10.33/3.48 WORST_CASE(NON_POLY, ?) 10.33/3.49 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 10.33/3.49 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 10.33/3.49 10.33/3.49 10.33/3.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 10.33/3.49 10.33/3.49 (0) CpxTRS 10.33/3.49 (1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 10.33/3.49 (2) TRS for Loop Detection 10.33/3.49 (3) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 10.33/3.49 (4) BEST 10.33/3.49 (5) proven lower bound 10.33/3.49 (6) LowerBoundPropagationProof [FINISHED, 0 ms] 10.33/3.49 (7) BOUNDS(n^1, INF) 10.33/3.49 (8) TRS for Loop Detection 10.33/3.49 (9) DecreasingLoopProof [FINISHED, 1279 ms] 10.33/3.49 (10) BOUNDS(EXP, INF) 10.33/3.49 10.33/3.49 10.33/3.49 ---------------------------------------- 10.33/3.49 10.33/3.49 (0) 10.33/3.49 Obligation: 10.33/3.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 10.33/3.49 10.33/3.49 10.33/3.49 The TRS R consists of the following rules: 10.33/3.49 10.33/3.49 U101(tt, M, N) -> U102(isNatKind(activate(M)), activate(M), activate(N)) 10.33/3.49 U102(tt, M, N) -> U103(isNat(activate(N)), activate(M), activate(N)) 10.33/3.49 U103(tt, M, N) -> U104(isNatKind(activate(N)), activate(M), activate(N)) 10.33/3.49 U104(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) 10.33/3.49 U11(tt, V1, V2) -> U12(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 U12(tt, V1, V2) -> U13(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U13(tt, V1, V2) -> U14(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U14(tt, V1, V2) -> U15(isNat(activate(V1)), activate(V2)) 10.33/3.49 U15(tt, V2) -> U16(isNat(activate(V2))) 10.33/3.49 U16(tt) -> tt 10.33/3.49 U21(tt, V1) -> U22(isNatKind(activate(V1)), activate(V1)) 10.33/3.49 U22(tt, V1) -> U23(isNat(activate(V1))) 10.33/3.49 U23(tt) -> tt 10.33/3.49 U31(tt, V1, V2) -> U32(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 U32(tt, V1, V2) -> U33(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U33(tt, V1, V2) -> U34(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U34(tt, V1, V2) -> U35(isNat(activate(V1)), activate(V2)) 10.33/3.49 U35(tt, V2) -> U36(isNat(activate(V2))) 10.33/3.49 U36(tt) -> tt 10.33/3.49 U41(tt, V2) -> U42(isNatKind(activate(V2))) 10.33/3.49 U42(tt) -> tt 10.33/3.49 U51(tt) -> tt 10.33/3.49 U61(tt, V2) -> U62(isNatKind(activate(V2))) 10.33/3.49 U62(tt) -> tt 10.33/3.49 U71(tt, N) -> U72(isNatKind(activate(N)), activate(N)) 10.33/3.49 U72(tt, N) -> activate(N) 10.33/3.49 U81(tt, M, N) -> U82(isNatKind(activate(M)), activate(M), activate(N)) 10.33/3.49 U82(tt, M, N) -> U83(isNat(activate(N)), activate(M), activate(N)) 10.33/3.49 U83(tt, M, N) -> U84(isNatKind(activate(N)), activate(M), activate(N)) 10.33/3.49 U84(tt, M, N) -> s(plus(activate(N), activate(M))) 10.33/3.49 U91(tt, N) -> U92(isNatKind(activate(N))) 10.33/3.49 U92(tt) -> 0 10.33/3.49 isNat(n__0) -> tt 10.33/3.49 isNat(n__plus(V1, V2)) -> U11(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 10.33/3.49 isNat(n__x(V1, V2)) -> U31(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 isNatKind(n__0) -> tt 10.33/3.49 isNatKind(n__plus(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V2)) 10.33/3.49 isNatKind(n__s(V1)) -> U51(isNatKind(activate(V1))) 10.33/3.49 isNatKind(n__x(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)) 10.33/3.49 plus(N, 0) -> U71(isNat(N), N) 10.33/3.49 plus(N, s(M)) -> U81(isNat(M), M, N) 10.33/3.49 x(N, 0) -> U91(isNat(N), N) 10.33/3.49 x(N, s(M)) -> U101(isNat(M), M, N) 10.33/3.49 0 -> n__0 10.33/3.49 plus(X1, X2) -> n__plus(X1, X2) 10.33/3.49 s(X) -> n__s(X) 10.33/3.49 x(X1, X2) -> n__x(X1, X2) 10.33/3.49 activate(n__0) -> 0 10.33/3.49 activate(n__plus(X1, X2)) -> plus(activate(X1), activate(X2)) 10.33/3.49 activate(n__s(X)) -> s(activate(X)) 10.33/3.49 activate(n__x(X1, X2)) -> x(activate(X1), activate(X2)) 10.33/3.49 activate(X) -> X 10.33/3.49 10.33/3.49 S is empty. 10.33/3.49 Rewrite Strategy: FULL 10.33/3.49 ---------------------------------------- 10.33/3.49 10.33/3.49 (1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 10.33/3.49 Transformed a relative TRS into a decreasing-loop problem. 10.33/3.49 ---------------------------------------- 10.33/3.49 10.33/3.49 (2) 10.33/3.49 Obligation: 10.33/3.49 Analyzing the following TRS for decreasing loops: 10.33/3.49 10.33/3.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 10.33/3.49 10.33/3.49 10.33/3.49 The TRS R consists of the following rules: 10.33/3.49 10.33/3.49 U101(tt, M, N) -> U102(isNatKind(activate(M)), activate(M), activate(N)) 10.33/3.49 U102(tt, M, N) -> U103(isNat(activate(N)), activate(M), activate(N)) 10.33/3.49 U103(tt, M, N) -> U104(isNatKind(activate(N)), activate(M), activate(N)) 10.33/3.49 U104(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) 10.33/3.49 U11(tt, V1, V2) -> U12(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 U12(tt, V1, V2) -> U13(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U13(tt, V1, V2) -> U14(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U14(tt, V1, V2) -> U15(isNat(activate(V1)), activate(V2)) 10.33/3.49 U15(tt, V2) -> U16(isNat(activate(V2))) 10.33/3.49 U16(tt) -> tt 10.33/3.49 U21(tt, V1) -> U22(isNatKind(activate(V1)), activate(V1)) 10.33/3.49 U22(tt, V1) -> U23(isNat(activate(V1))) 10.33/3.49 U23(tt) -> tt 10.33/3.49 U31(tt, V1, V2) -> U32(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 U32(tt, V1, V2) -> U33(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U33(tt, V1, V2) -> U34(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U34(tt, V1, V2) -> U35(isNat(activate(V1)), activate(V2)) 10.33/3.49 U35(tt, V2) -> U36(isNat(activate(V2))) 10.33/3.49 U36(tt) -> tt 10.33/3.49 U41(tt, V2) -> U42(isNatKind(activate(V2))) 10.33/3.49 U42(tt) -> tt 10.33/3.49 U51(tt) -> tt 10.33/3.49 U61(tt, V2) -> U62(isNatKind(activate(V2))) 10.33/3.49 U62(tt) -> tt 10.33/3.49 U71(tt, N) -> U72(isNatKind(activate(N)), activate(N)) 10.33/3.49 U72(tt, N) -> activate(N) 10.33/3.49 U81(tt, M, N) -> U82(isNatKind(activate(M)), activate(M), activate(N)) 10.33/3.49 U82(tt, M, N) -> U83(isNat(activate(N)), activate(M), activate(N)) 10.33/3.49 U83(tt, M, N) -> U84(isNatKind(activate(N)), activate(M), activate(N)) 10.33/3.49 U84(tt, M, N) -> s(plus(activate(N), activate(M))) 10.33/3.49 U91(tt, N) -> U92(isNatKind(activate(N))) 10.33/3.49 U92(tt) -> 0 10.33/3.49 isNat(n__0) -> tt 10.33/3.49 isNat(n__plus(V1, V2)) -> U11(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 10.33/3.49 isNat(n__x(V1, V2)) -> U31(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 isNatKind(n__0) -> tt 10.33/3.49 isNatKind(n__plus(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V2)) 10.33/3.49 isNatKind(n__s(V1)) -> U51(isNatKind(activate(V1))) 10.33/3.49 isNatKind(n__x(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)) 10.33/3.49 plus(N, 0) -> U71(isNat(N), N) 10.33/3.49 plus(N, s(M)) -> U81(isNat(M), M, N) 10.33/3.49 x(N, 0) -> U91(isNat(N), N) 10.33/3.49 x(N, s(M)) -> U101(isNat(M), M, N) 10.33/3.49 0 -> n__0 10.33/3.49 plus(X1, X2) -> n__plus(X1, X2) 10.33/3.49 s(X) -> n__s(X) 10.33/3.49 x(X1, X2) -> n__x(X1, X2) 10.33/3.49 activate(n__0) -> 0 10.33/3.49 activate(n__plus(X1, X2)) -> plus(activate(X1), activate(X2)) 10.33/3.49 activate(n__s(X)) -> s(activate(X)) 10.33/3.49 activate(n__x(X1, X2)) -> x(activate(X1), activate(X2)) 10.33/3.49 activate(X) -> X 10.33/3.49 10.33/3.49 S is empty. 10.33/3.49 Rewrite Strategy: FULL 10.33/3.49 ---------------------------------------- 10.33/3.49 10.33/3.49 (3) DecreasingLoopProof (LOWER BOUND(ID)) 10.33/3.49 The following loop(s) give(s) rise to the lower bound Omega(n^1): 10.33/3.49 10.33/3.49 The rewrite sequence 10.33/3.49 10.33/3.49 activate(n__s(X)) ->^+ s(activate(X)) 10.33/3.49 10.33/3.49 gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. 10.33/3.49 10.33/3.49 The pumping substitution is [X / n__s(X)]. 10.33/3.49 10.33/3.49 The result substitution is [ ]. 10.33/3.49 10.33/3.49 10.33/3.49 10.33/3.49 10.33/3.49 ---------------------------------------- 10.33/3.49 10.33/3.49 (4) 10.33/3.49 Complex Obligation (BEST) 10.33/3.49 10.33/3.49 ---------------------------------------- 10.33/3.49 10.33/3.49 (5) 10.33/3.49 Obligation: 10.33/3.49 Proved the lower bound n^1 for the following obligation: 10.33/3.49 10.33/3.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 10.33/3.49 10.33/3.49 10.33/3.49 The TRS R consists of the following rules: 10.33/3.49 10.33/3.49 U101(tt, M, N) -> U102(isNatKind(activate(M)), activate(M), activate(N)) 10.33/3.49 U102(tt, M, N) -> U103(isNat(activate(N)), activate(M), activate(N)) 10.33/3.49 U103(tt, M, N) -> U104(isNatKind(activate(N)), activate(M), activate(N)) 10.33/3.49 U104(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) 10.33/3.49 U11(tt, V1, V2) -> U12(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 U12(tt, V1, V2) -> U13(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U13(tt, V1, V2) -> U14(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U14(tt, V1, V2) -> U15(isNat(activate(V1)), activate(V2)) 10.33/3.49 U15(tt, V2) -> U16(isNat(activate(V2))) 10.33/3.49 U16(tt) -> tt 10.33/3.49 U21(tt, V1) -> U22(isNatKind(activate(V1)), activate(V1)) 10.33/3.49 U22(tt, V1) -> U23(isNat(activate(V1))) 10.33/3.49 U23(tt) -> tt 10.33/3.49 U31(tt, V1, V2) -> U32(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 U32(tt, V1, V2) -> U33(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U33(tt, V1, V2) -> U34(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U34(tt, V1, V2) -> U35(isNat(activate(V1)), activate(V2)) 10.33/3.49 U35(tt, V2) -> U36(isNat(activate(V2))) 10.33/3.49 U36(tt) -> tt 10.33/3.49 U41(tt, V2) -> U42(isNatKind(activate(V2))) 10.33/3.49 U42(tt) -> tt 10.33/3.49 U51(tt) -> tt 10.33/3.49 U61(tt, V2) -> U62(isNatKind(activate(V2))) 10.33/3.49 U62(tt) -> tt 10.33/3.49 U71(tt, N) -> U72(isNatKind(activate(N)), activate(N)) 10.33/3.49 U72(tt, N) -> activate(N) 10.33/3.49 U81(tt, M, N) -> U82(isNatKind(activate(M)), activate(M), activate(N)) 10.33/3.49 U82(tt, M, N) -> U83(isNat(activate(N)), activate(M), activate(N)) 10.33/3.49 U83(tt, M, N) -> U84(isNatKind(activate(N)), activate(M), activate(N)) 10.33/3.49 U84(tt, M, N) -> s(plus(activate(N), activate(M))) 10.33/3.49 U91(tt, N) -> U92(isNatKind(activate(N))) 10.33/3.49 U92(tt) -> 0 10.33/3.49 isNat(n__0) -> tt 10.33/3.49 isNat(n__plus(V1, V2)) -> U11(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 10.33/3.49 isNat(n__x(V1, V2)) -> U31(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 isNatKind(n__0) -> tt 10.33/3.49 isNatKind(n__plus(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V2)) 10.33/3.49 isNatKind(n__s(V1)) -> U51(isNatKind(activate(V1))) 10.33/3.49 isNatKind(n__x(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)) 10.33/3.49 plus(N, 0) -> U71(isNat(N), N) 10.33/3.49 plus(N, s(M)) -> U81(isNat(M), M, N) 10.33/3.49 x(N, 0) -> U91(isNat(N), N) 10.33/3.49 x(N, s(M)) -> U101(isNat(M), M, N) 10.33/3.49 0 -> n__0 10.33/3.49 plus(X1, X2) -> n__plus(X1, X2) 10.33/3.49 s(X) -> n__s(X) 10.33/3.49 x(X1, X2) -> n__x(X1, X2) 10.33/3.49 activate(n__0) -> 0 10.33/3.49 activate(n__plus(X1, X2)) -> plus(activate(X1), activate(X2)) 10.33/3.49 activate(n__s(X)) -> s(activate(X)) 10.33/3.49 activate(n__x(X1, X2)) -> x(activate(X1), activate(X2)) 10.33/3.49 activate(X) -> X 10.33/3.49 10.33/3.49 S is empty. 10.33/3.49 Rewrite Strategy: FULL 10.33/3.49 ---------------------------------------- 10.33/3.49 10.33/3.49 (6) LowerBoundPropagationProof (FINISHED) 10.33/3.49 Propagated lower bound. 10.33/3.49 ---------------------------------------- 10.33/3.49 10.33/3.49 (7) 10.33/3.49 BOUNDS(n^1, INF) 10.33/3.49 10.33/3.49 ---------------------------------------- 10.33/3.49 10.33/3.49 (8) 10.33/3.49 Obligation: 10.33/3.49 Analyzing the following TRS for decreasing loops: 10.33/3.49 10.33/3.49 The Runtime Complexity (full) of the given CpxTRS could be proven to be BOUNDS(EXP, INF). 10.33/3.49 10.33/3.49 10.33/3.49 The TRS R consists of the following rules: 10.33/3.49 10.33/3.49 U101(tt, M, N) -> U102(isNatKind(activate(M)), activate(M), activate(N)) 10.33/3.49 U102(tt, M, N) -> U103(isNat(activate(N)), activate(M), activate(N)) 10.33/3.49 U103(tt, M, N) -> U104(isNatKind(activate(N)), activate(M), activate(N)) 10.33/3.49 U104(tt, M, N) -> plus(x(activate(N), activate(M)), activate(N)) 10.33/3.49 U11(tt, V1, V2) -> U12(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 U12(tt, V1, V2) -> U13(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U13(tt, V1, V2) -> U14(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U14(tt, V1, V2) -> U15(isNat(activate(V1)), activate(V2)) 10.33/3.49 U15(tt, V2) -> U16(isNat(activate(V2))) 10.33/3.49 U16(tt) -> tt 10.33/3.49 U21(tt, V1) -> U22(isNatKind(activate(V1)), activate(V1)) 10.33/3.49 U22(tt, V1) -> U23(isNat(activate(V1))) 10.33/3.49 U23(tt) -> tt 10.33/3.49 U31(tt, V1, V2) -> U32(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 U32(tt, V1, V2) -> U33(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U33(tt, V1, V2) -> U34(isNatKind(activate(V2)), activate(V1), activate(V2)) 10.33/3.49 U34(tt, V1, V2) -> U35(isNat(activate(V1)), activate(V2)) 10.33/3.49 U35(tt, V2) -> U36(isNat(activate(V2))) 10.33/3.49 U36(tt) -> tt 10.33/3.49 U41(tt, V2) -> U42(isNatKind(activate(V2))) 10.33/3.49 U42(tt) -> tt 10.33/3.49 U51(tt) -> tt 10.33/3.49 U61(tt, V2) -> U62(isNatKind(activate(V2))) 10.33/3.49 U62(tt) -> tt 10.33/3.49 U71(tt, N) -> U72(isNatKind(activate(N)), activate(N)) 10.33/3.49 U72(tt, N) -> activate(N) 10.33/3.49 U81(tt, M, N) -> U82(isNatKind(activate(M)), activate(M), activate(N)) 10.33/3.49 U82(tt, M, N) -> U83(isNat(activate(N)), activate(M), activate(N)) 10.33/3.49 U83(tt, M, N) -> U84(isNatKind(activate(N)), activate(M), activate(N)) 10.33/3.49 U84(tt, M, N) -> s(plus(activate(N), activate(M))) 10.33/3.49 U91(tt, N) -> U92(isNatKind(activate(N))) 10.33/3.49 U92(tt) -> 0 10.33/3.49 isNat(n__0) -> tt 10.33/3.49 isNat(n__plus(V1, V2)) -> U11(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 isNat(n__s(V1)) -> U21(isNatKind(activate(V1)), activate(V1)) 10.33/3.49 isNat(n__x(V1, V2)) -> U31(isNatKind(activate(V1)), activate(V1), activate(V2)) 10.33/3.49 isNatKind(n__0) -> tt 10.33/3.49 isNatKind(n__plus(V1, V2)) -> U41(isNatKind(activate(V1)), activate(V2)) 10.33/3.49 isNatKind(n__s(V1)) -> U51(isNatKind(activate(V1))) 10.33/3.49 isNatKind(n__x(V1, V2)) -> U61(isNatKind(activate(V1)), activate(V2)) 10.33/3.49 plus(N, 0) -> U71(isNat(N), N) 10.33/3.49 plus(N, s(M)) -> U81(isNat(M), M, N) 10.33/3.49 x(N, 0) -> U91(isNat(N), N) 10.33/3.49 x(N, s(M)) -> U101(isNat(M), M, N) 10.33/3.49 0 -> n__0 10.33/3.49 plus(X1, X2) -> n__plus(X1, X2) 10.33/3.49 s(X) -> n__s(X) 10.33/3.49 x(X1, X2) -> n__x(X1, X2) 10.33/3.49 activate(n__0) -> 0 10.33/3.49 activate(n__plus(X1, X2)) -> plus(activate(X1), activate(X2)) 10.33/3.49 activate(n__s(X)) -> s(activate(X)) 10.33/3.49 activate(n__x(X1, X2)) -> x(activate(X1), activate(X2)) 10.33/3.49 activate(X) -> X 10.33/3.49 10.33/3.49 S is empty. 10.33/3.49 Rewrite Strategy: FULL 10.33/3.49 ---------------------------------------- 10.33/3.49 10.33/3.49 (9) DecreasingLoopProof (FINISHED) 10.33/3.49 The following loop(s) give(s) rise to the lower bound EXP: 10.33/3.49 10.33/3.49 The rewrite sequence 10.33/3.49 10.33/3.49 activate(n__x(X1, n__s(X1_0))) ->^+ U101(isNat(activate(X1_0)), activate(X1_0), activate(X1)) 10.33/3.49 10.33/3.49 gives rise to a decreasing loop by considering the right hand sides subterm at position [0,0]. 10.33/3.49 10.33/3.49 The pumping substitution is [X1_0 / n__x(X1, n__s(X1_0))]. 10.33/3.49 10.33/3.49 The result substitution is [ ]. 10.33/3.49 10.33/3.49 10.33/3.49 10.33/3.49 The rewrite sequence 10.33/3.49 10.33/3.49 activate(n__x(X1, n__s(X1_0))) ->^+ U101(isNat(activate(X1_0)), activate(X1_0), activate(X1)) 10.33/3.49 10.33/3.49 gives rise to a decreasing loop by considering the right hand sides subterm at position [1]. 10.33/3.49 10.33/3.49 The pumping substitution is [X1_0 / n__x(X1, n__s(X1_0))]. 10.33/3.49 10.33/3.49 The result substitution is [ ]. 10.33/3.49 10.33/3.49 10.33/3.49 10.33/3.49 10.33/3.49 ---------------------------------------- 10.33/3.49 10.33/3.49 (10) 10.33/3.49 BOUNDS(EXP, INF) 10.65/3.56 EOF