41.29/10.82 YES 41.61/10.83 41.61/10.83 Problem: 41.61/10.83 a(a(a(x1))) -> a(c(a(a(x1)))) 41.61/10.83 c(c(c(x1))) -> a(x1) 41.61/10.83 a(x1) -> x1 41.61/10.83 41.61/10.83 Proof: 41.61/10.83 DP Processor: 41.61/10.83 DPs: 41.61/10.83 a#(a(a(x1))) -> c#(a(a(x1))) 41.61/10.83 a#(a(a(x1))) -> a#(c(a(a(x1)))) 41.61/10.83 c#(c(c(x1))) -> a#(x1) 41.61/10.83 TRS: 41.61/10.83 a(a(a(x1))) -> a(c(a(a(x1)))) 41.61/10.83 c(c(c(x1))) -> a(x1) 41.61/10.83 a(x1) -> x1 41.61/10.83 TDG Processor: 41.61/10.83 DPs: 41.61/10.83 a#(a(a(x1))) -> c#(a(a(x1))) 41.61/10.83 a#(a(a(x1))) -> a#(c(a(a(x1)))) 41.61/10.83 c#(c(c(x1))) -> a#(x1) 41.61/10.83 TRS: 41.61/10.83 a(a(a(x1))) -> a(c(a(a(x1)))) 41.61/10.83 c(c(c(x1))) -> a(x1) 41.61/10.83 a(x1) -> x1 41.61/10.83 graph: 41.61/10.83 c#(c(c(x1))) -> a#(x1) -> a#(a(a(x1))) -> a#(c(a(a(x1)))) 41.61/10.83 c#(c(c(x1))) -> a#(x1) -> a#(a(a(x1))) -> c#(a(a(x1))) 41.61/10.83 a#(a(a(x1))) -> c#(a(a(x1))) -> c#(c(c(x1))) -> a#(x1) 41.61/10.83 a#(a(a(x1))) -> a#(c(a(a(x1)))) -> 41.61/10.83 a#(a(a(x1))) -> a#(c(a(a(x1)))) 41.61/10.83 a#(a(a(x1))) -> a#(c(a(a(x1)))) -> a#(a(a(x1))) -> c#(a(a(x1))) 41.61/10.83 Root-Labeling Processor: 41.61/10.83 DPs: 41.61/10.83 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 41.61/10.83 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 41.61/10.83 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) 41.61/10.83 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) 41.61/10.83 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) 41.61/10.83 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) 41.61/10.83 c{#,(f4)}(f4(c)(c(c)(c(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 41.61/10.83 c{#,(f4)}(f4(c)(c(c)(c(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 41.61/10.83 c{#,(f4)}(f4(c)(c(c)(c(c)(x1)))) -> a{#,(f4)}(f4(c)(x1)) 41.61/10.83 TRS: 41.61/10.83 a(a)(a(a)(a(f4)(x1))) -> a(c)(c(a)(a(a)(a(f4)(x1)))) 41.61/10.83 a(a)(a(a)(a(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) 41.61/10.83 a(a)(a(a)(a(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) 41.61/10.83 f4(c)(c(c)(c(c)(c(f4)(x1)))) -> f4(a)(a(f4)(x1)) 41.61/10.83 f4(c)(c(c)(c(c)(c(a)(x1)))) -> f4(a)(a(a)(x1)) 41.61/10.83 f4(c)(c(c)(c(c)(c(c)(x1)))) -> f4(a)(a(c)(x1)) 41.61/10.83 a(c)(c(c)(c(c)(c(f4)(x1)))) -> a(a)(a(f4)(x1)) 41.61/10.83 a(c)(c(c)(c(c)(c(a)(x1)))) -> a(a)(a(a)(x1)) 41.61/10.83 a(c)(c(c)(c(c)(c(c)(x1)))) -> a(a)(a(c)(x1)) 41.61/10.83 c(c)(c(c)(c(c)(c(f4)(x1)))) -> c(a)(a(f4)(x1)) 41.61/10.83 c(c)(c(c)(c(c)(c(a)(x1)))) -> c(a)(a(a)(x1)) 41.61/10.83 c(c)(c(c)(c(c)(c(c)(x1)))) -> c(a)(a(c)(x1)) 41.61/10.83 f4(a)(a(f4)(x1)) -> f4(f4)(x1) 41.61/10.83 f4(a)(a(a)(x1)) -> f4(a)(x1) 41.61/10.83 f4(a)(a(c)(x1)) -> f4(c)(x1) 41.61/10.83 a(a)(a(f4)(x1)) -> a(f4)(x1) 41.61/10.83 a(a)(a(a)(x1)) -> a(a)(x1) 41.61/10.83 a(a)(a(c)(x1)) -> a(c)(x1) 41.61/10.83 c(a)(a(f4)(x1)) -> c(f4)(x1) 41.61/10.83 c(a)(a(a)(x1)) -> c(a)(x1) 41.61/10.83 c(a)(a(c)(x1)) -> c(c)(x1) 41.61/10.83 TDG Processor: 41.61/10.83 DPs: 41.61/10.83 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 41.61/10.83 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 41.61/10.83 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) 41.61/10.83 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) 41.61/10.83 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) 41.61/10.83 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) 41.61/10.83 c{#,(f4)}(f4(c)(c(c)(c(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 41.61/10.83 c{#,(f4)}(f4(c)(c(c)(c(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 41.61/10.83 c{#,(f4)}(f4(c)(c(c)(c(c)(x1)))) -> a{#,(f4)}(f4(c)(x1)) 41.61/10.83 TRS: 41.61/10.83 a(a)(a(a)(a(f4)(x1))) -> a(c)(c(a)(a(a)(a(f4)(x1)))) 41.61/10.83 a(a)(a(a)(a(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) 41.61/10.83 a(a)(a(a)(a(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) 41.61/10.83 f4(c)(c(c)(c(c)(c(f4)(x1)))) -> f4(a)(a(f4)(x1)) 41.61/10.83 f4(c)(c(c)(c(c)(c(a)(x1)))) -> f4(a)(a(a)(x1)) 41.61/10.83 f4(c)(c(c)(c(c)(c(c)(x1)))) -> f4(a)(a(c)(x1)) 41.61/10.83 a(c)(c(c)(c(c)(c(f4)(x1)))) -> a(a)(a(f4)(x1)) 41.61/10.83 a(c)(c(c)(c(c)(c(a)(x1)))) -> a(a)(a(a)(x1)) 41.61/10.83 a(c)(c(c)(c(c)(c(c)(x1)))) -> a(a)(a(c)(x1)) 41.61/10.83 c(c)(c(c)(c(c)(c(f4)(x1)))) -> c(a)(a(f4)(x1)) 41.61/10.83 c(c)(c(c)(c(c)(c(a)(x1)))) -> c(a)(a(a)(x1)) 41.61/10.83 c(c)(c(c)(c(c)(c(c)(x1)))) -> c(a)(a(c)(x1)) 41.61/10.83 f4(a)(a(f4)(x1)) -> f4(f4)(x1) 41.61/10.83 f4(a)(a(a)(x1)) -> f4(a)(x1) 41.61/10.83 f4(a)(a(c)(x1)) -> f4(c)(x1) 41.61/10.83 a(a)(a(f4)(x1)) -> a(f4)(x1) 41.61/10.83 a(a)(a(a)(x1)) -> a(a)(x1) 41.61/10.83 a(a)(a(c)(x1)) -> a(c)(x1) 41.61/10.83 c(a)(a(f4)(x1)) -> c(f4)(x1) 41.61/10.83 c(a)(a(a)(x1)) -> c(a)(x1) 41.61/10.83 c(a)(a(c)(x1)) -> c(c)(x1) 41.61/10.84 graph: 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(c)(x1)))) -> a{#,(f4)}(f4(c)(x1)) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(c)(x1)))) -> a{#,(f4)}(f4(c)(x1)) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(c)(x1)))) -> a{#,(f4)}(f4(c)(x1)) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(c)(x1)))) -> a{#,(f4)}(f4(c)(x1)) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(c)(x1)))) -> a{#,(f4)}(f4(c)(x1)) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(c)(x1)))) -> a{#,(f4)}(f4(c)(x1)) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(c)(x1)))) -> a{#,(f4)}(f4(c)(x1)) 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> 41.61/10.84 c{#,(f4)}(f4(c)(c(c)(c(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) -> 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 41.61/10.84 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> 41.64/10.91 c{#,(f4)}(f4(c)(c(c)(c(c)(x1)))) -> a{#,(f4)}(f4(c)(x1)) 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> 41.64/10.91 c{#,(f4)}(f4(c)(c(c)(c(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> 41.64/10.91 c{#,(f4)}(f4(c)(c(c)(c(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) -> 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) -> 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) -> 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) -> 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) -> 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) -> 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> 41.64/10.91 c{#,(f4)}(f4(c)(c(c)(c(c)(x1)))) -> a{#,(f4)}(f4(c)(x1)) 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> 41.64/10.91 c{#,(f4)}(f4(c)(c(c)(c(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> 41.64/10.91 c{#,(f4)}(f4(c)(c(c)(c(f4)(x1)))) -> a{#,(f4)}(f4(f4)(x1)) 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) -> 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) -> 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) -> 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) -> 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) -> 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) -> 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 41.64/10.91 Polynomial Interpretation Processor: 41.64/10.91 dimension: 1 41.64/10.91 interpretation: 41.64/10.91 [f4(f4)](x0) = x0, 41.64/10.91 41.64/10.91 [c(f4)](x0) = x0 + 1, 41.64/10.91 41.64/10.91 [c(c)](x0) = x0, 41.64/10.91 41.64/10.91 [c(a)](x0) = x0, 41.64/10.91 41.64/10.91 [f4(c)](x0) = x0, 41.64/10.91 41.64/10.91 [a(c)](x0) = x0, 41.64/10.91 41.64/10.91 [c{#,(f4)}](x0) = x0 + 1, 41.64/10.91 41.64/10.91 [a(f4)](x0) = x0 + 1, 41.64/10.91 41.64/10.91 [a(a)](x0) = x0, 41.64/10.91 41.64/10.91 [f4(a)](x0) = x0, 41.64/10.91 41.64/10.91 [a{#,(f4)}](x0) = x0 + 1 41.64/10.91 orientation: 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) = x1 + 2 >= x1 + 2 = c{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 41.64/10.91 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) = x1 + 1 >= x1 + 1 = c{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 41.64/10.91 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) = x1 + 1 >= x1 + 1 = c{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) 41.64/10.91 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) = x1 + 2 >= x1 + 2 = a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) 41.64/10.91 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) 41.64/10.91 41.64/10.91 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) 41.64/10.91 41.64/10.91 c{#,(f4)}(f4(c)(c(c)(c(f4)(x1)))) = x1 + 2 >= x1 + 1 = a{#,(f4)}(f4(f4)(x1)) 41.64/10.91 41.64/10.91 c{#,(f4)}(f4(c)(c(c)(c(a)(x1)))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(a)(x1)) 41.64/10.91 41.64/10.91 c{#,(f4)}(f4(c)(c(c)(c(c)(x1)))) = x1 + 1 >= x1 + 1 = a{#,(f4)}(f4(c)(x1)) 41.70/10.93 41.70/10.93 a(a)(a(a)(a(f4)(x1))) = x1 + 1 >= x1 + 1 = a(c)(c(a)(a(a)(a(f4)(x1)))) 41.70/10.93 41.70/10.93 a(a)(a(a)(a(a)(x1))) = x1 >= x1 = a(c)(c(a)(a(a)(a(a)(x1)))) 41.70/10.93 41.70/10.93 a(a)(a(a)(a(c)(x1))) = x1 >= x1 = a(c)(c(a)(a(a)(a(c)(x1)))) 41.70/10.93 41.70/10.93 f4(c)(c(c)(c(c)(c(f4)(x1)))) = x1 + 1 >= x1 + 1 = f4(a)(a(f4)(x1)) 41.70/10.93 41.70/10.93 f4(c)(c(c)(c(c)(c(a)(x1)))) = x1 >= x1 = f4(a)(a(a)(x1)) 41.70/10.93 41.70/10.93 f4(c)(c(c)(c(c)(c(c)(x1)))) = x1 >= x1 = f4(a)(a(c)(x1)) 41.70/10.93 41.70/10.93 a(c)(c(c)(c(c)(c(f4)(x1)))) = x1 + 1 >= x1 + 1 = a(a)(a(f4)(x1)) 41.70/10.93 41.70/10.93 a(c)(c(c)(c(c)(c(a)(x1)))) = x1 >= x1 = a(a)(a(a)(x1)) 41.70/10.93 41.70/10.93 a(c)(c(c)(c(c)(c(c)(x1)))) = x1 >= x1 = a(a)(a(c)(x1)) 41.70/10.93 41.70/10.93 c(c)(c(c)(c(c)(c(f4)(x1)))) = x1 + 1 >= x1 + 1 = c(a)(a(f4)(x1)) 41.70/10.93 41.70/10.93 c(c)(c(c)(c(c)(c(a)(x1)))) = x1 >= x1 = c(a)(a(a)(x1)) 41.70/10.93 41.70/10.93 c(c)(c(c)(c(c)(c(c)(x1)))) = x1 >= x1 = c(a)(a(c)(x1)) 41.70/10.93 41.70/10.93 f4(a)(a(f4)(x1)) = x1 + 1 >= x1 = f4(f4)(x1) 41.70/10.93 41.70/10.93 f4(a)(a(a)(x1)) = x1 >= x1 = f4(a)(x1) 41.70/10.93 41.70/10.93 f4(a)(a(c)(x1)) = x1 >= x1 = f4(c)(x1) 41.70/10.93 41.70/10.93 a(a)(a(f4)(x1)) = x1 + 1 >= x1 + 1 = a(f4)(x1) 41.70/10.93 41.70/10.93 a(a)(a(a)(x1)) = x1 >= x1 = a(a)(x1) 41.70/10.93 41.70/10.93 a(a)(a(c)(x1)) = x1 >= x1 = a(c)(x1) 41.70/10.93 41.70/10.93 c(a)(a(f4)(x1)) = x1 + 1 >= x1 + 1 = c(f4)(x1) 41.70/10.93 41.70/10.93 c(a)(a(a)(x1)) = x1 >= x1 = c(a)(x1) 41.70/10.93 41.70/10.93 c(a)(a(c)(x1)) = x1 >= x1 = c(c)(x1) 41.70/10.93 problem: 41.70/10.93 DPs: 41.70/10.93 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 41.70/10.93 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 41.70/10.93 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> c{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) 41.70/10.93 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) 41.70/10.93 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) 41.70/10.93 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) 41.70/10.93 c{#,(f4)}(f4(c)(c(c)(c(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 41.70/10.93 c{#,(f4)}(f4(c)(c(c)(c(c)(x1)))) -> a{#,(f4)}(f4(c)(x1)) 41.70/10.93 TRS: 41.70/10.93 a(a)(a(a)(a(f4)(x1))) -> a(c)(c(a)(a(a)(a(f4)(x1)))) 41.70/10.93 a(a)(a(a)(a(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) 41.70/10.93 a(a)(a(a)(a(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) 41.70/10.93 f4(c)(c(c)(c(c)(c(f4)(x1)))) -> f4(a)(a(f4)(x1)) 41.70/10.93 f4(c)(c(c)(c(c)(c(a)(x1)))) -> f4(a)(a(a)(x1)) 41.70/10.93 f4(c)(c(c)(c(c)(c(c)(x1)))) -> f4(a)(a(c)(x1)) 41.70/10.93 a(c)(c(c)(c(c)(c(f4)(x1)))) -> a(a)(a(f4)(x1)) 41.70/10.93 a(c)(c(c)(c(c)(c(a)(x1)))) -> a(a)(a(a)(x1)) 41.70/10.93 a(c)(c(c)(c(c)(c(c)(x1)))) -> a(a)(a(c)(x1)) 41.70/10.93 c(c)(c(c)(c(c)(c(f4)(x1)))) -> c(a)(a(f4)(x1)) 41.70/10.93 c(c)(c(c)(c(c)(c(a)(x1)))) -> c(a)(a(a)(x1)) 41.70/10.93 c(c)(c(c)(c(c)(c(c)(x1)))) -> c(a)(a(c)(x1)) 41.70/10.93 f4(a)(a(a)(x1)) -> f4(a)(x1) 41.70/10.93 f4(a)(a(c)(x1)) -> f4(c)(x1) 41.70/10.93 a(a)(a(f4)(x1)) -> a(f4)(x1) 41.70/10.93 a(a)(a(a)(x1)) -> a(a)(x1) 41.70/10.93 a(a)(a(c)(x1)) -> a(c)(x1) 41.70/10.93 c(a)(a(f4)(x1)) -> c(f4)(x1) 41.70/10.93 c(a)(a(a)(x1)) -> c(a)(x1) 41.70/10.93 c(a)(a(c)(x1)) -> c(c)(x1) 41.70/10.93 Polynomial Interpretation Processor: 41.70/10.93 dimension: 1 41.70/10.93 usable rules: 41.70/10.93 a(a)(a(a)(a(f4)(x1))) -> a(c)(c(a)(a(a)(a(f4)(x1)))) 41.70/10.93 a(a)(a(a)(a(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) 41.70/10.93 a(a)(a(a)(a(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) 41.70/10.93 f4(c)(c(c)(c(c)(c(f4)(x1)))) -> f4(a)(a(f4)(x1)) 41.70/10.93 f4(c)(c(c)(c(c)(c(a)(x1)))) -> f4(a)(a(a)(x1)) 41.70/10.93 f4(c)(c(c)(c(c)(c(c)(x1)))) -> f4(a)(a(c)(x1)) 41.70/10.93 a(c)(c(c)(c(c)(c(f4)(x1)))) -> a(a)(a(f4)(x1)) 41.70/10.93 a(c)(c(c)(c(c)(c(a)(x1)))) -> a(a)(a(a)(x1)) 41.70/10.93 a(c)(c(c)(c(c)(c(c)(x1)))) -> a(a)(a(c)(x1)) 41.70/10.93 c(c)(c(c)(c(c)(c(f4)(x1)))) -> c(a)(a(f4)(x1)) 41.70/10.93 c(c)(c(c)(c(c)(c(a)(x1)))) -> c(a)(a(a)(x1)) 41.70/10.93 c(c)(c(c)(c(c)(c(c)(x1)))) -> c(a)(a(c)(x1)) 41.70/10.93 f4(a)(a(a)(x1)) -> f4(a)(x1) 41.70/10.93 f4(a)(a(c)(x1)) -> f4(c)(x1) 41.70/10.93 a(a)(a(f4)(x1)) -> a(f4)(x1) 41.70/10.93 a(a)(a(a)(x1)) -> a(a)(x1) 41.70/10.93 a(a)(a(c)(x1)) -> a(c)(x1) 41.70/10.93 c(a)(a(f4)(x1)) -> c(f4)(x1) 41.70/10.93 c(a)(a(a)(x1)) -> c(a)(x1) 41.70/10.93 c(a)(a(c)(x1)) -> c(c)(x1) 41.70/10.93 interpretation: 41.73/11.01 [c(f4)](x0) = 0, 41.73/11.01 41.73/11.01 [c(c)](x0) = x0 + 1, 41.73/11.01 41.73/11.01 [c(a)](x0) = x0 + 1, 41.73/11.01 41.73/11.01 [f4(c)](x0) = x0, 41.73/11.01 41.73/11.01 [a(c)](x0) = x0, 41.73/11.01 41.73/11.01 [c{#,(f4)}](x0) = x0, 41.73/11.01 41.73/11.01 [a(f4)](x0) = 0, 41.73/11.01 41.73/11.01 [a(a)](x0) = x0 + 1, 41.73/11.01 41.73/11.01 [f4(a)](x0) = x0 + 1, 41.73/11.01 41.73/11.01 [a{#,(f4)}](x0) = x0 + 1 41.73/11.01 orientation: 41.73/11.01 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) = 3 >= 2 = c{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) 41.73/11.01 41.73/11.01 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) = x1 + 4 >= x1 + 3 = c{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) 41.73/11.01 41.73/11.01 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) = x1 + 3 >= x1 + 2 = c{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) 41.73/11.01 41.73/11.01 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) = 3 >= 3 = a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) 41.73/11.01 41.73/11.01 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) = x1 + 4 >= x1 + 4 = a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) 41.73/11.01 41.73/11.01 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) = x1 + 3 >= x1 + 3 = a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) 41.73/11.01 41.73/11.01 c{#,(f4)}(f4(c)(c(c)(c(a)(x1)))) = x1 + 2 >= x1 + 2 = a{#,(f4)}(f4(a)(x1)) 41.73/11.01 41.73/11.01 c{#,(f4)}(f4(c)(c(c)(c(c)(x1)))) = x1 + 2 >= x1 + 1 = a{#,(f4)}(f4(c)(x1)) 41.73/11.01 41.73/11.01 a(a)(a(a)(a(f4)(x1))) = 2 >= 2 = a(c)(c(a)(a(a)(a(f4)(x1)))) 41.73/11.01 41.73/11.01 a(a)(a(a)(a(a)(x1))) = x1 + 3 >= x1 + 3 = a(c)(c(a)(a(a)(a(a)(x1)))) 41.73/11.01 41.73/11.01 a(a)(a(a)(a(c)(x1))) = x1 + 2 >= x1 + 2 = a(c)(c(a)(a(a)(a(c)(x1)))) 41.73/11.01 41.73/11.01 f4(c)(c(c)(c(c)(c(f4)(x1)))) = 2 >= 1 = f4(a)(a(f4)(x1)) 41.73/11.01 41.73/11.01 f4(c)(c(c)(c(c)(c(a)(x1)))) = x1 + 3 >= x1 + 2 = f4(a)(a(a)(x1)) 41.73/11.01 41.73/11.01 f4(c)(c(c)(c(c)(c(c)(x1)))) = x1 + 3 >= x1 + 1 = f4(a)(a(c)(x1)) 41.73/11.01 41.73/11.01 a(c)(c(c)(c(c)(c(f4)(x1)))) = 2 >= 1 = a(a)(a(f4)(x1)) 41.73/11.01 41.73/11.01 a(c)(c(c)(c(c)(c(a)(x1)))) = x1 + 3 >= x1 + 2 = a(a)(a(a)(x1)) 41.73/11.01 41.73/11.01 a(c)(c(c)(c(c)(c(c)(x1)))) = x1 + 3 >= x1 + 1 = a(a)(a(c)(x1)) 41.73/11.01 41.73/11.01 c(c)(c(c)(c(c)(c(f4)(x1)))) = 3 >= 1 = c(a)(a(f4)(x1)) 41.73/11.01 41.73/11.01 c(c)(c(c)(c(c)(c(a)(x1)))) = x1 + 4 >= x1 + 2 = c(a)(a(a)(x1)) 41.73/11.01 41.73/11.01 c(c)(c(c)(c(c)(c(c)(x1)))) = x1 + 4 >= x1 + 1 = c(a)(a(c)(x1)) 41.73/11.01 41.73/11.01 f4(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = f4(a)(x1) 41.73/11.01 41.73/11.01 f4(a)(a(c)(x1)) = x1 + 1 >= x1 = f4(c)(x1) 41.73/11.01 41.73/11.01 a(a)(a(f4)(x1)) = 1 >= 0 = a(f4)(x1) 41.73/11.01 41.73/11.01 a(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = a(a)(x1) 41.73/11.01 41.73/11.01 a(a)(a(c)(x1)) = x1 + 1 >= x1 = a(c)(x1) 41.73/11.01 41.73/11.01 c(a)(a(f4)(x1)) = 1 >= 0 = c(f4)(x1) 41.73/11.01 41.73/11.01 c(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = c(a)(x1) 41.73/11.01 41.73/11.01 c(a)(a(c)(x1)) = x1 + 1 >= x1 + 1 = c(c)(x1) 41.73/11.01 problem: 41.73/11.01 DPs: 41.73/11.01 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) 41.73/11.01 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) 41.73/11.01 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) 41.73/11.01 c{#,(f4)}(f4(c)(c(c)(c(a)(x1)))) -> a{#,(f4)}(f4(a)(x1)) 41.73/11.01 TRS: 41.73/11.01 a(a)(a(a)(a(f4)(x1))) -> a(c)(c(a)(a(a)(a(f4)(x1)))) 41.73/11.01 a(a)(a(a)(a(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) 41.73/11.01 a(a)(a(a)(a(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) 41.73/11.01 f4(c)(c(c)(c(c)(c(f4)(x1)))) -> f4(a)(a(f4)(x1)) 41.73/11.01 f4(c)(c(c)(c(c)(c(a)(x1)))) -> f4(a)(a(a)(x1)) 41.73/11.01 f4(c)(c(c)(c(c)(c(c)(x1)))) -> f4(a)(a(c)(x1)) 41.73/11.01 a(c)(c(c)(c(c)(c(f4)(x1)))) -> a(a)(a(f4)(x1)) 41.73/11.01 a(c)(c(c)(c(c)(c(a)(x1)))) -> a(a)(a(a)(x1)) 41.73/11.01 a(c)(c(c)(c(c)(c(c)(x1)))) -> a(a)(a(c)(x1)) 41.73/11.01 c(c)(c(c)(c(c)(c(f4)(x1)))) -> c(a)(a(f4)(x1)) 41.73/11.01 c(c)(c(c)(c(c)(c(a)(x1)))) -> c(a)(a(a)(x1)) 41.73/11.01 c(c)(c(c)(c(c)(c(c)(x1)))) -> c(a)(a(c)(x1)) 41.73/11.01 f4(a)(a(a)(x1)) -> f4(a)(x1) 41.73/11.01 f4(a)(a(c)(x1)) -> f4(c)(x1) 41.73/11.01 a(a)(a(f4)(x1)) -> a(f4)(x1) 41.73/11.01 a(a)(a(a)(x1)) -> a(a)(x1) 41.73/11.01 a(a)(a(c)(x1)) -> a(c)(x1) 41.73/11.01 c(a)(a(f4)(x1)) -> c(f4)(x1) 41.73/11.01 c(a)(a(a)(x1)) -> c(a)(x1) 41.73/11.01 c(a)(a(c)(x1)) -> c(c)(x1) 41.73/11.01 SCC Processor: 41.73/11.01 #sccs: 1 41.73/11.01 #rules: 3 41.73/11.01 #arcs: 45/16 41.73/11.01 DPs: 41.73/11.01 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) 41.85/11.08 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) 41.85/11.08 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) -> a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) 41.85/11.08 TRS: 41.85/11.08 a(a)(a(a)(a(f4)(x1))) -> a(c)(c(a)(a(a)(a(f4)(x1)))) 41.85/11.08 a(a)(a(a)(a(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) 41.85/11.08 a(a)(a(a)(a(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) 41.85/11.08 f4(c)(c(c)(c(c)(c(f4)(x1)))) -> f4(a)(a(f4)(x1)) 41.85/11.08 f4(c)(c(c)(c(c)(c(a)(x1)))) -> f4(a)(a(a)(x1)) 41.85/11.08 f4(c)(c(c)(c(c)(c(c)(x1)))) -> f4(a)(a(c)(x1)) 41.85/11.08 a(c)(c(c)(c(c)(c(f4)(x1)))) -> a(a)(a(f4)(x1)) 41.85/11.08 a(c)(c(c)(c(c)(c(a)(x1)))) -> a(a)(a(a)(x1)) 41.85/11.08 a(c)(c(c)(c(c)(c(c)(x1)))) -> a(a)(a(c)(x1)) 41.85/11.08 c(c)(c(c)(c(c)(c(f4)(x1)))) -> c(a)(a(f4)(x1)) 41.85/11.08 c(c)(c(c)(c(c)(c(a)(x1)))) -> c(a)(a(a)(x1)) 41.85/11.08 c(c)(c(c)(c(c)(c(c)(x1)))) -> c(a)(a(c)(x1)) 41.85/11.08 f4(a)(a(a)(x1)) -> f4(a)(x1) 41.85/11.08 f4(a)(a(c)(x1)) -> f4(c)(x1) 41.85/11.08 a(a)(a(f4)(x1)) -> a(f4)(x1) 41.85/11.08 a(a)(a(a)(x1)) -> a(a)(x1) 41.85/11.08 a(a)(a(c)(x1)) -> a(c)(x1) 41.85/11.08 c(a)(a(f4)(x1)) -> c(f4)(x1) 41.85/11.08 c(a)(a(a)(x1)) -> c(a)(x1) 41.85/11.08 c(a)(a(c)(x1)) -> c(c)(x1) 41.85/11.08 Polynomial Interpretation Processor: 41.85/11.08 dimension: 1 41.85/11.08 usable rules: 41.85/11.08 a(a)(a(a)(a(f4)(x1))) -> a(c)(c(a)(a(a)(a(f4)(x1)))) 41.85/11.08 a(a)(a(a)(a(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) 41.85/11.08 a(a)(a(a)(a(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) 41.85/11.08 f4(c)(c(c)(c(c)(c(f4)(x1)))) -> f4(a)(a(f4)(x1)) 41.85/11.08 f4(c)(c(c)(c(c)(c(a)(x1)))) -> f4(a)(a(a)(x1)) 41.85/11.08 f4(c)(c(c)(c(c)(c(c)(x1)))) -> f4(a)(a(c)(x1)) 41.85/11.08 a(c)(c(c)(c(c)(c(f4)(x1)))) -> a(a)(a(f4)(x1)) 41.85/11.08 a(c)(c(c)(c(c)(c(a)(x1)))) -> a(a)(a(a)(x1)) 41.85/11.08 a(c)(c(c)(c(c)(c(c)(x1)))) -> a(a)(a(c)(x1)) 41.85/11.08 c(c)(c(c)(c(c)(c(f4)(x1)))) -> c(a)(a(f4)(x1)) 41.85/11.08 c(c)(c(c)(c(c)(c(a)(x1)))) -> c(a)(a(a)(x1)) 41.85/11.08 c(c)(c(c)(c(c)(c(c)(x1)))) -> c(a)(a(c)(x1)) 41.85/11.08 f4(a)(a(a)(x1)) -> f4(a)(x1) 41.85/11.08 f4(a)(a(c)(x1)) -> f4(c)(x1) 41.85/11.08 a(a)(a(f4)(x1)) -> a(f4)(x1) 41.85/11.08 a(a)(a(a)(x1)) -> a(a)(x1) 41.85/11.08 a(a)(a(c)(x1)) -> a(c)(x1) 41.85/11.08 c(a)(a(f4)(x1)) -> c(f4)(x1) 41.85/11.08 c(a)(a(a)(x1)) -> c(a)(x1) 41.85/11.08 c(a)(a(c)(x1)) -> c(c)(x1) 41.85/11.08 interpretation: 41.85/11.08 [c(f4)](x0) = 0, 41.85/11.08 41.85/11.08 [c(c)](x0) = x0 + 1, 41.85/11.08 41.85/11.08 [c(a)](x0) = x0, 41.85/11.08 41.85/11.08 [f4(c)](x0) = x0, 41.85/11.08 41.85/11.08 [a(c)](x0) = x0 + 1, 41.85/11.08 41.85/11.08 [a(f4)](x0) = 1, 41.85/11.08 41.85/11.08 [a(a)](x0) = x0 + 1, 41.85/11.08 41.85/11.08 [f4(a)](x0) = x0 + 1, 41.85/11.08 41.85/11.08 [a{#,(f4)}](x0) = x0 41.85/11.08 orientation: 41.85/11.08 a{#,(f4)}(f4(a)(a(a)(a(f4)(x1)))) = 3 >= 2 = a{#,(f4)}(f4(c)(c(a)(a(a)(a(f4)(x1))))) 41.85/11.08 41.85/11.08 a{#,(f4)}(f4(a)(a(a)(a(a)(x1)))) = x1 + 3 >= x1 + 2 = a{#,(f4)}(f4(c)(c(a)(a(a)(a(a)(x1))))) 41.85/11.08 41.85/11.08 a{#,(f4)}(f4(a)(a(a)(a(c)(x1)))) = x1 + 3 >= x1 + 2 = a{#,(f4)}(f4(c)(c(a)(a(a)(a(c)(x1))))) 41.85/11.08 41.85/11.08 a(a)(a(a)(a(f4)(x1))) = 3 >= 3 = a(c)(c(a)(a(a)(a(f4)(x1)))) 41.85/11.08 41.85/11.08 a(a)(a(a)(a(a)(x1))) = x1 + 3 >= x1 + 3 = a(c)(c(a)(a(a)(a(a)(x1)))) 41.85/11.08 41.85/11.08 a(a)(a(a)(a(c)(x1))) = x1 + 3 >= x1 + 3 = a(c)(c(a)(a(a)(a(c)(x1)))) 41.85/11.08 41.85/11.08 f4(c)(c(c)(c(c)(c(f4)(x1)))) = 2 >= 2 = f4(a)(a(f4)(x1)) 41.85/11.08 41.85/11.08 f4(c)(c(c)(c(c)(c(a)(x1)))) = x1 + 2 >= x1 + 2 = f4(a)(a(a)(x1)) 41.85/11.08 41.85/11.08 f4(c)(c(c)(c(c)(c(c)(x1)))) = x1 + 3 >= x1 + 2 = f4(a)(a(c)(x1)) 41.85/11.08 41.85/11.08 a(c)(c(c)(c(c)(c(f4)(x1)))) = 3 >= 2 = a(a)(a(f4)(x1)) 41.85/11.08 41.85/11.08 a(c)(c(c)(c(c)(c(a)(x1)))) = x1 + 3 >= x1 + 2 = a(a)(a(a)(x1)) 41.85/11.08 41.85/11.08 a(c)(c(c)(c(c)(c(c)(x1)))) = x1 + 4 >= x1 + 2 = a(a)(a(c)(x1)) 41.85/11.08 41.85/11.08 c(c)(c(c)(c(c)(c(f4)(x1)))) = 3 >= 1 = c(a)(a(f4)(x1)) 41.85/11.08 41.85/11.08 c(c)(c(c)(c(c)(c(a)(x1)))) = x1 + 3 >= x1 + 1 = c(a)(a(a)(x1)) 41.85/11.08 41.85/11.08 c(c)(c(c)(c(c)(c(c)(x1)))) = x1 + 4 >= x1 + 1 = c(a)(a(c)(x1)) 41.85/11.08 41.85/11.08 f4(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = f4(a)(x1) 41.85/11.08 41.85/11.08 f4(a)(a(c)(x1)) = x1 + 2 >= x1 = f4(c)(x1) 41.85/11.08 41.85/11.08 a(a)(a(f4)(x1)) = 2 >= 1 = a(f4)(x1) 41.85/11.08 41.85/11.08 a(a)(a(a)(x1)) = x1 + 2 >= x1 + 1 = a(a)(x1) 41.85/11.08 41.85/11.08 a(a)(a(c)(x1)) = x1 + 2 >= x1 + 1 = a(c)(x1) 41.85/11.08 41.85/11.08 c(a)(a(f4)(x1)) = 1 >= 0 = c(f4)(x1) 41.85/11.08 41.85/11.08 c(a)(a(a)(x1)) = x1 + 1 >= x1 = c(a)(x1) 41.85/11.08 41.85/11.08 c(a)(a(c)(x1)) = x1 + 1 >= x1 + 1 = c(c)(x1) 41.85/11.08 problem: 41.85/11.08 DPs: 41.85/11.08 41.85/11.08 TRS: 41.85/11.08 a(a)(a(a)(a(f4)(x1))) -> a(c)(c(a)(a(a)(a(f4)(x1)))) 41.85/11.08 a(a)(a(a)(a(a)(x1))) -> a(c)(c(a)(a(a)(a(a)(x1)))) 41.85/11.08 a(a)(a(a)(a(c)(x1))) -> a(c)(c(a)(a(a)(a(c)(x1)))) 41.85/11.08 f4(c)(c(c)(c(c)(c(f4)(x1)))) -> f4(a)(a(f4)(x1)) 41.85/11.08 f4(c)(c(c)(c(c)(c(a)(x1)))) -> f4(a)(a(a)(x1)) 41.85/11.08 f4(c)(c(c)(c(c)(c(c)(x1)))) -> f4(a)(a(c)(x1)) 41.85/11.08 a(c)(c(c)(c(c)(c(f4)(x1)))) -> a(a)(a(f4)(x1)) 41.85/11.08 a(c)(c(c)(c(c)(c(a)(x1)))) -> a(a)(a(a)(x1)) 41.85/11.08 a(c)(c(c)(c(c)(c(c)(x1)))) -> a(a)(a(c)(x1)) 41.85/11.08 c(c)(c(c)(c(c)(c(f4)(x1)))) -> c(a)(a(f4)(x1)) 41.85/11.08 c(c)(c(c)(c(c)(c(a)(x1)))) -> c(a)(a(a)(x1)) 41.85/11.08 c(c)(c(c)(c(c)(c(c)(x1)))) -> c(a)(a(c)(x1)) 41.85/11.08 f4(a)(a(a)(x1)) -> f4(a)(x1) 41.85/11.08 f4(a)(a(c)(x1)) -> f4(c)(x1) 41.85/11.08 a(a)(a(f4)(x1)) -> a(f4)(x1) 41.85/11.08 a(a)(a(a)(x1)) -> a(a)(x1) 41.85/11.08 a(a)(a(c)(x1)) -> a(c)(x1) 41.85/11.08 c(a)(a(f4)(x1)) -> c(f4)(x1) 41.85/11.08 c(a)(a(a)(x1)) -> c(a)(x1) 41.85/11.08 c(a)(a(c)(x1)) -> c(c)(x1) 41.85/11.08 Qed 41.85/11.09 EOF