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HRS union beta 16688 pair #381734314
details
property
value
status
complete
benchmark
lambda_sum.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n004.star.cs.uiowa.edu
space
Hamana_17
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
0.278996944427 seconds
cpu usage
0.268994923
max memory
1.7068032E7
stage attributes
key
value
output-size
4393
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_HigherOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. Alphabet: app : [] --> arrAB -> A -> B case : [] --> SAB -> A -> C -> B -> C -> C inl : [] --> A -> SAB inr : [] --> B -> SAB lam : [] --> A -> B -> arrAB Rules: app (lam (/\x.f x)) y => f y lam (/\x.app y x) => y case (inl x) (/\y.f y) (/\z.g z) => f x case (inr x) (/\y.f y) (/\z.g z) => g x Using the transformations described in [Kop11], this system can be brought in a form without leading free variables in the left-hand side, and where the left-hand side of a variable is always a functional term or application headed by a functional term. We now transform the resulting AFS into an AFSM by replacing all free variables by meta-variables (with arity 0). This leads to the following AFSM: Alphabet: app : [arrAB * A] --> B case : [SAB * A -> C * B -> C] --> C inl : [A] --> SAB inr : [B] --> SAB lam : [A -> B] --> arrAB ~AP1 : [A -> B * A] --> B ~AP2 : [A -> C * A] --> C ~AP3 : [B -> C * B] --> C Rules: app(lam(/\x.~AP1(F, x)), X) => ~AP1(F, X) lam(/\x.app(X, x)) => X case(inl(X), /\x.~AP2(F, x), /\y.~AP3(G, y)) => ~AP2(F, X) case(inr(X), /\x.~AP2(F, x), /\y.~AP3(G, y)) => ~AP3(G, X) app(lam(/\x.app(X, x)), Y) => app(X, Y) ~AP1(F, X) => F X ~AP2(F, X) => F X ~AP3(F, X) => F X We use the dependency pair framework as described in [Kop12, Ch. 6/7], with static dependency pairs (see [KusIsoSakBla09] and the adaptation for AFSMs and accessible arguments in [Kop13]). We thus obtain the following dependency pair problem (P_0, R_0, static, all): Dependency Pairs P_0: 0] app#(lam(/\x.~AP1(F, x)), X) =#> ~AP1#(F, X) 1] case#(inl(X), /\x.~AP2(F, x), /\y.~AP3(G, y)) =#> ~AP2#(F, X) 2] case#(inr(X), /\x.~AP2(F, x), /\y.~AP3(G, y)) =#> ~AP3#(G, X) 3] app#(lam(/\x.app(X, x)), Y) =#> app#(X, Y) Rules R_0: app(lam(/\x.~AP1(F, x)), X) => ~AP1(F, X) lam(/\x.app(X, x)) => X case(inl(X), /\x.~AP2(F, x), /\y.~AP3(G, y)) => ~AP2(F, X) case(inr(X), /\x.~AP2(F, x), /\y.~AP3(G, y)) => ~AP3(G, X) app(lam(/\x.app(X, x)), Y) => app(X, Y) ~AP1(F, X) => F X ~AP2(F, X) => F X ~AP3(F, X) => F X Thus, the original system is terminating if (P_0, R_0, static, all) is finite. We consider the dependency pair problem (P_0, R_0, static, all). We place the elements of P in a dependency graph approximation G (see e.g. [Kop12, Thm. 7.27, 7.29], as follows: * 0 : * 1 : * 2 : * 3 : 0, 3 This graph has the following strongly connected components: P_1: app#(lam(/\x.app(X, x)), Y) =#> app#(X, Y) By [Kop12, Thm. 7.31], we may replace any dependency pair problem (P_0, R_0, m, f) by (P_1, R_0, m, f). Thus, the original system is terminating if (P_1, R_0, static, all) is finite. We consider the dependency pair problem (P_1, R_0, static, all). We apply the subterm criterion with the following projection function: nu(app#) = 1 Thus, we can orient the dependency pairs as follows:
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