0.00/0.09 YES 0.00/0.09 0.00/0.09 Problem 1: 0.00/0.09 0.00/0.09 (VAR v_NonEmpty:S X:S X1:S X2:S Y:S) 0.00/0.09 (RULES 0.00/0.09 a__adx(cons(X:S,Y:S)) -> a__incr(cons(X:S,adx(Y:S))) 0.00/0.09 a__adx(X:S) -> adx(X:S) 0.00/0.09 a__hd(cons(X:S,Y:S)) -> mark(X:S) 0.00/0.09 a__hd(X:S) -> hd(X:S) 0.00/0.09 a__incr(cons(X:S,Y:S)) -> cons(s(X:S),incr(Y:S)) 0.00/0.09 a__incr(X:S) -> incr(X:S) 0.00/0.09 a__nats -> a__adx(a__zeros) 0.00/0.09 a__nats -> nats 0.00/0.09 a__tl(cons(X:S,Y:S)) -> mark(Y:S) 0.00/0.09 a__tl(X:S) -> tl(X:S) 0.00/0.09 a__zeros -> cons(0,zeros) 0.00/0.09 a__zeros -> zeros 0.00/0.09 mark(0) -> 0 0.00/0.09 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.00/0.09 mark(cons(X1:S,X2:S)) -> cons(X1:S,X2:S) 0.00/0.09 mark(hd(X:S)) -> a__hd(mark(X:S)) 0.00/0.09 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.00/0.09 mark(nats) -> a__nats 0.00/0.09 mark(s(X:S)) -> s(X:S) 0.00/0.09 mark(tl(X:S)) -> a__tl(mark(X:S)) 0.00/0.09 mark(zeros) -> a__zeros 0.00/0.09 ) 0.00/0.09 (STRATEGY INNERMOST) 0.00/0.09 0.00/0.09 Problem 1: 0.00/0.09 0.00/0.09 Dependency Pairs Processor: 0.00/0.09 -> Pairs: 0.00/0.09 A__ADX(cons(X:S,Y:S)) -> A__INCR(cons(X:S,adx(Y:S))) 0.00/0.09 A__HD(cons(X:S,Y:S)) -> MARK(X:S) 0.00/0.09 A__NATS -> A__ADX(a__zeros) 0.00/0.09 A__NATS -> A__ZEROS 0.00/0.09 A__TL(cons(X:S,Y:S)) -> MARK(Y:S) 0.00/0.09 MARK(adx(X:S)) -> A__ADX(mark(X:S)) 0.00/0.09 MARK(adx(X:S)) -> MARK(X:S) 0.00/0.09 MARK(hd(X:S)) -> A__HD(mark(X:S)) 0.00/0.09 MARK(hd(X:S)) -> MARK(X:S) 0.00/0.09 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.00/0.09 MARK(incr(X:S)) -> MARK(X:S) 0.00/0.09 MARK(nats) -> A__NATS 0.00/0.09 MARK(tl(X:S)) -> A__TL(mark(X:S)) 0.00/0.09 MARK(tl(X:S)) -> MARK(X:S) 0.00/0.09 MARK(zeros) -> A__ZEROS 0.00/0.09 -> Rules: 0.00/0.09 a__adx(cons(X:S,Y:S)) -> a__incr(cons(X:S,adx(Y:S))) 0.00/0.09 a__adx(X:S) -> adx(X:S) 0.00/0.09 a__hd(cons(X:S,Y:S)) -> mark(X:S) 0.00/0.09 a__hd(X:S) -> hd(X:S) 0.00/0.09 a__incr(cons(X:S,Y:S)) -> cons(s(X:S),incr(Y:S)) 0.00/0.09 a__incr(X:S) -> incr(X:S) 0.00/0.09 a__nats -> a__adx(a__zeros) 0.00/0.09 a__nats -> nats 0.00/0.09 a__tl(cons(X:S,Y:S)) -> mark(Y:S) 0.00/0.09 a__tl(X:S) -> tl(X:S) 0.00/0.09 a__zeros -> cons(0,zeros) 0.00/0.09 a__zeros -> zeros 0.00/0.09 mark(0) -> 0 0.00/0.09 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.00/0.09 mark(cons(X1:S,X2:S)) -> cons(X1:S,X2:S) 0.00/0.09 mark(hd(X:S)) -> a__hd(mark(X:S)) 0.00/0.09 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.00/0.09 mark(nats) -> a__nats 0.00/0.09 mark(s(X:S)) -> s(X:S) 0.00/0.09 mark(tl(X:S)) -> a__tl(mark(X:S)) 0.00/0.09 mark(zeros) -> a__zeros 0.00/0.09 0.00/0.09 Problem 1: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 A__ADX(cons(X:S,Y:S)) -> A__INCR(cons(X:S,adx(Y:S))) 0.00/0.09 A__HD(cons(X:S,Y:S)) -> MARK(X:S) 0.00/0.09 A__NATS -> A__ADX(a__zeros) 0.00/0.09 A__NATS -> A__ZEROS 0.00/0.09 A__TL(cons(X:S,Y:S)) -> MARK(Y:S) 0.00/0.09 MARK(adx(X:S)) -> A__ADX(mark(X:S)) 0.00/0.09 MARK(adx(X:S)) -> MARK(X:S) 0.00/0.09 MARK(hd(X:S)) -> A__HD(mark(X:S)) 0.00/0.09 MARK(hd(X:S)) -> MARK(X:S) 0.00/0.09 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.00/0.09 MARK(incr(X:S)) -> MARK(X:S) 0.00/0.09 MARK(nats) -> A__NATS 0.00/0.09 MARK(tl(X:S)) -> A__TL(mark(X:S)) 0.00/0.09 MARK(tl(X:S)) -> MARK(X:S) 0.00/0.09 MARK(zeros) -> A__ZEROS 0.00/0.09 -> Rules: 0.00/0.09 a__adx(cons(X:S,Y:S)) -> a__incr(cons(X:S,adx(Y:S))) 0.00/0.09 a__adx(X:S) -> adx(X:S) 0.00/0.09 a__hd(cons(X:S,Y:S)) -> mark(X:S) 0.00/0.09 a__hd(X:S) -> hd(X:S) 0.00/0.09 a__incr(cons(X:S,Y:S)) -> cons(s(X:S),incr(Y:S)) 0.00/0.09 a__incr(X:S) -> incr(X:S) 0.00/0.09 a__nats -> a__adx(a__zeros) 0.00/0.09 a__nats -> nats 0.00/0.09 a__tl(cons(X:S,Y:S)) -> mark(Y:S) 0.00/0.09 a__tl(X:S) -> tl(X:S) 0.00/0.09 a__zeros -> cons(0,zeros) 0.00/0.09 a__zeros -> zeros 0.00/0.09 mark(0) -> 0 0.00/0.09 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.00/0.09 mark(cons(X1:S,X2:S)) -> cons(X1:S,X2:S) 0.00/0.09 mark(hd(X:S)) -> a__hd(mark(X:S)) 0.00/0.09 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.00/0.09 mark(nats) -> a__nats 0.00/0.09 mark(s(X:S)) -> s(X:S) 0.00/0.09 mark(tl(X:S)) -> a__tl(mark(X:S)) 0.00/0.09 mark(zeros) -> a__zeros 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 A__HD(cons(X:S,Y:S)) -> MARK(X:S) 0.00/0.09 A__TL(cons(X:S,Y:S)) -> MARK(Y:S) 0.00/0.09 MARK(adx(X:S)) -> MARK(X:S) 0.00/0.09 MARK(hd(X:S)) -> A__HD(mark(X:S)) 0.00/0.09 MARK(hd(X:S)) -> MARK(X:S) 0.00/0.09 MARK(incr(X:S)) -> MARK(X:S) 0.00/0.09 MARK(tl(X:S)) -> A__TL(mark(X:S)) 0.00/0.09 MARK(tl(X:S)) -> MARK(X:S) 0.00/0.09 ->->-> Rules: 0.00/0.09 a__adx(cons(X:S,Y:S)) -> a__incr(cons(X:S,adx(Y:S))) 0.00/0.09 a__adx(X:S) -> adx(X:S) 0.00/0.09 a__hd(cons(X:S,Y:S)) -> mark(X:S) 0.00/0.09 a__hd(X:S) -> hd(X:S) 0.00/0.09 a__incr(cons(X:S,Y:S)) -> cons(s(X:S),incr(Y:S)) 0.00/0.09 a__incr(X:S) -> incr(X:S) 0.00/0.09 a__nats -> a__adx(a__zeros) 0.00/0.09 a__nats -> nats 0.00/0.09 a__tl(cons(X:S,Y:S)) -> mark(Y:S) 0.00/0.09 a__tl(X:S) -> tl(X:S) 0.00/0.09 a__zeros -> cons(0,zeros) 0.00/0.09 a__zeros -> zeros 0.00/0.09 mark(0) -> 0 0.00/0.09 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.00/0.09 mark(cons(X1:S,X2:S)) -> cons(X1:S,X2:S) 0.00/0.09 mark(hd(X:S)) -> a__hd(mark(X:S)) 0.00/0.09 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.00/0.09 mark(nats) -> a__nats 0.00/0.09 mark(s(X:S)) -> s(X:S) 0.00/0.09 mark(tl(X:S)) -> a__tl(mark(X:S)) 0.00/0.09 mark(zeros) -> a__zeros 0.00/0.09 0.00/0.09 Problem 1: 0.00/0.09 0.00/0.09 Reduction Pairs Processor: 0.00/0.09 -> Pairs: 0.00/0.09 A__HD(cons(X:S,Y:S)) -> MARK(X:S) 0.00/0.09 A__TL(cons(X:S,Y:S)) -> MARK(Y:S) 0.00/0.09 MARK(adx(X:S)) -> MARK(X:S) 0.00/0.09 MARK(hd(X:S)) -> A__HD(mark(X:S)) 0.00/0.09 MARK(hd(X:S)) -> MARK(X:S) 0.00/0.09 MARK(incr(X:S)) -> MARK(X:S) 0.00/0.09 MARK(tl(X:S)) -> A__TL(mark(X:S)) 0.00/0.09 MARK(tl(X:S)) -> MARK(X:S) 0.00/0.09 -> Rules: 0.00/0.09 a__adx(cons(X:S,Y:S)) -> a__incr(cons(X:S,adx(Y:S))) 0.00/0.09 a__adx(X:S) -> adx(X:S) 0.00/0.09 a__hd(cons(X:S,Y:S)) -> mark(X:S) 0.00/0.09 a__hd(X:S) -> hd(X:S) 0.00/0.09 a__incr(cons(X:S,Y:S)) -> cons(s(X:S),incr(Y:S)) 0.00/0.09 a__incr(X:S) -> incr(X:S) 0.00/0.09 a__nats -> a__adx(a__zeros) 0.00/0.09 a__nats -> nats 0.00/0.09 a__tl(cons(X:S,Y:S)) -> mark(Y:S) 0.00/0.09 a__tl(X:S) -> tl(X:S) 0.00/0.09 a__zeros -> cons(0,zeros) 0.00/0.09 a__zeros -> zeros 0.00/0.09 mark(0) -> 0 0.00/0.09 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.00/0.09 mark(cons(X1:S,X2:S)) -> cons(X1:S,X2:S) 0.00/0.09 mark(hd(X:S)) -> a__hd(mark(X:S)) 0.00/0.09 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.00/0.09 mark(nats) -> a__nats 0.00/0.09 mark(s(X:S)) -> s(X:S) 0.00/0.09 mark(tl(X:S)) -> a__tl(mark(X:S)) 0.00/0.09 mark(zeros) -> a__zeros 0.00/0.09 -> Usable rules: 0.00/0.09 a__adx(cons(X:S,Y:S)) -> a__incr(cons(X:S,adx(Y:S))) 0.00/0.09 a__adx(X:S) -> adx(X:S) 0.00/0.09 a__hd(cons(X:S,Y:S)) -> mark(X:S) 0.00/0.09 a__hd(X:S) -> hd(X:S) 0.00/0.09 a__incr(cons(X:S,Y:S)) -> cons(s(X:S),incr(Y:S)) 0.00/0.09 a__incr(X:S) -> incr(X:S) 0.00/0.09 a__nats -> a__adx(a__zeros) 0.00/0.09 a__nats -> nats 0.00/0.09 a__tl(cons(X:S,Y:S)) -> mark(Y:S) 0.00/0.09 a__tl(X:S) -> tl(X:S) 0.00/0.09 a__zeros -> cons(0,zeros) 0.00/0.09 a__zeros -> zeros 0.00/0.09 mark(0) -> 0 0.00/0.09 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.00/0.09 mark(cons(X1:S,X2:S)) -> cons(X1:S,X2:S) 0.00/0.09 mark(hd(X:S)) -> a__hd(mark(X:S)) 0.00/0.09 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.00/0.09 mark(nats) -> a__nats 0.00/0.09 mark(s(X:S)) -> s(X:S) 0.00/0.09 mark(tl(X:S)) -> a__tl(mark(X:S)) 0.00/0.09 mark(zeros) -> a__zeros 0.00/0.09 ->Interpretation type: 0.00/0.09 Linear 0.00/0.09 ->Coefficients: 0.00/0.09 Natural Numbers 0.00/0.09 ->Dimension: 0.00/0.09 1 0.00/0.09 ->Bound: 0.00/0.09 2 0.00/0.09 ->Interpretation: 0.00/0.09 0.00/0.09 [a__adx](X) = 2.X + 2 0.00/0.09 [a__hd](X) = 2.X + 2 0.00/0.09 [a__incr](X) = X 0.00/0.09 [a__nats] = 2 0.00/0.09 [a__tl](X) = 2.X + 2 0.00/0.09 [a__zeros] = 0 0.00/0.09 [mark](X) = 2.X + 2 0.00/0.09 [0] = 0 0.00/0.09 [adx](X) = 2.X + 2 0.00/0.09 [cons](X1,X2) = 2.X1 + X2 0.00/0.09 [fSNonEmpty] = 0 0.00/0.09 [hd](X) = 2.X + 2 0.00/0.09 [incr](X) = X 0.00/0.09 [nats] = 2 0.00/0.09 [s](X) = X 0.00/0.09 [tl](X) = 2.X + 2 0.00/0.09 [zeros] = 0 0.00/0.09 [A__ADX](X) = 0 0.00/0.09 [A__HD](X) = X + 2 0.00/0.09 [A__INCR](X) = 0 0.00/0.09 [A__NATS] = 0 0.00/0.09 [A__TL](X) = 2.X + 1 0.00/0.09 [A__ZEROS] = 0 0.00/0.09 [MARK](X) = 2.X + 1 0.00/0.09 0.00/0.09 Problem 1: 0.00/0.09 0.00/0.09 SCC Processor: 0.00/0.09 -> Pairs: 0.00/0.09 A__TL(cons(X:S,Y:S)) -> MARK(Y:S) 0.00/0.09 MARK(adx(X:S)) -> MARK(X:S) 0.00/0.09 MARK(hd(X:S)) -> A__HD(mark(X:S)) 0.00/0.09 MARK(hd(X:S)) -> MARK(X:S) 0.00/0.09 MARK(incr(X:S)) -> MARK(X:S) 0.00/0.09 MARK(tl(X:S)) -> A__TL(mark(X:S)) 0.00/0.09 MARK(tl(X:S)) -> MARK(X:S) 0.00/0.09 -> Rules: 0.00/0.09 a__adx(cons(X:S,Y:S)) -> a__incr(cons(X:S,adx(Y:S))) 0.00/0.09 a__adx(X:S) -> adx(X:S) 0.00/0.09 a__hd(cons(X:S,Y:S)) -> mark(X:S) 0.00/0.09 a__hd(X:S) -> hd(X:S) 0.00/0.09 a__incr(cons(X:S,Y:S)) -> cons(s(X:S),incr(Y:S)) 0.00/0.09 a__incr(X:S) -> incr(X:S) 0.00/0.09 a__nats -> a__adx(a__zeros) 0.00/0.09 a__nats -> nats 0.00/0.09 a__tl(cons(X:S,Y:S)) -> mark(Y:S) 0.00/0.09 a__tl(X:S) -> tl(X:S) 0.00/0.09 a__zeros -> cons(0,zeros) 0.00/0.09 a__zeros -> zeros 0.00/0.09 mark(0) -> 0 0.00/0.09 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.00/0.09 mark(cons(X1:S,X2:S)) -> cons(X1:S,X2:S) 0.00/0.09 mark(hd(X:S)) -> a__hd(mark(X:S)) 0.00/0.09 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.00/0.09 mark(nats) -> a__nats 0.00/0.09 mark(s(X:S)) -> s(X:S) 0.00/0.09 mark(tl(X:S)) -> a__tl(mark(X:S)) 0.00/0.09 mark(zeros) -> a__zeros 0.00/0.09 ->Strongly Connected Components: 0.00/0.09 ->->Cycle: 0.00/0.09 ->->-> Pairs: 0.00/0.09 A__TL(cons(X:S,Y:S)) -> MARK(Y:S) 0.00/0.09 MARK(adx(X:S)) -> MARK(X:S) 0.00/0.09 MARK(hd(X:S)) -> MARK(X:S) 0.00/0.09 MARK(incr(X:S)) -> MARK(X:S) 0.00/0.09 MARK(tl(X:S)) -> A__TL(mark(X:S)) 0.00/0.09 MARK(tl(X:S)) -> MARK(X:S) 0.00/0.09 ->->-> Rules: 0.00/0.09 a__adx(cons(X:S,Y:S)) -> a__incr(cons(X:S,adx(Y:S))) 0.00/0.09 a__adx(X:S) -> adx(X:S) 0.00/0.09 a__hd(cons(X:S,Y:S)) -> mark(X:S) 0.00/0.09 a__hd(X:S) -> hd(X:S) 0.00/0.09 a__incr(cons(X:S,Y:S)) -> cons(s(X:S),incr(Y:S)) 0.00/0.09 a__incr(X:S) -> incr(X:S) 0.00/0.09 a__nats -> a__adx(a__zeros) 0.00/0.09 a__nats -> nats 0.00/0.09 a__tl(cons(X:S,Y:S)) -> mark(Y:S) 0.00/0.09 a__tl(X:S) -> tl(X:S) 0.00/0.09 a__zeros -> cons(0,zeros) 0.00/0.09 a__zeros -> zeros 0.00/0.09 mark(0) -> 0 0.00/0.09 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.00/0.09 mark(cons(X1:S,X2:S)) -> cons(X1:S,X2:S) 0.00/0.09 mark(hd(X:S)) -> a__hd(mark(X:S)) 0.00/0.09 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.00/0.09 mark(nats) -> a__nats 0.00/0.09 mark(s(X:S)) -> s(X:S) 0.00/0.09 mark(tl(X:S)) -> a__tl(mark(X:S)) 0.00/0.09 mark(zeros) -> a__zeros 0.00/0.09 0.00/0.09 Problem 1: 0.00/0.09 0.00/0.09 Reduction Pairs Processor: 0.00/0.09 -> Pairs: 0.00/0.09 A__TL(cons(X:S,Y:S)) -> MARK(Y:S) 0.00/0.09 MARK(adx(X:S)) -> MARK(X:S) 0.00/0.09 MARK(hd(X:S)) -> MARK(X:S) 0.00/0.09 MARK(incr(X:S)) -> MARK(X:S) 0.00/0.10 MARK(tl(X:S)) -> A__TL(mark(X:S)) 0.00/0.10 MARK(tl(X:S)) -> MARK(X:S) 0.00/0.10 -> Rules: 0.00/0.10 a__adx(cons(X:S,Y:S)) -> a__incr(cons(X:S,adx(Y:S))) 0.00/0.10 a__adx(X:S) -> adx(X:S) 0.00/0.10 a__hd(cons(X:S,Y:S)) -> mark(X:S) 0.00/0.10 a__hd(X:S) -> hd(X:S) 0.00/0.10 a__incr(cons(X:S,Y:S)) -> cons(s(X:S),incr(Y:S)) 0.00/0.10 a__incr(X:S) -> incr(X:S) 0.00/0.10 a__nats -> a__adx(a__zeros) 0.00/0.10 a__nats -> nats 0.00/0.10 a__tl(cons(X:S,Y:S)) -> mark(Y:S) 0.00/0.10 a__tl(X:S) -> tl(X:S) 0.00/0.10 a__zeros -> cons(0,zeros) 0.00/0.10 a__zeros -> zeros 0.00/0.10 mark(0) -> 0 0.00/0.10 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.00/0.10 mark(cons(X1:S,X2:S)) -> cons(X1:S,X2:S) 0.00/0.10 mark(hd(X:S)) -> a__hd(mark(X:S)) 0.00/0.10 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.00/0.10 mark(nats) -> a__nats 0.00/0.10 mark(s(X:S)) -> s(X:S) 0.00/0.10 mark(tl(X:S)) -> a__tl(mark(X:S)) 0.00/0.10 mark(zeros) -> a__zeros 0.00/0.10 -> Usable rules: 0.00/0.10 a__adx(cons(X:S,Y:S)) -> a__incr(cons(X:S,adx(Y:S))) 0.00/0.10 a__adx(X:S) -> adx(X:S) 0.00/0.10 a__hd(cons(X:S,Y:S)) -> mark(X:S) 0.00/0.10 a__hd(X:S) -> hd(X:S) 0.00/0.10 a__incr(cons(X:S,Y:S)) -> cons(s(X:S),incr(Y:S)) 0.00/0.10 a__incr(X:S) -> incr(X:S) 0.00/0.10 a__nats -> a__adx(a__zeros) 0.00/0.10 a__nats -> nats 0.00/0.10 a__tl(cons(X:S,Y:S)) -> mark(Y:S) 0.00/0.10 a__tl(X:S) -> tl(X:S) 0.00/0.10 a__zeros -> cons(0,zeros) 0.00/0.10 a__zeros -> zeros 0.00/0.10 mark(0) -> 0 0.00/0.10 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.00/0.10 mark(cons(X1:S,X2:S)) -> cons(X1:S,X2:S) 0.00/0.10 mark(hd(X:S)) -> a__hd(mark(X:S)) 0.00/0.10 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.00/0.10 mark(nats) -> a__nats 0.00/0.10 mark(s(X:S)) -> s(X:S) 0.00/0.10 mark(tl(X:S)) -> a__tl(mark(X:S)) 0.00/0.10 mark(zeros) -> a__zeros 0.00/0.10 ->Interpretation type: 0.00/0.10 Linear 0.00/0.10 ->Coefficients: 0.00/0.10 Natural Numbers 0.00/0.10 ->Dimension: 0.00/0.10 1 0.00/0.10 ->Bound: 0.00/0.10 2 0.00/0.10 ->Interpretation: 0.00/0.10 0.00/0.10 [a__adx](X) = X + 1 0.00/0.10 [a__hd](X) = 2.X + 2 0.00/0.10 [a__incr](X) = X 0.00/0.10 [a__nats] = 2 0.00/0.10 [a__tl](X) = 2.X + 2 0.00/0.10 [a__zeros] = 1 0.00/0.10 [mark](X) = 2.X + 1 0.00/0.10 [0] = 0 0.00/0.10 [adx](X) = X + 1 0.00/0.10 [cons](X1,X2) = 2.X1 + X2 + 1 0.00/0.10 [fSNonEmpty] = 0 0.00/0.10 [hd](X) = 2.X + 2 0.00/0.10 [incr](X) = X 0.00/0.10 [nats] = 1 0.00/0.10 [s](X) = X 0.00/0.10 [tl](X) = 2.X + 2 0.00/0.10 [zeros] = 0 0.00/0.10 [A__ADX](X) = 0 0.00/0.10 [A__HD](X) = 0 0.00/0.10 [A__INCR](X) = 0 0.00/0.10 [A__NATS] = 0 0.00/0.10 [A__TL](X) = 2.X + 1 0.00/0.10 [A__ZEROS] = 0 0.00/0.10 [MARK](X) = 2.X + 2 0.00/0.10 0.00/0.10 Problem 1: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 MARK(adx(X:S)) -> MARK(X:S) 0.00/0.10 MARK(hd(X:S)) -> MARK(X:S) 0.00/0.10 MARK(incr(X:S)) -> MARK(X:S) 0.00/0.10 MARK(tl(X:S)) -> A__TL(mark(X:S)) 0.00/0.10 MARK(tl(X:S)) -> MARK(X:S) 0.00/0.10 -> Rules: 0.00/0.10 a__adx(cons(X:S,Y:S)) -> a__incr(cons(X:S,adx(Y:S))) 0.00/0.10 a__adx(X:S) -> adx(X:S) 0.00/0.10 a__hd(cons(X:S,Y:S)) -> mark(X:S) 0.00/0.10 a__hd(X:S) -> hd(X:S) 0.00/0.10 a__incr(cons(X:S,Y:S)) -> cons(s(X:S),incr(Y:S)) 0.00/0.10 a__incr(X:S) -> incr(X:S) 0.00/0.10 a__nats -> a__adx(a__zeros) 0.00/0.10 a__nats -> nats 0.00/0.10 a__tl(cons(X:S,Y:S)) -> mark(Y:S) 0.00/0.10 a__tl(X:S) -> tl(X:S) 0.00/0.10 a__zeros -> cons(0,zeros) 0.00/0.10 a__zeros -> zeros 0.00/0.10 mark(0) -> 0 0.00/0.10 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.00/0.10 mark(cons(X1:S,X2:S)) -> cons(X1:S,X2:S) 0.00/0.10 mark(hd(X:S)) -> a__hd(mark(X:S)) 0.00/0.10 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.00/0.10 mark(nats) -> a__nats 0.00/0.10 mark(s(X:S)) -> s(X:S) 0.00/0.10 mark(tl(X:S)) -> a__tl(mark(X:S)) 0.00/0.10 mark(zeros) -> a__zeros 0.00/0.10 ->Strongly Connected Components: 0.00/0.10 ->->Cycle: 0.00/0.10 ->->-> Pairs: 0.00/0.10 MARK(adx(X:S)) -> MARK(X:S) 0.00/0.10 MARK(hd(X:S)) -> MARK(X:S) 0.00/0.10 MARK(incr(X:S)) -> MARK(X:S) 0.00/0.10 MARK(tl(X:S)) -> MARK(X:S) 0.00/0.10 ->->-> Rules: 0.00/0.10 a__adx(cons(X:S,Y:S)) -> a__incr(cons(X:S,adx(Y:S))) 0.00/0.10 a__adx(X:S) -> adx(X:S) 0.00/0.10 a__hd(cons(X:S,Y:S)) -> mark(X:S) 0.00/0.10 a__hd(X:S) -> hd(X:S) 0.00/0.10 a__incr(cons(X:S,Y:S)) -> cons(s(X:S),incr(Y:S)) 0.00/0.10 a__incr(X:S) -> incr(X:S) 0.00/0.10 a__nats -> a__adx(a__zeros) 0.00/0.10 a__nats -> nats 0.00/0.10 a__tl(cons(X:S,Y:S)) -> mark(Y:S) 0.00/0.10 a__tl(X:S) -> tl(X:S) 0.00/0.10 a__zeros -> cons(0,zeros) 0.00/0.10 a__zeros -> zeros 0.00/0.10 mark(0) -> 0 0.00/0.10 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.00/0.10 mark(cons(X1:S,X2:S)) -> cons(X1:S,X2:S) 0.00/0.10 mark(hd(X:S)) -> a__hd(mark(X:S)) 0.00/0.10 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.00/0.10 mark(nats) -> a__nats 0.00/0.10 mark(s(X:S)) -> s(X:S) 0.00/0.10 mark(tl(X:S)) -> a__tl(mark(X:S)) 0.00/0.10 mark(zeros) -> a__zeros 0.00/0.10 0.00/0.10 Problem 1: 0.00/0.10 0.00/0.10 Subterm Processor: 0.00/0.10 -> Pairs: 0.00/0.10 MARK(adx(X:S)) -> MARK(X:S) 0.00/0.10 MARK(hd(X:S)) -> MARK(X:S) 0.00/0.10 MARK(incr(X:S)) -> MARK(X:S) 0.00/0.10 MARK(tl(X:S)) -> MARK(X:S) 0.00/0.10 -> Rules: 0.00/0.10 a__adx(cons(X:S,Y:S)) -> a__incr(cons(X:S,adx(Y:S))) 0.00/0.10 a__adx(X:S) -> adx(X:S) 0.00/0.10 a__hd(cons(X:S,Y:S)) -> mark(X:S) 0.00/0.10 a__hd(X:S) -> hd(X:S) 0.00/0.10 a__incr(cons(X:S,Y:S)) -> cons(s(X:S),incr(Y:S)) 0.00/0.10 a__incr(X:S) -> incr(X:S) 0.00/0.10 a__nats -> a__adx(a__zeros) 0.00/0.10 a__nats -> nats 0.00/0.10 a__tl(cons(X:S,Y:S)) -> mark(Y:S) 0.00/0.10 a__tl(X:S) -> tl(X:S) 0.00/0.10 a__zeros -> cons(0,zeros) 0.00/0.10 a__zeros -> zeros 0.00/0.10 mark(0) -> 0 0.00/0.10 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.00/0.10 mark(cons(X1:S,X2:S)) -> cons(X1:S,X2:S) 0.00/0.10 mark(hd(X:S)) -> a__hd(mark(X:S)) 0.00/0.10 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.00/0.10 mark(nats) -> a__nats 0.00/0.10 mark(s(X:S)) -> s(X:S) 0.00/0.10 mark(tl(X:S)) -> a__tl(mark(X:S)) 0.00/0.10 mark(zeros) -> a__zeros 0.00/0.10 ->Projection: 0.00/0.10 pi(MARK) = 1 0.00/0.10 0.00/0.10 Problem 1: 0.00/0.10 0.00/0.10 SCC Processor: 0.00/0.10 -> Pairs: 0.00/0.10 Empty 0.00/0.10 -> Rules: 0.00/0.10 a__adx(cons(X:S,Y:S)) -> a__incr(cons(X:S,adx(Y:S))) 0.00/0.10 a__adx(X:S) -> adx(X:S) 0.00/0.10 a__hd(cons(X:S,Y:S)) -> mark(X:S) 0.00/0.10 a__hd(X:S) -> hd(X:S) 0.00/0.10 a__incr(cons(X:S,Y:S)) -> cons(s(X:S),incr(Y:S)) 0.00/0.10 a__incr(X:S) -> incr(X:S) 0.00/0.10 a__nats -> a__adx(a__zeros) 0.00/0.10 a__nats -> nats 0.00/0.10 a__tl(cons(X:S,Y:S)) -> mark(Y:S) 0.00/0.10 a__tl(X:S) -> tl(X:S) 0.00/0.10 a__zeros -> cons(0,zeros) 0.00/0.10 a__zeros -> zeros 0.00/0.10 mark(0) -> 0 0.00/0.10 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.00/0.10 mark(cons(X1:S,X2:S)) -> cons(X1:S,X2:S) 0.00/0.10 mark(hd(X:S)) -> a__hd(mark(X:S)) 0.00/0.10 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.00/0.10 mark(nats) -> a__nats 0.00/0.10 mark(s(X:S)) -> s(X:S) 0.00/0.10 mark(tl(X:S)) -> a__tl(mark(X:S)) 0.00/0.10 mark(zeros) -> a__zeros 0.00/0.10 ->Strongly Connected Components: 0.00/0.10 There is no strongly connected component 0.00/0.10 0.00/0.10 The problem is finite. 0.00/0.10 EOF