YES TPA v.1.0 Result: TRS is terminating Default interpretations for symbols are not printed. For polynomial interpretations and semantic labelling over N\{0,1} defaults are 2 for constants, identity for unary symbols and x+y-2 for binary symbols. For semantic labelling over {0,1} (booleans) defaults are 0 for constants, identity for unary symbols and disjunction for binary symbols. [1] TRS loaded from input file: (1) c(b(a(X))) -> a(a(b(b(c(c(X)))))) (2) a(X) -> e (3) b(X) -> e (4) c(X) -> e [2] Label this TRS using following interpretation that is a quasi-model: [c(x)] = 0 [b(x)] = 1 [a(x)] = 0 rest default thus obtaining new TRS: (1a) c$1(b$0(a$1(X))) -> a$0(a$1(b$1(b$0(c$0(c$1(X)))))) (1b) c$1(b$0(a$0(X))) -> a$0(a$1(b$1(b$0(c$0(c$0(X)))))) (2a) a$1(X) -> e (2b) a$0(X) -> e (3a) b$1(X) -> e (3b) b$0(X) -> e (4a) c$1(X) -> e (4b) c$0(X) -> e (D1) a$1(x) ->= a$0(x) (D2) b$1(x) ->= b$0(x) (D3) c$1(x) ->= c$0(x) [3] Use following polynomial interpretation: [c$1(x)] = x + 1 rest default Remove rules with left hand side strictly bigger than right hand side: (1b), (4a), (D3) [4] Use following polynomial interpretation: [a$1(x)] = x + 1 rest default Remove rules with left hand side strictly bigger than right hand side: (2a), (D1) [5] Use following polynomial interpretation: [a$1(x)] = x + 1 [c$1(x)] = 7x rest default Remove rules with left hand side strictly bigger than right hand side: (1a) [6] Unlabel this TRS to obtain the one consisting of the rules: (2)-(4) [7] Use following polynomial interpretation: [c(x)] = x + 1 rest default Remove rules with left hand side strictly bigger than right hand side: (4) [8] Use following polynomial interpretation: [b(x)] = x + 1 rest default Remove rules with left hand side strictly bigger than right hand side: (3) [9] Use following polynomial interpretation: [a(x)] = x + 1 rest default Remove rules with left hand side strictly bigger than right hand side: (2) [10] Since there are no remaining rules, termination is proved! ../tpdb/TRS/Rubio/lindau.trs, 0.01, Y Couldn't open file <60>: 60: No such file or directory