(fresh_constant, fresh_constant), y6)) -> app_flat(block(app(fresh_constant, fresh_constant)), down(y6)) 392.66/193.66 down(app(app(y581, app(y582, y583)), app(0, y584))) -> app_flat(down(app(y581, app(y582, y583))), block(app(0, y584))) 392.66/193.66 down(app(app(y581, app(y582, y583)), app(0, y584))) -> app_flat(block(app(y581, app(y582, y583))), down(app(0, y584))) 392.66/193.66 down(app(app(y619, hd), app(0, y620))) -> app_flat(down(app(y619, hd)), block(app(0, y620))) 392.66/193.66 down(app(app(y619, hd), app(0, y620))) -> app_flat(block(app(y619, hd)), down(app(0, y620))) 392.66/193.66 down(app(app(y630, map), app(0, y631))) -> app_flat(down(app(y630, map)), block(app(0, y631))) 392.66/193.66 down(app(app(y630, map), app(0, y631))) -> app_flat(block(app(y630, map)), down(app(0, y631))) 392.66/193.66 down(app(app(y641, cons), app(0, y642))) -> app_flat(down(app(y641, cons)), block(app(0, y642))) 392.66/193.66 down(app(app(y641, cons), app(0, y642))) -> app_flat(block(app(y641, cons)), down(app(0, y642))) 392.66/193.66 down(app(app(y652, nil), app(0, y653))) -> app_flat(down(app(y652, nil)), block(app(0, y653))) 392.66/193.66 down(app(app(y652, nil), app(0, y653))) -> app_flat(block(app(y652, nil)), down(app(0, y653))) 392.66/193.66 down(app(app(y663, fresh_constant), app(0, y664))) -> app_flat(down(app(y663, fresh_constant)), block(app(0, y664))) 392.66/193.66 down(app(app(y663, fresh_constant), app(0, y664))) -> app_flat(block(app(y663, fresh_constant)), down(app(0, y664))) 392.66/193.66 down(app(app(y693, app(y694, y695)), app(hd, y696))) -> app_flat(down(app(y693, app(y694, y695))), block(app(hd, y696))) 392.66/193.66 down(app(app(y693, app(y694, y695)), app(hd, y696))) -> app_flat(block(app(y693, app(y694, y695))), down(app(hd, y696))) 392.66/193.66 down(app(app(y731, hd), app(hd, y732))) -> app_flat(down(app(y731, hd)), block(app(hd, y732))) 392.66/193.66 down(app(app(y731, hd), app(hd, y732))) -> app_flat(block(app(y731, hd)), down(app(hd, y732))) 392.66/193.66 down(app(app(y742, map), app(hd, y743))) -> app_flat(down(app(y742, map)), block(app(hd, y743))) 392.66/193.66 down(app(app(y742, map), app(hd, y743))) -> app_flat(block(app(y742, map)), down(app(hd, y743))) 392.66/193.66 down(app(app(y753, cons), app(hd, y754))) -> app_flat(down(app(y753, cons)), block(app(hd, y754))) 392.66/193.66 down(app(app(y753, cons), app(hd, y754))) -> app_flat(block(app(y753, cons)), down(app(hd, y754))) 392.66/193.66 down(app(app(y764, nil), app(hd, y765))) -> app_flat(down(app(y764, nil)), block(app(hd, y765))) 392.66/193.66 down(app(app(y764, nil), app(hd, y765))) -> app_flat(block(app(y764, nil)), down(app(hd, y765))) 392.66/193.66 down(app(app(y775, fresh_constant), app(hd, y776))) -> app_flat(down(app(y775, fresh_constant)), block(app(hd, y776))) 392.66/193.66 down(app(app(y775, fresh_constant), app(hd, y776))) -> app_flat(block(app(y775, fresh_constant)), down(app(hd, y776))) 392.66/193.66 down(app(app(y805, app(y806, y807)), app(map, y808))) -> app_flat(down(app(y805, app(y806, y807))), block(app(map, y808))) 392.66/193.66 down(app(app(y805, app(y806, y807)), app(map, y808))) -> app_flat(block(app(y805, app(y806, y807))), down(app(map, y808))) 392.66/193.66 down(app(app(y843, hd), app(map, y844))) -> app_flat(down(app(y843, hd)), block(app(map, y844))) 392.66/193.66 down(app(app(y843, hd), app(map, y844))) -> app_flat(block(app(y843, hd)), down(app(map, y844))) 392.66/193.66 down(app(app(y854, map), app(map, y855))) -> app_flat(down(app(y854, map)), block(app(map, y855))) 392.66/193.66 down(app(app(y854, map), app(map, y855))) -> app_flat(block(app(y854, map)), down(app(map, y855))) 392.66/193.66 down(app(app(y865, cons), app(map, y866))) -> app_flat(down(app(y865, cons)), block(app(map, y866))) 392.66/193.66 down(app(app(y865, cons), app(map, y866))) -> app_flat(block(app(y865, cons)), down(app(map, y866))) 392.66/193.66 down(app(app(y876, nil), app(map, y877))) -> app_flat(down(app(y876, nil)), block(app(map, y877))) 392.66/193.66 down(app(app(y876, nil), app(map, y877))) -> app_flat(block(app(y876, nil)), down(app(map, y877))) 392.66/193.66 down(app(app(y887, fresh_constant), app(map, y888))) -> app_flat(down(app(y887, fresh_constant)), block(app(map, y888))) 392.66/193.66 down(app(app(y887, fresh_constant), app(map, y888))) -> app_flat(block(app(y887, fresh_constant)), down(app(map, y888))) 392.66/193.66 down(app(app(y917, app(y918, y919)), app(cons, y920))) -> app_flat(down(app(y917, app(y918, y919))), block(app(cons, y920))) 392.66/193.66 down(app(app(y917, app(y918, y919)), app(cons, y920))) -> app_flat(block(app(y917, app(y918, y919))), down(app(cons, y920))) 392.66/193.66 down(app(app(y955, hd), app(cons, y956))) -> app_flat(down(app(y955, hd)), block(app(cons, y956))) 392.66/193.66 down(app(app(y955, hd), app(cons, y956))) -> app_flat(block(app(y955, hd)), down(app(cons, y956))) 392.66/193.66 down(app(app(y966, map), app(cons, y967))) -> app_flat(down(app(y966, map)), block(app(cons, y967))) 392.66/193.66 down(app(app(y966, map), app(cons, y967))) -> app_flat(block(app(y966, map)), down(app(cons, y967))) 392.66/193.66 down(app(app(y977, cons), app(cons, y978))) -> app_flat(down(app(y977, cons)), block(app(cons, y978))) 392.66/193.66 down(app(app(y977, cons), app(cons, y978))) -> app_flat(block(app(y977, cons)), down(app(cons, y978))) 392.66/193.66 down(app(app(y988, nil), app(cons, y989))) -> app_flat(down(app(y988, nil)), block(app(cons, y989))) 392.66/193.66 down(app(app(y988, nil), app(cons, y989))) -> app_flat(block(app(y988, nil)), down(app(cons, y989))) 392.66/193.66 down(app(app(y999, fresh_constant), app(cons, y1000))) -> app_flat(down(app(y999, fresh_constant)), block(app(cons, y1000))) 392.66/193.66 down(app(app(y999, fresh_constant), app(cons, y1000))) -> app_flat(block(app(y999, fresh_constant)), down(app(cons, y1000))) 392.66/193.66 down(app(app(y1029, app(y1030, y1031)), app(nil, y1032))) -> app_flat(down(app(y1029, app(y1030, y1031))), block(app(nil, y1032))) 392.66/193.66 down(app(app(y1029, app(y1030, y1031)), app(nil, y1032))) -> app_flat(block(app(y1029, app(y1030, y1031))), down(app(nil, y1032))) 392.66/193.66 down(app(app(y1067, hd), app(nil, y1068))) -> app_flat(down(app(y1067, hd)), block(app(nil, y1068))) 392.66/193.66 down(app(app(y1067, hd), app(nil, y1068))) -> app_flat(block(app(y1067, hd)), down(app(nil, y1068))) 392.66/193.66 down(app(app(y1078, map), app(nil, y1079))) -> app_flat(down(app(y1078, map)), block(app(nil, y1079))) 392.66/193.66 down(app(app(y1078, map), app(nil, y1079))) -> app_flat(block(app(y1078, map)), down(app(nil, y1079))) 392.66/193.66 down(app(app(y1089, cons), app(nil, y1090))) -> app_flat(down(app(y1089, cons)), block(app(nil, y1090))) 392.66/193.66 down(app(app(y1089, cons), app(nil, y1090))) -> app_flat(block(app(y1089, cons)), down(app(nil, y1090))) 392.66/193.66 down(app(app(y1100, nil), app(nil, y1101))) -> app_flat(down(app(y1100, nil)), block(app(nil, y1101))) 392.66/193.66 down(app(app(y1100, nil), app(nil, y1101))) -> app_flat(block(app(y1100, nil)), down(app(nil, y1101))) 392.66/193.66 down(app(app(y1111, fresh_constant), app(nil, y1112))) -> app_flat(down(app(y1111, fresh_constant)), block(app(nil, y1112))) 392.66/193.66 down(app(app(y1111, fresh_constant), app(nil, y1112))) -> app_flat(block(app(y1111, fresh_constant)), down(app(nil, y1112))) 392.66/193.66 down(app(app(y1141, app(y1142, y1143)), app(fresh_constant, y1144))) -> app_flat(down(app(y1141, app(y1142, y1143))), block(app(fresh_constant, y1144))) 392.66/193.66 down(app(app(y1141, app(y1142, y1143)), app(fresh_constant, y1144))) -> app_flat(block(app(y1141, app(y1142, y1143))), down(app(fresh_constant, y1144))) 392.66/193.66 down(app(app(y1179, hd), app(fresh_constant, y1180))) -> app_flat(down(app(y1179, hd)), block(app(fresh_constant, y1180))) 392.66/193.66 down(app(app(y1179, hd), app(fresh_constant, y1180))) -> app_flat(block(app(y1179, hd)), down(app(fresh_constant, y1180))) 392.66/193.66 down(app(app(y1190, map), app(fresh_constant, y1191))) -> app_flat(down(app(y1190, map)), block(app(fresh_constant, y1191))) 392.66/193.66 down(app(app(y1190, map), app(fresh_constant, y1191))) -> app_flat(block(app(y1190, map)), down(app(fresh_constant, y1191))) 392.66/193.66 down(app(app(y1201, cons), app(fresh_constant, y1202))) -> app_flat(down(app(y1201, cons)), block(app(fresh_constant, y1202))) 392.66/193.66 down(app(app(y1201, cons), app(fresh_constant, y1202))) -> app_flat(block(app(y1201, cons)), down(app(fresh_constant, y1202))) 392.66/193.66 down(app(app(y1212, nil), app(fresh_constant, y1213))) -> app_flat(down(app(y1212, nil)), block(app(fresh_constant, y1213))) 392.66/193.66 down(app(app(y1212, nil), app(fresh_constant, y1213))) -> app_flat(block(app(y1212, nil)), down(app(fresh_constant, y1213))) 392.66/193.66 down(app(app(y1223, fresh_constant), app(fresh_constant, y1224))) -> app_flat(down(app(y1223, fresh_constant)), block(app(fresh_constant, y1224))) 392.66/193.66 down(app(app(y1223, fresh_constant), app(fresh_constant, y1224))) -> app_flat(block(app(y1223, fresh_constant)), down(app(fresh_constant, y1224))) 392.66/193.66 down(app(app(y6301, app(y6302, y6303)), 0)) -> app_flat(down(app(y6301, app(y6302, y6303))), block(0)) 392.66/193.66 down(app(app(y6301, app(y6302, y6303)), 0)) -> app_flat(block(app(y6301, app(y6302, y6303))), down(0)) 392.66/193.66 down(app(app(y6323, hd), 0)) -> app_flat(down(app(y6323, hd)), block(0)) 392.66/193.66 down(app(app(y6323, hd), 0)) -> app_flat(block(app(y6323, hd)), down(0)) 392.66/193.66 down(app(app(y6326, map), 0)) -> app_flat(down(app(y6326, map)), block(0)) 392.66/193.66 down(app(app(y6326, map), 0)) -> app_flat(block(app(y6326, map)), down(0)) 392.66/193.66 down(app(app(y6329, cons), 0)) -> app_flat(down(app(y6329, cons)), block(0)) 392.66/193.66 down(app(app(y6329, cons), 0)) -> app_flat(block(app(y6329, cons)), down(0)) 392.66/193.66 down(app(app(y6332, nil), 0)) -> app_flat(down(app(y6332, nil)), block(0)) 392.66/193.66 down(app(app(y6332, nil), 0)) -> app_flat(block(app(y6332, nil)), down(0)) 392.66/193.66 down(app(app(y6335, fresh_constant), 0)) -> app_flat(down(app(y6335, fresh_constant)), block(0)) 392.66/193.66 down(app(app(y6335, fresh_constant), 0)) -> app_flat(block(app(y6335, fresh_constant)), down(0)) 392.66/193.66 down(app(app(y6349, app(y6350, y6351)), hd)) -> app_flat(down(app(y6349, app(y6350, y6351))), block(hd)) 392.66/193.66 down(app(app(y6349, app(y6350, y6351)), hd)) -> app_flat(block(app(y6349, app(y6350, y6351))), down(hd)) 392.66/193.66 down(app(app(y6371, hd), hd)) -> app_flat(down(app(y6371, hd)), block(hd)) 392.66/193.66 down(app(app(y6371, hd), hd)) -> app_flat(block(app(y6371, hd)), down(hd)) 392.66/193.66 down(app(app(y6374, map), hd)) -> app_flat(down(app(y6374, map)), block(hd)) 392.66/193.66 down(app(app(y6374, map), hd)) -> app_flat(block(app(y6374, map)), down(hd)) 392.66/193.66 down(app(app(y6377, cons), hd)) -> app_flat(down(app(y6377, cons)), block(hd)) 392.66/193.66 down(app(app(y6377, cons), hd)) -> app_flat(block(app(y6377, cons)), down(hd)) 392.66/193.66 down(app(app(y6380, nil), hd)) -> app_flat(down(app(y6380, nil)), block(hd)) 392.66/193.66 down(app(app(y6380, nil), hd)) -> app_flat(block(app(y6380, nil)), down(hd)) 392.66/193.66 down(app(app(y6383, fresh_constant), hd)) -> app_flat(down(app(y6383, fresh_constant)), block(hd)) 392.66/193.66 down(app(app(y6383, fresh_constant), hd)) -> app_flat(block(app(y6383, fresh_constant)), down(hd)) 392.66/193.66 down(app(app(y6397, app(y6398, y6399)), map)) -> app_flat(down(app(y6397, app(y6398, y6399))), block(map)) 392.66/193.66 down(app(app(y6397, app(y6398, y6399)), map)) -> app_flat(block(app(y6397, app(y6398, y6399))), down(map)) 392.66/193.66 down(app(app(y6419, hd), map)) -> app_flat(down(app(y6419, hd)), block(map)) 392.66/193.66 down(app(app(y6419, hd), map)) -> app_flat(block(app(y6419, hd)), down(map)) 392.66/193.66 down(app(app(y6422, map), map)) -> app_flat(down(app(y6422, map)), block(map)) 392.66/193.66 down(app(app(y6422, map), map)) -> app_flat(block(app(y6422, map)), down(map)) 392.66/193.66 down(app(app(y6425, cons), map)) -> app_flat(down(app(y6425, cons)), block(map)) 392.66/193.66 down(app(app(y6425, cons), map)) -> app_flat(block(app(y6425, cons)), down(map)) 392.66/193.66 down(app(app(y6428, nil), map)) -> app_flat(down(app(y6428, nil)), block(map)) 392.66/193.66 down(app(app(y6428, nil), map)) -> app_flat(block(app(y6428, nil)), down(map)) 392.66/193.66 down(app(app(y6431, fresh_constant), map)) -> app_flat(down(app(y6431, fresh_constant)), block(map)) 392.66/193.66 down(app(app(y6431, fresh_constant), map)) -> app_flat(block(app(y6431, fresh_constant)), down(map)) 392.66/193.66 down(app(app(y6445, app(y6446, y6447)), cons)) -> app_flat(down(app(y6445, app(y6446, y6447))), block(cons)) 392.66/193.66 down(app(app(y6445, app(y6446, y6447)), cons)) -> app_flat(block(app(y6445, app(y6446, y6447))), down(cons)) 392.66/193.66 down(app(app(y6467, hd), cons)) -> app_flat(down(app(y6467, hd)), block(cons)) 392.66/193.66 down(app(app(y6467, hd), cons)) -> app_flat(block(app(y6467, hd)), down(cons)) 392.66/193.66 down(app(app(y6470, map), cons)) -> app_flat(down(app(y6470, map)), block(cons)) 392.66/193.66 down(app(app(y6470, map), cons)) -> app_flat(block(app(y6470, map)), down(cons)) 392.66/193.66 down(app(app(y6473, cons), cons)) -> app_flat(down(app(y6473, cons)), block(cons)) 392.66/193.66 down(app(app(y6473, cons), cons)) -> app_flat(block(app(y6473, cons)), down(cons)) 392.66/193.66 down(app(app(y6476, nil), cons)) -> app_flat(down(app(y6476, nil)), block(cons)) 392.66/193.66 down(app(app(y6476, nil), cons)) -> app_flat(block(app(y6476, nil)), down(cons)) 392.66/193.66 down(app(app(y6479, fresh_constant), cons)) -> app_flat(down(app(y6479, fresh_constant)), block(cons)) 392.66/193.66 down(app(app(y6479, fresh_constant), cons)) -> app_flat(block(app(y6479, fresh_constant)), down(cons)) 392.66/193.66 down(app(app(y6541, app(y6542, y6543)), fresh_constant)) -> app_flat(down(app(y6541, app(y6542, y6543))), block(fresh_constant)) 392.66/193.66 down(app(app(y6541, app(y6542, y6543)), fresh_constant)) -> app_flat(block(app(y6541, app(y6542, y6543))), down(fresh_constant)) 392.66/193.66 down(app(app(y6563, hd), fresh_constant)) -> app_flat(down(app(y6563, hd)), block(fresh_constant)) 392.66/193.66 down(app(app(y6563, hd), fresh_constant)) -> app_flat(block(app(y6563, hd)), down(fresh_constant)) 392.66/193.66 down(app(app(y6566, map), fresh_constant)) -> app_flat(down(app(y6566, map)), block(fresh_constant)) 392.66/193.66 down(app(app(y6566, map), fresh_constant)) -> app_flat(block(app(y6566, map)), down(fresh_constant)) 392.66/193.66 down(app(app(y6569, cons), fresh_constant)) -> app_flat(down(app(y6569, cons)), block(fresh_constant)) 392.66/193.66 down(app(app(y6569, cons), fresh_constant)) -> app_flat(block(app(y6569, cons)), down(fresh_constant)) 392.66/193.66 down(app(app(y6572, nil), fresh_constant)) -> app_flat(down(app(y6572, nil)), block(fresh_constant)) 392.66/193.66 down(app(app(y6572, nil), fresh_constant)) -> app_flat(block(app(y6572, nil)), down(fresh_constant)) 392.66/193.66 down(app(app(y6575, fresh_constant), fresh_constant)) -> app_flat(down(app(y6575, fresh_constant)), block(fresh_constant)) 392.66/193.66 down(app(app(y6575, fresh_constant), fresh_constant)) -> app_flat(block(app(y6575, fresh_constant)), down(fresh_constant)) 392.66/193.66 down(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> app_flat(down(app(y357, app(y20338, y20339))), block(app(app(app(y20340, y20341), y20342), y362))) 392.66/193.66 down(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> app_flat(block(app(y357, app(y20338, y20339))), down(app(app(app(y20340, y20341), y20342), y362))) 392.66/193.66 down(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> app_flat(down(app(y357, app(y20578, y20579))), block(app(app(0, y20580), y362))) 392.66/193.66 down(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> app_flat(block(app(y357, app(y20578, y20579))), down(app(app(0, y20580), y362))) 392.66/193.66 down(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> app_flat(down(app(y357, app(y20690, y20691))), block(app(app(hd, y20692), y362))) 392.66/193.66 down(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> app_flat(block(app(y357, app(y20690, y20691))), down(app(app(hd, y20692), y362))) 392.66/193.66 down(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> app_flat(down(app(y357, app(y20802, y20803))), block(app(app(map, y20804), y362))) 392.66/193.66 down(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> app_flat(block(app(y357, app(y20802, y20803))), down(app(app(map, y20804), y362))) 392.66/193.66 down(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> app_flat(down(app(y357, app(y21026, y21027))), block(app(app(nil, y21028), y362))) 392.66/193.66 down(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> app_flat(block(app(y357, app(y21026, y21027))), down(app(app(nil, y21028), y362))) 392.66/193.66 down(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> app_flat(down(app(y357, app(y21138, y21139))), block(app(app(fresh_constant, y21140), y362))) 392.66/193.66 down(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> app_flat(block(app(y357, app(y21138, y21139))), down(app(app(fresh_constant, y21140), y362))) 392.66/193.66 down(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> app_flat(down(app(y427, hd)), block(app(app(app(y32452, y32453), y32454), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> app_flat(block(app(y427, hd)), down(app(app(app(y32452, y32453), y32454), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(0, y32455), y430))) -> app_flat(down(app(y427, hd)), block(app(app(0, y32455), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(0, y32455), y430))) -> app_flat(block(app(y427, hd)), down(app(app(0, y32455), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(hd, y32456), y430))) -> app_flat(down(app(y427, hd)), block(app(app(hd, y32456), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(hd, y32456), y430))) -> app_flat(block(app(y427, hd)), down(app(app(hd, y32456), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(map, y32457), y430))) -> app_flat(down(app(y427, hd)), block(app(app(map, y32457), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(map, y32457), y430))) -> app_flat(block(app(y427, hd)), down(app(app(map, y32457), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(nil, y32459), y430))) -> app_flat(down(app(y427, hd)), block(app(app(nil, y32459), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(nil, y32459), y430))) -> app_flat(block(app(y427, hd)), down(app(app(nil, y32459), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(fresh_constant, y32460), y430))) -> app_flat(down(app(y427, hd)), block(app(app(fresh_constant, y32460), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(fresh_constant, y32460), y430))) -> app_flat(block(app(y427, hd)), down(app(app(fresh_constant, y32460), y430))) 392.66/193.66 down(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> app_flat(down(app(y454, map)), block(app(app(app(y32548, y32549), y32550), y457))) 392.66/193.66 down(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> app_flat(block(app(y454, map)), down(app(app(app(y32548, y32549), y32550), y457))) 392.66/193.66 down(app(app(y454, map), app(app(0, y32551), y457))) -> app_flat(down(app(y454, map)), block(app(app(0, y32551), y457))) 392.66/193.66 down(app(app(y454, map), app(app(0, y32551), y457))) -> app_flat(block(app(y454, map)), down(app(app(0, y32551), y457))) 392.66/193.66 down(app(app(y454, map), app(app(hd, y32552), y457))) -> app_flat(down(app(y454, map)), block(app(app(hd, y32552), y457))) 392.66/193.66 down(app(app(y454, map), app(app(hd, y32552), y457))) -> app_flat(block(app(y454, map)), down(app(app(hd, y32552), y457))) 392.66/193.66 down(app(app(y454, map), app(app(map, y32553), y457))) -> app_flat(down(app(y454, map)), block(app(app(map, y32553), y457))) 392.66/193.66 down(app(app(y454, map), app(app(map, y32553), y457))) -> app_flat(block(app(y454, map)), down(app(app(map, y32553), y457))) 392.66/193.66 down(app(app(y454, map), app(app(nil, y32555), y457))) -> app_flat(down(app(y454, map)), block(app(app(nil, y32555), y457))) 392.66/193.66 down(app(app(y454, map), app(app(nil, y32555), y457))) -> app_flat(block(app(y454, map)), down(app(app(nil, y32555), y457))) 392.66/193.66 down(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> app_flat(down(app(y454, map)), block(app(app(fresh_constant, y32556), y457))) 392.66/193.66 down(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> app_flat(block(app(y454, map)), down(app(app(fresh_constant, y32556), y457))) 392.66/193.66 down(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> app_flat(down(app(y481, cons)), block(app(app(app(y32644, y32645), y32646), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> app_flat(block(app(y481, cons)), down(app(app(app(y32644, y32645), y32646), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(0, y32647), y484))) -> app_flat(down(app(y481, cons)), block(app(app(0, y32647), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(0, y32647), y484))) -> app_flat(block(app(y481, cons)), down(app(app(0, y32647), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(hd, y32648), y484))) -> app_flat(down(app(y481, cons)), block(app(app(hd, y32648), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(hd, y32648), y484))) -> app_flat(block(app(y481, cons)), down(app(app(hd, y32648), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(map, y32649), y484))) -> app_flat(down(app(y481, cons)), block(app(app(map, y32649), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(map, y32649), y484))) -> app_flat(block(app(y481, cons)), down(app(app(map, y32649), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(nil, y32651), y484))) -> app_flat(down(app(y481, cons)), block(app(app(nil, y32651), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(nil, y32651), y484))) -> app_flat(block(app(y481, cons)), down(app(app(nil, y32651), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> app_flat(down(app(y481, cons)), block(app(app(fresh_constant, y32652), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> app_flat(block(app(y481, cons)), down(app(app(fresh_constant, y32652), y484))) 392.66/193.66 down(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> app_flat(down(app(y508, nil)), block(app(app(app(y32740, y32741), y32742), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> app_flat(block(app(y508, nil)), down(app(app(app(y32740, y32741), y32742), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(0, y32743), y511))) -> app_flat(down(app(y508, nil)), block(app(app(0, y32743), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(0, y32743), y511))) -> app_flat(block(app(y508, nil)), down(app(app(0, y32743), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(hd, y32744), y511))) -> app_flat(down(app(y508, nil)), block(app(app(hd, y32744), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(hd, y32744), y511))) -> app_flat(block(app(y508, nil)), down(app(app(hd, y32744), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(map, y32745), y511))) -> app_flat(down(app(y508, nil)), block(app(app(map, y32745), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(map, y32745), y511))) -> app_flat(block(app(y508, nil)), down(app(app(map, y32745), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(nil, y32747), y511))) -> app_flat(down(app(y508, nil)), block(app(app(nil, y32747), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(nil, y32747), y511))) -> app_flat(block(app(y508, nil)), down(app(app(nil, y32747), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(fresh_constant, y32748), y511))) -> app_flat(down(app(y508, nil)), block(app(app(fresh_constant, y32748), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(fresh_constant, y32748), y511))) -> app_flat(block(app(y508, nil)), down(app(app(fresh_constant, y32748), y511))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(app(y32836, y32837), y32838), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(app(y32836, y32837), y32838), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(0, y32839), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(0, y32839), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(0, y32839), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(0, y32839), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(hd, y32840), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(hd, y32840), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(hd, y32840), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(hd, y32840), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(map, y32841), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(map, y32841), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(nil, y32843), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(nil, y32843), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(nil, y32843), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(nil, y32843), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(fresh_constant, y32844), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(fresh_constant, y32844), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(fresh_constant, y32844), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(fresh_constant, y32844), y538))) 392.66/193.66 app_flat(up(x_1), block(x_2)) -> up(app(x_1, x_2)) 392.66/193.66 app_flat(block(x_1), up(x_2)) -> up(app(x_1, x_2)) 392.66/193.66 392.66/193.66 Q is empty. 392.66/193.66 We have to consider all minimal (P,Q,R)-chains. 392.66/193.66 ---------------------------------------- 392.66/193.66 392.66/193.66 (47) DependencyGraphProof (EQUIVALENT) 392.66/193.66 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 2 SCCs with 325 less nodes. 392.66/193.66 ---------------------------------------- 392.66/193.66 392.66/193.66 (48) 392.66/193.66 Complex Obligation (AND) 392.66/193.66 392.66/193.66 ---------------------------------------- 392.66/193.66 392.66/193.66 (49) 392.66/193.66 Obligation: 392.66/193.66 Q DP problem: 392.66/193.66 The TRS P consists of the following rules: 392.66/193.66 392.66/193.66 DOWN(app(hd, y8)) -> DOWN(y8) 392.66/193.66 DOWN(app(0, y7)) -> DOWN(y7) 392.66/193.66 DOWN(app(map, y9)) -> DOWN(y9) 392.66/193.66 DOWN(app(cons, y10)) -> DOWN(y10) 392.66/193.66 DOWN(app(nil, y11)) -> DOWN(y11) 392.66/193.66 DOWN(app(fresh_constant, y12)) -> DOWN(y12) 392.66/193.66 DOWN(app(app(app(y64, y65), app(y66, y67)), y6)) -> DOWN(app(app(y64, y65), app(y66, y67))) 392.66/193.66 DOWN(app(app(app(y64, y65), app(y66, y67)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, app(y68, y69)), y6)) -> DOWN(app(0, app(y68, y69))) 392.66/193.66 DOWN(app(app(0, app(y68, y69)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(hd, app(y70, y71)), y6)) -> DOWN(app(hd, app(y70, y71))) 392.66/193.66 DOWN(app(app(hd, app(y70, y71)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(cons, app(y74, y75)), y6)) -> DOWN(app(cons, app(y74, y75))) 392.66/193.66 DOWN(app(app(cons, app(y74, y75)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, app(y76, y77)), y6)) -> DOWN(app(nil, app(y76, y77))) 392.66/193.66 DOWN(app(app(nil, app(y76, y77)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(fresh_constant, app(y78, y79)), y6)) -> DOWN(app(fresh_constant, app(y78, y79))) 392.66/193.66 DOWN(app(app(fresh_constant, app(y78, y79)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(app(y84, y85), hd), y6)) -> DOWN(app(app(y84, y85), hd)) 392.66/193.66 DOWN(app(app(app(y84, y85), hd), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, hd), y6)) -> DOWN(app(0, hd)) 392.66/193.66 DOWN(app(app(0, hd), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(hd, hd), y6)) -> DOWN(app(hd, hd)) 392.66/193.66 DOWN(app(app(hd, hd), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(cons, hd), y6)) -> DOWN(app(cons, hd)) 392.66/193.66 DOWN(app(app(cons, hd), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, hd), y6)) -> DOWN(app(nil, hd)) 392.66/193.66 DOWN(app(app(nil, hd), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(fresh_constant, hd), y6)) -> DOWN(app(fresh_constant, hd)) 392.66/193.66 DOWN(app(app(fresh_constant, hd), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(app(y87, y88), map), y6)) -> DOWN(app(app(y87, y88), map)) 392.66/193.66 DOWN(app(app(app(y87, y88), map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, map), y6)) -> DOWN(app(0, map)) 392.66/193.66 DOWN(app(app(0, map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(hd, map), y6)) -> DOWN(app(hd, map)) 392.66/193.66 DOWN(app(app(hd, map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(cons, map), y6)) -> DOWN(app(cons, map)) 392.66/193.66 DOWN(app(app(cons, map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, map), y6)) -> DOWN(app(nil, map)) 392.66/193.66 DOWN(app(app(nil, map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(fresh_constant, map), y6)) -> DOWN(app(fresh_constant, map)) 392.66/193.66 DOWN(app(app(fresh_constant, map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(app(y90, y91), cons), y6)) -> DOWN(app(app(y90, y91), cons)) 392.66/193.66 DOWN(app(app(app(y90, y91), cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, cons), y6)) -> DOWN(app(0, cons)) 392.66/193.66 DOWN(app(app(0, cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(hd, cons), y6)) -> DOWN(app(hd, cons)) 392.66/193.66 DOWN(app(app(hd, cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(cons, cons), y6)) -> DOWN(app(cons, cons)) 392.66/193.66 DOWN(app(app(cons, cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, cons), y6)) -> DOWN(app(nil, cons)) 392.66/193.66 DOWN(app(app(nil, cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(fresh_constant, cons), y6)) -> DOWN(app(fresh_constant, cons)) 392.66/193.66 DOWN(app(app(fresh_constant, cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(app(y93, y94), nil), y6)) -> DOWN(app(app(y93, y94), nil)) 392.66/193.66 DOWN(app(app(app(y93, y94), nil), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, nil), y6)) -> DOWN(app(0, nil)) 392.66/193.66 DOWN(app(app(0, nil), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(hd, nil), y6)) -> DOWN(app(hd, nil)) 392.66/193.66 DOWN(app(app(hd, nil), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(cons, nil), y6)) -> DOWN(app(cons, nil)) 392.66/193.66 DOWN(app(app(cons, nil), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, nil), y6)) -> DOWN(app(nil, nil)) 392.66/193.66 DOWN(app(app(nil, nil), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(fresh_constant, nil), y6)) -> DOWN(app(fresh_constant, nil)) 392.66/193.66 DOWN(app(app(fresh_constant, nil), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(app(y96, y97), fresh_constant), y6)) -> DOWN(app(app(y96, y97), fresh_constant)) 392.66/193.66 DOWN(app(app(app(y96, y97), fresh_constant), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, fresh_constant), y6)) -> DOWN(app(0, fresh_constant)) 392.66/193.66 DOWN(app(app(0, fresh_constant), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(hd, fresh_constant), y6)) -> DOWN(app(hd, fresh_constant)) 392.66/193.66 DOWN(app(app(hd, fresh_constant), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(cons, fresh_constant), y6)) -> DOWN(app(cons, fresh_constant)) 392.66/193.66 DOWN(app(app(cons, fresh_constant), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, fresh_constant), y6)) -> DOWN(app(nil, fresh_constant)) 392.66/193.66 DOWN(app(app(nil, fresh_constant), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(fresh_constant, fresh_constant), y6)) -> DOWN(app(fresh_constant, fresh_constant)) 392.66/193.66 DOWN(app(app(fresh_constant, fresh_constant), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(y581, app(y582, y583)), app(0, y584))) -> DOWN(app(y581, app(y582, y583))) 392.66/193.66 DOWN(app(app(y581, app(y582, y583)), app(0, y584))) -> DOWN(app(0, y584)) 392.66/193.66 DOWN(app(app(y619, hd), app(0, y620))) -> DOWN(app(y619, hd)) 392.66/193.66 DOWN(app(app(y6349, app(y6350, y6351)), hd)) -> DOWN(app(y6349, app(y6350, y6351))) 392.66/193.66 DOWN(app(app(y619, hd), app(0, y620))) -> DOWN(app(0, y620)) 392.66/193.66 DOWN(app(app(y630, map), app(0, y631))) -> DOWN(app(y630, map)) 392.66/193.66 DOWN(app(app(y6397, app(y6398, y6399)), map)) -> DOWN(app(y6397, app(y6398, y6399))) 392.66/193.66 DOWN(app(app(y630, map), app(0, y631))) -> DOWN(app(0, y631)) 392.66/193.66 DOWN(app(app(y641, cons), app(0, y642))) -> DOWN(app(y641, cons)) 392.66/193.66 DOWN(app(app(y6445, app(y6446, y6447)), cons)) -> DOWN(app(y6445, app(y6446, y6447))) 392.66/193.66 DOWN(app(app(y641, cons), app(0, y642))) -> DOWN(app(0, y642)) 392.66/193.66 DOWN(app(app(y652, nil), app(0, y653))) -> DOWN(app(y652, nil)) 392.66/193.66 DOWN(app(app(y652, nil), app(0, y653))) -> DOWN(app(0, y653)) 392.66/193.66 DOWN(app(app(y663, fresh_constant), app(0, y664))) -> DOWN(app(y663, fresh_constant)) 392.66/193.66 DOWN(app(app(y6541, app(y6542, y6543)), fresh_constant)) -> DOWN(app(y6541, app(y6542, y6543))) 392.66/193.66 DOWN(app(app(y663, fresh_constant), app(0, y664))) -> DOWN(app(0, y664)) 392.66/193.66 DOWN(app(app(y693, app(y694, y695)), app(hd, y696))) -> DOWN(app(y693, app(y694, y695))) 392.66/193.66 DOWN(app(app(y693, app(y694, y695)), app(hd, y696))) -> DOWN(app(hd, y696)) 392.66/193.66 DOWN(app(app(y731, hd), app(hd, y732))) -> DOWN(app(y731, hd)) 392.66/193.66 DOWN(app(app(y6371, hd), hd)) -> DOWN(app(y6371, hd)) 392.66/193.66 DOWN(app(app(y6374, map), hd)) -> DOWN(app(y6374, map)) 392.66/193.66 DOWN(app(app(y6419, hd), map)) -> DOWN(app(y6419, hd)) 392.66/193.66 DOWN(app(app(y6377, cons), hd)) -> DOWN(app(y6377, cons)) 392.66/193.66 DOWN(app(app(y6467, hd), cons)) -> DOWN(app(y6467, hd)) 392.66/193.66 DOWN(app(app(y6380, nil), hd)) -> DOWN(app(y6380, nil)) 392.66/193.66 DOWN(app(app(y6383, fresh_constant), hd)) -> DOWN(app(y6383, fresh_constant)) 392.66/193.66 DOWN(app(app(y6563, hd), fresh_constant)) -> DOWN(app(y6563, hd)) 392.66/193.66 DOWN(app(app(y6566, map), fresh_constant)) -> DOWN(app(y6566, map)) 392.66/193.66 DOWN(app(app(y6422, map), map)) -> DOWN(app(y6422, map)) 392.66/193.66 DOWN(app(app(y6425, cons), map)) -> DOWN(app(y6425, cons)) 392.66/193.66 DOWN(app(app(y6470, map), cons)) -> DOWN(app(y6470, map)) 392.66/193.66 DOWN(app(app(y6428, nil), map)) -> DOWN(app(y6428, nil)) 392.66/193.66 DOWN(app(app(y6431, fresh_constant), map)) -> DOWN(app(y6431, fresh_constant)) 392.66/193.66 DOWN(app(app(y6569, cons), fresh_constant)) -> DOWN(app(y6569, cons)) 392.66/193.66 DOWN(app(app(y6473, cons), cons)) -> DOWN(app(y6473, cons)) 392.66/193.66 DOWN(app(app(y6476, nil), cons)) -> DOWN(app(y6476, nil)) 392.66/193.66 DOWN(app(app(y6479, fresh_constant), cons)) -> DOWN(app(y6479, fresh_constant)) 392.66/193.66 DOWN(app(app(y6572, nil), fresh_constant)) -> DOWN(app(y6572, nil)) 392.66/193.66 DOWN(app(app(y6575, fresh_constant), fresh_constant)) -> DOWN(app(y6575, fresh_constant)) 392.66/193.66 DOWN(app(app(y731, hd), app(hd, y732))) -> DOWN(app(hd, y732)) 392.66/193.66 DOWN(app(app(y742, map), app(hd, y743))) -> DOWN(app(y742, map)) 392.66/193.66 DOWN(app(app(y742, map), app(hd, y743))) -> DOWN(app(hd, y743)) 392.66/193.66 DOWN(app(app(y753, cons), app(hd, y754))) -> DOWN(app(y753, cons)) 392.66/193.66 DOWN(app(app(y753, cons), app(hd, y754))) -> DOWN(app(hd, y754)) 392.66/193.66 DOWN(app(app(y764, nil), app(hd, y765))) -> DOWN(app(y764, nil)) 392.66/193.66 DOWN(app(app(y764, nil), app(hd, y765))) -> DOWN(app(hd, y765)) 392.66/193.66 DOWN(app(app(y775, fresh_constant), app(hd, y776))) -> DOWN(app(y775, fresh_constant)) 392.66/193.66 DOWN(app(app(y775, fresh_constant), app(hd, y776))) -> DOWN(app(hd, y776)) 392.66/193.66 DOWN(app(app(y805, app(y806, y807)), app(map, y808))) -> DOWN(app(y805, app(y806, y807))) 392.66/193.66 DOWN(app(app(y805, app(y806, y807)), app(map, y808))) -> DOWN(app(map, y808)) 392.66/193.66 DOWN(app(app(y843, hd), app(map, y844))) -> DOWN(app(y843, hd)) 392.66/193.66 DOWN(app(app(y843, hd), app(map, y844))) -> DOWN(app(map, y844)) 392.66/193.66 DOWN(app(app(y854, map), app(map, y855))) -> DOWN(app(y854, map)) 392.66/193.66 DOWN(app(app(y854, map), app(map, y855))) -> DOWN(app(map, y855)) 392.66/193.66 DOWN(app(app(y865, cons), app(map, y866))) -> DOWN(app(y865, cons)) 392.66/193.66 DOWN(app(app(y865, cons), app(map, y866))) -> DOWN(app(map, y866)) 392.66/193.66 DOWN(app(app(y876, nil), app(map, y877))) -> DOWN(app(y876, nil)) 392.66/193.66 DOWN(app(app(y876, nil), app(map, y877))) -> DOWN(app(map, y877)) 392.66/193.66 DOWN(app(app(y887, fresh_constant), app(map, y888))) -> DOWN(app(y887, fresh_constant)) 392.66/193.66 DOWN(app(app(y887, fresh_constant), app(map, y888))) -> DOWN(app(map, y888)) 392.66/193.66 DOWN(app(app(y917, app(y918, y919)), app(cons, y920))) -> DOWN(app(y917, app(y918, y919))) 392.66/193.66 DOWN(app(app(y917, app(y918, y919)), app(cons, y920))) -> DOWN(app(cons, y920)) 392.66/193.66 DOWN(app(app(y955, hd), app(cons, y956))) -> DOWN(app(y955, hd)) 392.66/193.66 DOWN(app(app(y955, hd), app(cons, y956))) -> DOWN(app(cons, y956)) 392.66/193.66 DOWN(app(app(y966, map), app(cons, y967))) -> DOWN(app(y966, map)) 392.66/193.66 DOWN(app(app(y966, map), app(cons, y967))) -> DOWN(app(cons, y967)) 392.66/193.66 DOWN(app(app(y977, cons), app(cons, y978))) -> DOWN(app(y977, cons)) 392.66/193.66 DOWN(app(app(y977, cons), app(cons, y978))) -> DOWN(app(cons, y978)) 392.66/193.66 DOWN(app(app(y988, nil), app(cons, y989))) -> DOWN(app(y988, nil)) 392.66/193.66 DOWN(app(app(y988, nil), app(cons, y989))) -> DOWN(app(cons, y989)) 392.66/193.66 DOWN(app(app(y999, fresh_constant), app(cons, y1000))) -> DOWN(app(y999, fresh_constant)) 392.66/193.66 DOWN(app(app(y999, fresh_constant), app(cons, y1000))) -> DOWN(app(cons, y1000)) 392.66/193.66 DOWN(app(app(y1029, app(y1030, y1031)), app(nil, y1032))) -> DOWN(app(y1029, app(y1030, y1031))) 392.66/193.66 DOWN(app(app(y1029, app(y1030, y1031)), app(nil, y1032))) -> DOWN(app(nil, y1032)) 392.66/193.66 DOWN(app(app(y1067, hd), app(nil, y1068))) -> DOWN(app(y1067, hd)) 392.66/193.66 DOWN(app(app(y1067, hd), app(nil, y1068))) -> DOWN(app(nil, y1068)) 392.66/193.66 DOWN(app(app(y1078, map), app(nil, y1079))) -> DOWN(app(y1078, map)) 392.66/193.66 DOWN(app(app(y1078, map), app(nil, y1079))) -> DOWN(app(nil, y1079)) 392.66/193.66 DOWN(app(app(y1089, cons), app(nil, y1090))) -> DOWN(app(y1089, cons)) 392.66/193.66 DOWN(app(app(y1089, cons), app(nil, y1090))) -> DOWN(app(nil, y1090)) 392.66/193.66 DOWN(app(app(y1100, nil), app(nil, y1101))) -> DOWN(app(y1100, nil)) 392.66/193.66 DOWN(app(app(y1100, nil), app(nil, y1101))) -> DOWN(app(nil, y1101)) 392.66/193.66 DOWN(app(app(y1111, fresh_constant), app(nil, y1112))) -> DOWN(app(y1111, fresh_constant)) 392.66/193.66 DOWN(app(app(y1111, fresh_constant), app(nil, y1112))) -> DOWN(app(nil, y1112)) 392.66/193.66 DOWN(app(app(y1141, app(y1142, y1143)), app(fresh_constant, y1144))) -> DOWN(app(y1141, app(y1142, y1143))) 392.66/193.66 DOWN(app(app(y1141, app(y1142, y1143)), app(fresh_constant, y1144))) -> DOWN(app(fresh_constant, y1144)) 392.66/193.66 DOWN(app(app(y1179, hd), app(fresh_constant, y1180))) -> DOWN(app(y1179, hd)) 392.66/193.66 DOWN(app(app(y1179, hd), app(fresh_constant, y1180))) -> DOWN(app(fresh_constant, y1180)) 392.66/193.66 DOWN(app(app(y1190, map), app(fresh_constant, y1191))) -> DOWN(app(y1190, map)) 392.66/193.66 DOWN(app(app(y1190, map), app(fresh_constant, y1191))) -> DOWN(app(fresh_constant, y1191)) 392.66/193.66 DOWN(app(app(y1201, cons), app(fresh_constant, y1202))) -> DOWN(app(y1201, cons)) 392.66/193.66 DOWN(app(app(y1201, cons), app(fresh_constant, y1202))) -> DOWN(app(fresh_constant, y1202)) 392.66/193.66 DOWN(app(app(y1212, nil), app(fresh_constant, y1213))) -> DOWN(app(y1212, nil)) 392.66/193.66 DOWN(app(app(y1212, nil), app(fresh_constant, y1213))) -> DOWN(app(fresh_constant, y1213)) 392.66/193.66 DOWN(app(app(y1223, fresh_constant), app(fresh_constant, y1224))) -> DOWN(app(y1223, fresh_constant)) 392.66/193.66 DOWN(app(app(y1223, fresh_constant), app(fresh_constant, y1224))) -> DOWN(app(fresh_constant, y1224)) 392.66/193.66 DOWN(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> DOWN(app(y357, app(y20338, y20339))) 392.66/193.66 DOWN(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> DOWN(app(app(app(y20340, y20341), y20342), y362)) 392.66/193.66 DOWN(app(app(y6301, app(y6302, y6303)), 0)) -> DOWN(app(y6301, app(y6302, y6303))) 392.66/193.66 DOWN(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> DOWN(app(y357, app(y20578, y20579))) 392.66/193.66 DOWN(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> DOWN(app(app(0, y20580), y362)) 392.66/193.66 DOWN(app(app(y6323, hd), 0)) -> DOWN(app(y6323, hd)) 392.66/193.66 DOWN(app(app(y6326, map), 0)) -> DOWN(app(y6326, map)) 392.66/193.66 DOWN(app(app(y6329, cons), 0)) -> DOWN(app(y6329, cons)) 392.66/193.66 DOWN(app(app(y6332, nil), 0)) -> DOWN(app(y6332, nil)) 392.66/193.66 DOWN(app(app(y6335, fresh_constant), 0)) -> DOWN(app(y6335, fresh_constant)) 392.66/193.66 DOWN(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> DOWN(app(y357, app(y20690, y20691))) 392.66/193.66 DOWN(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> DOWN(app(app(hd, y20692), y362)) 392.66/193.66 DOWN(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> DOWN(app(y357, app(y20802, y20803))) 392.66/193.66 DOWN(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> DOWN(app(app(map, y20804), y362)) 392.66/193.66 DOWN(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> DOWN(app(y357, app(y21026, y21027))) 392.66/193.66 DOWN(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> DOWN(app(app(nil, y21028), y362)) 392.66/193.66 DOWN(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> DOWN(app(y357, app(y21138, y21139))) 392.66/193.66 DOWN(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> DOWN(app(app(fresh_constant, y21140), y362)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> DOWN(app(app(app(y32452, y32453), y32454), y430)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(0, y32455), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(0, y32455), y430))) -> DOWN(app(app(0, y32455), y430)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(hd, y32456), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(hd, y32456), y430))) -> DOWN(app(app(hd, y32456), y430)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(map, y32457), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(map, y32457), y430))) -> DOWN(app(app(map, y32457), y430)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(nil, y32459), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(nil, y32459), y430))) -> DOWN(app(app(nil, y32459), y430)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(fresh_constant, y32460), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(fresh_constant, y32460), y430))) -> DOWN(app(app(fresh_constant, y32460), y430)) 392.66/193.66 DOWN(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> DOWN(app(app(app(y32548, y32549), y32550), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(0, y32551), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(0, y32551), y457))) -> DOWN(app(app(0, y32551), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(hd, y32552), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(hd, y32552), y457))) -> DOWN(app(app(hd, y32552), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(map, y32553), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(map, y32553), y457))) -> DOWN(app(app(map, y32553), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(nil, y32555), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(nil, y32555), y457))) -> DOWN(app(app(nil, y32555), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> DOWN(app(app(fresh_constant, y32556), y457)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> DOWN(app(app(app(y32644, y32645), y32646), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(0, y32647), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(0, y32647), y484))) -> DOWN(app(app(0, y32647), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(hd, y32648), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(hd, y32648), y484))) -> DOWN(app(app(hd, y32648), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(map, y32649), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(map, y32649), y484))) -> DOWN(app(app(map, y32649), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(nil, y32651), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(nil, y32651), y484))) -> DOWN(app(app(nil, y32651), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> DOWN(app(app(fresh_constant, y32652), y484)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> DOWN(app(app(app(y32740, y32741), y32742), y511)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(0, y32743), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(0, y32743), y511))) -> DOWN(app(app(0, y32743), y511)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(hd, y32744), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(hd, y32744), y511))) -> DOWN(app(app(hd, y32744), y511)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(map, y32745), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(map, y32745), y511))) -> DOWN(app(app(map, y32745), y511)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(nil, y32747), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(nil, y32747), y511))) -> DOWN(app(app(nil, y32747), y511)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(fresh_constant, y32748), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(fresh_constant, y32748), y511))) -> DOWN(app(app(fresh_constant, y32748), y511)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> DOWN(app(app(app(y32836, y32837), y32838), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(0, y32839), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(0, y32839), y538))) -> DOWN(app(app(0, y32839), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(hd, y32840), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(hd, y32840), y538))) -> DOWN(app(app(hd, y32840), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> DOWN(app(app(map, y32841), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(nil, y32843), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(nil, y32843), y538))) -> DOWN(app(app(nil, y32843), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(fresh_constant, y32844), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(fresh_constant, y32844), y538))) -> DOWN(app(app(fresh_constant, y32844), y538)) 392.66/193.66 392.66/193.66 The TRS R consists of the following rules: 392.66/193.66 392.66/193.66 down(app(app(f, 0), n)) -> up(app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)) 392.66/193.66 down(app(app(map, f), nil)) -> up(nil) 392.66/193.66 down(app(app(map, f), app(app(cons, x), xs))) -> up(app(app(cons, app(f, x)), app(app(map, f), xs))) 392.66/193.66 top(up(x)) -> top(down(x)) 392.66/193.66 down(app(0, y7)) -> app_flat(down(0), block(y7)) 392.66/193.66 down(app(0, y7)) -> app_flat(block(0), down(y7)) 392.66/193.66 down(app(hd, y8)) -> app_flat(down(hd), block(y8)) 392.66/193.66 down(app(hd, y8)) -> app_flat(block(hd), down(y8)) 392.66/193.66 down(app(map, y9)) -> app_flat(down(map), block(y9)) 392.66/193.66 down(app(map, y9)) -> app_flat(block(map), down(y9)) 392.66/193.66 down(app(cons, y10)) -> app_flat(down(cons), block(y10)) 392.66/193.66 down(app(cons, y10)) -> app_flat(block(cons), down(y10)) 392.66/193.66 down(app(nil, y11)) -> app_flat(down(nil), block(y11)) 392.66/193.66 down(app(nil, y11)) -> app_flat(block(nil), down(y11)) 392.66/193.66 down(app(fresh_constant, y12)) -> app_flat(down(fresh_constant), block(y12)) 392.66/193.66 down(app(fresh_constant, y12)) -> app_flat(block(fresh_constant), down(y12)) 392.66/193.66 down(app(app(app(y64, y65), app(y66, y67)), y6)) -> app_flat(down(app(app(y64, y65), app(y66, y67))), block(y6)) 392.66/193.66 down(app(app(app(y64, y65), app(y66, y67)), y6)) -> app_flat(block(app(app(y64, y65), app(y66, y67))), down(y6)) 392.66/193.66 down(app(app(0, app(y68, y69)), y6)) -> app_flat(down(app(0, app(y68, y69))), block(y6)) 392.66/193.66 down(app(app(0, app(y68, y69)), y6)) -> app_flat(block(app(0, app(y68, y69))), down(y6)) 392.66/193.66 down(app(app(hd, app(y70, y71)), y6)) -> app_flat(down(app(hd, app(y70, y71))), block(y6)) 392.66/193.66 down(app(app(hd, app(y70, y71)), y6)) -> app_flat(block(app(hd, app(y70, y71))), down(y6)) 392.66/193.66 down(app(app(cons, app(y74, y75)), y6)) -> app_flat(down(app(cons, app(y74, y75))), block(y6)) 392.66/193.66 down(app(app(cons, app(y74, y75)), y6)) -> app_flat(block(app(cons, app(y74, y75))), down(y6)) 392.66/193.66 down(app(app(nil, app(y76, y77)), y6)) -> app_flat(down(app(nil, app(y76, y77))), block(y6)) 392.66/193.66 down(app(app(nil, app(y76, y77)), y6)) -> app_flat(block(app(nil, app(y76, y77))), down(y6)) 392.66/193.66 down(app(app(fresh_constant, app(y78, y79)), y6)) -> app_flat(down(app(fresh_constant, app(y78, y79))), block(y6)) 392.66/193.66 down(app(app(fresh_constant, app(y78, y79)), y6)) -> app_flat(block(app(fresh_constant, app(y78, y79))), down(y6)) 392.66/193.66 down(app(app(app(y84, y85), hd), y6)) -> app_flat(down(app(app(y84, y85), hd)), block(y6)) 392.66/193.66 down(app(app(app(y84, y85), hd), y6)) -> app_flat(block(app(app(y84, y85), hd)), down(y6)) 392.66/193.66 down(app(app(0, hd), y6)) -> app_flat(down(app(0, hd)), block(y6)) 392.66/193.66 down(app(app(0, hd), y6)) -> app_flat(block(app(0, hd)), down(y6)) 392.66/193.66 down(app(app(hd, hd), y6)) -> app_flat(down(app(hd, hd)), block(y6)) 392.66/193.66 down(app(app(hd, hd), y6)) -> app_flat(block(app(hd, hd)), down(y6)) 392.66/193.66 down(app(app(cons, hd), y6)) -> app_flat(down(app(cons, hd)), block(y6)) 392.66/193.66 down(app(app(cons, hd), y6)) -> app_flat(block(app(cons, hd)), down(y6)) 392.66/193.66 down(app(app(nil, hd), y6)) -> app_flat(down(app(nil, hd)), block(y6)) 392.66/193.66 down(app(app(nil, hd), y6)) -> app_flat(block(app(nil, hd)), down(y6)) 392.66/193.66 down(app(app(fresh_constant, hd), y6)) -> app_flat(down(app(fresh_constant, hd)), block(y6)) 392.66/193.66 down(app(app(fresh_constant, hd), y6)) -> app_flat(block(app(fresh_constant, hd)), down(y6)) 392.66/193.66 down(app(app(app(y87, y88), map), y6)) -> app_flat(down(app(app(y87, y88), map)), block(y6)) 392.66/193.66 down(app(app(app(y87, y88), map), y6)) -> app_flat(block(app(app(y87, y88), map)), down(y6)) 392.66/193.66 down(app(app(0, map), y6)) -> app_flat(down(app(0, map)), block(y6)) 392.66/193.66 down(app(app(0, map), y6)) -> app_flat(block(app(0, map)), down(y6)) 392.66/193.66 down(app(app(hd, map), y6)) -> app_flat(down(app(hd, map)), block(y6)) 392.66/193.66 down(app(app(hd, map), y6)) -> app_flat(block(app(hd, map)), down(y6)) 392.66/193.66 down(app(app(cons, map), y6)) -> app_flat(down(app(cons, map)), block(y6)) 392.66/193.66 down(app(app(cons, map), y6)) -> app_flat(block(app(cons, map)), down(y6)) 392.66/193.66 down(app(app(nil, map), y6)) -> app_flat(down(app(nil, map)), block(y6)) 392.66/193.66 down(app(app(nil, map), y6)) -> app_flat(block(app(nil, map)), down(y6)) 392.66/193.66 down(app(app(fresh_constant, map), y6)) -> app_flat(down(app(fresh_constant, map)), block(y6)) 392.66/193.66 down(app(app(fresh_constant, map), y6)) -> app_flat(block(app(fresh_constant, map)), down(y6)) 392.66/193.66 down(app(app(app(y90, y91), cons), y6)) -> app_flat(down(app(app(y90, y91), cons)), block(y6)) 392.66/193.66 down(app(app(app(y90, y91), cons), y6)) -> app_flat(block(app(app(y90, y91), cons)), down(y6)) 392.66/193.66 down(app(app(0, cons), y6)) -> app_flat(down(app(0, cons)), block(y6)) 392.66/193.66 down(app(app(0, cons), y6)) -> app_flat(block(app(0, cons)), down(y6)) 392.66/193.66 down(app(app(hd, cons), y6)) -> app_flat(down(app(hd, cons)), block(y6)) 392.66/193.66 down(app(app(hd, cons), y6)) -> app_flat(block(app(hd, cons)), down(y6)) 392.66/193.66 down(app(app(cons, cons), y6)) -> app_flat(down(app(cons, cons)), block(y6)) 392.66/193.66 down(app(app(cons, cons), y6)) -> app_flat(block(app(cons, cons)), down(y6)) 392.66/193.66 down(app(app(nil, cons), y6)) -> app_flat(down(app(nil, cons)), block(y6)) 392.66/193.66 down(app(app(nil, cons), y6)) -> app_flat(block(app(nil, cons)), down(y6)) 392.66/193.66 down(app(app(fresh_constant, cons), y6)) -> app_flat(down(app(fresh_constant, cons)), block(y6)) 392.66/193.66 down(app(app(fresh_constant, cons), y6)) -> app_flat(block(app(fresh_constant, cons)), down(y6)) 392.66/193.66 down(app(app(app(y93, y94), nil), y6)) -> app_flat(down(app(app(y93, y94), nil)), block(y6)) 392.66/193.66 down(app(app(app(y93, y94), nil), y6)) -> app_flat(block(app(app(y93, y94), nil)), down(y6)) 392.66/193.66 down(app(app(0, nil), y6)) -> app_flat(down(app(0, nil)), block(y6)) 392.66/193.66 down(app(app(0, nil), y6)) -> app_flat(block(app(0, nil)), down(y6)) 392.66/193.66 down(app(app(hd, nil), y6)) -> app_flat(down(app(hd, nil)), block(y6)) 392.66/193.66 down(app(app(hd, nil), y6)) -> app_flat(block(app(hd, nil)), down(y6)) 392.66/193.66 down(app(app(cons, nil), y6)) -> app_flat(down(app(cons, nil)), block(y6)) 392.66/193.66 down(app(app(cons, nil), y6)) -> app_flat(block(app(cons, nil)), down(y6)) 392.66/193.66 down(app(app(nil, nil), y6)) -> app_flat(down(app(nil, nil)), block(y6)) 392.66/193.66 down(app(app(nil, nil), y6)) -> app_flat(block(app(nil, nil)), down(y6)) 392.66/193.66 down(app(app(fresh_constant, nil), y6)) -> app_flat(down(app(fresh_constant, nil)), block(y6)) 392.66/193.66 down(app(app(fresh_constant, nil), y6)) -> app_flat(block(app(fresh_constant, nil)), down(y6)) 392.66/193.66 down(app(app(app(y96, y97), fresh_constant), y6)) -> app_flat(down(app(app(y96, y97), fresh_constant)), block(y6)) 392.66/193.66 down(app(app(app(y96, y97), fresh_constant), y6)) -> app_flat(block(app(app(y96, y97), fresh_constant)), down(y6)) 392.66/193.66 down(app(app(0, fresh_constant), y6)) -> app_flat(down(app(0, fresh_constant)), block(y6)) 392.66/193.66 down(app(app(0, fresh_constant), y6)) -> app_flat(block(app(0, fresh_constant)), down(y6)) 392.66/193.66 down(app(app(hd, fresh_constant), y6)) -> app_flat(down(app(hd, fresh_constant)), block(y6)) 392.66/193.66 down(app(app(hd, fresh_constant), y6)) -> app_flat(block(app(hd, fresh_constant)), down(y6)) 392.66/193.66 down(app(app(cons, fresh_constant), y6)) -> app_flat(down(app(cons, fresh_constant)), block(y6)) 392.66/193.66 down(app(app(cons, fresh_constant), y6)) -> app_flat(block(app(cons, fresh_constant)), down(y6)) 392.66/193.66 down(app(app(nil, fresh_constant), y6)) -> app_flat(down(app(nil, fresh_constant)), block(y6)) 392.66/193.66 down(app(app(nil, fresh_constant), y6)) -> app_flat(block(app(nil, fresh_constant)), down(y6)) 392.66/193.66 down(app(app(fresh_constant, fresh_constant), y6)) -> app_flat(down(app(fresh_constant, fresh_constant)), block(y6)) 392.66/193.66 down(app(app(fresh_constant, fresh_constant), y6)) -> app_flat(block(app(fresh_constant, fresh_constant)), down(y6)) 392.66/193.66 down(app(app(y581, app(y582, y583)), app(0, y584))) -> app_flat(down(app(y581, app(y582, y583))), block(app(0, y584))) 392.66/193.66 down(app(app(y581, app(y582, y583)), app(0, y584))) -> app_flat(block(app(y581, app(y582, y583))), down(app(0, y584))) 392.66/193.66 down(app(app(y619, hd), app(0, y620))) -> app_flat(down(app(y619, hd)), block(app(0, y620))) 392.66/193.66 down(app(app(y619, hd), app(0, y620))) -> app_flat(block(app(y619, hd)), down(app(0, y620))) 392.66/193.66 down(app(app(y630, map), app(0, y631))) -> app_flat(down(app(y630, map)), block(app(0, y631))) 392.66/193.66 down(app(app(y630, map), app(0, y631))) -> app_flat(block(app(y630, map)), down(app(0, y631))) 392.66/193.66 down(app(app(y641, cons), app(0, y642))) -> app_flat(down(app(y641, cons)), block(app(0, y642))) 392.66/193.66 down(app(app(y641, cons), app(0, y642))) -> app_flat(block(app(y641, cons)), down(app(0, y642))) 392.66/193.66 down(app(app(y652, nil), app(0, y653))) -> app_flat(down(app(y652, nil)), block(app(0, y653))) 392.66/193.66 down(app(app(y652, nil), app(0, y653))) -> app_flat(block(app(y652, nil)), down(app(0, y653))) 392.66/193.66 down(app(app(y663, fresh_constant), app(0, y664))) -> app_flat(down(app(y663, fresh_constant)), block(app(0, y664))) 392.66/193.66 down(app(app(y663, fresh_constant), app(0, y664))) -> app_flat(block(app(y663, fresh_constant)), down(app(0, y664))) 392.66/193.66 down(app(app(y693, app(y694, y695)), app(hd, y696))) -> app_flat(down(app(y693, app(y694, y695))), block(app(hd, y696))) 392.66/193.66 down(app(app(y693, app(y694, y695)), app(hd, y696))) -> app_flat(block(app(y693, app(y694, y695))), down(app(hd, y696))) 392.66/193.66 down(app(app(y731, hd), app(hd, y732))) -> app_flat(down(app(y731, hd)), block(app(hd, y732))) 392.66/193.66 down(app(app(y731, hd), app(hd, y732))) -> app_flat(block(app(y731, hd)), down(app(hd, y732))) 392.66/193.66 down(app(app(y742, map), app(hd, y743))) -> app_flat(down(app(y742, map)), block(app(hd, y743))) 392.66/193.66 down(app(app(y742, map), app(hd, y743))) -> app_flat(block(app(y742, map)), down(app(hd, y743))) 392.66/193.66 down(app(app(y753, cons), app(hd, y754))) -> app_flat(down(app(y753, cons)), block(app(hd, y754))) 392.66/193.66 down(app(app(y753, cons), app(hd, y754))) -> app_flat(block(app(y753, cons)), down(app(hd, y754))) 392.66/193.66 down(app(app(y764, nil), app(hd, y765))) -> app_flat(down(app(y764, nil)), block(app(hd, y765))) 392.66/193.66 down(app(app(y764, nil), app(hd, y765))) -> app_flat(block(app(y764, nil)), down(app(hd, y765))) 392.66/193.66 down(app(app(y775, fresh_constant), app(hd, y776))) -> app_flat(down(app(y775, fresh_constant)), block(app(hd, y776))) 392.66/193.66 down(app(app(y775, fresh_constant), app(hd, y776))) -> app_flat(block(app(y775, fresh_constant)), down(app(hd, y776))) 392.66/193.66 down(app(app(y805, app(y806, y807)), app(map, y808))) -> app_flat(down(app(y805, app(y806, y807))), block(app(map, y808))) 392.66/193.66 down(app(app(y805, app(y806, y807)), app(map, y808))) -> app_flat(block(app(y805, app(y806, y807))), down(app(map, y808))) 392.66/193.66 down(app(app(y843, hd), app(map, y844))) -> app_flat(down(app(y843, hd)), block(app(map, y844))) 392.66/193.66 down(app(app(y843, hd), app(map, y844))) -> app_flat(block(app(y843, hd)), down(app(map, y844))) 392.66/193.66 down(app(app(y854, map), app(map, y855))) -> app_flat(down(app(y854, map)), block(app(map, y855))) 392.66/193.66 down(app(app(y854, map), app(map, y855))) -> app_flat(block(app(y854, map)), down(app(map, y855))) 392.66/193.66 down(app(app(y865, cons), app(map, y866))) -> app_flat(down(app(y865, cons)), block(app(map, y866))) 392.66/193.66 down(app(app(y865, cons), app(map, y866))) -> app_flat(block(app(y865, cons)), down(app(map, y866))) 392.66/193.66 down(app(app(y876, nil), app(map, y877))) -> app_flat(down(app(y876, nil)), block(app(map, y877))) 392.66/193.66 down(app(app(y876, nil), app(map, y877))) -> app_flat(block(app(y876, nil)), down(app(map, y877))) 392.66/193.66 down(app(app(y887, fresh_constant), app(map, y888))) -> app_flat(down(app(y887, fresh_constant)), block(app(map, y888))) 392.66/193.66 down(app(app(y887, fresh_constant), app(map, y888))) -> app_flat(block(app(y887, fresh_constant)), down(app(map, y888))) 392.66/193.66 down(app(app(y917, app(y918, y919)), app(cons, y920))) -> app_flat(down(app(y917, app(y918, y919))), block(app(cons, y920))) 392.66/193.66 down(app(app(y917, app(y918, y919)), app(cons, y920))) -> app_flat(block(app(y917, app(y918, y919))), down(app(cons, y920))) 392.66/193.66 down(app(app(y955, hd), app(cons, y956))) -> app_flat(down(app(y955, hd)), block(app(cons, y956))) 392.66/193.66 down(app(app(y955, hd), app(cons, y956))) -> app_flat(block(app(y955, hd)), down(app(cons, y956))) 392.66/193.66 down(app(app(y966, map), app(cons, y967))) -> app_flat(down(app(y966, map)), block(app(cons, y967))) 392.66/193.66 down(app(app(y966, map), app(cons, y967))) -> app_flat(block(app(y966, map)), down(app(cons, y967))) 392.66/193.66 down(app(app(y977, cons), app(cons, y978))) -> app_flat(down(app(y977, cons)), block(app(cons, y978))) 392.66/193.66 down(app(app(y977, cons), app(cons, y978))) -> app_flat(block(app(y977, cons)), down(app(cons, y978))) 392.66/193.66 down(app(app(y988, nil), app(cons, y989))) -> app_flat(down(app(y988, nil)), block(app(cons, y989))) 392.66/193.66 down(app(app(y988, nil), app(cons, y989))) -> app_flat(block(app(y988, nil)), down(app(cons, y989))) 392.66/193.66 down(app(app(y999, fresh_constant), app(cons, y1000))) -> app_flat(down(app(y999, fresh_constant)), block(app(cons, y1000))) 392.66/193.66 down(app(app(y999, fresh_constant), app(cons, y1000))) -> app_flat(block(app(y999, fresh_constant)), down(app(cons, y1000))) 392.66/193.66 down(app(app(y1029, app(y1030, y1031)), app(nil, y1032))) -> app_flat(down(app(y1029, app(y1030, y1031))), block(app(nil, y1032))) 392.66/193.66 down(app(app(y1029, app(y1030, y1031)), app(nil, y1032))) -> app_flat(block(app(y1029, app(y1030, y1031))), down(app(nil, y1032))) 392.66/193.66 down(app(app(y1067, hd), app(nil, y1068))) -> app_flat(down(app(y1067, hd)), block(app(nil, y1068))) 392.66/193.66 down(app(app(y1067, hd), app(nil, y1068))) -> app_flat(block(app(y1067, hd)), down(app(nil, y1068))) 392.66/193.66 down(app(app(y1078, map), app(nil, y1079))) -> app_flat(down(app(y1078, map)), block(app(nil, y1079))) 392.66/193.66 down(app(app(y1078, map), app(nil, y1079))) -> app_flat(block(app(y1078, map)), down(app(nil, y1079))) 392.66/193.66 down(app(app(y1089, cons), app(nil, y1090))) -> app_flat(down(app(y1089, cons)), block(app(nil, y1090))) 392.66/193.66 down(app(app(y1089, cons), app(nil, y1090))) -> app_flat(block(app(y1089, cons)), down(app(nil, y1090))) 392.66/193.66 down(app(app(y1100, nil), app(nil, y1101))) -> app_flat(down(app(y1100, nil)), block(app(nil, y1101))) 392.66/193.66 down(app(app(y1100, nil), app(nil, y1101))) -> app_flat(block(app(y1100, nil)), down(app(nil, y1101))) 392.66/193.66 down(app(app(y1111, fresh_constant), app(nil, y1112))) -> app_flat(down(app(y1111, fresh_constant)), block(app(nil, y1112))) 392.66/193.66 down(app(app(y1111, fresh_constant), app(nil, y1112))) -> app_flat(block(app(y1111, fresh_constant)), down(app(nil, y1112))) 392.66/193.66 down(app(app(y1141, app(y1142, y1143)), app(fresh_constant, y1144))) -> app_flat(down(app(y1141, app(y1142, y1143))), block(app(fresh_constant, y1144))) 392.66/193.66 down(app(app(y1141, app(y1142, y1143)), app(fresh_constant, y1144))) -> app_flat(block(app(y1141, app(y1142, y1143))), down(app(fresh_constant, y1144))) 392.66/193.66 down(app(app(y1179, hd), app(fresh_constant, y1180))) -> app_flat(down(app(y1179, hd)), block(app(fresh_constant, y1180))) 392.66/193.66 down(app(app(y1179, hd), app(fresh_constant, y1180))) -> app_flat(block(app(y1179, hd)), down(app(fresh_constant, y1180))) 392.66/193.66 down(app(app(y1190, map), app(fresh_constant, y1191))) -> app_flat(down(app(y1190, map)), block(app(fresh_constant, y1191))) 392.66/193.66 down(app(app(y1190, map), app(fresh_constant, y1191))) -> app_flat(block(app(y1190, map)), down(app(fresh_constant, y1191))) 392.66/193.66 down(app(app(y1201, cons), app(fresh_constant, y1202))) -> app_flat(down(app(y1201, cons)), block(app(fresh_constant, y1202))) 392.66/193.66 down(app(app(y1201, cons), app(fresh_constant, y1202))) -> app_flat(block(app(y1201, cons)), down(app(fresh_constant, y1202))) 392.66/193.66 down(app(app(y1212, nil), app(fresh_constant, y1213))) -> app_flat(down(app(y1212, nil)), block(app(fresh_constant, y1213))) 392.66/193.66 down(app(app(y1212, nil), app(fresh_constant, y1213))) -> app_flat(block(app(y1212, nil)), down(app(fresh_constant, y1213))) 392.66/193.66 down(app(app(y1223, fresh_constant), app(fresh_constant, y1224))) -> app_flat(down(app(y1223, fresh_constant)), block(app(fresh_constant, y1224))) 392.66/193.66 down(app(app(y1223, fresh_constant), app(fresh_constant, y1224))) -> app_flat(block(app(y1223, fresh_constant)), down(app(fresh_constant, y1224))) 392.66/193.66 down(app(app(y6301, app(y6302, y6303)), 0)) -> app_flat(down(app(y6301, app(y6302, y6303))), block(0)) 392.66/193.66 down(app(app(y6301, app(y6302, y6303)), 0)) -> app_flat(block(app(y6301, app(y6302, y6303))), down(0)) 392.66/193.66 down(app(app(y6323, hd), 0)) -> app_flat(down(app(y6323, hd)), block(0)) 392.66/193.66 down(app(app(y6323, hd), 0)) -> app_flat(block(app(y6323, hd)), down(0)) 392.66/193.66 down(app(app(y6326, map), 0)) -> app_flat(down(app(y6326, map)), block(0)) 392.66/193.66 down(app(app(y6326, map), 0)) -> app_flat(block(app(y6326, map)), down(0)) 392.66/193.66 down(app(app(y6329, cons), 0)) -> app_flat(down(app(y6329, cons)), block(0)) 392.66/193.66 down(app(app(y6329, cons), 0)) -> app_flat(block(app(y6329, cons)), down(0)) 392.66/193.66 down(app(app(y6332, nil), 0)) -> app_flat(down(app(y6332, nil)), block(0)) 392.66/193.66 down(app(app(y6332, nil), 0)) -> app_flat(block(app(y6332, nil)), down(0)) 392.66/193.66 down(app(app(y6335, fresh_constant), 0)) -> app_flat(down(app(y6335, fresh_constant)), block(0)) 392.66/193.66 down(app(app(y6335, fresh_constant), 0)) -> app_flat(block(app(y6335, fresh_constant)), down(0)) 392.66/193.66 down(app(app(y6349, app(y6350, y6351)), hd)) -> app_flat(down(app(y6349, app(y6350, y6351))), block(hd)) 392.66/193.66 down(app(app(y6349, app(y6350, y6351)), hd)) -> app_flat(block(app(y6349, app(y6350, y6351))), down(hd)) 392.66/193.66 down(app(app(y6371, hd), hd)) -> app_flat(down(app(y6371, hd)), block(hd)) 392.66/193.66 down(app(app(y6371, hd), hd)) -> app_flat(block(app(y6371, hd)), down(hd)) 392.66/193.66 down(app(app(y6374, map), hd)) -> app_flat(down(app(y6374, map)), block(hd)) 392.66/193.66 down(app(app(y6374, map), hd)) -> app_flat(block(app(y6374, map)), down(hd)) 392.66/193.66 down(app(app(y6377, cons), hd)) -> app_flat(down(app(y6377, cons)), block(hd)) 392.66/193.66 down(app(app(y6377, cons), hd)) -> app_flat(block(app(y6377, cons)), down(hd)) 392.66/193.66 down(app(app(y6380, nil), hd)) -> app_flat(down(app(y6380, nil)), block(hd)) 392.66/193.66 down(app(app(y6380, nil), hd)) -> app_flat(block(app(y6380, nil)), down(hd)) 392.66/193.66 down(app(app(y6383, fresh_constant), hd)) -> app_flat(down(app(y6383, fresh_constant)), block(hd)) 392.66/193.66 down(app(app(y6383, fresh_constant), hd)) -> app_flat(block(app(y6383, fresh_constant)), down(hd)) 392.66/193.66 down(app(app(y6397, app(y6398, y6399)), map)) -> app_flat(down(app(y6397, app(y6398, y6399))), block(map)) 392.66/193.66 down(app(app(y6397, app(y6398, y6399)), map)) -> app_flat(block(app(y6397, app(y6398, y6399))), down(map)) 392.66/193.66 down(app(app(y6419, hd), map)) -> app_flat(down(app(y6419, hd)), block(map)) 392.66/193.66 down(app(app(y6419, hd), map)) -> app_flat(block(app(y6419, hd)), down(map)) 392.66/193.66 down(app(app(y6422, map), map)) -> app_flat(down(app(y6422, map)), block(map)) 392.66/193.66 down(app(app(y6422, map), map)) -> app_flat(block(app(y6422, map)), down(map)) 392.66/193.66 down(app(app(y6425, cons), map)) -> app_flat(down(app(y6425, cons)), block(map)) 392.66/193.66 down(app(app(y6425, cons), map)) -> app_flat(block(app(y6425, cons)), down(map)) 392.66/193.66 down(app(app(y6428, nil), map)) -> app_flat(down(app(y6428, nil)), block(map)) 392.66/193.66 down(app(app(y6428, nil), map)) -> app_flat(block(app(y6428, nil)), down(map)) 392.66/193.66 down(app(app(y6431, fresh_constant), map)) -> app_flat(down(app(y6431, fresh_constant)), block(map)) 392.66/193.66 down(app(app(y6431, fresh_constant), map)) -> app_flat(block(app(y6431, fresh_constant)), down(map)) 392.66/193.66 down(app(app(y6445, app(y6446, y6447)), cons)) -> app_flat(down(app(y6445, app(y6446, y6447))), block(cons)) 392.66/193.66 down(app(app(y6445, app(y6446, y6447)), cons)) -> app_flat(block(app(y6445, app(y6446, y6447))), down(cons)) 392.66/193.66 down(app(app(y6467, hd), cons)) -> app_flat(down(app(y6467, hd)), block(cons)) 392.66/193.66 down(app(app(y6467, hd), cons)) -> app_flat(block(app(y6467, hd)), down(cons)) 392.66/193.66 down(app(app(y6470, map), cons)) -> app_flat(down(app(y6470, map)), block(cons)) 392.66/193.66 down(app(app(y6470, map), cons)) -> app_flat(block(app(y6470, map)), down(cons)) 392.66/193.66 down(app(app(y6473, cons), cons)) -> app_flat(down(app(y6473, cons)), block(cons)) 392.66/193.66 down(app(app(y6473, cons), cons)) -> app_flat(block(app(y6473, cons)), down(cons)) 392.66/193.66 down(app(app(y6476, nil), cons)) -> app_flat(down(app(y6476, nil)), block(cons)) 392.66/193.66 down(app(app(y6476, nil), cons)) -> app_flat(block(app(y6476, nil)), down(cons)) 392.66/193.66 down(app(app(y6479, fresh_constant), cons)) -> app_flat(down(app(y6479, fresh_constant)), block(cons)) 392.66/193.66 down(app(app(y6479, fresh_constant), cons)) -> app_flat(block(app(y6479, fresh_constant)), down(cons)) 392.66/193.66 down(app(app(y6541, app(y6542, y6543)), fresh_constant)) -> app_flat(down(app(y6541, app(y6542, y6543))), block(fresh_constant)) 392.66/193.66 down(app(app(y6541, app(y6542, y6543)), fresh_constant)) -> app_flat(block(app(y6541, app(y6542, y6543))), down(fresh_constant)) 392.66/193.66 down(app(app(y6563, hd), fresh_constant)) -> app_flat(down(app(y6563, hd)), block(fresh_constant)) 392.66/193.66 down(app(app(y6563, hd), fresh_constant)) -> app_flat(block(app(y6563, hd)), down(fresh_constant)) 392.66/193.66 down(app(app(y6566, map), fresh_constant)) -> app_flat(down(app(y6566, map)), block(fresh_constant)) 392.66/193.66 down(app(app(y6566, map), fresh_constant)) -> app_flat(block(app(y6566, map)), down(fresh_constant)) 392.66/193.66 down(app(app(y6569, cons), fresh_constant)) -> app_flat(down(app(y6569, cons)), block(fresh_constant)) 392.66/193.66 down(app(app(y6569, cons), fresh_constant)) -> app_flat(block(app(y6569, cons)), down(fresh_constant)) 392.66/193.66 down(app(app(y6572, nil), fresh_constant)) -> app_flat(down(app(y6572, nil)), block(fresh_constant)) 392.66/193.66 down(app(app(y6572, nil), fresh_constant)) -> app_flat(block(app(y6572, nil)), down(fresh_constant)) 392.66/193.66 down(app(app(y6575, fresh_constant), fresh_constant)) -> app_flat(down(app(y6575, fresh_constant)), block(fresh_constant)) 392.66/193.66 down(app(app(y6575, fresh_constant), fresh_constant)) -> app_flat(block(app(y6575, fresh_constant)), down(fresh_constant)) 392.66/193.66 down(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> app_flat(down(app(y357, app(y20338, y20339))), block(app(app(app(y20340, y20341), y20342), y362))) 392.66/193.66 down(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> app_flat(block(app(y357, app(y20338, y20339))), down(app(app(app(y20340, y20341), y20342), y362))) 392.66/193.66 down(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> app_flat(down(app(y357, app(y20578, y20579))), block(app(app(0, y20580), y362))) 392.66/193.66 down(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> app_flat(block(app(y357, app(y20578, y20579))), down(app(app(0, y20580), y362))) 392.66/193.66 down(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> app_flat(down(app(y357, app(y20690, y20691))), block(app(app(hd, y20692), y362))) 392.66/193.66 down(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> app_flat(block(app(y357, app(y20690, y20691))), down(app(app(hd, y20692), y362))) 392.66/193.66 down(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> app_flat(down(app(y357, app(y20802, y20803))), block(app(app(map, y20804), y362))) 392.66/193.66 down(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> app_flat(block(app(y357, app(y20802, y20803))), down(app(app(map, y20804), y362))) 392.66/193.66 down(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> app_flat(down(app(y357, app(y21026, y21027))), block(app(app(nil, y21028), y362))) 392.66/193.66 down(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> app_flat(block(app(y357, app(y21026, y21027))), down(app(app(nil, y21028), y362))) 392.66/193.66 down(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> app_flat(down(app(y357, app(y21138, y21139))), block(app(app(fresh_constant, y21140), y362))) 392.66/193.66 down(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> app_flat(block(app(y357, app(y21138, y21139))), down(app(app(fresh_constant, y21140), y362))) 392.66/193.66 down(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> app_flat(down(app(y427, hd)), block(app(app(app(y32452, y32453), y32454), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> app_flat(block(app(y427, hd)), down(app(app(app(y32452, y32453), y32454), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(0, y32455), y430))) -> app_flat(down(app(y427, hd)), block(app(app(0, y32455), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(0, y32455), y430))) -> app_flat(block(app(y427, hd)), down(app(app(0, y32455), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(hd, y32456), y430))) -> app_flat(down(app(y427, hd)), block(app(app(hd, y32456), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(hd, y32456), y430))) -> app_flat(block(app(y427, hd)), down(app(app(hd, y32456), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(map, y32457), y430))) -> app_flat(down(app(y427, hd)), block(app(app(map, y32457), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(map, y32457), y430))) -> app_flat(block(app(y427, hd)), down(app(app(map, y32457), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(nil, y32459), y430))) -> app_flat(down(app(y427, hd)), block(app(app(nil, y32459), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(nil, y32459), y430))) -> app_flat(block(app(y427, hd)), down(app(app(nil, y32459), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(fresh_constant, y32460), y430))) -> app_flat(down(app(y427, hd)), block(app(app(fresh_constant, y32460), y430))) 392.66/193.66 down(app(app(y427, hd), app(app(fresh_constant, y32460), y430))) -> app_flat(block(app(y427, hd)), down(app(app(fresh_constant, y32460), y430))) 392.66/193.66 down(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> app_flat(down(app(y454, map)), block(app(app(app(y32548, y32549), y32550), y457))) 392.66/193.66 down(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> app_flat(block(app(y454, map)), down(app(app(app(y32548, y32549), y32550), y457))) 392.66/193.66 down(app(app(y454, map), app(app(0, y32551), y457))) -> app_flat(down(app(y454, map)), block(app(app(0, y32551), y457))) 392.66/193.66 down(app(app(y454, map), app(app(0, y32551), y457))) -> app_flat(block(app(y454, map)), down(app(app(0, y32551), y457))) 392.66/193.66 down(app(app(y454, map), app(app(hd, y32552), y457))) -> app_flat(down(app(y454, map)), block(app(app(hd, y32552), y457))) 392.66/193.66 down(app(app(y454, map), app(app(hd, y32552), y457))) -> app_flat(block(app(y454, map)), down(app(app(hd, y32552), y457))) 392.66/193.66 down(app(app(y454, map), app(app(map, y32553), y457))) -> app_flat(down(app(y454, map)), block(app(app(map, y32553), y457))) 392.66/193.66 down(app(app(y454, map), app(app(map, y32553), y457))) -> app_flat(block(app(y454, map)), down(app(app(map, y32553), y457))) 392.66/193.66 down(app(app(y454, map), app(app(nil, y32555), y457))) -> app_flat(down(app(y454, map)), block(app(app(nil, y32555), y457))) 392.66/193.66 down(app(app(y454, map), app(app(nil, y32555), y457))) -> app_flat(block(app(y454, map)), down(app(app(nil, y32555), y457))) 392.66/193.66 down(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> app_flat(down(app(y454, map)), block(app(app(fresh_constant, y32556), y457))) 392.66/193.66 down(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> app_flat(block(app(y454, map)), down(app(app(fresh_constant, y32556), y457))) 392.66/193.66 down(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> app_flat(down(app(y481, cons)), block(app(app(app(y32644, y32645), y32646), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> app_flat(block(app(y481, cons)), down(app(app(app(y32644, y32645), y32646), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(0, y32647), y484))) -> app_flat(down(app(y481, cons)), block(app(app(0, y32647), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(0, y32647), y484))) -> app_flat(block(app(y481, cons)), down(app(app(0, y32647), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(hd, y32648), y484))) -> app_flat(down(app(y481, cons)), block(app(app(hd, y32648), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(hd, y32648), y484))) -> app_flat(block(app(y481, cons)), down(app(app(hd, y32648), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(map, y32649), y484))) -> app_flat(down(app(y481, cons)), block(app(app(map, y32649), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(map, y32649), y484))) -> app_flat(block(app(y481, cons)), down(app(app(map, y32649), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(nil, y32651), y484))) -> app_flat(down(app(y481, cons)), block(app(app(nil, y32651), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(nil, y32651), y484))) -> app_flat(block(app(y481, cons)), down(app(app(nil, y32651), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> app_flat(down(app(y481, cons)), block(app(app(fresh_constant, y32652), y484))) 392.66/193.66 down(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> app_flat(block(app(y481, cons)), down(app(app(fresh_constant, y32652), y484))) 392.66/193.66 down(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> app_flat(down(app(y508, nil)), block(app(app(app(y32740, y32741), y32742), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> app_flat(block(app(y508, nil)), down(app(app(app(y32740, y32741), y32742), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(0, y32743), y511))) -> app_flat(down(app(y508, nil)), block(app(app(0, y32743), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(0, y32743), y511))) -> app_flat(block(app(y508, nil)), down(app(app(0, y32743), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(hd, y32744), y511))) -> app_flat(down(app(y508, nil)), block(app(app(hd, y32744), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(hd, y32744), y511))) -> app_flat(block(app(y508, nil)), down(app(app(hd, y32744), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(map, y32745), y511))) -> app_flat(down(app(y508, nil)), block(app(app(map, y32745), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(map, y32745), y511))) -> app_flat(block(app(y508, nil)), down(app(app(map, y32745), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(nil, y32747), y511))) -> app_flat(down(app(y508, nil)), block(app(app(nil, y32747), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(nil, y32747), y511))) -> app_flat(block(app(y508, nil)), down(app(app(nil, y32747), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(fresh_constant, y32748), y511))) -> app_flat(down(app(y508, nil)), block(app(app(fresh_constant, y32748), y511))) 392.66/193.66 down(app(app(y508, nil), app(app(fresh_constant, y32748), y511))) -> app_flat(block(app(y508, nil)), down(app(app(fresh_constant, y32748), y511))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(app(y32836, y32837), y32838), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(app(y32836, y32837), y32838), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(0, y32839), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(0, y32839), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(0, y32839), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(0, y32839), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(hd, y32840), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(hd, y32840), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(hd, y32840), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(hd, y32840), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(map, y32841), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(map, y32841), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(nil, y32843), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(nil, y32843), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(nil, y32843), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(nil, y32843), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(fresh_constant, y32844), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(fresh_constant, y32844), y538))) 392.66/193.66 down(app(app(y535, fresh_constant), app(app(fresh_constant, y32844), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(fresh_constant, y32844), y538))) 392.66/193.66 app_flat(up(x_1), block(x_2)) -> up(app(x_1, x_2)) 392.66/193.66 app_flat(block(x_1), up(x_2)) -> up(app(x_1, x_2)) 392.66/193.66 392.66/193.66 Q is empty. 392.66/193.66 We have to consider all minimal (P,Q,R)-chains. 392.66/193.66 ---------------------------------------- 392.66/193.66 392.66/193.66 (50) UsableRulesProof (EQUIVALENT) 392.66/193.66 We can use the usable rules and reduction pair processor [LPAR04] with the Ce-compatible extension of the polynomial order that maps every function symbol to the sum of its arguments. Then, we can delete all non-usable rules [FROCOS05] from R. 392.66/193.66 ---------------------------------------- 392.66/193.66 392.66/193.66 (51) 392.66/193.66 Obligation: 392.66/193.66 Q DP problem: 392.66/193.66 The TRS P consists of the following rules: 392.66/193.66 392.66/193.66 DOWN(app(hd, y8)) -> DOWN(y8) 392.66/193.66 DOWN(app(0, y7)) -> DOWN(y7) 392.66/193.66 DOWN(app(map, y9)) -> DOWN(y9) 392.66/193.66 DOWN(app(cons, y10)) -> DOWN(y10) 392.66/193.66 DOWN(app(nil, y11)) -> DOWN(y11) 392.66/193.66 DOWN(app(fresh_constant, y12)) -> DOWN(y12) 392.66/193.66 DOWN(app(app(app(y64, y65), app(y66, y67)), y6)) -> DOWN(app(app(y64, y65), app(y66, y67))) 392.66/193.66 DOWN(app(app(app(y64, y65), app(y66, y67)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, app(y68, y69)), y6)) -> DOWN(app(0, app(y68, y69))) 392.66/193.66 DOWN(app(app(0, app(y68, y69)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(hd, app(y70, y71)), y6)) -> DOWN(app(hd, app(y70, y71))) 392.66/193.66 DOWN(app(app(hd, app(y70, y71)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(cons, app(y74, y75)), y6)) -> DOWN(app(cons, app(y74, y75))) 392.66/193.66 DOWN(app(app(cons, app(y74, y75)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, app(y76, y77)), y6)) -> DOWN(app(nil, app(y76, y77))) 392.66/193.66 DOWN(app(app(nil, app(y76, y77)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(fresh_constant, app(y78, y79)), y6)) -> DOWN(app(fresh_constant, app(y78, y79))) 392.66/193.66 DOWN(app(app(fresh_constant, app(y78, y79)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(app(y84, y85), hd), y6)) -> DOWN(app(app(y84, y85), hd)) 392.66/193.66 DOWN(app(app(app(y84, y85), hd), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, hd), y6)) -> DOWN(app(0, hd)) 392.66/193.66 DOWN(app(app(0, hd), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(hd, hd), y6)) -> DOWN(app(hd, hd)) 392.66/193.66 DOWN(app(app(hd, hd), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(cons, hd), y6)) -> DOWN(app(cons, hd)) 392.66/193.66 DOWN(app(app(cons, hd), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, hd), y6)) -> DOWN(app(nil, hd)) 392.66/193.66 DOWN(app(app(nil, hd), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(fresh_constant, hd), y6)) -> DOWN(app(fresh_constant, hd)) 392.66/193.66 DOWN(app(app(fresh_constant, hd), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(app(y87, y88), map), y6)) -> DOWN(app(app(y87, y88), map)) 392.66/193.66 DOWN(app(app(app(y87, y88), map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, map), y6)) -> DOWN(app(0, map)) 392.66/193.66 DOWN(app(app(0, map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(hd, map), y6)) -> DOWN(app(hd, map)) 392.66/193.66 DOWN(app(app(hd, map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(cons, map), y6)) -> DOWN(app(cons, map)) 392.66/193.66 DOWN(app(app(cons, map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, map), y6)) -> DOWN(app(nil, map)) 392.66/193.66 DOWN(app(app(nil, map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(fresh_constant, map), y6)) -> DOWN(app(fresh_constant, map)) 392.66/193.66 DOWN(app(app(fresh_constant, map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(app(y90, y91), cons), y6)) -> DOWN(app(app(y90, y91), cons)) 392.66/193.66 DOWN(app(app(app(y90, y91), cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, cons), y6)) -> DOWN(app(0, cons)) 392.66/193.66 DOWN(app(app(0, cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(hd, cons), y6)) -> DOWN(app(hd, cons)) 392.66/193.66 DOWN(app(app(hd, cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(cons, cons), y6)) -> DOWN(app(cons, cons)) 392.66/193.66 DOWN(app(app(cons, cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, cons), y6)) -> DOWN(app(nil, cons)) 392.66/193.66 DOWN(app(app(nil, cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(fresh_constant, cons), y6)) -> DOWN(app(fresh_constant, cons)) 392.66/193.66 DOWN(app(app(fresh_constant, cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(app(y93, y94), nil), y6)) -> DOWN(app(app(y93, y94), nil)) 392.66/193.66 DOWN(app(app(app(y93, y94), nil), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, nil), y6)) -> DOWN(app(0, nil)) 392.66/193.66 DOWN(app(app(0, nil), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(hd, nil), y6)) -> DOWN(app(hd, nil)) 392.66/193.66 DOWN(app(app(hd, nil), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(cons, nil), y6)) -> DOWN(app(cons, nil)) 392.66/193.66 DOWN(app(app(cons, nil), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, nil), y6)) -> DOWN(app(nil, nil)) 392.66/193.66 DOWN(app(app(nil, nil), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(fresh_constant, nil), y6)) -> DOWN(app(fresh_constant, nil)) 392.66/193.66 DOWN(app(app(fresh_constant, nil), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(app(y96, y97), fresh_constant), y6)) -> DOWN(app(app(y96, y97), fresh_constant)) 392.66/193.66 DOWN(app(app(app(y96, y97), fresh_constant), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, fresh_constant), y6)) -> DOWN(app(0, fresh_constant)) 392.66/193.66 DOWN(app(app(0, fresh_constant), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(hd, fresh_constant), y6)) -> DOWN(app(hd, fresh_constant)) 392.66/193.66 DOWN(app(app(hd, fresh_constant), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(cons, fresh_constant), y6)) -> DOWN(app(cons, fresh_constant)) 392.66/193.66 DOWN(app(app(cons, fresh_constant), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, fresh_constant), y6)) -> DOWN(app(nil, fresh_constant)) 392.66/193.66 DOWN(app(app(nil, fresh_constant), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(fresh_constant, fresh_constant), y6)) -> DOWN(app(fresh_constant, fresh_constant)) 392.66/193.66 DOWN(app(app(fresh_constant, fresh_constant), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(y581, app(y582, y583)), app(0, y584))) -> DOWN(app(y581, app(y582, y583))) 392.66/193.66 DOWN(app(app(y581, app(y582, y583)), app(0, y584))) -> DOWN(app(0, y584)) 392.66/193.66 DOWN(app(app(y619, hd), app(0, y620))) -> DOWN(app(y619, hd)) 392.66/193.66 DOWN(app(app(y6349, app(y6350, y6351)), hd)) -> DOWN(app(y6349, app(y6350, y6351))) 392.66/193.66 DOWN(app(app(y619, hd), app(0, y620))) -> DOWN(app(0, y620)) 392.66/193.66 DOWN(app(app(y630, map), app(0, y631))) -> DOWN(app(y630, map)) 392.66/193.66 DOWN(app(app(y6397, app(y6398, y6399)), map)) -> DOWN(app(y6397, app(y6398, y6399))) 392.66/193.66 DOWN(app(app(y630, map), app(0, y631))) -> DOWN(app(0, y631)) 392.66/193.66 DOWN(app(app(y641, cons), app(0, y642))) -> DOWN(app(y641, cons)) 392.66/193.66 DOWN(app(app(y6445, app(y6446, y6447)), cons)) -> DOWN(app(y6445, app(y6446, y6447))) 392.66/193.66 DOWN(app(app(y641, cons), app(0, y642))) -> DOWN(app(0, y642)) 392.66/193.66 DOWN(app(app(y652, nil), app(0, y653))) -> DOWN(app(y652, nil)) 392.66/193.66 DOWN(app(app(y652, nil), app(0, y653))) -> DOWN(app(0, y653)) 392.66/193.66 DOWN(app(app(y663, fresh_constant), app(0, y664))) -> DOWN(app(y663, fresh_constant)) 392.66/193.66 DOWN(app(app(y6541, app(y6542, y6543)), fresh_constant)) -> DOWN(app(y6541, app(y6542, y6543))) 392.66/193.66 DOWN(app(app(y663, fresh_constant), app(0, y664))) -> DOWN(app(0, y664)) 392.66/193.66 DOWN(app(app(y693, app(y694, y695)), app(hd, y696))) -> DOWN(app(y693, app(y694, y695))) 392.66/193.66 DOWN(app(app(y693, app(y694, y695)), app(hd, y696))) -> DOWN(app(hd, y696)) 392.66/193.66 DOWN(app(app(y731, hd), app(hd, y732))) -> DOWN(app(y731, hd)) 392.66/193.66 DOWN(app(app(y6371, hd), hd)) -> DOWN(app(y6371, hd)) 392.66/193.66 DOWN(app(app(y6374, map), hd)) -> DOWN(app(y6374, map)) 392.66/193.66 DOWN(app(app(y6419, hd), map)) -> DOWN(app(y6419, hd)) 392.66/193.66 DOWN(app(app(y6377, cons), hd)) -> DOWN(app(y6377, cons)) 392.66/193.66 DOWN(app(app(y6467, hd), cons)) -> DOWN(app(y6467, hd)) 392.66/193.66 DOWN(app(app(y6380, nil), hd)) -> DOWN(app(y6380, nil)) 392.66/193.66 DOWN(app(app(y6383, fresh_constant), hd)) -> DOWN(app(y6383, fresh_constant)) 392.66/193.66 DOWN(app(app(y6563, hd), fresh_constant)) -> DOWN(app(y6563, hd)) 392.66/193.66 DOWN(app(app(y6566, map), fresh_constant)) -> DOWN(app(y6566, map)) 392.66/193.66 DOWN(app(app(y6422, map), map)) -> DOWN(app(y6422, map)) 392.66/193.66 DOWN(app(app(y6425, cons), map)) -> DOWN(app(y6425, cons)) 392.66/193.66 DOWN(app(app(y6470, map), cons)) -> DOWN(app(y6470, map)) 392.66/193.66 DOWN(app(app(y6428, nil), map)) -> DOWN(app(y6428, nil)) 392.66/193.66 DOWN(app(app(y6431, fresh_constant), map)) -> DOWN(app(y6431, fresh_constant)) 392.66/193.66 DOWN(app(app(y6569, cons), fresh_constant)) -> DOWN(app(y6569, cons)) 392.66/193.66 DOWN(app(app(y6473, cons), cons)) -> DOWN(app(y6473, cons)) 392.66/193.66 DOWN(app(app(y6476, nil), cons)) -> DOWN(app(y6476, nil)) 392.66/193.66 DOWN(app(app(y6479, fresh_constant), cons)) -> DOWN(app(y6479, fresh_constant)) 392.66/193.66 DOWN(app(app(y6572, nil), fresh_constant)) -> DOWN(app(y6572, nil)) 392.66/193.66 DOWN(app(app(y6575, fresh_constant), fresh_constant)) -> DOWN(app(y6575, fresh_constant)) 392.66/193.66 DOWN(app(app(y731, hd), app(hd, y732))) -> DOWN(app(hd, y732)) 392.66/193.66 DOWN(app(app(y742, map), app(hd, y743))) -> DOWN(app(y742, map)) 392.66/193.66 DOWN(app(app(y742, map), app(hd, y743))) -> DOWN(app(hd, y743)) 392.66/193.66 DOWN(app(app(y753, cons), app(hd, y754))) -> DOWN(app(y753, cons)) 392.66/193.66 DOWN(app(app(y753, cons), app(hd, y754))) -> DOWN(app(hd, y754)) 392.66/193.66 DOWN(app(app(y764, nil), app(hd, y765))) -> DOWN(app(y764, nil)) 392.66/193.66 DOWN(app(app(y764, nil), app(hd, y765))) -> DOWN(app(hd, y765)) 392.66/193.66 DOWN(app(app(y775, fresh_constant), app(hd, y776))) -> DOWN(app(y775, fresh_constant)) 392.66/193.66 DOWN(app(app(y775, fresh_constant), app(hd, y776))) -> DOWN(app(hd, y776)) 392.66/193.66 DOWN(app(app(y805, app(y806, y807)), app(map, y808))) -> DOWN(app(y805, app(y806, y807))) 392.66/193.66 DOWN(app(app(y805, app(y806, y807)), app(map, y808))) -> DOWN(app(map, y808)) 392.66/193.66 DOWN(app(app(y843, hd), app(map, y844))) -> DOWN(app(y843, hd)) 392.66/193.66 DOWN(app(app(y843, hd), app(map, y844))) -> DOWN(app(map, y844)) 392.66/193.66 DOWN(app(app(y854, map), app(map, y855))) -> DOWN(app(y854, map)) 392.66/193.66 DOWN(app(app(y854, map), app(map, y855))) -> DOWN(app(map, y855)) 392.66/193.66 DOWN(app(app(y865, cons), app(map, y866))) -> DOWN(app(y865, cons)) 392.66/193.66 DOWN(app(app(y865, cons), app(map, y866))) -> DOWN(app(map, y866)) 392.66/193.66 DOWN(app(app(y876, nil), app(map, y877))) -> DOWN(app(y876, nil)) 392.66/193.66 DOWN(app(app(y876, nil), app(map, y877))) -> DOWN(app(map, y877)) 392.66/193.66 DOWN(app(app(y887, fresh_constant), app(map, y888))) -> DOWN(app(y887, fresh_constant)) 392.66/193.66 DOWN(app(app(y887, fresh_constant), app(map, y888))) -> DOWN(app(map, y888)) 392.66/193.66 DOWN(app(app(y917, app(y918, y919)), app(cons, y920))) -> DOWN(app(y917, app(y918, y919))) 392.66/193.66 DOWN(app(app(y917, app(y918, y919)), app(cons, y920))) -> DOWN(app(cons, y920)) 392.66/193.66 DOWN(app(app(y955, hd), app(cons, y956))) -> DOWN(app(y955, hd)) 392.66/193.66 DOWN(app(app(y955, hd), app(cons, y956))) -> DOWN(app(cons, y956)) 392.66/193.66 DOWN(app(app(y966, map), app(cons, y967))) -> DOWN(app(y966, map)) 392.66/193.66 DOWN(app(app(y966, map), app(cons, y967))) -> DOWN(app(cons, y967)) 392.66/193.66 DOWN(app(app(y977, cons), app(cons, y978))) -> DOWN(app(y977, cons)) 392.66/193.66 DOWN(app(app(y977, cons), app(cons, y978))) -> DOWN(app(cons, y978)) 392.66/193.66 DOWN(app(app(y988, nil), app(cons, y989))) -> DOWN(app(y988, nil)) 392.66/193.66 DOWN(app(app(y988, nil), app(cons, y989))) -> DOWN(app(cons, y989)) 392.66/193.66 DOWN(app(app(y999, fresh_constant), app(cons, y1000))) -> DOWN(app(y999, fresh_constant)) 392.66/193.66 DOWN(app(app(y999, fresh_constant), app(cons, y1000))) -> DOWN(app(cons, y1000)) 392.66/193.66 DOWN(app(app(y1029, app(y1030, y1031)), app(nil, y1032))) -> DOWN(app(y1029, app(y1030, y1031))) 392.66/193.66 DOWN(app(app(y1029, app(y1030, y1031)), app(nil, y1032))) -> DOWN(app(nil, y1032)) 392.66/193.66 DOWN(app(app(y1067, hd), app(nil, y1068))) -> DOWN(app(y1067, hd)) 392.66/193.66 DOWN(app(app(y1067, hd), app(nil, y1068))) -> DOWN(app(nil, y1068)) 392.66/193.66 DOWN(app(app(y1078, map), app(nil, y1079))) -> DOWN(app(y1078, map)) 392.66/193.66 DOWN(app(app(y1078, map), app(nil, y1079))) -> DOWN(app(nil, y1079)) 392.66/193.66 DOWN(app(app(y1089, cons), app(nil, y1090))) -> DOWN(app(y1089, cons)) 392.66/193.66 DOWN(app(app(y1089, cons), app(nil, y1090))) -> DOWN(app(nil, y1090)) 392.66/193.66 DOWN(app(app(y1100, nil), app(nil, y1101))) -> DOWN(app(y1100, nil)) 392.66/193.66 DOWN(app(app(y1100, nil), app(nil, y1101))) -> DOWN(app(nil, y1101)) 392.66/193.66 DOWN(app(app(y1111, fresh_constant), app(nil, y1112))) -> DOWN(app(y1111, fresh_constant)) 392.66/193.66 DOWN(app(app(y1111, fresh_constant), app(nil, y1112))) -> DOWN(app(nil, y1112)) 392.66/193.66 DOWN(app(app(y1141, app(y1142, y1143)), app(fresh_constant, y1144))) -> DOWN(app(y1141, app(y1142, y1143))) 392.66/193.66 DOWN(app(app(y1141, app(y1142, y1143)), app(fresh_constant, y1144))) -> DOWN(app(fresh_constant, y1144)) 392.66/193.66 DOWN(app(app(y1179, hd), app(fresh_constant, y1180))) -> DOWN(app(y1179, hd)) 392.66/193.66 DOWN(app(app(y1179, hd), app(fresh_constant, y1180))) -> DOWN(app(fresh_constant, y1180)) 392.66/193.66 DOWN(app(app(y1190, map), app(fresh_constant, y1191))) -> DOWN(app(y1190, map)) 392.66/193.66 DOWN(app(app(y1190, map), app(fresh_constant, y1191))) -> DOWN(app(fresh_constant, y1191)) 392.66/193.66 DOWN(app(app(y1201, cons), app(fresh_constant, y1202))) -> DOWN(app(y1201, cons)) 392.66/193.66 DOWN(app(app(y1201, cons), app(fresh_constant, y1202))) -> DOWN(app(fresh_constant, y1202)) 392.66/193.66 DOWN(app(app(y1212, nil), app(fresh_constant, y1213))) -> DOWN(app(y1212, nil)) 392.66/193.66 DOWN(app(app(y1212, nil), app(fresh_constant, y1213))) -> DOWN(app(fresh_constant, y1213)) 392.66/193.66 DOWN(app(app(y1223, fresh_constant), app(fresh_constant, y1224))) -> DOWN(app(y1223, fresh_constant)) 392.66/193.66 DOWN(app(app(y1223, fresh_constant), app(fresh_constant, y1224))) -> DOWN(app(fresh_constant, y1224)) 392.66/193.66 DOWN(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> DOWN(app(y357, app(y20338, y20339))) 392.66/193.66 DOWN(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> DOWN(app(app(app(y20340, y20341), y20342), y362)) 392.66/193.66 DOWN(app(app(y6301, app(y6302, y6303)), 0)) -> DOWN(app(y6301, app(y6302, y6303))) 392.66/193.66 DOWN(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> DOWN(app(y357, app(y20578, y20579))) 392.66/193.66 DOWN(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> DOWN(app(app(0, y20580), y362)) 392.66/193.66 DOWN(app(app(y6323, hd), 0)) -> DOWN(app(y6323, hd)) 392.66/193.66 DOWN(app(app(y6326, map), 0)) -> DOWN(app(y6326, map)) 392.66/193.66 DOWN(app(app(y6329, cons), 0)) -> DOWN(app(y6329, cons)) 392.66/193.66 DOWN(app(app(y6332, nil), 0)) -> DOWN(app(y6332, nil)) 392.66/193.66 DOWN(app(app(y6335, fresh_constant), 0)) -> DOWN(app(y6335, fresh_constant)) 392.66/193.66 DOWN(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> DOWN(app(y357, app(y20690, y20691))) 392.66/193.66 DOWN(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> DOWN(app(app(hd, y20692), y362)) 392.66/193.66 DOWN(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> DOWN(app(y357, app(y20802, y20803))) 392.66/193.66 DOWN(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> DOWN(app(app(map, y20804), y362)) 392.66/193.66 DOWN(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> DOWN(app(y357, app(y21026, y21027))) 392.66/193.66 DOWN(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> DOWN(app(app(nil, y21028), y362)) 392.66/193.66 DOWN(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> DOWN(app(y357, app(y21138, y21139))) 392.66/193.66 DOWN(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> DOWN(app(app(fresh_constant, y21140), y362)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> DOWN(app(app(app(y32452, y32453), y32454), y430)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(0, y32455), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(0, y32455), y430))) -> DOWN(app(app(0, y32455), y430)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(hd, y32456), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(hd, y32456), y430))) -> DOWN(app(app(hd, y32456), y430)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(map, y32457), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(map, y32457), y430))) -> DOWN(app(app(map, y32457), y430)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(nil, y32459), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(nil, y32459), y430))) -> DOWN(app(app(nil, y32459), y430)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(fresh_constant, y32460), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(fresh_constant, y32460), y430))) -> DOWN(app(app(fresh_constant, y32460), y430)) 392.66/193.66 DOWN(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> DOWN(app(app(app(y32548, y32549), y32550), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(0, y32551), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(0, y32551), y457))) -> DOWN(app(app(0, y32551), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(hd, y32552), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(hd, y32552), y457))) -> DOWN(app(app(hd, y32552), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(map, y32553), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(map, y32553), y457))) -> DOWN(app(app(map, y32553), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(nil, y32555), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(nil, y32555), y457))) -> DOWN(app(app(nil, y32555), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> DOWN(app(app(fresh_constant, y32556), y457)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> DOWN(app(app(app(y32644, y32645), y32646), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(0, y32647), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(0, y32647), y484))) -> DOWN(app(app(0, y32647), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(hd, y32648), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(hd, y32648), y484))) -> DOWN(app(app(hd, y32648), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(map, y32649), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(map, y32649), y484))) -> DOWN(app(app(map, y32649), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(nil, y32651), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(nil, y32651), y484))) -> DOWN(app(app(nil, y32651), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> DOWN(app(app(fresh_constant, y32652), y484)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> DOWN(app(app(app(y32740, y32741), y32742), y511)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(0, y32743), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(0, y32743), y511))) -> DOWN(app(app(0, y32743), y511)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(hd, y32744), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(hd, y32744), y511))) -> DOWN(app(app(hd, y32744), y511)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(map, y32745), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(map, y32745), y511))) -> DOWN(app(app(map, y32745), y511)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(nil, y32747), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(nil, y32747), y511))) -> DOWN(app(app(nil, y32747), y511)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(fresh_constant, y32748), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(fresh_constant, y32748), y511))) -> DOWN(app(app(fresh_constant, y32748), y511)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> DOWN(app(app(app(y32836, y32837), y32838), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(0, y32839), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(0, y32839), y538))) -> DOWN(app(app(0, y32839), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(hd, y32840), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(hd, y32840), y538))) -> DOWN(app(app(hd, y32840), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> DOWN(app(app(map, y32841), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(nil, y32843), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(nil, y32843), y538))) -> DOWN(app(app(nil, y32843), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(fresh_constant, y32844), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(fresh_constant, y32844), y538))) -> DOWN(app(app(fresh_constant, y32844), y538)) 392.66/193.66 392.66/193.66 R is empty. 392.66/193.66 Q is empty. 392.66/193.66 We have to consider all minimal (P,Q,R)-chains. 392.66/193.66 ---------------------------------------- 392.66/193.66 392.66/193.66 (52) QDPOrderProof (EQUIVALENT) 392.66/193.66 We use the reduction pair processor [LPAR04,JAR06]. 392.66/193.66 392.66/193.66 392.66/193.66 The following pairs can be oriented strictly and are deleted. 392.66/193.66 392.66/193.66 DOWN(app(hd, y8)) -> DOWN(y8) 392.66/193.66 DOWN(app(0, y7)) -> DOWN(y7) 392.66/193.66 DOWN(app(nil, y11)) -> DOWN(y11) 392.66/193.66 DOWN(app(fresh_constant, y12)) -> DOWN(y12) 392.66/193.66 DOWN(app(app(0, app(y68, y69)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(hd, app(y70, y71)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, app(y76, y77)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(fresh_constant, app(y78, y79)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(app(y84, y85), hd), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, hd), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(hd, hd), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(cons, hd), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, hd), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(fresh_constant, hd), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(hd, map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(fresh_constant, map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(hd, cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(fresh_constant, cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(app(y93, y94), nil), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, nil), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(hd, nil), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(cons, nil), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, nil), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(fresh_constant, nil), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(app(y96, y97), fresh_constant), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, fresh_constant), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(hd, fresh_constant), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(cons, fresh_constant), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, fresh_constant), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(fresh_constant, fresh_constant), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(y581, app(y582, y583)), app(0, y584))) -> DOWN(app(y581, app(y582, y583))) 392.66/193.66 DOWN(app(app(y619, hd), app(0, y620))) -> DOWN(app(y619, hd)) 392.66/193.66 DOWN(app(app(y6349, app(y6350, y6351)), hd)) -> DOWN(app(y6349, app(y6350, y6351))) 392.66/193.66 DOWN(app(app(y619, hd), app(0, y620))) -> DOWN(app(0, y620)) 392.66/193.66 DOWN(app(app(y630, map), app(0, y631))) -> DOWN(app(y630, map)) 392.66/193.66 DOWN(app(app(y641, cons), app(0, y642))) -> DOWN(app(y641, cons)) 392.66/193.66 DOWN(app(app(y652, nil), app(0, y653))) -> DOWN(app(y652, nil)) 392.66/193.66 DOWN(app(app(y652, nil), app(0, y653))) -> DOWN(app(0, y653)) 392.66/193.66 DOWN(app(app(y663, fresh_constant), app(0, y664))) -> DOWN(app(y663, fresh_constant)) 392.66/193.66 DOWN(app(app(y6541, app(y6542, y6543)), fresh_constant)) -> DOWN(app(y6541, app(y6542, y6543))) 392.66/193.66 DOWN(app(app(y663, fresh_constant), app(0, y664))) -> DOWN(app(0, y664)) 392.66/193.66 DOWN(app(app(y693, app(y694, y695)), app(hd, y696))) -> DOWN(app(y693, app(y694, y695))) 392.66/193.66 DOWN(app(app(y731, hd), app(hd, y732))) -> DOWN(app(y731, hd)) 392.66/193.66 DOWN(app(app(y6371, hd), hd)) -> DOWN(app(y6371, hd)) 392.66/193.66 DOWN(app(app(y6374, map), hd)) -> DOWN(app(y6374, map)) 392.66/193.66 DOWN(app(app(y6377, cons), hd)) -> DOWN(app(y6377, cons)) 392.66/193.66 DOWN(app(app(y6380, nil), hd)) -> DOWN(app(y6380, nil)) 392.66/193.66 DOWN(app(app(y6383, fresh_constant), hd)) -> DOWN(app(y6383, fresh_constant)) 392.66/193.66 DOWN(app(app(y6563, hd), fresh_constant)) -> DOWN(app(y6563, hd)) 392.66/193.66 DOWN(app(app(y6566, map), fresh_constant)) -> DOWN(app(y6566, map)) 392.66/193.66 DOWN(app(app(y6569, cons), fresh_constant)) -> DOWN(app(y6569, cons)) 392.66/193.66 DOWN(app(app(y6572, nil), fresh_constant)) -> DOWN(app(y6572, nil)) 392.66/193.66 DOWN(app(app(y6575, fresh_constant), fresh_constant)) -> DOWN(app(y6575, fresh_constant)) 392.66/193.66 DOWN(app(app(y731, hd), app(hd, y732))) -> DOWN(app(hd, y732)) 392.66/193.66 DOWN(app(app(y742, map), app(hd, y743))) -> DOWN(app(y742, map)) 392.66/193.66 DOWN(app(app(y753, cons), app(hd, y754))) -> DOWN(app(y753, cons)) 392.66/193.66 DOWN(app(app(y764, nil), app(hd, y765))) -> DOWN(app(y764, nil)) 392.66/193.66 DOWN(app(app(y764, nil), app(hd, y765))) -> DOWN(app(hd, y765)) 392.66/193.66 DOWN(app(app(y775, fresh_constant), app(hd, y776))) -> DOWN(app(y775, fresh_constant)) 392.66/193.66 DOWN(app(app(y775, fresh_constant), app(hd, y776))) -> DOWN(app(hd, y776)) 392.66/193.66 DOWN(app(app(y843, hd), app(map, y844))) -> DOWN(app(map, y844)) 392.66/193.66 DOWN(app(app(y876, nil), app(map, y877))) -> DOWN(app(map, y877)) 392.66/193.66 DOWN(app(app(y887, fresh_constant), app(map, y888))) -> DOWN(app(map, y888)) 392.66/193.66 DOWN(app(app(y955, hd), app(cons, y956))) -> DOWN(app(cons, y956)) 392.66/193.66 DOWN(app(app(y988, nil), app(cons, y989))) -> DOWN(app(cons, y989)) 392.66/193.66 DOWN(app(app(y999, fresh_constant), app(cons, y1000))) -> DOWN(app(cons, y1000)) 392.66/193.66 DOWN(app(app(y1029, app(y1030, y1031)), app(nil, y1032))) -> DOWN(app(y1029, app(y1030, y1031))) 392.66/193.66 DOWN(app(app(y1067, hd), app(nil, y1068))) -> DOWN(app(y1067, hd)) 392.66/193.66 DOWN(app(app(y1067, hd), app(nil, y1068))) -> DOWN(app(nil, y1068)) 392.66/193.66 DOWN(app(app(y1078, map), app(nil, y1079))) -> DOWN(app(y1078, map)) 392.66/193.66 DOWN(app(app(y1089, cons), app(nil, y1090))) -> DOWN(app(y1089, cons)) 392.66/193.66 DOWN(app(app(y1100, nil), app(nil, y1101))) -> DOWN(app(y1100, nil)) 392.66/193.66 DOWN(app(app(y1100, nil), app(nil, y1101))) -> DOWN(app(nil, y1101)) 392.66/193.66 DOWN(app(app(y1111, fresh_constant), app(nil, y1112))) -> DOWN(app(y1111, fresh_constant)) 392.66/193.66 DOWN(app(app(y1111, fresh_constant), app(nil, y1112))) -> DOWN(app(nil, y1112)) 392.66/193.66 DOWN(app(app(y1141, app(y1142, y1143)), app(fresh_constant, y1144))) -> DOWN(app(y1141, app(y1142, y1143))) 392.66/193.66 DOWN(app(app(y1179, hd), app(fresh_constant, y1180))) -> DOWN(app(y1179, hd)) 392.66/193.66 DOWN(app(app(y1179, hd), app(fresh_constant, y1180))) -> DOWN(app(fresh_constant, y1180)) 392.66/193.66 DOWN(app(app(y1190, map), app(fresh_constant, y1191))) -> DOWN(app(y1190, map)) 392.66/193.66 DOWN(app(app(y1201, cons), app(fresh_constant, y1202))) -> DOWN(app(y1201, cons)) 392.66/193.66 DOWN(app(app(y1212, nil), app(fresh_constant, y1213))) -> DOWN(app(y1212, nil)) 392.66/193.66 DOWN(app(app(y1212, nil), app(fresh_constant, y1213))) -> DOWN(app(fresh_constant, y1213)) 392.66/193.66 DOWN(app(app(y1223, fresh_constant), app(fresh_constant, y1224))) -> DOWN(app(y1223, fresh_constant)) 392.66/193.66 DOWN(app(app(y1223, fresh_constant), app(fresh_constant, y1224))) -> DOWN(app(fresh_constant, y1224)) 392.66/193.66 DOWN(app(app(y6301, app(y6302, y6303)), 0)) -> DOWN(app(y6301, app(y6302, y6303))) 392.66/193.66 DOWN(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> DOWN(app(y357, app(y20578, y20579))) 392.66/193.66 DOWN(app(app(y6323, hd), 0)) -> DOWN(app(y6323, hd)) 392.66/193.66 DOWN(app(app(y6326, map), 0)) -> DOWN(app(y6326, map)) 392.66/193.66 DOWN(app(app(y6329, cons), 0)) -> DOWN(app(y6329, cons)) 392.66/193.66 DOWN(app(app(y6332, nil), 0)) -> DOWN(app(y6332, nil)) 392.66/193.66 DOWN(app(app(y6335, fresh_constant), 0)) -> DOWN(app(y6335, fresh_constant)) 392.66/193.66 DOWN(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> DOWN(app(y357, app(y20690, y20691))) 392.66/193.66 DOWN(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> DOWN(app(y357, app(y21026, y21027))) 392.66/193.66 DOWN(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> DOWN(app(y357, app(y21138, y21139))) 392.66/193.66 DOWN(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> DOWN(app(app(app(y32452, y32453), y32454), y430)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(0, y32455), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(0, y32455), y430))) -> DOWN(app(app(0, y32455), y430)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(hd, y32456), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(hd, y32456), y430))) -> DOWN(app(app(hd, y32456), y430)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(map, y32457), y430))) -> DOWN(app(app(map, y32457), y430)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(nil, y32459), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(nil, y32459), y430))) -> DOWN(app(app(nil, y32459), y430)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(fresh_constant, y32460), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(fresh_constant, y32460), y430))) -> DOWN(app(app(fresh_constant, y32460), y430)) 392.66/193.66 DOWN(app(app(y454, map), app(app(0, y32551), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(hd, y32552), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(nil, y32555), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(0, y32647), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(hd, y32648), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(nil, y32651), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> DOWN(app(app(app(y32740, y32741), y32742), y511)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(0, y32743), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(0, y32743), y511))) -> DOWN(app(app(0, y32743), y511)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(hd, y32744), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(hd, y32744), y511))) -> DOWN(app(app(hd, y32744), y511)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(map, y32745), y511))) -> DOWN(app(app(map, y32745), y511)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(nil, y32747), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(nil, y32747), y511))) -> DOWN(app(app(nil, y32747), y511)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(fresh_constant, y32748), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(fresh_constant, y32748), y511))) -> DOWN(app(app(fresh_constant, y32748), y511)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> DOWN(app(app(app(y32836, y32837), y32838), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(0, y32839), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(0, y32839), y538))) -> DOWN(app(app(0, y32839), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(hd, y32840), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(hd, y32840), y538))) -> DOWN(app(app(hd, y32840), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> DOWN(app(app(map, y32841), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(nil, y32843), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(nil, y32843), y538))) -> DOWN(app(app(nil, y32843), y538)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(fresh_constant, y32844), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(fresh_constant, y32844), y538))) -> DOWN(app(app(fresh_constant, y32844), y538)) 392.66/193.66 The remaining pairs can at least be oriented weakly. 392.66/193.66 Used ordering: Polynomial interpretation [POLO]: 392.66/193.66 392.66/193.66 POL(0) = 1 392.66/193.66 POL(DOWN(x_1)) = x_1 392.66/193.66 POL(app(x_1, x_2)) = x_1 + x_2 392.66/193.66 POL(cons) = 0 392.66/193.66 POL(fresh_constant) = 1 392.66/193.66 POL(hd) = 1 392.66/193.66 POL(map) = 0 392.66/193.66 POL(nil) = 1 392.66/193.66 392.66/193.66 The following usable rules [FROCOS05] with respect to the argument filtering of the ordering [JAR06] were oriented: 392.66/193.66 none 392.66/193.66 392.66/193.66 392.66/193.66 ---------------------------------------- 392.66/193.66 392.66/193.66 (53) 392.66/193.66 Obligation: 392.66/193.66 Q DP problem: 392.66/193.66 The TRS P consists of the following rules: 392.66/193.66 392.66/193.66 DOWN(app(map, y9)) -> DOWN(y9) 392.66/193.66 DOWN(app(cons, y10)) -> DOWN(y10) 392.66/193.66 DOWN(app(app(app(y64, y65), app(y66, y67)), y6)) -> DOWN(app(app(y64, y65), app(y66, y67))) 392.66/193.66 DOWN(app(app(app(y64, y65), app(y66, y67)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, app(y68, y69)), y6)) -> DOWN(app(0, app(y68, y69))) 392.66/193.66 DOWN(app(app(hd, app(y70, y71)), y6)) -> DOWN(app(hd, app(y70, y71))) 392.66/193.66 DOWN(app(app(cons, app(y74, y75)), y6)) -> DOWN(app(cons, app(y74, y75))) 392.66/193.66 DOWN(app(app(cons, app(y74, y75)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, app(y76, y77)), y6)) -> DOWN(app(nil, app(y76, y77))) 392.66/193.66 DOWN(app(app(fresh_constant, app(y78, y79)), y6)) -> DOWN(app(fresh_constant, app(y78, y79))) 392.66/193.66 DOWN(app(app(app(y84, y85), hd), y6)) -> DOWN(app(app(y84, y85), hd)) 392.66/193.66 DOWN(app(app(0, hd), y6)) -> DOWN(app(0, hd)) 392.66/193.66 DOWN(app(app(hd, hd), y6)) -> DOWN(app(hd, hd)) 392.66/193.66 DOWN(app(app(cons, hd), y6)) -> DOWN(app(cons, hd)) 392.66/193.66 DOWN(app(app(nil, hd), y6)) -> DOWN(app(nil, hd)) 392.66/193.66 DOWN(app(app(fresh_constant, hd), y6)) -> DOWN(app(fresh_constant, hd)) 392.66/193.66 DOWN(app(app(app(y87, y88), map), y6)) -> DOWN(app(app(y87, y88), map)) 392.66/193.66 DOWN(app(app(app(y87, y88), map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, map), y6)) -> DOWN(app(0, map)) 392.66/193.66 DOWN(app(app(hd, map), y6)) -> DOWN(app(hd, map)) 392.66/193.66 DOWN(app(app(cons, map), y6)) -> DOWN(app(cons, map)) 392.66/193.66 DOWN(app(app(cons, map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, map), y6)) -> DOWN(app(nil, map)) 392.66/193.66 DOWN(app(app(fresh_constant, map), y6)) -> DOWN(app(fresh_constant, map)) 392.66/193.66 DOWN(app(app(app(y90, y91), cons), y6)) -> DOWN(app(app(y90, y91), cons)) 392.66/193.66 DOWN(app(app(app(y90, y91), cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(0, cons), y6)) -> DOWN(app(0, cons)) 392.66/193.66 DOWN(app(app(hd, cons), y6)) -> DOWN(app(hd, cons)) 392.66/193.66 DOWN(app(app(cons, cons), y6)) -> DOWN(app(cons, cons)) 392.66/193.66 DOWN(app(app(cons, cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(nil, cons), y6)) -> DOWN(app(nil, cons)) 392.66/193.66 DOWN(app(app(fresh_constant, cons), y6)) -> DOWN(app(fresh_constant, cons)) 392.66/193.66 DOWN(app(app(app(y93, y94), nil), y6)) -> DOWN(app(app(y93, y94), nil)) 392.66/193.66 DOWN(app(app(0, nil), y6)) -> DOWN(app(0, nil)) 392.66/193.66 DOWN(app(app(hd, nil), y6)) -> DOWN(app(hd, nil)) 392.66/193.66 DOWN(app(app(cons, nil), y6)) -> DOWN(app(cons, nil)) 392.66/193.66 DOWN(app(app(nil, nil), y6)) -> DOWN(app(nil, nil)) 392.66/193.66 DOWN(app(app(fresh_constant, nil), y6)) -> DOWN(app(fresh_constant, nil)) 392.66/193.66 DOWN(app(app(app(y96, y97), fresh_constant), y6)) -> DOWN(app(app(y96, y97), fresh_constant)) 392.66/193.66 DOWN(app(app(0, fresh_constant), y6)) -> DOWN(app(0, fresh_constant)) 392.66/193.66 DOWN(app(app(hd, fresh_constant), y6)) -> DOWN(app(hd, fresh_constant)) 392.66/193.66 DOWN(app(app(cons, fresh_constant), y6)) -> DOWN(app(cons, fresh_constant)) 392.66/193.66 DOWN(app(app(nil, fresh_constant), y6)) -> DOWN(app(nil, fresh_constant)) 392.66/193.66 DOWN(app(app(fresh_constant, fresh_constant), y6)) -> DOWN(app(fresh_constant, fresh_constant)) 392.66/193.66 DOWN(app(app(y581, app(y582, y583)), app(0, y584))) -> DOWN(app(0, y584)) 392.66/193.66 DOWN(app(app(y6397, app(y6398, y6399)), map)) -> DOWN(app(y6397, app(y6398, y6399))) 392.66/193.66 DOWN(app(app(y630, map), app(0, y631))) -> DOWN(app(0, y631)) 392.66/193.66 DOWN(app(app(y6445, app(y6446, y6447)), cons)) -> DOWN(app(y6445, app(y6446, y6447))) 392.66/193.66 DOWN(app(app(y641, cons), app(0, y642))) -> DOWN(app(0, y642)) 392.66/193.66 DOWN(app(app(y693, app(y694, y695)), app(hd, y696))) -> DOWN(app(hd, y696)) 392.66/193.66 DOWN(app(app(y6419, hd), map)) -> DOWN(app(y6419, hd)) 392.66/193.66 DOWN(app(app(y6467, hd), cons)) -> DOWN(app(y6467, hd)) 392.66/193.66 DOWN(app(app(y6422, map), map)) -> DOWN(app(y6422, map)) 392.66/193.66 DOWN(app(app(y6425, cons), map)) -> DOWN(app(y6425, cons)) 392.66/193.66 DOWN(app(app(y6470, map), cons)) -> DOWN(app(y6470, map)) 392.66/193.66 DOWN(app(app(y6428, nil), map)) -> DOWN(app(y6428, nil)) 392.66/193.66 DOWN(app(app(y6431, fresh_constant), map)) -> DOWN(app(y6431, fresh_constant)) 392.66/193.66 DOWN(app(app(y6473, cons), cons)) -> DOWN(app(y6473, cons)) 392.66/193.66 DOWN(app(app(y6476, nil), cons)) -> DOWN(app(y6476, nil)) 392.66/193.66 DOWN(app(app(y6479, fresh_constant), cons)) -> DOWN(app(y6479, fresh_constant)) 392.66/193.66 DOWN(app(app(y742, map), app(hd, y743))) -> DOWN(app(hd, y743)) 392.66/193.66 DOWN(app(app(y753, cons), app(hd, y754))) -> DOWN(app(hd, y754)) 392.66/193.66 DOWN(app(app(y805, app(y806, y807)), app(map, y808))) -> DOWN(app(y805, app(y806, y807))) 392.66/193.66 DOWN(app(app(y805, app(y806, y807)), app(map, y808))) -> DOWN(app(map, y808)) 392.66/193.66 DOWN(app(app(y843, hd), app(map, y844))) -> DOWN(app(y843, hd)) 392.66/193.66 DOWN(app(app(y854, map), app(map, y855))) -> DOWN(app(y854, map)) 392.66/193.66 DOWN(app(app(y854, map), app(map, y855))) -> DOWN(app(map, y855)) 392.66/193.66 DOWN(app(app(y865, cons), app(map, y866))) -> DOWN(app(y865, cons)) 392.66/193.66 DOWN(app(app(y865, cons), app(map, y866))) -> DOWN(app(map, y866)) 392.66/193.66 DOWN(app(app(y876, nil), app(map, y877))) -> DOWN(app(y876, nil)) 392.66/193.66 DOWN(app(app(y887, fresh_constant), app(map, y888))) -> DOWN(app(y887, fresh_constant)) 392.66/193.66 DOWN(app(app(y917, app(y918, y919)), app(cons, y920))) -> DOWN(app(y917, app(y918, y919))) 392.66/193.66 DOWN(app(app(y917, app(y918, y919)), app(cons, y920))) -> DOWN(app(cons, y920)) 392.66/193.66 DOWN(app(app(y955, hd), app(cons, y956))) -> DOWN(app(y955, hd)) 392.66/193.66 DOWN(app(app(y966, map), app(cons, y967))) -> DOWN(app(y966, map)) 392.66/193.66 DOWN(app(app(y966, map), app(cons, y967))) -> DOWN(app(cons, y967)) 392.66/193.66 DOWN(app(app(y977, cons), app(cons, y978))) -> DOWN(app(y977, cons)) 392.66/193.66 DOWN(app(app(y977, cons), app(cons, y978))) -> DOWN(app(cons, y978)) 392.66/193.66 DOWN(app(app(y988, nil), app(cons, y989))) -> DOWN(app(y988, nil)) 392.66/193.66 DOWN(app(app(y999, fresh_constant), app(cons, y1000))) -> DOWN(app(y999, fresh_constant)) 392.66/193.66 DOWN(app(app(y1029, app(y1030, y1031)), app(nil, y1032))) -> DOWN(app(nil, y1032)) 392.66/193.66 DOWN(app(app(y1078, map), app(nil, y1079))) -> DOWN(app(nil, y1079)) 392.66/193.66 DOWN(app(app(y1089, cons), app(nil, y1090))) -> DOWN(app(nil, y1090)) 392.66/193.66 DOWN(app(app(y1141, app(y1142, y1143)), app(fresh_constant, y1144))) -> DOWN(app(fresh_constant, y1144)) 392.66/193.66 DOWN(app(app(y1190, map), app(fresh_constant, y1191))) -> DOWN(app(fresh_constant, y1191)) 392.66/193.66 DOWN(app(app(y1201, cons), app(fresh_constant, y1202))) -> DOWN(app(fresh_constant, y1202)) 392.66/193.66 DOWN(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> DOWN(app(y357, app(y20338, y20339))) 392.66/193.66 DOWN(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> DOWN(app(app(app(y20340, y20341), y20342), y362)) 392.66/193.66 DOWN(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> DOWN(app(app(0, y20580), y362)) 392.66/193.66 DOWN(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> DOWN(app(app(hd, y20692), y362)) 392.66/193.66 DOWN(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> DOWN(app(y357, app(y20802, y20803))) 392.66/193.66 DOWN(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> DOWN(app(app(map, y20804), y362)) 392.66/193.66 DOWN(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> DOWN(app(app(nil, y21028), y362)) 392.66/193.66 DOWN(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> DOWN(app(app(fresh_constant, y21140), y362)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(map, y32457), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> DOWN(app(app(app(y32548, y32549), y32550), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(0, y32551), y457))) -> DOWN(app(app(0, y32551), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(hd, y32552), y457))) -> DOWN(app(app(hd, y32552), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(map, y32553), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(map, y32553), y457))) -> DOWN(app(app(map, y32553), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(nil, y32555), y457))) -> DOWN(app(app(nil, y32555), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> DOWN(app(app(fresh_constant, y32556), y457)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> DOWN(app(app(app(y32644, y32645), y32646), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(0, y32647), y484))) -> DOWN(app(app(0, y32647), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(hd, y32648), y484))) -> DOWN(app(app(hd, y32648), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(map, y32649), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(map, y32649), y484))) -> DOWN(app(app(map, y32649), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(nil, y32651), y484))) -> DOWN(app(app(nil, y32651), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> DOWN(app(app(fresh_constant, y32652), y484)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(map, y32745), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 392.66/193.66 R is empty. 392.66/193.66 Q is empty. 392.66/193.66 We have to consider all minimal (P,Q,R)-chains. 392.66/193.66 ---------------------------------------- 392.66/193.66 392.66/193.66 (54) DependencyGraphProof (EQUIVALENT) 392.66/193.66 The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 36 less nodes. 392.66/193.66 ---------------------------------------- 392.66/193.66 392.66/193.66 (55) 392.66/193.66 Obligation: 392.66/193.66 Q DP problem: 392.66/193.66 The TRS P consists of the following rules: 392.66/193.66 392.66/193.66 DOWN(app(cons, y10)) -> DOWN(y10) 392.66/193.66 DOWN(app(map, y9)) -> DOWN(y9) 392.66/193.66 DOWN(app(app(app(y64, y65), app(y66, y67)), y6)) -> DOWN(app(app(y64, y65), app(y66, y67))) 392.66/193.66 DOWN(app(app(app(y64, y65), app(y66, y67)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(cons, app(y74, y75)), y6)) -> DOWN(app(cons, app(y74, y75))) 392.66/193.66 DOWN(app(app(cons, app(y74, y75)), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(app(y84, y85), hd), y6)) -> DOWN(app(app(y84, y85), hd)) 392.66/193.66 DOWN(app(app(cons, hd), y6)) -> DOWN(app(cons, hd)) 392.66/193.66 DOWN(app(app(app(y87, y88), map), y6)) -> DOWN(app(app(y87, y88), map)) 392.66/193.66 DOWN(app(app(app(y87, y88), map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(cons, map), y6)) -> DOWN(app(cons, map)) 392.66/193.66 DOWN(app(app(cons, map), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(app(y90, y91), cons), y6)) -> DOWN(app(app(y90, y91), cons)) 392.66/193.66 DOWN(app(app(app(y90, y91), cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(cons, cons), y6)) -> DOWN(app(cons, cons)) 392.66/193.66 DOWN(app(app(cons, cons), y6)) -> DOWN(y6) 392.66/193.66 DOWN(app(app(app(y93, y94), nil), y6)) -> DOWN(app(app(y93, y94), nil)) 392.66/193.66 DOWN(app(app(cons, nil), y6)) -> DOWN(app(cons, nil)) 392.66/193.66 DOWN(app(app(app(y96, y97), fresh_constant), y6)) -> DOWN(app(app(y96, y97), fresh_constant)) 392.66/193.66 DOWN(app(app(cons, fresh_constant), y6)) -> DOWN(app(cons, fresh_constant)) 392.66/193.66 DOWN(app(app(y805, app(y806, y807)), app(map, y808))) -> DOWN(app(y805, app(y806, y807))) 392.66/193.66 DOWN(app(app(y805, app(y806, y807)), app(map, y808))) -> DOWN(app(map, y808)) 392.66/193.66 DOWN(app(app(y843, hd), app(map, y844))) -> DOWN(app(y843, hd)) 392.66/193.66 DOWN(app(app(y854, map), app(map, y855))) -> DOWN(app(y854, map)) 392.66/193.66 DOWN(app(app(y6397, app(y6398, y6399)), map)) -> DOWN(app(y6397, app(y6398, y6399))) 392.66/193.66 DOWN(app(app(y854, map), app(map, y855))) -> DOWN(app(map, y855)) 392.66/193.66 DOWN(app(app(y865, cons), app(map, y866))) -> DOWN(app(y865, cons)) 392.66/193.66 DOWN(app(app(y6445, app(y6446, y6447)), cons)) -> DOWN(app(y6445, app(y6446, y6447))) 392.66/193.66 DOWN(app(app(y865, cons), app(map, y866))) -> DOWN(app(map, y866)) 392.66/193.66 DOWN(app(app(y876, nil), app(map, y877))) -> DOWN(app(y876, nil)) 392.66/193.66 DOWN(app(app(y887, fresh_constant), app(map, y888))) -> DOWN(app(y887, fresh_constant)) 392.66/193.66 DOWN(app(app(y917, app(y918, y919)), app(cons, y920))) -> DOWN(app(y917, app(y918, y919))) 392.66/193.66 DOWN(app(app(y917, app(y918, y919)), app(cons, y920))) -> DOWN(app(cons, y920)) 392.66/193.66 DOWN(app(app(y955, hd), app(cons, y956))) -> DOWN(app(y955, hd)) 392.66/193.66 DOWN(app(app(y966, map), app(cons, y967))) -> DOWN(app(y966, map)) 392.66/193.66 DOWN(app(app(y6419, hd), map)) -> DOWN(app(y6419, hd)) 392.66/193.66 DOWN(app(app(y6422, map), map)) -> DOWN(app(y6422, map)) 392.66/193.66 DOWN(app(app(y6425, cons), map)) -> DOWN(app(y6425, cons)) 392.66/193.66 DOWN(app(app(y6467, hd), cons)) -> DOWN(app(y6467, hd)) 392.66/193.66 DOWN(app(app(y6470, map), cons)) -> DOWN(app(y6470, map)) 392.66/193.66 DOWN(app(app(y6428, nil), map)) -> DOWN(app(y6428, nil)) 392.66/193.66 DOWN(app(app(y6431, fresh_constant), map)) -> DOWN(app(y6431, fresh_constant)) 392.66/193.66 DOWN(app(app(y6473, cons), cons)) -> DOWN(app(y6473, cons)) 392.66/193.66 DOWN(app(app(y6476, nil), cons)) -> DOWN(app(y6476, nil)) 392.66/193.66 DOWN(app(app(y6479, fresh_constant), cons)) -> DOWN(app(y6479, fresh_constant)) 392.66/193.66 DOWN(app(app(y966, map), app(cons, y967))) -> DOWN(app(cons, y967)) 392.66/193.66 DOWN(app(app(y977, cons), app(cons, y978))) -> DOWN(app(y977, cons)) 392.66/193.66 DOWN(app(app(y977, cons), app(cons, y978))) -> DOWN(app(cons, y978)) 392.66/193.66 DOWN(app(app(y988, nil), app(cons, y989))) -> DOWN(app(y988, nil)) 392.66/193.66 DOWN(app(app(y999, fresh_constant), app(cons, y1000))) -> DOWN(app(y999, fresh_constant)) 392.66/193.66 DOWN(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> DOWN(app(y357, app(y20338, y20339))) 392.66/193.66 DOWN(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> DOWN(app(app(app(y20340, y20341), y20342), y362)) 392.66/193.66 DOWN(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> DOWN(app(app(0, y20580), y362)) 392.66/193.66 DOWN(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> DOWN(app(app(hd, y20692), y362)) 392.66/193.66 DOWN(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> DOWN(app(y357, app(y20802, y20803))) 392.66/193.66 DOWN(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> DOWN(app(app(map, y20804), y362)) 392.66/193.66 DOWN(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> DOWN(app(app(nil, y21028), y362)) 392.66/193.66 DOWN(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> DOWN(app(app(fresh_constant, y21140), y362)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y427, hd), app(app(map, y32457), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 DOWN(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> DOWN(app(app(app(y32548, y32549), y32550), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(0, y32551), y457))) -> DOWN(app(app(0, y32551), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(hd, y32552), y457))) -> DOWN(app(app(hd, y32552), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(map, y32553), y457))) -> DOWN(app(y454, map)) 392.66/193.66 DOWN(app(app(y454, map), app(app(map, y32553), y457))) -> DOWN(app(app(map, y32553), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(nil, y32555), y457))) -> DOWN(app(app(nil, y32555), y457)) 392.66/193.66 DOWN(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> DOWN(app(app(fresh_constant, y32556), y457)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> DOWN(app(app(app(y32644, y32645), y32646), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(0, y32647), y484))) -> DOWN(app(app(0, y32647), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(hd, y32648), y484))) -> DOWN(app(app(hd, y32648), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(map, y32649), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(map, y32649), y484))) -> DOWN(app(app(map, y32649), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(nil, y32651), y484))) -> DOWN(app(app(nil, y32651), y484)) 392.66/193.66 DOWN(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> DOWN(app(app(fresh_constant, y32652), y484)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y508, nil), app(app(map, y32745), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 DOWN(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 392.66/193.66 R is empty. 392.66/193.66 Q is empty. 392.66/193.66 We have to consider all minimal (P,Q,R)-chains. 392.66/193.66 ---------------------------------------- 392.66/193.66 392.66/193.66 (56) QDPSizeChangeProof (EQUIVALENT) 392.66/193.66 By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. 392.66/193.66 392.66/193.66 From the DPs we obtained the following set of size-change graphs: 392.66/193.66 *DOWN(app(cons, y10)) -> DOWN(y10) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(map, y9)) -> DOWN(y9) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y6397, app(y6398, y6399)), map)) -> DOWN(app(y6397, app(y6398, y6399))) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y6445, app(y6446, y6447)), cons)) -> DOWN(app(y6445, app(y6446, y6447))) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(app(y64, y65), app(y66, y67)), y6)) -> DOWN(app(app(y64, y65), app(y66, y67))) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y6422, map), map)) -> DOWN(app(y6422, map)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y6470, map), cons)) -> DOWN(app(y6470, map)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(app(y87, y88), map), y6)) -> DOWN(app(app(y87, y88), map)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y6425, cons), map)) -> DOWN(app(y6425, cons)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y6473, cons), cons)) -> DOWN(app(y6473, cons)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(app(y90, y91), cons), y6)) -> DOWN(app(app(y90, y91), cons)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(app(y64, y65), app(y66, y67)), y6)) -> DOWN(y6) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(app(y87, y88), map), y6)) -> DOWN(y6) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(app(y90, y91), cons), y6)) -> DOWN(y6) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(cons, app(y74, y75)), y6)) -> DOWN(y6) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(cons, map), y6)) -> DOWN(y6) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(cons, cons), y6)) -> DOWN(y6) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y805, app(y806, y807)), app(map, y808))) -> DOWN(app(y805, app(y806, y807))) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y917, app(y918, y919)), app(cons, y920))) -> DOWN(app(y917, app(y918, y919))) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> DOWN(app(y357, app(y20338, y20339))) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> DOWN(app(y357, app(y20802, y20803))) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y854, map), app(map, y855))) -> DOWN(app(y854, map)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y966, map), app(cons, y967))) -> DOWN(app(y966, map)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> DOWN(app(y454, map)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y454, map), app(app(map, y32553), y457))) -> DOWN(app(y454, map)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y865, cons), app(map, y866))) -> DOWN(app(y865, cons)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y977, cons), app(cons, y978))) -> DOWN(app(y977, cons)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y481, cons), app(app(map, y32649), y484))) -> DOWN(app(y481, cons)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y843, hd), app(map, y844))) -> DOWN(app(y843, hd)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y876, nil), app(map, y877))) -> DOWN(app(y876, nil)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y887, fresh_constant), app(map, y888))) -> DOWN(app(y887, fresh_constant)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y955, hd), app(cons, y956))) -> DOWN(app(y955, hd)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y988, nil), app(cons, y989))) -> DOWN(app(y988, nil)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y999, fresh_constant), app(cons, y1000))) -> DOWN(app(y999, fresh_constant)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y427, hd), app(app(map, y32457), y430))) -> DOWN(app(y427, hd)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y508, nil), app(app(map, y32745), y511))) -> DOWN(app(y508, nil)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> DOWN(app(y535, fresh_constant)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y6419, hd), map)) -> DOWN(app(y6419, hd)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y6428, nil), map)) -> DOWN(app(y6428, nil)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y6431, fresh_constant), map)) -> DOWN(app(y6431, fresh_constant)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y6467, hd), cons)) -> DOWN(app(y6467, hd)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y6476, nil), cons)) -> DOWN(app(y6476, nil)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y6479, fresh_constant), cons)) -> DOWN(app(y6479, fresh_constant)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(cons, app(y74, y75)), y6)) -> DOWN(app(cons, app(y74, y75))) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(cons, hd), y6)) -> DOWN(app(cons, hd)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(cons, map), y6)) -> DOWN(app(cons, map)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(cons, cons), y6)) -> DOWN(app(cons, cons)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(cons, nil), y6)) -> DOWN(app(cons, nil)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(cons, fresh_constant), y6)) -> DOWN(app(cons, fresh_constant)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y917, app(y918, y919)), app(cons, y920))) -> DOWN(app(cons, y920)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y966, map), app(cons, y967))) -> DOWN(app(cons, y967)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y977, cons), app(cons, y978))) -> DOWN(app(cons, y978)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y805, app(y806, y807)), app(map, y808))) -> DOWN(app(map, y808)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y854, map), app(map, y855))) -> DOWN(app(map, y855)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y865, cons), app(map, y866))) -> DOWN(app(map, y866)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(app(y84, y85), hd), y6)) -> DOWN(app(app(y84, y85), hd)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(app(y93, y94), nil), y6)) -> DOWN(app(app(y93, y94), nil)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(app(y96, y97), fresh_constant), y6)) -> DOWN(app(app(y96, y97), fresh_constant)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> DOWN(app(app(app(y20340, y20341), y20342), y362)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> DOWN(app(app(app(y32548, y32549), y32550), y457)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> DOWN(app(app(app(y32644, y32645), y32646), y484)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> DOWN(app(app(0, y20580), y362)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> DOWN(app(app(hd, y20692), y362)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> DOWN(app(app(map, y20804), y362)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> DOWN(app(app(nil, y21028), y362)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> DOWN(app(app(fresh_constant, y21140), y362)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y454, map), app(app(0, y32551), y457))) -> DOWN(app(app(0, y32551), y457)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y454, map), app(app(hd, y32552), y457))) -> DOWN(app(app(hd, y32552), y457)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y454, map), app(app(map, y32553), y457))) -> DOWN(app(app(map, y32553), y457)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y454, map), app(app(nil, y32555), y457))) -> DOWN(app(app(nil, y32555), y457)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> DOWN(app(app(fresh_constant, y32556), y457)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y481, cons), app(app(0, y32647), y484))) -> DOWN(app(app(0, y32647), y484)) 392.66/193.66 The graph contains the following edges 1 > 1 392.66/193.66 392.66/193.66 392.66/193.66 *DOWN(app(app(y481, cons), app(app(hd, y32648), y484))) -> DOWN(app(app(hd, y32648), y484)) 392.66/193.67 The graph contains the following edges 1 > 1 392.66/193.67 392.66/193.67 392.66/193.67 *DOWN(app(app(y481, cons), app(app(map, y32649), y484))) -> DOWN(app(app(map, y32649), y484)) 392.66/193.67 The graph contains the following edges 1 > 1 392.66/193.67 392.66/193.67 392.66/193.67 *DOWN(app(app(y481, cons), app(app(nil, y32651), y484))) -> DOWN(app(app(nil, y32651), y484)) 392.66/193.67 The graph contains the following edges 1 > 1 392.66/193.67 392.66/193.67 392.66/193.67 *DOWN(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> DOWN(app(app(fresh_constant, y32652), y484)) 392.66/193.67 The graph contains the following edges 1 > 1 392.66/193.67 392.66/193.67 392.66/193.67 ---------------------------------------- 392.66/193.67 392.66/193.67 (57) 392.66/193.67 YES 392.66/193.67 392.66/193.67 ---------------------------------------- 392.66/193.67 392.66/193.67 (58) 392.66/193.67 Obligation: 392.66/193.67 Q DP problem: 392.66/193.67 The TRS P consists of the following rules: 392.66/193.67 392.66/193.67 TOP(up(x)) -> TOP(down(x)) 392.66/193.67 392.66/193.67 The TRS R consists of the following rules: 392.66/193.67 392.66/193.67 down(app(app(f, 0), n)) -> up(app(app(hd, app(app(map, f), app(app(cons, 0), nil))), n)) 392.66/193.67 down(app(app(map, f), nil)) -> up(nil) 392.66/193.67 down(app(app(map, f), app(app(cons, x), xs))) -> up(app(app(cons, app(f, x)), app(app(map, f), xs))) 392.66/193.67 top(up(x)) -> top(down(x)) 392.66/193.67 down(app(0, y7)) -> app_flat(down(0), block(y7)) 392.66/193.67 down(app(0, y7)) -> app_flat(block(0), down(y7)) 392.66/193.67 down(app(hd, y8)) -> app_flat(down(hd), block(y8)) 392.66/193.67 down(app(hd, y8)) -> app_flat(block(hd), down(y8)) 392.66/193.67 down(app(map, y9)) -> app_flat(down(map), block(y9)) 392.66/193.67 down(app(map, y9)) -> app_flat(block(map), down(y9)) 392.66/193.67 down(app(cons, y10)) -> app_flat(down(cons), block(y10)) 392.66/193.67 down(app(cons, y10)) -> app_flat(block(cons), down(y10)) 392.66/193.67 down(app(nil, y11)) -> app_flat(down(nil), block(y11)) 392.66/193.67 down(app(nil, y11)) -> app_flat(block(nil), down(y11)) 392.66/193.67 down(app(fresh_constant, y12)) -> app_flat(down(fresh_constant), block(y12)) 392.66/193.67 down(app(fresh_constant, y12)) -> app_flat(block(fresh_constant), down(y12)) 392.66/193.67 down(app(app(app(y64, y65), app(y66, y67)), y6)) -> app_flat(down(app(app(y64, y65), app(y66, y67))), block(y6)) 392.66/193.67 down(app(app(app(y64, y65), app(y66, y67)), y6)) -> app_flat(block(app(app(y64, y65), app(y66, y67))), down(y6)) 392.66/193.67 down(app(app(0, app(y68, y69)), y6)) -> app_flat(down(app(0, app(y68, y69))), block(y6)) 392.66/193.67 down(app(app(0, app(y68, y69)), y6)) -> app_flat(block(app(0, app(y68, y69))), down(y6)) 392.66/193.67 down(app(app(hd, app(y70, y71)), y6)) -> app_flat(down(app(hd, app(y70, y71))), block(y6)) 392.66/193.67 down(app(app(hd, app(y70, y71)), y6)) -> app_flat(block(app(hd, app(y70, y71))), down(y6)) 392.66/193.67 down(app(app(cons, app(y74, y75)), y6)) -> app_flat(down(app(cons, app(y74, y75))), block(y6)) 392.66/193.67 down(app(app(cons, app(y74, y75)), y6)) -> app_flat(block(app(cons, app(y74, y75))), down(y6)) 392.66/193.67 down(app(app(nil, app(y76, y77)), y6)) -> app_flat(down(app(nil, app(y76, y77))), block(y6)) 392.66/193.67 down(app(app(nil, app(y76, y77)), y6)) -> app_flat(block(app(nil, app(y76, y77))), down(y6)) 392.66/193.67 down(app(app(fresh_constant, app(y78, y79)), y6)) -> app_flat(down(app(fresh_constant, app(y78, y79))), block(y6)) 392.66/193.67 down(app(app(fresh_constant, app(y78, y79)), y6)) -> app_flat(block(app(fresh_constant, app(y78, y79))), down(y6)) 392.66/193.67 down(app(app(app(y84, y85), hd), y6)) -> app_flat(down(app(app(y84, y85), hd)), block(y6)) 392.66/193.67 down(app(app(app(y84, y85), hd), y6)) -> app_flat(block(app(app(y84, y85), hd)), down(y6)) 392.66/193.67 down(app(app(0, hd), y6)) -> app_flat(down(app(0, hd)), block(y6)) 392.66/193.67 down(app(app(0, hd), y6)) -> app_flat(block(app(0, hd)), down(y6)) 392.66/193.67 down(app(app(hd, hd), y6)) -> app_flat(down(app(hd, hd)), block(y6)) 392.66/193.67 down(app(app(hd, hd), y6)) -> app_flat(block(app(hd, hd)), down(y6)) 392.66/193.67 down(app(app(cons, hd), y6)) -> app_flat(down(app(cons, hd)), block(y6)) 392.66/193.67 down(app(app(cons, hd), y6)) -> app_flat(block(app(cons, hd)), down(y6)) 392.66/193.67 down(app(app(nil, hd), y6)) -> app_flat(down(app(nil, hd)), block(y6)) 392.66/193.67 down(app(app(nil, hd), y6)) -> app_flat(block(app(nil, hd)), down(y6)) 392.66/193.67 down(app(app(fresh_constant, hd), y6)) -> app_flat(down(app(fresh_constant, hd)), block(y6)) 392.66/193.67 down(app(app(fresh_constant, hd), y6)) -> app_flat(block(app(fresh_constant, hd)), down(y6)) 392.66/193.67 down(app(app(app(y87, y88), map), y6)) -> app_flat(down(app(app(y87, y88), map)), block(y6)) 392.66/193.67 down(app(app(app(y87, y88), map), y6)) -> app_flat(block(app(app(y87, y88), map)), down(y6)) 392.66/193.67 down(app(app(0, map), y6)) -> app_flat(down(app(0, map)), block(y6)) 392.66/193.67 down(app(app(0, map), y6)) -> app_flat(block(app(0, map)), down(y6)) 392.66/193.67 down(app(app(hd, map), y6)) -> app_flat(down(app(hd, map)), block(y6)) 392.66/193.67 down(app(app(hd, map), y6)) -> app_flat(block(app(hd, map)), down(y6)) 392.66/193.67 down(app(app(cons, map), y6)) -> app_flat(down(app(cons, map)), block(y6)) 392.66/193.67 down(app(app(cons, map), y6)) -> app_flat(block(app(cons, map)), down(y6)) 392.66/193.67 down(app(app(nil, map), y6)) -> app_flat(down(app(nil, map)), block(y6)) 392.66/193.67 down(app(app(nil, map), y6)) -> app_flat(block(app(nil, map)), down(y6)) 392.66/193.67 down(app(app(fresh_constant, map), y6)) -> app_flat(down(app(fresh_constant, map)), block(y6)) 392.66/193.67 down(app(app(fresh_constant, map), y6)) -> app_flat(block(app(fresh_constant, map)), down(y6)) 392.66/193.67 down(app(app(app(y90, y91), cons), y6)) -> app_flat(down(app(app(y90, y91), cons)), block(y6)) 392.66/193.67 down(app(app(app(y90, y91), cons), y6)) -> app_flat(block(app(app(y90, y91), cons)), down(y6)) 392.66/193.67 down(app(app(0, cons), y6)) -> app_flat(down(app(0, cons)), block(y6)) 392.66/193.67 down(app(app(0, cons), y6)) -> app_flat(block(app(0, cons)), down(y6)) 392.66/193.67 down(app(app(hd, cons), y6)) -> app_flat(down(app(hd, cons)), block(y6)) 392.66/193.67 down(app(app(hd, cons), y6)) -> app_flat(block(app(hd, cons)), down(y6)) 392.66/193.67 down(app(app(cons, cons), y6)) -> app_flat(down(app(cons, cons)), block(y6)) 392.66/193.67 down(app(app(cons, cons), y6)) -> app_flat(block(app(cons, cons)), down(y6)) 392.66/193.67 down(app(app(nil, cons), y6)) -> app_flat(down(app(nil, cons)), block(y6)) 392.66/193.67 down(app(app(nil, cons), y6)) -> app_flat(block(app(nil, cons)), down(y6)) 392.66/193.67 down(app(app(fresh_constant, cons), y6)) -> app_flat(down(app(fresh_constant, cons)), block(y6)) 392.66/193.67 down(app(app(fresh_constant, cons), y6)) -> app_flat(block(app(fresh_constant, cons)), down(y6)) 392.66/193.67 down(app(app(app(y93, y94), nil), y6)) -> app_flat(down(app(app(y93, y94), nil)), block(y6)) 392.66/193.67 down(app(app(app(y93, y94), nil), y6)) -> app_flat(block(app(app(y93, y94), nil)), down(y6)) 392.66/193.67 down(app(app(0, nil), y6)) -> app_flat(down(app(0, nil)), block(y6)) 392.66/193.67 down(app(app(0, nil), y6)) -> app_flat(block(app(0, nil)), down(y6)) 392.66/193.67 down(app(app(hd, nil), y6)) -> app_flat(down(app(hd, nil)), block(y6)) 392.66/193.67 down(app(app(hd, nil), y6)) -> app_flat(block(app(hd, nil)), down(y6)) 392.66/193.67 down(app(app(cons, nil), y6)) -> app_flat(down(app(cons, nil)), block(y6)) 392.66/193.67 down(app(app(cons, nil), y6)) -> app_flat(block(app(cons, nil)), down(y6)) 392.66/193.67 down(app(app(nil, nil), y6)) -> app_flat(down(app(nil, nil)), block(y6)) 392.66/193.67 down(app(app(nil, nil), y6)) -> app_flat(block(app(nil, nil)), down(y6)) 392.66/193.67 down(app(app(fresh_constant, nil), y6)) -> app_flat(down(app(fresh_constant, nil)), block(y6)) 392.66/193.67 down(app(app(fresh_constant, nil), y6)) -> app_flat(block(app(fresh_constant, nil)), down(y6)) 392.66/193.67 down(app(app(app(y96, y97), fresh_constant), y6)) -> app_flat(down(app(app(y96, y97), fresh_constant)), block(y6)) 392.66/193.67 down(app(app(app(y96, y97), fresh_constant), y6)) -> app_flat(block(app(app(y96, y97), fresh_constant)), down(y6)) 392.66/193.67 down(app(app(0, fresh_constant), y6)) -> app_flat(down(app(0, fresh_constant)), block(y6)) 392.66/193.67 down(app(app(0, fresh_constant), y6)) -> app_flat(block(app(0, fresh_constant)), down(y6)) 392.66/193.67 down(app(app(hd, fresh_constant), y6)) -> app_flat(down(app(hd, fresh_constant)), block(y6)) 392.66/193.67 down(app(app(hd, fresh_constant), y6)) -> app_flat(block(app(hd, fresh_constant)), down(y6)) 392.66/193.67 down(app(app(cons, fresh_constant), y6)) -> app_flat(down(app(cons, fresh_constant)), block(y6)) 392.66/193.67 down(app(app(cons, fresh_constant), y6)) -> app_flat(block(app(cons, fresh_constant)), down(y6)) 392.66/193.67 down(app(app(nil, fresh_constant), y6)) -> app_flat(down(app(nil, fresh_constant)), block(y6)) 392.66/193.67 down(app(app(nil, fresh_constant), y6)) -> app_flat(block(app(nil, fresh_constant)), down(y6)) 392.66/193.67 down(app(app(fresh_constant, fresh_constant), y6)) -> app_flat(down(app(fresh_constant, fresh_constant)), block(y6)) 392.66/193.67 down(app(app(fresh_constant, fresh_constant), y6)) -> app_flat(block(app(fresh_constant, fresh_constant)), down(y6)) 392.66/193.67 down(app(app(y581, app(y582, y583)), app(0, y584))) -> app_flat(down(app(y581, app(y582, y583))), block(app(0, y584))) 392.66/193.67 down(app(app(y581, app(y582, y583)), app(0, y584))) -> app_flat(block(app(y581, app(y582, y583))), down(app(0, y584))) 392.66/193.67 down(app(app(y619, hd), app(0, y620))) -> app_flat(down(app(y619, hd)), block(app(0, y620))) 392.66/193.67 down(app(app(y619, hd), app(0, y620))) -> app_flat(block(app(y619, hd)), down(app(0, y620))) 392.66/193.67 down(app(app(y630, map), app(0, y631))) -> app_flat(down(app(y630, map)), block(app(0, y631))) 392.66/193.67 down(app(app(y630, map), app(0, y631))) -> app_flat(block(app(y630, map)), down(app(0, y631))) 392.66/193.67 down(app(app(y641, cons), app(0, y642))) -> app_flat(down(app(y641, cons)), block(app(0, y642))) 392.66/193.67 down(app(app(y641, cons), app(0, y642))) -> app_flat(block(app(y641, cons)), down(app(0, y642))) 392.66/193.67 down(app(app(y652, nil), app(0, y653))) -> app_flat(down(app(y652, nil)), block(app(0, y653))) 392.66/193.67 down(app(app(y652, nil), app(0, y653))) -> app_flat(block(app(y652, nil)), down(app(0, y653))) 392.66/193.67 down(app(app(y663, fresh_constant), app(0, y664))) -> app_flat(down(app(y663, fresh_constant)), block(app(0, y664))) 392.66/193.67 down(app(app(y663, fresh_constant), app(0, y664))) -> app_flat(block(app(y663, fresh_constant)), down(app(0, y664))) 392.66/193.67 down(app(app(y693, app(y694, y695)), app(hd, y696))) -> app_flat(down(app(y693, app(y694, y695))), block(app(hd, y696))) 392.66/193.67 down(app(app(y693, app(y694, y695)), app(hd, y696))) -> app_flat(block(app(y693, app(y694, y695))), down(app(hd, y696))) 392.66/193.67 down(app(app(y731, hd), app(hd, y732))) -> app_flat(down(app(y731, hd)), block(app(hd, y732))) 392.66/193.67 down(app(app(y731, hd), app(hd, y732))) -> app_flat(block(app(y731, hd)), down(app(hd, y732))) 392.66/193.67 down(app(app(y742, map), app(hd, y743))) -> app_flat(down(app(y742, map)), block(app(hd, y743))) 392.66/193.67 down(app(app(y742, map), app(hd, y743))) -> app_flat(block(app(y742, map)), down(app(hd, y743))) 392.66/193.67 down(app(app(y753, cons), app(hd, y754))) -> app_flat(down(app(y753, cons)), block(app(hd, y754))) 392.66/193.67 down(app(app(y753, cons), app(hd, y754))) -> app_flat(block(app(y753, cons)), down(app(hd, y754))) 392.66/193.67 down(app(app(y764, nil), app(hd, y765))) -> app_flat(down(app(y764, nil)), block(app(hd, y765))) 392.66/193.67 down(app(app(y764, nil), app(hd, y765))) -> app_flat(block(app(y764, nil)), down(app(hd, y765))) 392.66/193.67 down(app(app(y775, fresh_constant), app(hd, y776))) -> app_flat(down(app(y775, fresh_constant)), block(app(hd, y776))) 392.66/193.67 down(app(app(y775, fresh_constant), app(hd, y776))) -> app_flat(block(app(y775, fresh_constant)), down(app(hd, y776))) 392.66/193.67 down(app(app(y805, app(y806, y807)), app(map, y808))) -> app_flat(down(app(y805, app(y806, y807))), block(app(map, y808))) 392.66/193.67 down(app(app(y805, app(y806, y807)), app(map, y808))) -> app_flat(block(app(y805, app(y806, y807))), down(app(map, y808))) 392.66/193.67 down(app(app(y843, hd), app(map, y844))) -> app_flat(down(app(y843, hd)), block(app(map, y844))) 392.66/193.67 down(app(app(y843, hd), app(map, y844))) -> app_flat(block(app(y843, hd)), down(app(map, y844))) 392.66/193.67 down(app(app(y854, map), app(map, y855))) -> app_flat(down(app(y854, map)), block(app(map, y855))) 392.66/193.67 down(app(app(y854, map), app(map, y855))) -> app_flat(block(app(y854, map)), down(app(map, y855))) 392.66/193.67 down(app(app(y865, cons), app(map, y866))) -> app_flat(down(app(y865, cons)), block(app(map, y866))) 392.66/193.67 down(app(app(y865, cons), app(map, y866))) -> app_flat(block(app(y865, cons)), down(app(map, y866))) 392.66/193.67 down(app(app(y876, nil), app(map, y877))) -> app_flat(down(app(y876, nil)), block(app(map, y877))) 392.66/193.67 down(app(app(y876, nil), app(map, y877))) -> app_flat(block(app(y876, nil)), down(app(map, y877))) 392.66/193.67 down(app(app(y887, fresh_constant), app(map, y888))) -> app_flat(down(app(y887, fresh_constant)), block(app(map, y888))) 392.66/193.67 down(app(app(y887, fresh_constant), app(map, y888))) -> app_flat(block(app(y887, fresh_constant)), down(app(map, y888))) 392.66/193.67 down(app(app(y917, app(y918, y919)), app(cons, y920))) -> app_flat(down(app(y917, app(y918, y919))), block(app(cons, y920))) 392.66/193.67 down(app(app(y917, app(y918, y919)), app(cons, y920))) -> app_flat(block(app(y917, app(y918, y919))), down(app(cons, y920))) 392.66/193.67 down(app(app(y955, hd), app(cons, y956))) -> app_flat(down(app(y955, hd)), block(app(cons, y956))) 392.66/193.67 down(app(app(y955, hd), app(cons, y956))) -> app_flat(block(app(y955, hd)), down(app(cons, y956))) 392.66/193.67 down(app(app(y966, map), app(cons, y967))) -> app_flat(down(app(y966, map)), block(app(cons, y967))) 392.66/193.67 down(app(app(y966, map), app(cons, y967))) -> app_flat(block(app(y966, map)), down(app(cons, y967))) 392.66/193.67 down(app(app(y977, cons), app(cons, y978))) -> app_flat(down(app(y977, cons)), block(app(cons, y978))) 392.66/193.67 down(app(app(y977, cons), app(cons, y978))) -> app_flat(block(app(y977, cons)), down(app(cons, y978))) 392.66/193.67 down(app(app(y988, nil), app(cons, y989))) -> app_flat(down(app(y988, nil)), block(app(cons, y989))) 392.66/193.67 down(app(app(y988, nil), app(cons, y989))) -> app_flat(block(app(y988, nil)), down(app(cons, y989))) 392.66/193.67 down(app(app(y999, fresh_constant), app(cons, y1000))) -> app_flat(down(app(y999, fresh_constant)), block(app(cons, y1000))) 392.66/193.67 down(app(app(y999, fresh_constant), app(cons, y1000))) -> app_flat(block(app(y999, fresh_constant)), down(app(cons, y1000))) 392.66/193.67 down(app(app(y1029, app(y1030, y1031)), app(nil, y1032))) -> app_flat(down(app(y1029, app(y1030, y1031))), block(app(nil, y1032))) 392.66/193.67 down(app(app(y1029, app(y1030, y1031)), app(nil, y1032))) -> app_flat(block(app(y1029, app(y1030, y1031))), down(app(nil, y1032))) 392.66/193.67 down(app(app(y1067, hd), app(nil, y1068))) -> app_flat(down(app(y1067, hd)), block(app(nil, y1068))) 392.66/193.67 down(app(app(y1067, hd), app(nil, y1068))) -> app_flat(block(app(y1067, hd)), down(app(nil, y1068))) 392.66/193.67 down(app(app(y1078, map), app(nil, y1079))) -> app_flat(down(app(y1078, map)), block(app(nil, y1079))) 392.66/193.67 down(app(app(y1078, map), app(nil, y1079))) -> app_flat(block(app(y1078, map)), down(app(nil, y1079))) 392.66/193.67 down(app(app(y1089, cons), app(nil, y1090))) -> app_flat(down(app(y1089, cons)), block(app(nil, y1090))) 392.66/193.67 down(app(app(y1089, cons), app(nil, y1090))) -> app_flat(block(app(y1089, cons)), down(app(nil, y1090))) 392.66/193.67 down(app(app(y1100, nil), app(nil, y1101))) -> app_flat(down(app(y1100, nil)), block(app(nil, y1101))) 392.66/193.67 down(app(app(y1100, nil), app(nil, y1101))) -> app_flat(block(app(y1100, nil)), down(app(nil, y1101))) 392.66/193.67 down(app(app(y1111, fresh_constant), app(nil, y1112))) -> app_flat(down(app(y1111, fresh_constant)), block(app(nil, y1112))) 392.66/193.67 down(app(app(y1111, fresh_constant), app(nil, y1112))) -> app_flat(block(app(y1111, fresh_constant)), down(app(nil, y1112))) 392.66/193.67 down(app(app(y1141, app(y1142, y1143)), app(fresh_constant, y1144))) -> app_flat(down(app(y1141, app(y1142, y1143))), block(app(fresh_constant, y1144))) 392.66/193.67 down(app(app(y1141, app(y1142, y1143)), app(fresh_constant, y1144))) -> app_flat(block(app(y1141, app(y1142, y1143))), down(app(fresh_constant, y1144))) 392.66/193.67 down(app(app(y1179, hd), app(fresh_constant, y1180))) -> app_flat(down(app(y1179, hd)), block(app(fresh_constant, y1180))) 392.66/193.67 down(app(app(y1179, hd), app(fresh_constant, y1180))) -> app_flat(block(app(y1179, hd)), down(app(fresh_constant, y1180))) 392.66/193.67 down(app(app(y1190, map), app(fresh_constant, y1191))) -> app_flat(down(app(y1190, map)), block(app(fresh_constant, y1191))) 392.66/193.67 down(app(app(y1190, map), app(fresh_constant, y1191))) -> app_flat(block(app(y1190, map)), down(app(fresh_constant, y1191))) 392.66/193.67 down(app(app(y1201, cons), app(fresh_constant, y1202))) -> app_flat(down(app(y1201, cons)), block(app(fresh_constant, y1202))) 392.66/193.67 down(app(app(y1201, cons), app(fresh_constant, y1202))) -> app_flat(block(app(y1201, cons)), down(app(fresh_constant, y1202))) 392.66/193.67 down(app(app(y1212, nil), app(fresh_constant, y1213))) -> app_flat(down(app(y1212, nil)), block(app(fresh_constant, y1213))) 392.66/193.67 down(app(app(y1212, nil), app(fresh_constant, y1213))) -> app_flat(block(app(y1212, nil)), down(app(fresh_constant, y1213))) 392.66/193.67 down(app(app(y1223, fresh_constant), app(fresh_constant, y1224))) -> app_flat(down(app(y1223, fresh_constant)), block(app(fresh_constant, y1224))) 392.66/193.67 down(app(app(y1223, fresh_constant), app(fresh_constant, y1224))) -> app_flat(block(app(y1223, fresh_constant)), down(app(fresh_constant, y1224))) 392.66/193.67 down(app(app(y6301, app(y6302, y6303)), 0)) -> app_flat(down(app(y6301, app(y6302, y6303))), block(0)) 392.66/193.67 down(app(app(y6301, app(y6302, y6303)), 0)) -> app_flat(block(app(y6301, app(y6302, y6303))), down(0)) 392.66/193.67 down(app(app(y6323, hd), 0)) -> app_flat(down(app(y6323, hd)), block(0)) 392.66/193.67 down(app(app(y6323, hd), 0)) -> app_flat(block(app(y6323, hd)), down(0)) 392.66/193.67 down(app(app(y6326, map), 0)) -> app_flat(down(app(y6326, map)), block(0)) 392.66/193.67 down(app(app(y6326, map), 0)) -> app_flat(block(app(y6326, map)), down(0)) 392.66/193.67 down(app(app(y6329, cons), 0)) -> app_flat(down(app(y6329, cons)), block(0)) 392.66/193.67 down(app(app(y6329, cons), 0)) -> app_flat(block(app(y6329, cons)), down(0)) 392.66/193.67 down(app(app(y6332, nil), 0)) -> app_flat(down(app(y6332, nil)), block(0)) 392.66/193.67 down(app(app(y6332, nil), 0)) -> app_flat(block(app(y6332, nil)), down(0)) 392.66/193.67 down(app(app(y6335, fresh_constant), 0)) -> app_flat(down(app(y6335, fresh_constant)), block(0)) 392.66/193.67 down(app(app(y6335, fresh_constant), 0)) -> app_flat(block(app(y6335, fresh_constant)), down(0)) 392.66/193.67 down(app(app(y6349, app(y6350, y6351)), hd)) -> app_flat(down(app(y6349, app(y6350, y6351))), block(hd)) 392.66/193.67 down(app(app(y6349, app(y6350, y6351)), hd)) -> app_flat(block(app(y6349, app(y6350, y6351))), down(hd)) 392.66/193.67 down(app(app(y6371, hd), hd)) -> app_flat(down(app(y6371, hd)), block(hd)) 392.66/193.67 down(app(app(y6371, hd), hd)) -> app_flat(block(app(y6371, hd)), down(hd)) 392.66/193.67 down(app(app(y6374, map), hd)) -> app_flat(down(app(y6374, map)), block(hd)) 392.66/193.67 down(app(app(y6374, map), hd)) -> app_flat(block(app(y6374, map)), down(hd)) 392.66/193.67 down(app(app(y6377, cons), hd)) -> app_flat(down(app(y6377, cons)), block(hd)) 392.66/193.67 down(app(app(y6377, cons), hd)) -> app_flat(block(app(y6377, cons)), down(hd)) 392.66/193.67 down(app(app(y6380, nil), hd)) -> app_flat(down(app(y6380, nil)), block(hd)) 392.66/193.67 down(app(app(y6380, nil), hd)) -> app_flat(block(app(y6380, nil)), down(hd)) 392.66/193.67 down(app(app(y6383, fresh_constant), hd)) -> app_flat(down(app(y6383, fresh_constant)), block(hd)) 392.66/193.67 down(app(app(y6383, fresh_constant), hd)) -> app_flat(block(app(y6383, fresh_constant)), down(hd)) 392.66/193.67 down(app(app(y6397, app(y6398, y6399)), map)) -> app_flat(down(app(y6397, app(y6398, y6399))), block(map)) 392.66/193.67 down(app(app(y6397, app(y6398, y6399)), map)) -> app_flat(block(app(y6397, app(y6398, y6399))), down(map)) 392.66/193.67 down(app(app(y6419, hd), map)) -> app_flat(down(app(y6419, hd)), block(map)) 392.66/193.67 down(app(app(y6419, hd), map)) -> app_flat(block(app(y6419, hd)), down(map)) 392.66/193.67 down(app(app(y6422, map), map)) -> app_flat(down(app(y6422, map)), block(map)) 392.66/193.67 down(app(app(y6422, map), map)) -> app_flat(block(app(y6422, map)), down(map)) 392.66/193.67 down(app(app(y6425, cons), map)) -> app_flat(down(app(y6425, cons)), block(map)) 392.66/193.67 down(app(app(y6425, cons), map)) -> app_flat(block(app(y6425, cons)), down(map)) 392.66/193.67 down(app(app(y6428, nil), map)) -> app_flat(down(app(y6428, nil)), block(map)) 392.66/193.67 down(app(app(y6428, nil), map)) -> app_flat(block(app(y6428, nil)), down(map)) 392.66/193.67 down(app(app(y6431, fresh_constant), map)) -> app_flat(down(app(y6431, fresh_constant)), block(map)) 392.66/193.67 down(app(app(y6431, fresh_constant), map)) -> app_flat(block(app(y6431, fresh_constant)), down(map)) 392.66/193.67 down(app(app(y6445, app(y6446, y6447)), cons)) -> app_flat(down(app(y6445, app(y6446, y6447))), block(cons)) 392.66/193.67 down(app(app(y6445, app(y6446, y6447)), cons)) -> app_flat(block(app(y6445, app(y6446, y6447))), down(cons)) 392.66/193.67 down(app(app(y6467, hd), cons)) -> app_flat(down(app(y6467, hd)), block(cons)) 392.66/193.67 down(app(app(y6467, hd), cons)) -> app_flat(block(app(y6467, hd)), down(cons)) 392.66/193.67 down(app(app(y6470, map), cons)) -> app_flat(down(app(y6470, map)), block(cons)) 392.66/193.67 down(app(app(y6470, map), cons)) -> app_flat(block(app(y6470, map)), down(cons)) 392.66/193.67 down(app(app(y6473, cons), cons)) -> app_flat(down(app(y6473, cons)), block(cons)) 392.66/193.67 down(app(app(y6473, cons), cons)) -> app_flat(block(app(y6473, cons)), down(cons)) 392.66/193.67 down(app(app(y6476, nil), cons)) -> app_flat(down(app(y6476, nil)), block(cons)) 392.66/193.67 down(app(app(y6476, nil), cons)) -> app_flat(block(app(y6476, nil)), down(cons)) 392.66/193.67 down(app(app(y6479, fresh_constant), cons)) -> app_flat(down(app(y6479, fresh_constant)), block(cons)) 392.66/193.67 down(app(app(y6479, fresh_constant), cons)) -> app_flat(block(app(y6479, fresh_constant)), down(cons)) 392.66/193.67 down(app(app(y6541, app(y6542, y6543)), fresh_constant)) -> app_flat(down(app(y6541, app(y6542, y6543))), block(fresh_constant)) 392.66/193.67 down(app(app(y6541, app(y6542, y6543)), fresh_constant)) -> app_flat(block(app(y6541, app(y6542, y6543))), down(fresh_constant)) 392.66/193.67 down(app(app(y6563, hd), fresh_constant)) -> app_flat(down(app(y6563, hd)), block(fresh_constant)) 392.66/193.67 down(app(app(y6563, hd), fresh_constant)) -> app_flat(block(app(y6563, hd)), down(fresh_constant)) 392.66/193.67 down(app(app(y6566, map), fresh_constant)) -> app_flat(down(app(y6566, map)), block(fresh_constant)) 392.66/193.67 down(app(app(y6566, map), fresh_constant)) -> app_flat(block(app(y6566, map)), down(fresh_constant)) 392.66/193.67 down(app(app(y6569, cons), fresh_constant)) -> app_flat(down(app(y6569, cons)), block(fresh_constant)) 392.66/193.67 down(app(app(y6569, cons), fresh_constant)) -> app_flat(block(app(y6569, cons)), down(fresh_constant)) 392.66/193.67 down(app(app(y6572, nil), fresh_constant)) -> app_flat(down(app(y6572, nil)), block(fresh_constant)) 392.66/193.67 down(app(app(y6572, nil), fresh_constant)) -> app_flat(block(app(y6572, nil)), down(fresh_constant)) 392.66/193.67 down(app(app(y6575, fresh_constant), fresh_constant)) -> app_flat(down(app(y6575, fresh_constant)), block(fresh_constant)) 392.66/193.67 down(app(app(y6575, fresh_constant), fresh_constant)) -> app_flat(block(app(y6575, fresh_constant)), down(fresh_constant)) 392.66/193.67 down(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> app_flat(down(app(y357, app(y20338, y20339))), block(app(app(app(y20340, y20341), y20342), y362))) 392.66/193.67 down(app(app(y357, app(y20338, y20339)), app(app(app(y20340, y20341), y20342), y362))) -> app_flat(block(app(y357, app(y20338, y20339))), down(app(app(app(y20340, y20341), y20342), y362))) 392.66/193.67 down(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> app_flat(down(app(y357, app(y20578, y20579))), block(app(app(0, y20580), y362))) 392.66/193.67 down(app(app(y357, app(y20578, y20579)), app(app(0, y20580), y362))) -> app_flat(block(app(y357, app(y20578, y20579))), down(app(app(0, y20580), y362))) 392.66/193.67 down(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> app_flat(down(app(y357, app(y20690, y20691))), block(app(app(hd, y20692), y362))) 392.66/193.67 down(app(app(y357, app(y20690, y20691)), app(app(hd, y20692), y362))) -> app_flat(block(app(y357, app(y20690, y20691))), down(app(app(hd, y20692), y362))) 392.66/193.67 down(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> app_flat(down(app(y357, app(y20802, y20803))), block(app(app(map, y20804), y362))) 392.66/193.67 down(app(app(y357, app(y20802, y20803)), app(app(map, y20804), y362))) -> app_flat(block(app(y357, app(y20802, y20803))), down(app(app(map, y20804), y362))) 392.66/193.67 down(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> app_flat(down(app(y357, app(y21026, y21027))), block(app(app(nil, y21028), y362))) 392.66/193.67 down(app(app(y357, app(y21026, y21027)), app(app(nil, y21028), y362))) -> app_flat(block(app(y357, app(y21026, y21027))), down(app(app(nil, y21028), y362))) 392.66/193.67 down(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> app_flat(down(app(y357, app(y21138, y21139))), block(app(app(fresh_constant, y21140), y362))) 392.66/193.67 down(app(app(y357, app(y21138, y21139)), app(app(fresh_constant, y21140), y362))) -> app_flat(block(app(y357, app(y21138, y21139))), down(app(app(fresh_constant, y21140), y362))) 392.66/193.67 down(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> app_flat(down(app(y427, hd)), block(app(app(app(y32452, y32453), y32454), y430))) 392.66/193.67 down(app(app(y427, hd), app(app(app(y32452, y32453), y32454), y430))) -> app_flat(block(app(y427, hd)), down(app(app(app(y32452, y32453), y32454), y430))) 392.66/193.67 down(app(app(y427, hd), app(app(0, y32455), y430))) -> app_flat(down(app(y427, hd)), block(app(app(0, y32455), y430))) 392.66/193.67 down(app(app(y427, hd), app(app(0, y32455), y430))) -> app_flat(block(app(y427, hd)), down(app(app(0, y32455), y430))) 392.66/193.67 down(app(app(y427, hd), app(app(hd, y32456), y430))) -> app_flat(down(app(y427, hd)), block(app(app(hd, y32456), y430))) 392.66/193.67 down(app(app(y427, hd), app(app(hd, y32456), y430))) -> app_flat(block(app(y427, hd)), down(app(app(hd, y32456), y430))) 392.66/193.67 down(app(app(y427, hd), app(app(map, y32457), y430))) -> app_flat(down(app(y427, hd)), block(app(app(map, y32457), y430))) 392.66/193.67 down(app(app(y427, hd), app(app(map, y32457), y430))) -> app_flat(block(app(y427, hd)), down(app(app(map, y32457), y430))) 392.66/193.67 down(app(app(y427, hd), app(app(nil, y32459), y430))) -> app_flat(down(app(y427, hd)), block(app(app(nil, y32459), y430))) 392.66/193.67 down(app(app(y427, hd), app(app(nil, y32459), y430))) -> app_flat(block(app(y427, hd)), down(app(app(nil, y32459), y430))) 392.66/193.67 down(app(app(y427, hd), app(app(fresh_constant, y32460), y430))) -> app_flat(down(app(y427, hd)), block(app(app(fresh_constant, y32460), y430))) 392.66/193.67 down(app(app(y427, hd), app(app(fresh_constant, y32460), y430))) -> app_flat(block(app(y427, hd)), down(app(app(fresh_constant, y32460), y430))) 392.66/193.67 down(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> app_flat(down(app(y454, map)), block(app(app(app(y32548, y32549), y32550), y457))) 392.66/193.67 down(app(app(y454, map), app(app(app(y32548, y32549), y32550), y457))) -> app_flat(block(app(y454, map)), down(app(app(app(y32548, y32549), y32550), y457))) 392.66/193.67 down(app(app(y454, map), app(app(0, y32551), y457))) -> app_flat(down(app(y454, map)), block(app(app(0, y32551), y457))) 392.66/193.67 down(app(app(y454, map), app(app(0, y32551), y457))) -> app_flat(block(app(y454, map)), down(app(app(0, y32551), y457))) 392.66/193.67 down(app(app(y454, map), app(app(hd, y32552), y457))) -> app_flat(down(app(y454, map)), block(app(app(hd, y32552), y457))) 392.66/193.67 down(app(app(y454, map), app(app(hd, y32552), y457))) -> app_flat(block(app(y454, map)), down(app(app(hd, y32552), y457))) 392.66/193.67 down(app(app(y454, map), app(app(map, y32553), y457))) -> app_flat(down(app(y454, map)), block(app(app(map, y32553), y457))) 392.66/193.67 down(app(app(y454, map), app(app(map, y32553), y457))) -> app_flat(block(app(y454, map)), down(app(app(map, y32553), y457))) 392.66/193.67 down(app(app(y454, map), app(app(nil, y32555), y457))) -> app_flat(down(app(y454, map)), block(app(app(nil, y32555), y457))) 392.66/193.67 down(app(app(y454, map), app(app(nil, y32555), y457))) -> app_flat(block(app(y454, map)), down(app(app(nil, y32555), y457))) 392.66/193.67 down(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> app_flat(down(app(y454, map)), block(app(app(fresh_constant, y32556), y457))) 392.66/193.67 down(app(app(y454, map), app(app(fresh_constant, y32556), y457))) -> app_flat(block(app(y454, map)), down(app(app(fresh_constant, y32556), y457))) 392.66/193.67 down(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> app_flat(down(app(y481, cons)), block(app(app(app(y32644, y32645), y32646), y484))) 392.66/193.67 down(app(app(y481, cons), app(app(app(y32644, y32645), y32646), y484))) -> app_flat(block(app(y481, cons)), down(app(app(app(y32644, y32645), y32646), y484))) 392.66/193.67 down(app(app(y481, cons), app(app(0, y32647), y484))) -> app_flat(down(app(y481, cons)), block(app(app(0, y32647), y484))) 392.66/193.67 down(app(app(y481, cons), app(app(0, y32647), y484))) -> app_flat(block(app(y481, cons)), down(app(app(0, y32647), y484))) 392.66/193.67 down(app(app(y481, cons), app(app(hd, y32648), y484))) -> app_flat(down(app(y481, cons)), block(app(app(hd, y32648), y484))) 392.66/193.67 down(app(app(y481, cons), app(app(hd, y32648), y484))) -> app_flat(block(app(y481, cons)), down(app(app(hd, y32648), y484))) 392.66/193.67 down(app(app(y481, cons), app(app(map, y32649), y484))) -> app_flat(down(app(y481, cons)), block(app(app(map, y32649), y484))) 392.66/193.67 down(app(app(y481, cons), app(app(map, y32649), y484))) -> app_flat(block(app(y481, cons)), down(app(app(map, y32649), y484))) 392.66/193.67 down(app(app(y481, cons), app(app(nil, y32651), y484))) -> app_flat(down(app(y481, cons)), block(app(app(nil, y32651), y484))) 392.66/193.67 down(app(app(y481, cons), app(app(nil, y32651), y484))) -> app_flat(block(app(y481, cons)), down(app(app(nil, y32651), y484))) 392.66/193.67 down(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> app_flat(down(app(y481, cons)), block(app(app(fresh_constant, y32652), y484))) 392.66/193.67 down(app(app(y481, cons), app(app(fresh_constant, y32652), y484))) -> app_flat(block(app(y481, cons)), down(app(app(fresh_constant, y32652), y484))) 392.66/193.67 down(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> app_flat(down(app(y508, nil)), block(app(app(app(y32740, y32741), y32742), y511))) 392.66/193.67 down(app(app(y508, nil), app(app(app(y32740, y32741), y32742), y511))) -> app_flat(block(app(y508, nil)), down(app(app(app(y32740, y32741), y32742), y511))) 392.66/193.67 down(app(app(y508, nil), app(app(0, y32743), y511))) -> app_flat(down(app(y508, nil)), block(app(app(0, y32743), y511))) 392.66/193.67 down(app(app(y508, nil), app(app(0, y32743), y511))) -> app_flat(block(app(y508, nil)), down(app(app(0, y32743), y511))) 392.66/193.67 down(app(app(y508, nil), app(app(hd, y32744), y511))) -> app_flat(down(app(y508, nil)), block(app(app(hd, y32744), y511))) 392.66/193.67 down(app(app(y508, nil), app(app(hd, y32744), y511))) -> app_flat(block(app(y508, nil)), down(app(app(hd, y32744), y511))) 392.66/193.67 down(app(app(y508, nil), app(app(map, y32745), y511))) -> app_flat(down(app(y508, nil)), block(app(app(map, y32745), y511))) 392.66/193.67 down(app(app(y508, nil), app(app(map, y32745), y511))) -> app_flat(block(app(y508, nil)), down(app(app(map, y32745), y511))) 392.66/193.67 down(app(app(y508, nil), app(app(nil, y32747), y511))) -> app_flat(down(app(y508, nil)), block(app(app(nil, y32747), y511))) 392.66/193.67 down(app(app(y508, nil), app(app(nil, y32747), y511))) -> app_flat(block(app(y508, nil)), down(app(app(nil, y32747), y511))) 392.66/193.67 down(app(app(y508, nil), app(app(fresh_constant, y32748), y511))) -> app_flat(down(app(y508, nil)), block(app(app(fresh_constant, y32748), y511))) 392.66/193.67 down(app(app(y508, nil), app(app(fresh_constant, y32748), y511))) -> app_flat(block(app(y508, nil)), down(app(app(fresh_constant, y32748), y511))) 392.66/193.67 down(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(app(y32836, y32837), y32838), y538))) 392.66/193.67 down(app(app(y535, fresh_constant), app(app(app(y32836, y32837), y32838), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(app(y32836, y32837), y32838), y538))) 392.66/193.67 down(app(app(y535, fresh_constant), app(app(0, y32839), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(0, y32839), y538))) 392.66/193.67 down(app(app(y535, fresh_constant), app(app(0, y32839), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(0, y32839), y538))) 392.66/193.67 down(app(app(y535, fresh_constant), app(app(hd, y32840), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(hd, y32840), y538))) 392.66/193.67 down(app(app(y535, fresh_constant), app(app(hd, y32840), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(hd, y32840), y538))) 392.66/193.67 down(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(map, y32841), y538))) 392.66/193.67 down(app(app(y535, fresh_constant), app(app(map, y32841), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(map, y32841), y538))) 392.66/193.67 down(app(app(y535, fresh_constant), app(app(nil, y32843), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(nil, y32843), y538))) 392.66/193.67 down(app(app(y535, fresh_constant), app(app(nil, y32843), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(nil, y32843), y538))) 392.66/193.67 down(app(app(y535, fresh_constant), app(app(fresh_constant, y32844), y538))) -> app_flat(down(app(y535, fresh_constant)), block(app(app(fresh_constant, y32844), y538))) 392.66/193.67 down(app(app(y535, fresh_constant), app(app(fresh_constant, y32844), y538))) -> app_flat(block(app(y535, fresh_constant)), down(app(app(fresh_constant, y32844), y538))) 392.66/193.67 app_flat(up(x_1), block(x_2)) -> up(app(x_1, x_2)) 392.66/193.67 app_flat(block(x_1), up(x_2)) -> up(app(x_1, x_2)) 392.66/193.67 392.66/193.67 Q is empty. 392.66/193.67 We have to consider all minimal (P,Q,R)-chains. 392.66/193.72 EOF