MAYBE Time: 0.009147 TRS: {cond(true(), x) -> cond(odd x, 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 x), cond#(true(), x) -> odd# x, cond#(true(), x) -> p# x, odd# s s x -> odd# x} TRS: {cond(true(), x) -> cond(odd x, 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 x), cond#(true(), x) -> p# x) (cond#(true(), x) -> cond#(odd x, p x), cond#(true(), x) -> odd# x) (cond#(true(), x) -> cond#(odd x, p x), cond#(true(), x) -> cond#(odd x, 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: 0.687500 SCCS (2): Scc: {cond#(true(), x) -> cond#(odd x, p x)} Scc: {odd# s s x -> odd# x} SCC (1): Strict: {cond#(true(), x) -> cond#(odd x, p x)} Weak: {cond(true(), x) -> cond(odd x, 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 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, [p](x0) = x0, [s](x0) = x0 + 1, [true] = 1, [false] = 0, [0] = 0, [odd#](x0) = x0 Strict: odd# s s x -> odd# x 2 + 1x >= 0 + 1x Weak: p s x -> x 1 + 1x >= 1x p 0() -> 0() 0 >= 0 odd s s x -> odd x 2 + 1x >= 0 + 1x odd s 0() -> true() 1 >= 1 odd 0() -> false() 0 >= 0 cond(true(), x) -> cond(odd x, p x) 2 + 1x >= 1 + 2x Qed