0.85/0.98 YES 0.85/0.98 0.85/0.98 Problem 1: 0.85/0.98 0.85/0.98 (VAR v_NonEmpty:S L:S X:S X1:S X2:S) 0.85/0.98 (RULES 0.85/0.98 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.98 a__adx(nil) -> nil 0.85/0.98 a__adx(X:S) -> adx(X:S) 0.85/0.98 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.98 a__head(X:S) -> head(X:S) 0.85/0.98 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.98 a__incr(nil) -> nil 0.85/0.98 a__incr(X:S) -> incr(X:S) 0.85/0.98 a__nats -> a__adx(a__zeros) 0.85/0.98 a__nats -> nats 0.85/0.98 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.98 a__tail(X:S) -> tail(X:S) 0.85/0.98 a__zeros -> cons(0,zeros) 0.85/0.98 a__zeros -> zeros 0.85/0.98 mark(0) -> 0 0.85/0.98 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.98 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.98 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.98 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.98 mark(nats) -> a__nats 0.85/0.98 mark(nil) -> nil 0.85/0.98 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.98 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.98 mark(zeros) -> a__zeros 0.85/0.98 ) 0.85/0.98 (STRATEGY INNERMOST) 0.85/0.98 0.85/0.98 Problem 1: 0.85/0.98 0.85/0.98 Dependency Pairs Processor: 0.85/0.98 -> Pairs: 0.85/0.98 A__ADX(cons(X:S,L:S)) -> A__INCR(cons(mark(X:S),adx(L:S))) 0.85/0.98 A__ADX(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__HEAD(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__NATS -> A__ADX(a__zeros) 0.85/0.98 A__NATS -> A__ZEROS 0.85/0.98 A__TAIL(cons(X:S,L:S)) -> MARK(L:S) 0.85/0.98 MARK(adx(X:S)) -> A__ADX(mark(X:S)) 0.85/0.98 MARK(adx(X:S)) -> MARK(X:S) 0.85/0.98 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.98 MARK(head(X:S)) -> A__HEAD(mark(X:S)) 0.85/0.98 MARK(head(X:S)) -> MARK(X:S) 0.85/0.98 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.98 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.98 MARK(nats) -> A__NATS 0.85/0.98 MARK(s(X:S)) -> MARK(X:S) 0.85/0.98 MARK(tail(X:S)) -> A__TAIL(mark(X:S)) 0.85/0.98 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.98 MARK(zeros) -> A__ZEROS 0.85/0.98 -> Rules: 0.85/0.98 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.98 a__adx(nil) -> nil 0.85/0.98 a__adx(X:S) -> adx(X:S) 0.85/0.98 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.98 a__head(X:S) -> head(X:S) 0.85/0.98 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.98 a__incr(nil) -> nil 0.85/0.98 a__incr(X:S) -> incr(X:S) 0.85/0.98 a__nats -> a__adx(a__zeros) 0.85/0.98 a__nats -> nats 0.85/0.98 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.98 a__tail(X:S) -> tail(X:S) 0.85/0.98 a__zeros -> cons(0,zeros) 0.85/0.98 a__zeros -> zeros 0.85/0.98 mark(0) -> 0 0.85/0.98 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.98 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.98 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.98 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.98 mark(nats) -> a__nats 0.85/0.98 mark(nil) -> nil 0.85/0.98 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.98 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.98 mark(zeros) -> a__zeros 0.85/0.98 0.85/0.98 Problem 1: 0.85/0.98 0.85/0.98 SCC Processor: 0.85/0.98 -> Pairs: 0.85/0.98 A__ADX(cons(X:S,L:S)) -> A__INCR(cons(mark(X:S),adx(L:S))) 0.85/0.98 A__ADX(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__HEAD(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__NATS -> A__ADX(a__zeros) 0.85/0.98 A__NATS -> A__ZEROS 0.85/0.98 A__TAIL(cons(X:S,L:S)) -> MARK(L:S) 0.85/0.98 MARK(adx(X:S)) -> A__ADX(mark(X:S)) 0.85/0.98 MARK(adx(X:S)) -> MARK(X:S) 0.85/0.98 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.98 MARK(head(X:S)) -> A__HEAD(mark(X:S)) 0.85/0.98 MARK(head(X:S)) -> MARK(X:S) 0.85/0.98 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.98 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.98 MARK(nats) -> A__NATS 0.85/0.98 MARK(s(X:S)) -> MARK(X:S) 0.85/0.98 MARK(tail(X:S)) -> A__TAIL(mark(X:S)) 0.85/0.98 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.98 MARK(zeros) -> A__ZEROS 0.85/0.98 -> Rules: 0.85/0.98 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.98 a__adx(nil) -> nil 0.85/0.98 a__adx(X:S) -> adx(X:S) 0.85/0.98 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.98 a__head(X:S) -> head(X:S) 0.85/0.98 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.98 a__incr(nil) -> nil 0.85/0.98 a__incr(X:S) -> incr(X:S) 0.85/0.98 a__nats -> a__adx(a__zeros) 0.85/0.98 a__nats -> nats 0.85/0.98 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.98 a__tail(X:S) -> tail(X:S) 0.85/0.98 a__zeros -> cons(0,zeros) 0.85/0.98 a__zeros -> zeros 0.85/0.98 mark(0) -> 0 0.85/0.98 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.98 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.98 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.98 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.98 mark(nats) -> a__nats 0.85/0.98 mark(nil) -> nil 0.85/0.98 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.98 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.98 mark(zeros) -> a__zeros 0.85/0.98 ->Strongly Connected Components: 0.85/0.98 ->->Cycle: 0.85/0.98 ->->-> Pairs: 0.85/0.98 A__ADX(cons(X:S,L:S)) -> A__INCR(cons(mark(X:S),adx(L:S))) 0.85/0.98 A__ADX(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__HEAD(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__NATS -> A__ADX(a__zeros) 0.85/0.98 A__TAIL(cons(X:S,L:S)) -> MARK(L:S) 0.85/0.98 MARK(adx(X:S)) -> A__ADX(mark(X:S)) 0.85/0.98 MARK(adx(X:S)) -> MARK(X:S) 0.85/0.98 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.98 MARK(head(X:S)) -> A__HEAD(mark(X:S)) 0.85/0.98 MARK(head(X:S)) -> MARK(X:S) 0.85/0.98 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.98 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.98 MARK(nats) -> A__NATS 0.85/0.98 MARK(s(X:S)) -> MARK(X:S) 0.85/0.98 MARK(tail(X:S)) -> A__TAIL(mark(X:S)) 0.85/0.98 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.98 ->->-> Rules: 0.85/0.98 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.98 a__adx(nil) -> nil 0.85/0.98 a__adx(X:S) -> adx(X:S) 0.85/0.98 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.98 a__head(X:S) -> head(X:S) 0.85/0.98 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.98 a__incr(nil) -> nil 0.85/0.98 a__incr(X:S) -> incr(X:S) 0.85/0.98 a__nats -> a__adx(a__zeros) 0.85/0.98 a__nats -> nats 0.85/0.98 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.98 a__tail(X:S) -> tail(X:S) 0.85/0.98 a__zeros -> cons(0,zeros) 0.85/0.98 a__zeros -> zeros 0.85/0.98 mark(0) -> 0 0.85/0.98 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.98 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.98 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.98 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.98 mark(nats) -> a__nats 0.85/0.98 mark(nil) -> nil 0.85/0.98 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.98 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.98 mark(zeros) -> a__zeros 0.85/0.98 0.85/0.98 Problem 1: 0.85/0.98 0.85/0.98 Reduction Pairs Processor: 0.85/0.98 -> Pairs: 0.85/0.98 A__ADX(cons(X:S,L:S)) -> A__INCR(cons(mark(X:S),adx(L:S))) 0.85/0.98 A__ADX(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__HEAD(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__NATS -> A__ADX(a__zeros) 0.85/0.98 A__TAIL(cons(X:S,L:S)) -> MARK(L:S) 0.85/0.98 MARK(adx(X:S)) -> A__ADX(mark(X:S)) 0.85/0.98 MARK(adx(X:S)) -> MARK(X:S) 0.85/0.98 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.98 MARK(head(X:S)) -> A__HEAD(mark(X:S)) 0.85/0.98 MARK(head(X:S)) -> MARK(X:S) 0.85/0.98 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.98 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.98 MARK(nats) -> A__NATS 0.85/0.98 MARK(s(X:S)) -> MARK(X:S) 0.85/0.98 MARK(tail(X:S)) -> A__TAIL(mark(X:S)) 0.85/0.98 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.98 -> Rules: 0.85/0.98 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.98 a__adx(nil) -> nil 0.85/0.98 a__adx(X:S) -> adx(X:S) 0.85/0.98 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.98 a__head(X:S) -> head(X:S) 0.85/0.98 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.98 a__incr(nil) -> nil 0.85/0.98 a__incr(X:S) -> incr(X:S) 0.85/0.98 a__nats -> a__adx(a__zeros) 0.85/0.98 a__nats -> nats 0.85/0.98 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.98 a__tail(X:S) -> tail(X:S) 0.85/0.98 a__zeros -> cons(0,zeros) 0.85/0.98 a__zeros -> zeros 0.85/0.98 mark(0) -> 0 0.85/0.98 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.98 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.98 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.98 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.98 mark(nats) -> a__nats 0.85/0.98 mark(nil) -> nil 0.85/0.98 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.98 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.98 mark(zeros) -> a__zeros 0.85/0.98 -> Usable rules: 0.85/0.98 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.98 a__adx(nil) -> nil 0.85/0.98 a__adx(X:S) -> adx(X:S) 0.85/0.98 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.98 a__head(X:S) -> head(X:S) 0.85/0.98 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.98 a__incr(nil) -> nil 0.85/0.98 a__incr(X:S) -> incr(X:S) 0.85/0.98 a__nats -> a__adx(a__zeros) 0.85/0.98 a__nats -> nats 0.85/0.98 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.98 a__tail(X:S) -> tail(X:S) 0.85/0.98 a__zeros -> cons(0,zeros) 0.85/0.98 a__zeros -> zeros 0.85/0.98 mark(0) -> 0 0.85/0.98 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.98 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.98 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.98 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.98 mark(nats) -> a__nats 0.85/0.98 mark(nil) -> nil 0.85/0.98 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.98 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.98 mark(zeros) -> a__zeros 0.85/0.98 ->Interpretation type: 0.85/0.98 Linear 0.85/0.98 ->Coefficients: 0.85/0.98 Natural Numbers 0.85/0.98 ->Dimension: 0.85/0.98 1 0.85/0.98 ->Bound: 0.85/0.98 2 0.85/0.98 ->Interpretation: 0.85/0.98 0.85/0.98 [a__adx](X) = 2.X + 1 0.85/0.98 [a__head](X) = X + 2 0.85/0.98 [a__incr](X) = X 0.85/0.98 [a__nats] = 2 0.85/0.98 [a__tail](X) = 2.X + 2 0.85/0.98 [a__zeros] = 0 0.85/0.98 [mark](X) = X 0.85/0.98 [0] = 0 0.85/0.98 [adx](X) = 2.X + 1 0.85/0.98 [cons](X1,X2) = 2.X1 + X2 0.85/0.98 [fSNonEmpty] = 0 0.85/0.98 [head](X) = X + 2 0.85/0.98 [incr](X) = X 0.85/0.98 [nats] = 2 0.85/0.98 [nil] = 1 0.85/0.98 [s](X) = X 0.85/0.98 [tail](X) = 2.X + 2 0.85/0.98 [zeros] = 0 0.85/0.98 [A__ADX](X) = 2.X + 2 0.85/0.98 [A__HEAD](X) = X 0.85/0.98 [A__INCR](X) = X 0.85/0.98 [A__NATS] = 2 0.85/0.98 [A__TAIL](X) = 2.X + 1 0.85/0.98 [A__ZEROS] = 0 0.85/0.98 [MARK](X) = 2.X 0.85/0.98 0.85/0.98 Problem 1: 0.85/0.98 0.85/0.98 SCC Processor: 0.85/0.98 -> Pairs: 0.85/0.98 A__ADX(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__HEAD(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__NATS -> A__ADX(a__zeros) 0.85/0.98 A__TAIL(cons(X:S,L:S)) -> MARK(L:S) 0.85/0.98 MARK(adx(X:S)) -> A__ADX(mark(X:S)) 0.85/0.98 MARK(adx(X:S)) -> MARK(X:S) 0.85/0.98 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.98 MARK(head(X:S)) -> A__HEAD(mark(X:S)) 0.85/0.98 MARK(head(X:S)) -> MARK(X:S) 0.85/0.98 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.98 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.98 MARK(nats) -> A__NATS 0.85/0.98 MARK(s(X:S)) -> MARK(X:S) 0.85/0.98 MARK(tail(X:S)) -> A__TAIL(mark(X:S)) 0.85/0.98 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.98 -> Rules: 0.85/0.98 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.98 a__adx(nil) -> nil 0.85/0.98 a__adx(X:S) -> adx(X:S) 0.85/0.98 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.98 a__head(X:S) -> head(X:S) 0.85/0.98 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.98 a__incr(nil) -> nil 0.85/0.98 a__incr(X:S) -> incr(X:S) 0.85/0.98 a__nats -> a__adx(a__zeros) 0.85/0.98 a__nats -> nats 0.85/0.98 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.98 a__tail(X:S) -> tail(X:S) 0.85/0.98 a__zeros -> cons(0,zeros) 0.85/0.98 a__zeros -> zeros 0.85/0.98 mark(0) -> 0 0.85/0.98 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.98 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.98 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.98 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.98 mark(nats) -> a__nats 0.85/0.98 mark(nil) -> nil 0.85/0.98 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.98 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.98 mark(zeros) -> a__zeros 0.85/0.98 ->Strongly Connected Components: 0.85/0.98 ->->Cycle: 0.85/0.98 ->->-> Pairs: 0.85/0.98 A__ADX(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__HEAD(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__NATS -> A__ADX(a__zeros) 0.85/0.98 A__TAIL(cons(X:S,L:S)) -> MARK(L:S) 0.85/0.98 MARK(adx(X:S)) -> A__ADX(mark(X:S)) 0.85/0.98 MARK(adx(X:S)) -> MARK(X:S) 0.85/0.98 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.98 MARK(head(X:S)) -> A__HEAD(mark(X:S)) 0.85/0.98 MARK(head(X:S)) -> MARK(X:S) 0.85/0.98 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.98 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.98 MARK(nats) -> A__NATS 0.85/0.98 MARK(s(X:S)) -> MARK(X:S) 0.85/0.98 MARK(tail(X:S)) -> A__TAIL(mark(X:S)) 0.85/0.98 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.98 ->->-> Rules: 0.85/0.98 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.98 a__adx(nil) -> nil 0.85/0.98 a__adx(X:S) -> adx(X:S) 0.85/0.98 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.98 a__head(X:S) -> head(X:S) 0.85/0.98 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.98 a__incr(nil) -> nil 0.85/0.98 a__incr(X:S) -> incr(X:S) 0.85/0.98 a__nats -> a__adx(a__zeros) 0.85/0.98 a__nats -> nats 0.85/0.98 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.98 a__tail(X:S) -> tail(X:S) 0.85/0.98 a__zeros -> cons(0,zeros) 0.85/0.98 a__zeros -> zeros 0.85/0.98 mark(0) -> 0 0.85/0.98 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.98 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.98 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.98 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.98 mark(nats) -> a__nats 0.85/0.98 mark(nil) -> nil 0.85/0.98 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.98 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.98 mark(zeros) -> a__zeros 0.85/0.98 0.85/0.98 Problem 1: 0.85/0.98 0.85/0.98 Reduction Pairs Processor: 0.85/0.98 -> Pairs: 0.85/0.98 A__ADX(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__HEAD(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__NATS -> A__ADX(a__zeros) 0.85/0.98 A__TAIL(cons(X:S,L:S)) -> MARK(L:S) 0.85/0.98 MARK(adx(X:S)) -> A__ADX(mark(X:S)) 0.85/0.98 MARK(adx(X:S)) -> MARK(X:S) 0.85/0.98 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.98 MARK(head(X:S)) -> A__HEAD(mark(X:S)) 0.85/0.98 MARK(head(X:S)) -> MARK(X:S) 0.85/0.98 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.98 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.98 MARK(nats) -> A__NATS 0.85/0.98 MARK(s(X:S)) -> MARK(X:S) 0.85/0.98 MARK(tail(X:S)) -> A__TAIL(mark(X:S)) 0.85/0.98 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.98 -> Rules: 0.85/0.98 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.98 a__adx(nil) -> nil 0.85/0.98 a__adx(X:S) -> adx(X:S) 0.85/0.98 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.98 a__head(X:S) -> head(X:S) 0.85/0.98 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.98 a__incr(nil) -> nil 0.85/0.98 a__incr(X:S) -> incr(X:S) 0.85/0.98 a__nats -> a__adx(a__zeros) 0.85/0.98 a__nats -> nats 0.85/0.98 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.98 a__tail(X:S) -> tail(X:S) 0.85/0.98 a__zeros -> cons(0,zeros) 0.85/0.98 a__zeros -> zeros 0.85/0.98 mark(0) -> 0 0.85/0.98 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.98 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.98 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.98 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.98 mark(nats) -> a__nats 0.85/0.98 mark(nil) -> nil 0.85/0.98 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.98 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.98 mark(zeros) -> a__zeros 0.85/0.98 -> Usable rules: 0.85/0.98 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.98 a__adx(nil) -> nil 0.85/0.98 a__adx(X:S) -> adx(X:S) 0.85/0.98 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.98 a__head(X:S) -> head(X:S) 0.85/0.98 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.98 a__incr(nil) -> nil 0.85/0.98 a__incr(X:S) -> incr(X:S) 0.85/0.98 a__nats -> a__adx(a__zeros) 0.85/0.98 a__nats -> nats 0.85/0.98 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.98 a__tail(X:S) -> tail(X:S) 0.85/0.98 a__zeros -> cons(0,zeros) 0.85/0.98 a__zeros -> zeros 0.85/0.98 mark(0) -> 0 0.85/0.98 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.98 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.98 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.98 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.98 mark(nats) -> a__nats 0.85/0.98 mark(nil) -> nil 0.85/0.98 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.98 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.98 mark(zeros) -> a__zeros 0.85/0.98 ->Interpretation type: 0.85/0.98 Linear 0.85/0.98 ->Coefficients: 0.85/0.98 Natural Numbers 0.85/0.98 ->Dimension: 0.85/0.98 1 0.85/0.98 ->Bound: 0.85/0.98 2 0.85/0.98 ->Interpretation: 0.85/0.98 0.85/0.98 [a__adx](X) = 2.X + 2 0.85/0.98 [a__head](X) = 2.X + 2 0.85/0.98 [a__incr](X) = X 0.85/0.98 [a__nats] = 2 0.85/0.98 [a__tail](X) = 2.X + 2 0.85/0.98 [a__zeros] = 0 0.85/0.98 [mark](X) = X 0.85/0.98 [0] = 0 0.85/0.98 [adx](X) = 2.X + 2 0.85/0.98 [cons](X1,X2) = 2.X1 + X2 0.85/0.98 [fSNonEmpty] = 0 0.85/0.98 [head](X) = 2.X + 2 0.85/0.98 [incr](X) = X 0.85/0.98 [nats] = 2 0.85/0.98 [nil] = 2 0.85/0.98 [s](X) = X 0.85/0.98 [tail](X) = 2.X + 2 0.85/0.98 [zeros] = 0 0.85/0.98 [A__ADX](X) = 2.X + 2 0.85/0.98 [A__HEAD](X) = 2.X + 2 0.85/0.98 [A__INCR](X) = X + 1 0.85/0.98 [A__NATS] = 2 0.85/0.98 [A__TAIL](X) = 2.X + 1 0.85/0.98 [A__ZEROS] = 0 0.85/0.98 [MARK](X) = 2.X + 1 0.85/0.98 0.85/0.98 Problem 1: 0.85/0.98 0.85/0.98 SCC Processor: 0.85/0.98 -> Pairs: 0.85/0.98 A__HEAD(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__NATS -> A__ADX(a__zeros) 0.85/0.98 A__TAIL(cons(X:S,L:S)) -> MARK(L:S) 0.85/0.98 MARK(adx(X:S)) -> A__ADX(mark(X:S)) 0.85/0.98 MARK(adx(X:S)) -> MARK(X:S) 0.85/0.98 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.98 MARK(head(X:S)) -> A__HEAD(mark(X:S)) 0.85/0.98 MARK(head(X:S)) -> MARK(X:S) 0.85/0.98 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.98 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.98 MARK(nats) -> A__NATS 0.85/0.98 MARK(s(X:S)) -> MARK(X:S) 0.85/0.98 MARK(tail(X:S)) -> A__TAIL(mark(X:S)) 0.85/0.98 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.98 -> Rules: 0.85/0.98 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.98 a__adx(nil) -> nil 0.85/0.98 a__adx(X:S) -> adx(X:S) 0.85/0.98 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.98 a__head(X:S) -> head(X:S) 0.85/0.98 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.98 a__incr(nil) -> nil 0.85/0.98 a__incr(X:S) -> incr(X:S) 0.85/0.98 a__nats -> a__adx(a__zeros) 0.85/0.98 a__nats -> nats 0.85/0.98 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.98 a__tail(X:S) -> tail(X:S) 0.85/0.98 a__zeros -> cons(0,zeros) 0.85/0.98 a__zeros -> zeros 0.85/0.98 mark(0) -> 0 0.85/0.98 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.98 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.98 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.98 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.98 mark(nats) -> a__nats 0.85/0.98 mark(nil) -> nil 0.85/0.98 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.98 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.98 mark(zeros) -> a__zeros 0.85/0.98 ->Strongly Connected Components: 0.85/0.98 ->->Cycle: 0.85/0.98 ->->-> Pairs: 0.85/0.98 A__HEAD(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.98 A__TAIL(cons(X:S,L:S)) -> MARK(L:S) 0.85/0.98 MARK(adx(X:S)) -> MARK(X:S) 0.85/0.98 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.98 MARK(head(X:S)) -> A__HEAD(mark(X:S)) 0.85/0.98 MARK(head(X:S)) -> MARK(X:S) 0.85/0.98 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.98 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.98 MARK(s(X:S)) -> MARK(X:S) 0.85/0.98 MARK(tail(X:S)) -> A__TAIL(mark(X:S)) 0.85/0.98 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.98 ->->-> Rules: 0.85/0.98 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.98 a__adx(nil) -> nil 0.85/0.98 a__adx(X:S) -> adx(X:S) 0.85/0.98 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.98 a__head(X:S) -> head(X:S) 0.85/0.98 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.98 a__incr(nil) -> nil 0.85/0.98 a__incr(X:S) -> incr(X:S) 0.85/0.98 a__nats -> a__adx(a__zeros) 0.85/0.98 a__nats -> nats 0.85/0.98 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.98 a__tail(X:S) -> tail(X:S) 0.85/0.98 a__zeros -> cons(0,zeros) 0.85/0.98 a__zeros -> zeros 0.85/0.98 mark(0) -> 0 0.85/0.98 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.98 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 0.85/0.99 Problem 1: 0.85/0.99 0.85/0.99 Reduction Pairs Processor: 0.85/0.99 -> Pairs: 0.85/0.99 A__HEAD(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.99 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.99 A__TAIL(cons(X:S,L:S)) -> MARK(L:S) 0.85/0.99 MARK(adx(X:S)) -> MARK(X:S) 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(head(X:S)) -> A__HEAD(mark(X:S)) 0.85/0.99 MARK(head(X:S)) -> MARK(X:S) 0.85/0.99 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 MARK(tail(X:S)) -> A__TAIL(mark(X:S)) 0.85/0.99 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.99 -> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 -> Usable rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 ->Interpretation type: 0.85/0.99 Linear 0.85/0.99 ->Coefficients: 0.85/0.99 Natural Numbers 0.85/0.99 ->Dimension: 0.85/0.99 1 0.85/0.99 ->Bound: 0.85/0.99 2 0.85/0.99 ->Interpretation: 0.85/0.99 0.85/0.99 [a__adx](X) = 2.X + 2 0.85/0.99 [a__head](X) = 2.X + 2 0.85/0.99 [a__incr](X) = X 0.85/0.99 [a__nats] = 2 0.85/0.99 [a__tail](X) = 2.X + 2 0.85/0.99 [a__zeros] = 0 0.85/0.99 [mark](X) = X 0.85/0.99 [0] = 0 0.85/0.99 [adx](X) = 2.X + 2 0.85/0.99 [cons](X1,X2) = 2.X1 + X2 0.85/0.99 [fSNonEmpty] = 0 0.85/0.99 [head](X) = 2.X + 2 0.85/0.99 [incr](X) = X 0.85/0.99 [nats] = 2 0.85/0.99 [nil] = 2 0.85/0.99 [s](X) = X 0.85/0.99 [tail](X) = 2.X + 2 0.85/0.99 [zeros] = 0 0.85/0.99 [A__ADX](X) = 0 0.85/0.99 [A__HEAD](X) = X + 2 0.85/0.99 [A__INCR](X) = X + 1 0.85/0.99 [A__NATS] = 0 0.85/0.99 [A__TAIL](X) = 2.X + 2 0.85/0.99 [A__ZEROS] = 0 0.85/0.99 [MARK](X) = 2.X + 1 0.85/0.99 0.85/0.99 Problem 1: 0.85/0.99 0.85/0.99 SCC Processor: 0.85/0.99 -> Pairs: 0.85/0.99 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.99 A__TAIL(cons(X:S,L:S)) -> MARK(L:S) 0.85/0.99 MARK(adx(X:S)) -> MARK(X:S) 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(head(X:S)) -> A__HEAD(mark(X:S)) 0.85/0.99 MARK(head(X:S)) -> MARK(X:S) 0.85/0.99 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 MARK(tail(X:S)) -> A__TAIL(mark(X:S)) 0.85/0.99 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.99 -> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 ->Strongly Connected Components: 0.85/0.99 ->->Cycle: 0.85/0.99 ->->-> Pairs: 0.85/0.99 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.99 A__TAIL(cons(X:S,L:S)) -> MARK(L:S) 0.85/0.99 MARK(adx(X:S)) -> MARK(X:S) 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(head(X:S)) -> MARK(X:S) 0.85/0.99 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 MARK(tail(X:S)) -> A__TAIL(mark(X:S)) 0.85/0.99 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.99 ->->-> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 0.85/0.99 Problem 1: 0.85/0.99 0.85/0.99 Reduction Pairs Processor: 0.85/0.99 -> Pairs: 0.85/0.99 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.99 A__TAIL(cons(X:S,L:S)) -> MARK(L:S) 0.85/0.99 MARK(adx(X:S)) -> MARK(X:S) 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(head(X:S)) -> MARK(X:S) 0.85/0.99 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 MARK(tail(X:S)) -> A__TAIL(mark(X:S)) 0.85/0.99 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.99 -> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 -> Usable rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 ->Interpretation type: 0.85/0.99 Linear 0.85/0.99 ->Coefficients: 0.85/0.99 Natural Numbers 0.85/0.99 ->Dimension: 0.85/0.99 1 0.85/0.99 ->Bound: 0.85/0.99 2 0.85/0.99 ->Interpretation: 0.85/0.99 0.85/0.99 [a__adx](X) = 2.X 0.85/0.99 [a__head](X) = 2.X + 2 0.85/0.99 [a__incr](X) = X 0.85/0.99 [a__nats] = 2 0.85/0.99 [a__tail](X) = 2.X + 1 0.85/0.99 [a__zeros] = 0 0.85/0.99 [mark](X) = X 0.85/0.99 [0] = 0 0.85/0.99 [adx](X) = 2.X 0.85/0.99 [cons](X1,X2) = X1 + 2.X2 0.85/0.99 [fSNonEmpty] = 0 0.85/0.99 [head](X) = 2.X + 2 0.85/0.99 [incr](X) = X 0.85/0.99 [nats] = 2 0.85/0.99 [nil] = 1 0.85/0.99 [s](X) = X 0.85/0.99 [tail](X) = 2.X + 1 0.85/0.99 [zeros] = 0 0.85/0.99 [A__ADX](X) = 0 0.85/0.99 [A__HEAD](X) = 0 0.85/0.99 [A__INCR](X) = 2.X + 1 0.85/0.99 [A__NATS] = 0 0.85/0.99 [A__TAIL](X) = X + 2 0.85/0.99 [A__ZEROS] = 0 0.85/0.99 [MARK](X) = 2.X + 1 0.85/0.99 0.85/0.99 Problem 1: 0.85/0.99 0.85/0.99 SCC Processor: 0.85/0.99 -> Pairs: 0.85/0.99 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.99 MARK(adx(X:S)) -> MARK(X:S) 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(head(X:S)) -> MARK(X:S) 0.85/0.99 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 MARK(tail(X:S)) -> A__TAIL(mark(X:S)) 0.85/0.99 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.99 -> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 ->Strongly Connected Components: 0.85/0.99 ->->Cycle: 0.85/0.99 ->->-> Pairs: 0.85/0.99 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.99 MARK(adx(X:S)) -> MARK(X:S) 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(head(X:S)) -> MARK(X:S) 0.85/0.99 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.99 ->->-> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 0.85/0.99 Problem 1: 0.85/0.99 0.85/0.99 Reduction Pairs Processor: 0.85/0.99 -> Pairs: 0.85/0.99 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.99 MARK(adx(X:S)) -> MARK(X:S) 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(head(X:S)) -> MARK(X:S) 0.85/0.99 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.99 -> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 -> Usable rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 ->Interpretation type: 0.85/0.99 Linear 0.85/0.99 ->Coefficients: 0.85/0.99 Natural Numbers 0.85/0.99 ->Dimension: 0.85/0.99 1 0.85/0.99 ->Bound: 0.85/0.99 2 0.85/0.99 ->Interpretation: 0.85/0.99 0.85/0.99 [a__adx](X) = 2.X + 2 0.85/0.99 [a__head](X) = 2.X + 2 0.85/0.99 [a__incr](X) = X 0.85/0.99 [a__nats] = 2 0.85/0.99 [a__tail](X) = X + 1 0.85/0.99 [a__zeros] = 0 0.85/0.99 [mark](X) = X 0.85/0.99 [0] = 0 0.85/0.99 [adx](X) = 2.X + 2 0.85/0.99 [cons](X1,X2) = 2.X1 + X2 0.85/0.99 [fSNonEmpty] = 0 0.85/0.99 [head](X) = 2.X + 2 0.85/0.99 [incr](X) = X 0.85/0.99 [nats] = 2 0.85/0.99 [nil] = 1 0.85/0.99 [s](X) = X 0.85/0.99 [tail](X) = X + 1 0.85/0.99 [zeros] = 0 0.85/0.99 [A__ADX](X) = 0 0.85/0.99 [A__HEAD](X) = 0 0.85/0.99 [A__INCR](X) = 2.X + 2 0.85/0.99 [A__NATS] = 0 0.85/0.99 [A__TAIL](X) = 0 0.85/0.99 [A__ZEROS] = 0 0.85/0.99 [MARK](X) = 2.X + 2 0.85/0.99 0.85/0.99 Problem 1: 0.85/0.99 0.85/0.99 SCC Processor: 0.85/0.99 -> Pairs: 0.85/0.99 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(head(X:S)) -> MARK(X:S) 0.85/0.99 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.99 -> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 ->Strongly Connected Components: 0.85/0.99 ->->Cycle: 0.85/0.99 ->->-> Pairs: 0.85/0.99 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(head(X:S)) -> MARK(X:S) 0.85/0.99 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.99 ->->-> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 0.85/0.99 Problem 1: 0.85/0.99 0.85/0.99 Reduction Pairs Processor: 0.85/0.99 -> Pairs: 0.85/0.99 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(head(X:S)) -> MARK(X:S) 0.85/0.99 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.99 -> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 -> Usable rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 ->Interpretation type: 0.85/0.99 Linear 0.85/0.99 ->Coefficients: 0.85/0.99 Natural Numbers 0.85/0.99 ->Dimension: 0.85/0.99 1 0.85/0.99 ->Bound: 0.85/0.99 2 0.85/0.99 ->Interpretation: 0.85/0.99 0.85/0.99 [a__adx](X) = X 0.85/0.99 [a__head](X) = X + 2 0.85/0.99 [a__incr](X) = X 0.85/0.99 [a__nats] = 2 0.85/0.99 [a__tail](X) = X + 1 0.85/0.99 [a__zeros] = 2 0.85/0.99 [mark](X) = X 0.85/0.99 [0] = 0 0.85/0.99 [adx](X) = X 0.85/0.99 [cons](X1,X2) = X1 + X2 0.85/0.99 [fSNonEmpty] = 0 0.85/0.99 [head](X) = X + 2 0.85/0.99 [incr](X) = X 0.85/0.99 [nats] = 2 0.85/0.99 [nil] = 1 0.85/0.99 [s](X) = X 0.85/0.99 [tail](X) = X + 1 0.85/0.99 [zeros] = 2 0.85/0.99 [A__ADX](X) = 0 0.85/0.99 [A__HEAD](X) = 0 0.85/0.99 [A__INCR](X) = 2.X + 2 0.85/0.99 [A__NATS] = 0 0.85/0.99 [A__TAIL](X) = 0 0.85/0.99 [A__ZEROS] = 0 0.85/0.99 [MARK](X) = 2.X + 2 0.85/0.99 0.85/0.99 Problem 1: 0.85/0.99 0.85/0.99 SCC Processor: 0.85/0.99 -> Pairs: 0.85/0.99 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.99 -> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 ->Strongly Connected Components: 0.85/0.99 ->->Cycle: 0.85/0.99 ->->-> Pairs: 0.85/0.99 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.99 ->->-> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 0.85/0.99 Problem 1: 0.85/0.99 0.85/0.99 Reduction Pairs Processor: 0.85/0.99 -> Pairs: 0.85/0.99 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 MARK(tail(X:S)) -> MARK(X:S) 0.85/0.99 -> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 -> Usable rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 ->Interpretation type: 0.85/0.99 Linear 0.85/0.99 ->Coefficients: 0.85/0.99 Natural Numbers 0.85/0.99 ->Dimension: 0.85/0.99 1 0.85/0.99 ->Bound: 0.85/0.99 2 0.85/0.99 ->Interpretation: 0.85/0.99 0.85/0.99 [a__adx](X) = X + 1 0.85/0.99 [a__head](X) = 2.X + 1 0.85/0.99 [a__incr](X) = X 0.85/0.99 [a__nats] = 2 0.85/0.99 [a__tail](X) = 2.X + 2 0.85/0.99 [a__zeros] = 1 0.85/0.99 [mark](X) = X 0.85/0.99 [0] = 0 0.85/0.99 [adx](X) = X + 1 0.85/0.99 [cons](X1,X2) = 2.X1 + X2 0.85/0.99 [fSNonEmpty] = 0 0.85/0.99 [head](X) = 2.X + 1 0.85/0.99 [incr](X) = X 0.85/0.99 [nats] = 2 0.85/0.99 [nil] = 0 0.85/0.99 [s](X) = X 0.85/0.99 [tail](X) = 2.X + 2 0.85/0.99 [zeros] = 1 0.85/0.99 [A__ADX](X) = 0 0.85/0.99 [A__HEAD](X) = 0 0.85/0.99 [A__INCR](X) = 2.X + 2 0.85/0.99 [A__NATS] = 0 0.85/0.99 [A__TAIL](X) = 0 0.85/0.99 [A__ZEROS] = 0 0.85/0.99 [MARK](X) = 2.X + 2 0.85/0.99 0.85/0.99 Problem 1: 0.85/0.99 0.85/0.99 SCC Processor: 0.85/0.99 -> Pairs: 0.85/0.99 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 -> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 ->Strongly Connected Components: 0.85/0.99 ->->Cycle: 0.85/0.99 ->->-> Pairs: 0.85/0.99 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 ->->-> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 0.85/0.99 Problem 1: 0.85/0.99 0.85/0.99 Reduction Pairs Processor: 0.85/0.99 -> Pairs: 0.85/0.99 A__INCR(cons(X:S,L:S)) -> MARK(X:S) 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 -> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 -> Usable rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 ->Interpretation type: 0.85/0.99 Linear 0.85/0.99 ->Coefficients: 0.85/0.99 All rationals 0.85/0.99 ->Dimension: 0.85/0.99 1 0.85/0.99 ->Bound: 0.85/0.99 2 0.85/0.99 ->Interpretation: 0.85/0.99 0.85/0.99 [a__adx](X) = 2.X 0.85/0.99 [a__head](X) = 2.X + 2 0.85/0.99 [a__incr](X) = X + 1/2 0.85/0.99 [a__nats] = 2 0.85/0.99 [a__tail](X) = 2.X 0.85/0.99 [a__zeros] = 1 0.85/0.99 [mark](X) = X 0.85/0.99 [0] = 0 0.85/0.99 [adx](X) = 2.X 0.85/0.99 [cons](X1,X2) = 2.X1 + 1/2.X2 + 1/2 0.85/0.99 [fSNonEmpty] = 0 0.85/0.99 [head](X) = 2.X + 2 0.85/0.99 [incr](X) = X + 1/2 0.85/0.99 [nats] = 2 0.85/0.99 [nil] = 2 0.85/0.99 [s](X) = X 0.85/0.99 [tail](X) = 2.X 0.85/0.99 [zeros] = 1 0.85/0.99 [A__ADX](X) = 0 0.85/0.99 [A__HEAD](X) = 0 0.85/0.99 [A__INCR](X) = X 0.85/0.99 [A__NATS] = 0 0.85/0.99 [A__TAIL](X) = 0 0.85/0.99 [A__ZEROS] = 0 0.85/0.99 [MARK](X) = 2.X 0.85/0.99 0.85/0.99 Problem 1: 0.85/0.99 0.85/0.99 SCC Processor: 0.85/0.99 -> Pairs: 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(incr(X:S)) -> A__INCR(mark(X:S)) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 -> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 ->Strongly Connected Components: 0.85/0.99 ->->Cycle: 0.85/0.99 ->->-> Pairs: 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 ->->-> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 0.85/0.99 Problem 1: 0.85/0.99 0.85/0.99 Subterm Processor: 0.85/0.99 -> Pairs: 0.85/0.99 MARK(cons(X1:S,X2:S)) -> MARK(X1:S) 0.85/0.99 MARK(incr(X:S)) -> MARK(X:S) 0.85/0.99 MARK(s(X:S)) -> MARK(X:S) 0.85/0.99 -> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 ->Projection: 0.85/0.99 pi(MARK) = 1 0.85/0.99 0.85/0.99 Problem 1: 0.85/0.99 0.85/0.99 SCC Processor: 0.85/0.99 -> Pairs: 0.85/0.99 Empty 0.85/0.99 -> Rules: 0.85/0.99 a__adx(cons(X:S,L:S)) -> a__incr(cons(mark(X:S),adx(L:S))) 0.85/0.99 a__adx(nil) -> nil 0.85/0.99 a__adx(X:S) -> adx(X:S) 0.85/0.99 a__head(cons(X:S,L:S)) -> mark(X:S) 0.85/0.99 a__head(X:S) -> head(X:S) 0.85/0.99 a__incr(cons(X:S,L:S)) -> cons(s(mark(X:S)),incr(L:S)) 0.85/0.99 a__incr(nil) -> nil 0.85/0.99 a__incr(X:S) -> incr(X:S) 0.85/0.99 a__nats -> a__adx(a__zeros) 0.85/0.99 a__nats -> nats 0.85/0.99 a__tail(cons(X:S,L:S)) -> mark(L:S) 0.85/0.99 a__tail(X:S) -> tail(X:S) 0.85/0.99 a__zeros -> cons(0,zeros) 0.85/0.99 a__zeros -> zeros 0.85/0.99 mark(0) -> 0 0.85/0.99 mark(adx(X:S)) -> a__adx(mark(X:S)) 0.85/0.99 mark(cons(X1:S,X2:S)) -> cons(mark(X1:S),X2:S) 0.85/0.99 mark(head(X:S)) -> a__head(mark(X:S)) 0.85/0.99 mark(incr(X:S)) -> a__incr(mark(X:S)) 0.85/0.99 mark(nats) -> a__nats 0.85/0.99 mark(nil) -> nil 0.85/0.99 mark(s(X:S)) -> s(mark(X:S)) 0.85/0.99 mark(tail(X:S)) -> a__tail(mark(X:S)) 0.85/0.99 mark(zeros) -> a__zeros 0.85/0.99 ->Strongly Connected Components: 0.85/0.99 There is no strongly connected component 0.85/0.99 0.85/0.99 The problem is finite. 0.85/0.99 EOF