10.47/3.59 YES 10.80/3.60 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 10.80/3.60 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.80/3.60 10.80/3.60 10.80/3.60 Termination of the given RelTRS could be proven: 10.80/3.60 10.80/3.60 (0) RelTRS 10.80/3.60 (1) RelTRSRRRProof [EQUIVALENT, 111 ms] 10.80/3.60 (2) RelTRS 10.80/3.60 (3) RelTRSRRRProof [EQUIVALENT, 56 ms] 10.80/3.60 (4) RelTRS 10.80/3.60 (5) RelTRSRRRProof [EQUIVALENT, 25 ms] 10.80/3.60 (6) RelTRS 10.80/3.60 (7) RelTRSRRRProof [EQUIVALENT, 30 ms] 10.80/3.60 (8) RelTRS 10.80/3.60 (9) RelTRSRRRProof [EQUIVALENT, 172 ms] 10.80/3.60 (10) RelTRS 10.80/3.60 (11) RelTRSRRRProof [EQUIVALENT, 15 ms] 10.80/3.60 (12) RelTRS 10.80/3.60 (13) RelTRSRRRProof [EQUIVALENT, 5 ms] 10.80/3.60 (14) RelTRS 10.80/3.60 (15) RelTRSRRRProof [EQUIVALENT, 7 ms] 10.80/3.60 (16) RelTRS 10.80/3.60 (17) RIsEmptyProof [EQUIVALENT, 0 ms] 10.80/3.60 (18) YES 10.80/3.60 10.80/3.60 10.80/3.60 ---------------------------------------- 10.80/3.60 10.80/3.60 (0) 10.80/3.60 Obligation: 10.80/3.60 Relative term rewrite system: 10.80/3.60 The relative TRS consists of the following R rules: 10.80/3.60 10.80/3.60 RAo(R) -> R 10.80/3.60 RAn(R) -> R 10.80/3.60 WAo(W) -> W 10.80/3.60 WAn(W) -> W 10.80/3.60 10.80/3.60 The relative TRS consists of the following S rules: 10.80/3.60 10.80/3.60 Rw -> RIn(Rw) 10.80/3.60 Ww -> WIn(Ww) 10.80/3.60 top(ok(sys_r(read(r, RIo(x)), write(W, Ww)))) -> top(check(sys_r(read(RAo(r), x), write(W, Ww)))) 10.80/3.60 top(ok(sys_w(read(r, RIo(x)), write(W, Ww)))) -> top(check(sys_w(read(RAo(r), x), write(W, Ww)))) 10.80/3.60 top(ok(sys_r(read(r, RIn(x)), write(W, Ww)))) -> top(check(sys_r(read(RAn(r), x), write(W, Ww)))) 10.80/3.60 top(ok(sys_w(read(r, RIn(x)), write(W, Ww)))) -> top(check(sys_w(read(RAn(r), x), write(W, Ww)))) 10.80/3.60 top(ok(sys_r(read(R, Rw), write(W, WIn(y))))) -> top(check(sys_r(read(R, Rw), write(WAn(W), y)))) 10.80/3.60 top(ok(sys_w(read(R, Rw), write(W, WIn(y))))) -> top(check(sys_w(read(R, Rw), write(WAn(W), y)))) 10.80/3.60 top(ok(sys_r(read(R, Rw), write(W, WIo(y))))) -> top(check(sys_r(read(R, Rw), write(WAo(W), y)))) 10.80/3.60 top(ok(sys_w(read(R, Rw), write(W, WIo(y))))) -> top(check(sys_w(read(R, Rw), write(WAo(W), y)))) 10.80/3.60 top(ok(sys_r(read(r, RIo(x)), write(W, y)))) -> top(check(sys_w(read(RAo(r), x), write(W, y)))) 10.80/3.60 top(ok(sys_r(read(r, RIn(x)), write(W, y)))) -> top(check(sys_w(read(RAn(r), x), write(W, y)))) 10.80/3.60 top(ok(sys_w(read(R, x), write(W, WIo(y))))) -> top(check(sys_r(read(R, x), write(WAo(W), y)))) 10.80/3.60 top(ok(sys_w(read(R, x), write(W, WIn(y))))) -> top(check(sys_r(read(R, x), write(WAn(W), y)))) 10.80/3.60 check(RIo(x)) -> ok(RIo(x)) 10.80/3.60 check(RAo(x)) -> RAo(check(x)) 10.80/3.60 check(RAn(x)) -> RAn(check(x)) 10.80/3.60 check(WAo(x)) -> WAo(check(x)) 10.80/3.60 check(WAn(x)) -> WAn(check(x)) 10.80/3.60 check(RIo(x)) -> RIo(check(x)) 10.80/3.60 check(RIn(x)) -> RIn(check(x)) 10.80/3.60 check(WIo(x)) -> WIo(check(x)) 10.80/3.60 check(WIn(x)) -> WIn(check(x)) 10.80/3.60 check(sys_r(x, y)) -> sys_r(check(x), y) 10.80/3.60 check(sys_r(x, y)) -> sys_r(x, check(y)) 10.80/3.60 check(sys_w(x, y)) -> sys_w(check(x), y) 10.80/3.60 check(sys_w(x, y)) -> sys_w(x, check(y)) 10.80/3.60 RAo(ok(x)) -> ok(RAo(x)) 10.80/3.60 RAn(ok(x)) -> ok(RAn(x)) 10.80/3.60 WAo(ok(x)) -> ok(WAo(x)) 10.80/3.60 WAn(ok(x)) -> ok(WAn(x)) 10.80/3.60 RIn(ok(x)) -> ok(RIn(x)) 10.80/3.60 WIo(ok(x)) -> ok(WIo(x)) 10.80/3.60 WIn(ok(x)) -> ok(WIn(x)) 10.80/3.60 sys_r(ok(x), y) -> ok(sys_r(x, y)) 10.80/3.60 sys_r(x, ok(y)) -> ok(sys_r(x, y)) 10.80/3.60 sys_w(ok(x), y) -> ok(sys_w(x, y)) 10.80/3.60 sys_w(x, ok(y)) -> ok(sys_w(x, y)) 10.80/3.60 10.80/3.60 10.80/3.60 ---------------------------------------- 10.80/3.60 10.80/3.60 (1) RelTRSRRRProof (EQUIVALENT) 10.80/3.60 We used the following monotonic ordering for rule removal: 10.80/3.60 Polynomial interpretation [POLO]: 10.80/3.60 10.80/3.60 POL(R) = 0 10.80/3.60 POL(RAn(x_1)) = x_1 10.80/3.60 POL(RAo(x_1)) = x_1 10.80/3.60 POL(RIn(x_1)) = x_1 10.80/3.60 POL(RIo(x_1)) = x_1 10.80/3.60 POL(Rw) = 0 10.80/3.60 POL(W) = 0 10.80/3.60 POL(WAn(x_1)) = x_1 10.80/3.60 POL(WAo(x_1)) = x_1 10.80/3.60 POL(WIn(x_1)) = x_1 10.80/3.60 POL(WIo(x_1)) = 1 + x_1 10.80/3.60 POL(Ww) = 0 10.80/3.60 POL(check(x_1)) = x_1 10.80/3.60 POL(ok(x_1)) = x_1 10.80/3.60 POL(read(x_1, x_2)) = x_1 + x_2 10.80/3.60 POL(sys_r(x_1, x_2)) = x_1 + x_2 10.80/3.60 POL(sys_w(x_1, x_2)) = x_1 + x_2 10.80/3.60 POL(top(x_1)) = x_1 10.80/3.60 POL(write(x_1, x_2)) = x_1 + x_2 10.80/3.60 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 10.80/3.60 Rules from R: 10.80/3.60 none 10.80/3.60 Rules from S: 10.80/3.60 10.80/3.60 top(ok(sys_r(read(R, Rw), write(W, WIo(y))))) -> top(check(sys_r(read(R, Rw), write(WAo(W), y)))) 10.80/3.60 top(ok(sys_w(read(R, Rw), write(W, WIo(y))))) -> top(check(sys_w(read(R, Rw), write(WAo(W), y)))) 10.80/3.60 top(ok(sys_w(read(R, x), write(W, WIo(y))))) -> top(check(sys_r(read(R, x), write(WAo(W), y)))) 10.80/3.60 10.80/3.60 10.80/3.60 10.80/3.60 10.80/3.60 ---------------------------------------- 10.80/3.60 10.80/3.60 (2) 10.80/3.60 Obligation: 10.80/3.60 Relative term rewrite system: 10.80/3.60 The relative TRS consists of the following R rules: 10.80/3.60 10.80/3.60 RAo(R) -> R 10.80/3.60 RAn(R) -> R 10.80/3.60 WAo(W) -> W 10.80/3.60 WAn(W) -> W 10.80/3.60 10.80/3.60 The relative TRS consists of the following S rules: 10.80/3.60 10.80/3.60 Rw -> RIn(Rw) 10.80/3.60 Ww -> WIn(Ww) 10.80/3.60 top(ok(sys_r(read(r, RIo(x)), write(W, Ww)))) -> top(check(sys_r(read(RAo(r), x), write(W, Ww)))) 10.80/3.60 top(ok(sys_w(read(r, RIo(x)), write(W, Ww)))) -> top(check(sys_w(read(RAo(r), x), write(W, Ww)))) 10.80/3.60 top(ok(sys_r(read(r, RIn(x)), write(W, Ww)))) -> top(check(sys_r(read(RAn(r), x), write(W, Ww)))) 10.80/3.60 top(ok(sys_w(read(r, RIn(x)), write(W, Ww)))) -> top(check(sys_w(read(RAn(r), x), write(W, Ww)))) 10.80/3.60 top(ok(sys_r(read(R, Rw), write(W, WIn(y))))) -> top(check(sys_r(read(R, Rw), write(WAn(W), y)))) 10.80/3.60 top(ok(sys_w(read(R, Rw), write(W, WIn(y))))) -> top(check(sys_w(read(R, Rw), write(WAn(W), y)))) 10.80/3.60 top(ok(sys_r(read(r, RIo(x)), write(W, y)))) -> top(check(sys_w(read(RAo(r), x), write(W, y)))) 10.80/3.60 top(ok(sys_r(read(r, RIn(x)), write(W, y)))) -> top(check(sys_w(read(RAn(r), x), write(W, y)))) 10.80/3.60 top(ok(sys_w(read(R, x), write(W, WIn(y))))) -> top(check(sys_r(read(R, x), write(WAn(W), y)))) 10.80/3.60 check(RIo(x)) -> ok(RIo(x)) 10.80/3.60 check(RAo(x)) -> RAo(check(x)) 10.80/3.60 check(RAn(x)) -> RAn(check(x)) 10.80/3.60 check(WAo(x)) -> WAo(check(x)) 10.80/3.60 check(WAn(x)) -> WAn(check(x)) 10.80/3.60 check(RIo(x)) -> RIo(check(x)) 10.80/3.60 check(RIn(x)) -> RIn(check(x)) 10.80/3.60 check(WIo(x)) -> WIo(check(x)) 10.80/3.60 check(WIn(x)) -> WIn(check(x)) 10.80/3.60 check(sys_r(x, y)) -> sys_r(check(x), y) 10.80/3.60 check(sys_r(x, y)) -> sys_r(x, check(y)) 10.80/3.60 check(sys_w(x, y)) -> sys_w(check(x), y) 10.80/3.60 check(sys_w(x, y)) -> sys_w(x, check(y)) 10.80/3.60 RAo(ok(x)) -> ok(RAo(x)) 10.80/3.60 RAn(ok(x)) -> ok(RAn(x)) 10.80/3.60 WAo(ok(x)) -> ok(WAo(x)) 10.80/3.60 WAn(ok(x)) -> ok(WAn(x)) 10.80/3.60 RIn(ok(x)) -> ok(RIn(x)) 10.80/3.60 WIo(ok(x)) -> ok(WIo(x)) 10.80/3.60 WIn(ok(x)) -> ok(WIn(x)) 10.80/3.60 sys_r(ok(x), y) -> ok(sys_r(x, y)) 10.80/3.60 sys_r(x, ok(y)) -> ok(sys_r(x, y)) 10.80/3.60 sys_w(ok(x), y) -> ok(sys_w(x, y)) 10.80/3.60 sys_w(x, ok(y)) -> ok(sys_w(x, y)) 10.80/3.60 10.80/3.60 10.80/3.60 ---------------------------------------- 10.80/3.60 10.80/3.60 (3) RelTRSRRRProof (EQUIVALENT) 10.80/3.60 We used the following monotonic ordering for rule removal: 10.80/3.60 Polynomial interpretation [POLO]: 10.80/3.60 10.80/3.60 POL(R) = 0 10.80/3.60 POL(RAn(x_1)) = x_1 10.80/3.60 POL(RAo(x_1)) = 1 + x_1 10.80/3.60 POL(RIn(x_1)) = x_1 10.80/3.60 POL(RIo(x_1)) = 1 + x_1 10.80/3.60 POL(Rw) = 0 10.80/3.60 POL(W) = 0 10.80/3.60 POL(WAn(x_1)) = x_1 10.80/3.60 POL(WAo(x_1)) = x_1 10.80/3.60 POL(WIn(x_1)) = x_1 10.80/3.60 POL(WIo(x_1)) = x_1 10.80/3.60 POL(Ww) = 0 10.80/3.60 POL(check(x_1)) = x_1 10.80/3.60 POL(ok(x_1)) = x_1 10.80/3.60 POL(read(x_1, x_2)) = x_1 + x_2 10.80/3.60 POL(sys_r(x_1, x_2)) = 1 + x_1 + x_2 10.80/3.60 POL(sys_w(x_1, x_2)) = 1 + x_1 + x_2 10.80/3.60 POL(top(x_1)) = x_1 10.80/3.60 POL(write(x_1, x_2)) = x_1 + x_2 10.80/3.60 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 10.80/3.60 Rules from R: 10.80/3.60 10.80/3.60 RAo(R) -> R 10.80/3.60 Rules from S: 10.80/3.60 none 10.80/3.60 10.80/3.60 10.80/3.60 10.80/3.60 10.80/3.60 ---------------------------------------- 10.80/3.60 10.80/3.60 (4) 10.80/3.60 Obligation: 10.80/3.60 Relative term rewrite system: 10.80/3.60 The relative TRS consists of the following R rules: 10.80/3.60 10.80/3.60 RAn(R) -> R 10.80/3.60 WAo(W) -> W 10.80/3.60 WAn(W) -> W 10.80/3.60 10.80/3.60 The relative TRS consists of the following S rules: 10.80/3.60 10.80/3.60 Rw -> RIn(Rw) 10.80/3.60 Ww -> WIn(Ww) 10.80/3.60 top(ok(sys_r(read(r, RIo(x)), write(W, Ww)))) -> top(check(sys_r(read(RAo(r), x), write(W, Ww)))) 10.80/3.60 top(ok(sys_w(read(r, RIo(x)), write(W, Ww)))) -> top(check(sys_w(read(RAo(r), x), write(W, Ww)))) 10.80/3.60 top(ok(sys_r(read(r, RIn(x)), write(W, Ww)))) -> top(check(sys_r(read(RAn(r), x), write(W, Ww)))) 10.80/3.60 top(ok(sys_w(read(r, RIn(x)), write(W, Ww)))) -> top(check(sys_w(read(RAn(r), x), write(W, Ww)))) 10.80/3.60 top(ok(sys_r(read(R, Rw), write(W, WIn(y))))) -> top(check(sys_r(read(R, Rw), write(WAn(W), y)))) 10.80/3.60 top(ok(sys_w(read(R, Rw), write(W, WIn(y))))) -> top(check(sys_w(read(R, Rw), write(WAn(W), y)))) 10.80/3.60 top(ok(sys_r(read(r, RIo(x)), write(W, y)))) -> top(check(sys_w(read(RAo(r), x), write(W, y)))) 10.80/3.60 top(ok(sys_r(read(r, RIn(x)), write(W, y)))) -> top(check(sys_w(read(RAn(r), x), write(W, y)))) 10.80/3.60 top(ok(sys_w(read(R, x), write(W, WIn(y))))) -> top(check(sys_r(read(R, x), write(WAn(W), y)))) 10.80/3.60 check(RIo(x)) -> ok(RIo(x)) 10.80/3.60 check(RAo(x)) -> RAo(check(x)) 10.80/3.60 check(RAn(x)) -> RAn(check(x)) 10.80/3.60 check(WAo(x)) -> WAo(check(x)) 10.80/3.60 check(WAn(x)) -> WAn(check(x)) 10.80/3.61 check(RIo(x)) -> RIo(check(x)) 10.80/3.61 check(RIn(x)) -> RIn(check(x)) 10.80/3.61 check(WIo(x)) -> WIo(check(x)) 10.80/3.61 check(WIn(x)) -> WIn(check(x)) 10.80/3.61 check(sys_r(x, y)) -> sys_r(check(x), y) 10.80/3.61 check(sys_r(x, y)) -> sys_r(x, check(y)) 10.80/3.61 check(sys_w(x, y)) -> sys_w(check(x), y) 10.80/3.61 check(sys_w(x, y)) -> sys_w(x, check(y)) 10.80/3.61 RAo(ok(x)) -> ok(RAo(x)) 10.80/3.61 RAn(ok(x)) -> ok(RAn(x)) 10.80/3.61 WAo(ok(x)) -> ok(WAo(x)) 10.80/3.61 WAn(ok(x)) -> ok(WAn(x)) 10.80/3.61 RIn(ok(x)) -> ok(RIn(x)) 10.80/3.61 WIo(ok(x)) -> ok(WIo(x)) 10.80/3.61 WIn(ok(x)) -> ok(WIn(x)) 10.80/3.61 sys_r(ok(x), y) -> ok(sys_r(x, y)) 10.80/3.61 sys_r(x, ok(y)) -> ok(sys_r(x, y)) 10.80/3.61 sys_w(ok(x), y) -> ok(sys_w(x, y)) 10.80/3.61 sys_w(x, ok(y)) -> ok(sys_w(x, y)) 10.80/3.61 10.80/3.61 10.80/3.61 ---------------------------------------- 10.80/3.61 10.80/3.61 (5) RelTRSRRRProof (EQUIVALENT) 10.80/3.61 We used the following monotonic ordering for rule removal: 10.80/3.61 Polynomial interpretation [POLO]: 10.80/3.61 10.80/3.61 POL(R) = 0 10.80/3.61 POL(RAn(x_1)) = x_1 10.80/3.61 POL(RAo(x_1)) = 1 + x_1 10.80/3.61 POL(RIn(x_1)) = x_1 10.80/3.61 POL(RIo(x_1)) = 1 + x_1 10.80/3.61 POL(Rw) = 0 10.80/3.61 POL(W) = 0 10.80/3.61 POL(WAn(x_1)) = x_1 10.80/3.61 POL(WAo(x_1)) = 1 + x_1 10.80/3.61 POL(WIn(x_1)) = x_1 10.80/3.61 POL(WIo(x_1)) = x_1 10.80/3.61 POL(Ww) = 0 10.80/3.61 POL(check(x_1)) = x_1 10.80/3.61 POL(ok(x_1)) = x_1 10.80/3.61 POL(read(x_1, x_2)) = x_1 + x_2 10.80/3.61 POL(sys_r(x_1, x_2)) = 1 + x_1 + x_2 10.80/3.61 POL(sys_w(x_1, x_2)) = 1 + x_1 + x_2 10.80/3.61 POL(top(x_1)) = x_1 10.80/3.61 POL(write(x_1, x_2)) = x_1 + x_2 10.80/3.61 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 10.80/3.61 Rules from R: 10.80/3.61 10.80/3.61 WAo(W) -> W 10.80/3.61 Rules from S: 10.80/3.61 none 10.80/3.61 10.80/3.61 10.80/3.61 10.80/3.61 10.80/3.61 ---------------------------------------- 10.80/3.61 10.80/3.61 (6) 10.80/3.61 Obligation: 10.80/3.61 Relative term rewrite system: 10.80/3.61 The relative TRS consists of the following R rules: 10.80/3.61 10.80/3.61 RAn(R) -> R 10.80/3.61 WAn(W) -> W 10.80/3.61 10.80/3.61 The relative TRS consists of the following S rules: 10.80/3.61 10.80/3.61 Rw -> RIn(Rw) 10.80/3.61 Ww -> WIn(Ww) 10.80/3.61 top(ok(sys_r(read(r, RIo(x)), write(W, Ww)))) -> top(check(sys_r(read(RAo(r), x), write(W, Ww)))) 10.80/3.61 top(ok(sys_w(read(r, RIo(x)), write(W, Ww)))) -> top(check(sys_w(read(RAo(r), x), write(W, Ww)))) 10.80/3.61 top(ok(sys_r(read(r, RIn(x)), write(W, Ww)))) -> top(check(sys_r(read(RAn(r), x), write(W, Ww)))) 10.80/3.61 top(ok(sys_w(read(r, RIn(x)), write(W, Ww)))) -> top(check(sys_w(read(RAn(r), x), write(W, Ww)))) 10.80/3.61 top(ok(sys_r(read(R, Rw), write(W, WIn(y))))) -> top(check(sys_r(read(R, Rw), write(WAn(W), y)))) 10.80/3.61 top(ok(sys_w(read(R, Rw), write(W, WIn(y))))) -> top(check(sys_w(read(R, Rw), write(WAn(W), y)))) 10.80/3.61 top(ok(sys_r(read(r, RIo(x)), write(W, y)))) -> top(check(sys_w(read(RAo(r), x), write(W, y)))) 10.80/3.61 top(ok(sys_r(read(r, RIn(x)), write(W, y)))) -> top(check(sys_w(read(RAn(r), x), write(W, y)))) 10.80/3.61 top(ok(sys_w(read(R, x), write(W, WIn(y))))) -> top(check(sys_r(read(R, x), write(WAn(W), y)))) 10.80/3.61 check(RIo(x)) -> ok(RIo(x)) 10.80/3.61 check(RAo(x)) -> RAo(check(x)) 10.80/3.61 check(RAn(x)) -> RAn(check(x)) 10.80/3.61 check(WAo(x)) -> WAo(check(x)) 10.80/3.61 check(WAn(x)) -> WAn(check(x)) 10.80/3.61 check(RIo(x)) -> RIo(check(x)) 10.80/3.61 check(RIn(x)) -> RIn(check(x)) 10.80/3.61 check(WIo(x)) -> WIo(check(x)) 10.80/3.61 check(WIn(x)) -> WIn(check(x)) 10.80/3.61 check(sys_r(x, y)) -> sys_r(check(x), y) 10.80/3.61 check(sys_r(x, y)) -> sys_r(x, check(y)) 10.80/3.61 check(sys_w(x, y)) -> sys_w(check(x), y) 10.80/3.61 check(sys_w(x, y)) -> sys_w(x, check(y)) 10.80/3.61 RAo(ok(x)) -> ok(RAo(x)) 10.80/3.61 RAn(ok(x)) -> ok(RAn(x)) 10.80/3.61 WAo(ok(x)) -> ok(WAo(x)) 10.80/3.61 WAn(ok(x)) -> ok(WAn(x)) 10.80/3.61 RIn(ok(x)) -> ok(RIn(x)) 10.80/3.61 WIo(ok(x)) -> ok(WIo(x)) 10.80/3.61 WIn(ok(x)) -> ok(WIn(x)) 10.80/3.61 sys_r(ok(x), y) -> ok(sys_r(x, y)) 10.80/3.61 sys_r(x, ok(y)) -> ok(sys_r(x, y)) 10.80/3.61 sys_w(ok(x), y) -> ok(sys_w(x, y)) 10.80/3.61 sys_w(x, ok(y)) -> ok(sys_w(x, y)) 10.80/3.61 10.80/3.61 10.80/3.61 ---------------------------------------- 10.80/3.61 10.80/3.61 (7) RelTRSRRRProof (EQUIVALENT) 10.80/3.61 We used the following monotonic ordering for rule removal: 10.80/3.61 Polynomial interpretation [POLO]: 10.80/3.61 10.80/3.61 POL(R) = 0 10.80/3.61 POL(RAn(x_1)) = x_1 10.80/3.61 POL(RAo(x_1)) = x_1 10.80/3.61 POL(RIn(x_1)) = x_1 10.80/3.61 POL(RIo(x_1)) = 1 + x_1 10.80/3.61 POL(Rw) = 0 10.80/3.61 POL(W) = 0 10.80/3.61 POL(WAn(x_1)) = x_1 10.80/3.61 POL(WAo(x_1)) = x_1 10.80/3.61 POL(WIn(x_1)) = x_1 10.80/3.61 POL(WIo(x_1)) = x_1 10.80/3.61 POL(Ww) = 0 10.80/3.61 POL(check(x_1)) = x_1 10.80/3.61 POL(ok(x_1)) = x_1 10.80/3.61 POL(read(x_1, x_2)) = x_1 + x_2 10.80/3.61 POL(sys_r(x_1, x_2)) = x_1 + x_2 10.80/3.61 POL(sys_w(x_1, x_2)) = x_1 + x_2 10.80/3.61 POL(top(x_1)) = x_1 10.80/3.61 POL(write(x_1, x_2)) = x_1 + x_2 10.80/3.61 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 10.80/3.61 Rules from R: 10.80/3.61 none 10.80/3.61 Rules from S: 10.80/3.61 10.80/3.61 top(ok(sys_r(read(r, RIo(x)), write(W, Ww)))) -> top(check(sys_r(read(RAo(r), x), write(W, Ww)))) 10.80/3.61 top(ok(sys_w(read(r, RIo(x)), write(W, Ww)))) -> top(check(sys_w(read(RAo(r), x), write(W, Ww)))) 10.80/3.61 top(ok(sys_r(read(r, RIo(x)), write(W, y)))) -> top(check(sys_w(read(RAo(r), x), write(W, y)))) 10.80/3.61 10.80/3.61 10.80/3.61 10.80/3.61 10.80/3.61 ---------------------------------------- 10.80/3.61 10.80/3.61 (8) 10.80/3.61 Obligation: 10.80/3.61 Relative term rewrite system: 10.80/3.61 The relative TRS consists of the following R rules: 10.80/3.61 10.80/3.61 RAn(R) -> R 10.80/3.61 WAn(W) -> W 10.80/3.61 10.80/3.61 The relative TRS consists of the following S rules: 10.80/3.61 10.80/3.61 Rw -> RIn(Rw) 10.80/3.61 Ww -> WIn(Ww) 10.80/3.61 top(ok(sys_r(read(r, RIn(x)), write(W, Ww)))) -> top(check(sys_r(read(RAn(r), x), write(W, Ww)))) 10.80/3.61 top(ok(sys_w(read(r, RIn(x)), write(W, Ww)))) -> top(check(sys_w(read(RAn(r), x), write(W, Ww)))) 10.80/3.61 top(ok(sys_r(read(R, Rw), write(W, WIn(y))))) -> top(check(sys_r(read(R, Rw), write(WAn(W), y)))) 10.80/3.61 top(ok(sys_w(read(R, Rw), write(W, WIn(y))))) -> top(check(sys_w(read(R, Rw), write(WAn(W), y)))) 10.80/3.61 top(ok(sys_r(read(r, RIn(x)), write(W, y)))) -> top(check(sys_w(read(RAn(r), x), write(W, y)))) 10.80/3.61 top(ok(sys_w(read(R, x), write(W, WIn(y))))) -> top(check(sys_r(read(R, x), write(WAn(W), y)))) 10.80/3.61 check(RIo(x)) -> ok(RIo(x)) 10.80/3.61 check(RAo(x)) -> RAo(check(x)) 10.80/3.61 check(RAn(x)) -> RAn(check(x)) 10.80/3.61 check(WAo(x)) -> WAo(check(x)) 10.80/3.61 check(WAn(x)) -> WAn(check(x)) 10.80/3.61 check(RIo(x)) -> RIo(check(x)) 10.80/3.61 check(RIn(x)) -> RIn(check(x)) 10.80/3.61 check(WIo(x)) -> WIo(check(x)) 10.80/3.61 check(WIn(x)) -> WIn(check(x)) 10.80/3.61 check(sys_r(x, y)) -> sys_r(check(x), y) 10.80/3.61 check(sys_r(x, y)) -> sys_r(x, check(y)) 10.80/3.61 check(sys_w(x, y)) -> sys_w(check(x), y) 10.80/3.61 check(sys_w(x, y)) -> sys_w(x, check(y)) 10.80/3.61 RAo(ok(x)) -> ok(RAo(x)) 10.80/3.61 RAn(ok(x)) -> ok(RAn(x)) 10.80/3.61 WAo(ok(x)) -> ok(WAo(x)) 10.80/3.61 WAn(ok(x)) -> ok(WAn(x)) 10.80/3.61 RIn(ok(x)) -> ok(RIn(x)) 10.80/3.61 WIo(ok(x)) -> ok(WIo(x)) 10.80/3.61 WIn(ok(x)) -> ok(WIn(x)) 10.80/3.61 sys_r(ok(x), y) -> ok(sys_r(x, y)) 10.80/3.61 sys_r(x, ok(y)) -> ok(sys_r(x, y)) 10.80/3.61 sys_w(ok(x), y) -> ok(sys_w(x, y)) 10.80/3.61 sys_w(x, ok(y)) -> ok(sys_w(x, y)) 10.80/3.61 10.80/3.61 10.80/3.61 ---------------------------------------- 10.80/3.61 10.80/3.61 (9) RelTRSRRRProof (EQUIVALENT) 10.80/3.61 We used the following monotonic ordering for rule removal: 10.80/3.61 Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(RAn(x_1)) = [[0], [0]] + [[1, 0], [0, 1]] * x_1 10.80/3.61 >>> 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(R) = [[0], [0]] 10.80/3.61 >>> 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(WAn(x_1)) = [[0], [0]] + [[1, 0], [0, 1]] * x_1 10.80/3.61 >>> 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(W) = [[0], [0]] 10.80/3.61 >>> 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(Rw) = [[0], [0]] 10.80/3.61 >>> 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(RIn(x_1)) = [[0], [0]] + [[1, 0], [0, 1]] * x_1 10.80/3.61 >>> 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(Ww) = [[0], [0]] 10.80/3.61 >>> 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(WIn(x_1)) = [[0], [0]] + [[1, 0], [0, 1]] * x_1 10.80/3.61 >>> 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(top(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 10.80/3.61 >>> 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(ok(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 10.80/3.61 >>> 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(sys_r(x_1, x_2)) = [[0], [0]] + [[1, 0], [0, 1]] * x_1 + [[1, 0], [0, 1]] * x_2 10.80/3.61 >>> 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(read(x_1, x_2)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 + [[1, 0], [0, 0]] * x_2 10.80/3.61 >>> 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(write(x_1, x_2)) = [[0], [0]] + [[1, 1], [1, 1]] * x_1 + [[1, 0], [0, 0]] * x_2 10.80/3.61 >>> 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(check(x_1)) = [[0], [0]] + [[1, 1], [0, 1]] * x_1 10.80/3.61 >>> 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(sys_w(x_1, x_2)) = [[0], [0]] + [[1, 0], [0, 1]] * x_1 + [[1, 0], [0, 1]] * x_2 10.80/3.61 >>> 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(RIo(x_1)) = [[1], [1]] + [[1, 1], [0, 1]] * x_1 10.80/3.61 >>> 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(RAo(x_1)) = [[0], [0]] + [[1, 0], [0, 1]] * x_1 10.80/3.61 >>> 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(WAo(x_1)) = [[0], [0]] + [[1, 0], [0, 1]] * x_1 10.80/3.61 >>> 10.80/3.61 10.80/3.61 <<< 10.80/3.61 POL(WIo(x_1)) = [[0], [0]] + [[1, 0], [0, 1]] * x_1 10.80/3.61 >>> 10.80/3.61 10.80/3.61 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 10.80/3.61 Rules from R: 10.80/3.61 none 10.80/3.61 Rules from S: 10.80/3.61 10.80/3.61 check(RIo(x)) -> ok(RIo(x)) 10.80/3.61 check(RIo(x)) -> RIo(check(x)) 10.80/3.61 10.80/3.61 10.80/3.61 10.80/3.61 10.80/3.61 ---------------------------------------- 10.80/3.61 10.80/3.61 (10) 10.80/3.61 Obligation: 10.80/3.61 Relative term rewrite system: 10.80/3.61 The relative TRS consists of the following R rules: 10.80/3.61 10.80/3.61 RAn(R) -> R 10.80/3.61 WAn(W) -> W 10.80/3.61 10.80/3.61 The relative TRS consists of the following S rules: 10.80/3.61 10.80/3.61 Rw -> RIn(Rw) 10.80/3.61 Ww -> WIn(Ww) 10.80/3.61 top(ok(sys_r(read(r, RIn(x)), write(W, Ww)))) -> top(check(sys_r(read(RAn(r), x), write(W, Ww)))) 10.80/3.61 top(ok(sys_w(read(r, RIn(x)), write(W, Ww)))) -> top(check(sys_w(read(RAn(r), x), write(W, Ww)))) 10.80/3.61 top(ok(sys_r(read(R, Rw), write(W, WIn(y))))) -> top(check(sys_r(read(R, Rw), write(WAn(W), y)))) 10.80/3.61 top(ok(sys_w(read(R, Rw), write(W, WIn(y))))) -> top(check(sys_w(read(R, Rw), write(WAn(W), y)))) 10.80/3.61 top(ok(sys_r(read(r, RIn(x)), write(W, y)))) -> top(check(sys_w(read(RAn(r), x), write(W, y)))) 10.80/3.61 top(ok(sys_w(read(R, x), write(W, WIn(y))))) -> top(check(sys_r(read(R, x), write(WAn(W), y)))) 10.80/3.61 check(RAo(x)) -> RAo(check(x)) 10.80/3.61 check(RAn(x)) -> RAn(check(x)) 10.80/3.61 check(WAo(x)) -> WAo(check(x)) 10.80/3.61 check(WAn(x)) -> WAn(check(x)) 10.80/3.61 check(RIn(x)) -> RIn(check(x)) 10.80/3.61 check(WIo(x)) -> WIo(check(x)) 10.80/3.61 check(WIn(x)) -> WIn(check(x)) 10.80/3.61 check(sys_r(x, y)) -> sys_r(check(x), y) 10.80/3.61 check(sys_r(x, y)) -> sys_r(x, check(y)) 10.80/3.61 check(sys_w(x, y)) -> sys_w(check(x), y) 10.80/3.61 check(sys_w(x, y)) -> sys_w(x, check(y)) 10.80/3.61 RAo(ok(x)) -> ok(RAo(x)) 10.80/3.61 RAn(ok(x)) -> ok(RAn(x)) 10.80/3.61 WAo(ok(x)) -> ok(WAo(x)) 10.80/3.61 WAn(ok(x)) -> ok(WAn(x)) 10.80/3.61 RIn(ok(x)) -> ok(RIn(x)) 10.80/3.61 WIo(ok(x)) -> ok(WIo(x)) 10.80/3.61 WIn(ok(x)) -> ok(WIn(x)) 10.80/3.61 sys_r(ok(x), y) -> ok(sys_r(x, y)) 10.80/3.61 sys_r(x, ok(y)) -> ok(sys_r(x, y)) 10.80/3.61 sys_w(ok(x), y) -> ok(sys_w(x, y)) 10.80/3.61 sys_w(x, ok(y)) -> ok(sys_w(x, y)) 10.80/3.61 10.80/3.61 10.80/3.61 ---------------------------------------- 10.80/3.61 10.80/3.61 (11) RelTRSRRRProof (EQUIVALENT) 10.80/3.61 We used the following monotonic ordering for rule removal: 10.80/3.61 Polynomial interpretation [POLO]: 10.80/3.61 10.80/3.61 POL(R) = 0 10.80/3.61 POL(RAn(x_1)) = x_1 10.80/3.61 POL(RAo(x_1)) = x_1 10.80/3.61 POL(RIn(x_1)) = x_1 10.80/3.61 POL(Rw) = 0 10.80/3.61 POL(W) = 0 10.80/3.61 POL(WAn(x_1)) = x_1 10.80/3.61 POL(WAo(x_1)) = x_1 10.80/3.61 POL(WIn(x_1)) = x_1 10.80/3.61 POL(WIo(x_1)) = x_1 10.80/3.61 POL(Ww) = 0 10.80/3.61 POL(check(x_1)) = x_1 10.80/3.61 POL(ok(x_1)) = 1 + x_1 10.80/3.61 POL(read(x_1, x_2)) = x_1 + x_2 10.80/3.61 POL(sys_r(x_1, x_2)) = x_1 + x_2 10.80/3.61 POL(sys_w(x_1, x_2)) = x_1 + x_2 10.80/3.61 POL(top(x_1)) = x_1 10.80/3.61 POL(write(x_1, x_2)) = x_1 + x_2 10.80/3.61 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 10.80/3.61 Rules from R: 10.80/3.61 none 10.80/3.61 Rules from S: 10.80/3.61 10.80/3.61 top(ok(sys_r(read(r, RIn(x)), write(W, Ww)))) -> top(check(sys_r(read(RAn(r), x), write(W, Ww)))) 10.80/3.61 top(ok(sys_w(read(r, RIn(x)), write(W, Ww)))) -> top(check(sys_w(read(RAn(r), x), write(W, Ww)))) 10.80/3.61 top(ok(sys_r(read(R, Rw), write(W, WIn(y))))) -> top(check(sys_r(read(R, Rw), write(WAn(W), y)))) 10.80/3.61 top(ok(sys_w(read(R, Rw), write(W, WIn(y))))) -> top(check(sys_w(read(R, Rw), write(WAn(W), y)))) 10.80/3.61 top(ok(sys_r(read(r, RIn(x)), write(W, y)))) -> top(check(sys_w(read(RAn(r), x), write(W, y)))) 10.80/3.61 top(ok(sys_w(read(R, x), write(W, WIn(y))))) -> top(check(sys_r(read(R, x), write(WAn(W), y)))) 10.80/3.61 10.80/3.61 10.80/3.61 10.80/3.61 10.80/3.61 ---------------------------------------- 10.80/3.61 10.80/3.61 (12) 10.80/3.61 Obligation: 10.80/3.61 Relative term rewrite system: 10.80/3.61 The relative TRS consists of the following R rules: 10.80/3.61 10.80/3.61 RAn(R) -> R 10.80/3.61 WAn(W) -> W 10.80/3.61 10.80/3.61 The relative TRS consists of the following S rules: 10.80/3.61 10.80/3.61 Rw -> RIn(Rw) 10.80/3.61 Ww -> WIn(Ww) 10.80/3.61 check(RAo(x)) -> RAo(check(x)) 10.80/3.61 check(RAn(x)) -> RAn(check(x)) 10.80/3.61 check(WAo(x)) -> WAo(check(x)) 10.80/3.61 check(WAn(x)) -> WAn(check(x)) 10.80/3.61 check(RIn(x)) -> RIn(check(x)) 10.80/3.61 check(WIo(x)) -> WIo(check(x)) 10.80/3.61 check(WIn(x)) -> WIn(check(x)) 10.80/3.61 check(sys_r(x, y)) -> sys_r(check(x), y) 10.80/3.61 check(sys_r(x, y)) -> sys_r(x, check(y)) 10.80/3.61 check(sys_w(x, y)) -> sys_w(check(x), y) 10.80/3.61 check(sys_w(x, y)) -> sys_w(x, check(y)) 10.80/3.61 RAo(ok(x)) -> ok(RAo(x)) 10.80/3.61 RAn(ok(x)) -> ok(RAn(x)) 10.80/3.61 WAo(ok(x)) -> ok(WAo(x)) 10.80/3.61 WAn(ok(x)) -> ok(WAn(x)) 10.80/3.61 RIn(ok(x)) -> ok(RIn(x)) 10.80/3.61 WIo(ok(x)) -> ok(WIo(x)) 10.80/3.61 WIn(ok(x)) -> ok(WIn(x)) 10.80/3.61 sys_r(ok(x), y) -> ok(sys_r(x, y)) 10.80/3.61 sys_r(x, ok(y)) -> ok(sys_r(x, y)) 10.80/3.61 sys_w(ok(x), y) -> ok(sys_w(x, y)) 10.80/3.61 sys_w(x, ok(y)) -> ok(sys_w(x, y)) 10.80/3.61 10.80/3.61 10.80/3.61 ---------------------------------------- 10.80/3.61 10.80/3.61 (13) RelTRSRRRProof (EQUIVALENT) 10.80/3.61 We used the following monotonic ordering for rule removal: 10.80/3.61 Polynomial interpretation [POLO]: 10.80/3.61 10.80/3.61 POL(R) = 0 10.80/3.61 POL(RAn(x_1)) = 1 + x_1 10.80/3.61 POL(RAo(x_1)) = x_1 10.80/3.61 POL(RIn(x_1)) = x_1 10.80/3.61 POL(Rw) = 0 10.80/3.61 POL(W) = 0 10.80/3.61 POL(WAn(x_1)) = x_1 10.80/3.61 POL(WAo(x_1)) = x_1 10.80/3.61 POL(WIn(x_1)) = x_1 10.80/3.61 POL(WIo(x_1)) = x_1 10.80/3.61 POL(Ww) = 0 10.80/3.61 POL(check(x_1)) = x_1 10.80/3.61 POL(ok(x_1)) = x_1 10.80/3.61 POL(sys_r(x_1, x_2)) = x_1 + x_2 10.80/3.61 POL(sys_w(x_1, x_2)) = x_1 + x_2 10.80/3.61 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 10.80/3.61 Rules from R: 10.80/3.61 10.80/3.61 RAn(R) -> R 10.80/3.61 Rules from S: 10.80/3.61 none 10.80/3.61 10.80/3.61 10.80/3.61 10.80/3.61 10.80/3.61 ---------------------------------------- 10.80/3.61 10.80/3.61 (14) 10.80/3.61 Obligation: 10.80/3.61 Relative term rewrite system: 10.80/3.61 The relative TRS consists of the following R rules: 10.80/3.61 10.80/3.61 WAn(W) -> W 10.80/3.61 10.80/3.61 The relative TRS consists of the following S rules: 10.80/3.61 10.80/3.61 Rw -> RIn(Rw) 10.80/3.61 Ww -> WIn(Ww) 10.80/3.61 check(RAo(x)) -> RAo(check(x)) 10.80/3.61 check(RAn(x)) -> RAn(check(x)) 10.80/3.61 check(WAo(x)) -> WAo(check(x)) 10.80/3.61 check(WAn(x)) -> WAn(check(x)) 10.80/3.61 check(RIn(x)) -> RIn(check(x)) 10.80/3.61 check(WIo(x)) -> WIo(check(x)) 10.80/3.61 check(WIn(x)) -> WIn(check(x)) 10.80/3.61 check(sys_r(x, y)) -> sys_r(check(x), y) 10.80/3.61 check(sys_r(x, y)) -> sys_r(x, check(y)) 10.80/3.61 check(sys_w(x, y)) -> sys_w(check(x), y) 10.80/3.61 check(sys_w(x, y)) -> sys_w(x, check(y)) 10.80/3.62 RAo(ok(x)) -> ok(RAo(x)) 10.80/3.62 RAn(ok(x)) -> ok(RAn(x)) 10.80/3.62 WAo(ok(x)) -> ok(WAo(x)) 10.80/3.62 WAn(ok(x)) -> ok(WAn(x)) 10.80/3.62 RIn(ok(x)) -> ok(RIn(x)) 10.80/3.62 WIo(ok(x)) -> ok(WIo(x)) 10.80/3.62 WIn(ok(x)) -> ok(WIn(x)) 10.80/3.62 sys_r(ok(x), y) -> ok(sys_r(x, y)) 10.80/3.62 sys_r(x, ok(y)) -> ok(sys_r(x, y)) 10.80/3.62 sys_w(ok(x), y) -> ok(sys_w(x, y)) 10.80/3.62 sys_w(x, ok(y)) -> ok(sys_w(x, y)) 10.80/3.62 10.80/3.62 10.80/3.62 ---------------------------------------- 10.80/3.62 10.80/3.62 (15) RelTRSRRRProof (EQUIVALENT) 10.80/3.62 We used the following monotonic ordering for rule removal: 10.80/3.62 Polynomial interpretation [POLO]: 10.80/3.62 10.80/3.62 POL(RAn(x_1)) = x_1 10.80/3.62 POL(RAo(x_1)) = x_1 10.80/3.62 POL(RIn(x_1)) = x_1 10.80/3.62 POL(Rw) = 0 10.80/3.62 POL(W) = 0 10.80/3.62 POL(WAn(x_1)) = 1 + x_1 10.80/3.62 POL(WAo(x_1)) = x_1 10.80/3.62 POL(WIn(x_1)) = x_1 10.80/3.62 POL(WIo(x_1)) = x_1 10.80/3.62 POL(Ww) = 0 10.80/3.62 POL(check(x_1)) = x_1 10.80/3.62 POL(ok(x_1)) = x_1 10.80/3.62 POL(sys_r(x_1, x_2)) = x_1 + x_2 10.80/3.62 POL(sys_w(x_1, x_2)) = x_1 + x_2 10.80/3.62 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 10.80/3.62 Rules from R: 10.80/3.62 10.80/3.62 WAn(W) -> W 10.80/3.62 Rules from S: 10.80/3.62 none 10.80/3.62 10.80/3.62 10.80/3.62 10.80/3.62 10.80/3.62 ---------------------------------------- 10.80/3.62 10.80/3.62 (16) 10.80/3.62 Obligation: 10.80/3.62 Relative term rewrite system: 10.80/3.62 R is empty. 10.80/3.62 The relative TRS consists of the following S rules: 10.80/3.62 10.80/3.62 Rw -> RIn(Rw) 10.80/3.62 Ww -> WIn(Ww) 10.80/3.62 check(RAo(x)) -> RAo(check(x)) 10.80/3.62 check(RAn(x)) -> RAn(check(x)) 10.80/3.62 check(WAo(x)) -> WAo(check(x)) 10.80/3.62 check(WAn(x)) -> WAn(check(x)) 10.80/3.62 check(RIn(x)) -> RIn(check(x)) 10.80/3.62 check(WIo(x)) -> WIo(check(x)) 10.80/3.62 check(WIn(x)) -> WIn(check(x)) 10.80/3.62 check(sys_r(x, y)) -> sys_r(check(x), y) 10.80/3.62 check(sys_r(x, y)) -> sys_r(x, check(y)) 10.80/3.62 check(sys_w(x, y)) -> sys_w(check(x), y) 10.80/3.62 check(sys_w(x, y)) -> sys_w(x, check(y)) 10.80/3.62 RAo(ok(x)) -> ok(RAo(x)) 10.80/3.62 RAn(ok(x)) -> ok(RAn(x)) 10.80/3.62 WAo(ok(x)) -> ok(WAo(x)) 10.80/3.62 WAn(ok(x)) -> ok(WAn(x)) 10.80/3.62 RIn(ok(x)) -> ok(RIn(x)) 10.80/3.62 WIo(ok(x)) -> ok(WIo(x)) 10.80/3.62 WIn(ok(x)) -> ok(WIn(x)) 10.80/3.62 sys_r(ok(x), y) -> ok(sys_r(x, y)) 10.80/3.62 sys_r(x, ok(y)) -> ok(sys_r(x, y)) 10.80/3.62 sys_w(ok(x), y) -> ok(sys_w(x, y)) 10.80/3.62 sys_w(x, ok(y)) -> ok(sys_w(x, y)) 10.80/3.62 10.80/3.62 10.80/3.62 ---------------------------------------- 10.80/3.62 10.80/3.62 (17) RIsEmptyProof (EQUIVALENT) 10.80/3.62 The TRS R is empty. Hence, termination is trivially proven. 10.80/3.62 ---------------------------------------- 10.80/3.62 10.80/3.62 (18) 10.80/3.62 YES 10.80/3.66 EOF