; @xtcfilename "./TRS_Relative/INVY_15/quicktest_sum.xml"
(format TRS)
(fun true 0)
(fun rands 2)
(fun done 1)
(fun sum1 1)
(fun and 2)
(fun rand 1)
(fun g 1)
(fun nil 0)
(fun s 1)
(fun eq 2)
(fun + 2)
(fun |::| 2)
(fun tests 1)
(fun f 1)
(fun |0| 0)
(fun cons 2)
(fun test 1)
(fun sum2 2)
(rule (+ |0| y) y)
(rule (+ (s x) y) (s (+ x y)))
(rule (sum1 nil) |0|)
(rule (sum1 (cons x y)) (+ x (sum1 y)))
(rule (sum2 nil z) z)
(rule (sum2 (cons x y) z) (sum2 y (+ x z)))
(rule (tests |0|) true)
(rule (tests (s x)) (and (test (rands (rand |0|) nil)) x))
(rule (test (done y)) (eq (f y) (g y)))
(rule (eq x x) true)
(rule (rands |0| y) (done y))
(rule (rands (s x) y) (rands x (|::| (rand |0|) y)))
(rule (rand x) x :cost 0)
(rule (rand x) (rand (s x)) :cost 0)