MAYBE Time: 0.057786 TRS: {cond(true(), x) -> cond(odd x, p p p x), odd 0() -> false(), odd s 0() -> true(), odd s s x -> odd x, p 0() -> 0(), p s x -> x} DP: DP: {cond#(true(), x) -> cond#(odd x, p p p x), cond#(true(), x) -> odd# x, cond#(true(), x) -> p# x, cond#(true(), x) -> p# p x, cond#(true(), x) -> p# p p x, odd# s s x -> odd# x} TRS: {cond(true(), x) -> cond(odd x, p p p x), odd 0() -> false(), odd s 0() -> true(), odd s s x -> odd x, p 0() -> 0(), p s x -> x} UR: { odd 0() -> false(), odd s 0() -> true(), odd s s x -> odd x, p 0() -> 0(), p s x -> x, a(y, z) -> y, a(y, z) -> z} EDG: {(cond#(true(), x) -> cond#(odd x, p p p x), cond#(true(), x) -> p# p p x) (cond#(true(), x) -> cond#(odd x, p p p x), cond#(true(), x) -> p# p x) (cond#(true(), x) -> cond#(odd x, p p p x), cond#(true(), x) -> p# x) (cond#(true(), x) -> cond#(odd x, p p p x), cond#(true(), x) -> odd# x) (cond#(true(), x) -> cond#(odd x, p p p x), cond#(true(), x) -> cond#(odd x, p p p x)) (odd# s s x -> odd# x, odd# s s x -> odd# x) (cond#(true(), x) -> odd# x, odd# s s x -> odd# x)} STATUS: arrows: 0.805556 SCCS (2): Scc: {cond#(true(), x) -> cond#(odd x, p p p x)} Scc: {odd# s s x -> odd# x} SCC (1): Strict: {cond#(true(), x) -> cond#(odd x, p p p x)} Weak: {cond(true(), x) -> cond(odd x, p p p x), odd 0() -> false(), odd s 0() -> true(), odd s s x -> odd x, p 0() -> 0(), p s x -> x} Fail SCC (1): Strict: {odd# s s x -> odd# x} Weak: {cond(true(), x) -> cond(odd x, p p p x), odd 0() -> false(), odd s 0() -> true(), odd s s x -> odd x, p 0() -> 0(), p s x -> x} POLY: Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true Interpretation: [cond](x0, x1) = x0 + x1 + 1, [odd](x0) = x0 + 1, [p](x0) = x0 + 1, [s](x0) = x0 + 1, [true] = 0, [false] = 0, [0] = 1, [odd#](x0) = x0 Strict: odd# s s x -> odd# x 2 + 1x >= 0 + 1x Weak: p s x -> x 2 + 1x >= 1x p 0() -> 0() 2 >= 1 odd s s x -> odd x 3 + 1x >= 1 + 1x odd s 0() -> true() 3 >= 0 odd 0() -> false() 2 >= 0 cond(true(), x) -> cond(odd x, p p p x) 1 + 1x >= 5 + 2x Qed