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HRS union beta 16688 pair #381734911
details
property
value
status
complete
benchmark
Applicative_first_order_05__13.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n029.star.cs.uiowa.edu
space
Uncurried_Applicative_11
run statistics
property
value
solver
Wanda
configuration
HigherOrder
runtime (wallclock)
13.2180011272 seconds
cpu usage
34.333123232
max memory
1.621286912E9
stage attributes
key
value
output-size
15200
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_HigherOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. Alphabet: !facplus : [a * a] --> a !factimes : [a * a] --> a cons : [c * d] --> d false : [] --> b filter : [c -> b * d] --> d filter2 : [b * c -> b * c * d] --> d map : [c -> c * d] --> d nil : [] --> d true : [] --> b Rules: !factimes(x, !facplus(y, z)) => !facplus(!factimes(x, y), !factimes(x, z)) !factimes(!facplus(x, y), z) => !facplus(!factimes(z, x), !factimes(z, y)) !factimes(!factimes(x, y), z) => !factimes(x, !factimes(y, z)) !facplus(!facplus(x, y), z) => !facplus(x, !facplus(y, z)) map(f, nil) => nil map(f, cons(x, y)) => cons(f x, map(f, y)) filter(f, nil) => nil filter(f, cons(x, y)) => filter2(f x, f, x, y) filter2(true, f, x, y) => cons(x, filter(f, y)) filter2(false, f, x, y) => filter(f, y) This AFS is converted to an AFSM simply by replacing all free variables by meta-variables (with arity 0). We observe that the rules contain a first-order subset: !factimes(X, !facplus(Y, Z)) => !facplus(!factimes(X, Y), !factimes(X, Z)) !factimes(!facplus(X, Y), Z) => !facplus(!factimes(Z, X), !factimes(Z, Y)) !factimes(!factimes(X, Y), Z) => !factimes(X, !factimes(Y, Z)) !facplus(!facplus(X, Y), Z) => !facplus(X, !facplus(Y, Z)) Moreover, the system is finitely branching. Thus, by [Kop12, Thm. 7.55], we may omit all first-order dependency pairs from the dependency pair problem (DP(R), R) if this first-order part is Ce-terminating when seen as a many-sorted first-order TRS. According to the external first-order termination prover, this system is indeed Ce-terminating: || proof of resources/system.trs || # AProVE Commit ID: d84c10301d352dfd14de2104819581f4682260f5 fuhs 20130616 || || || Termination w.r.t. Q of the given QTRS could be proven: || || (0) QTRS || (1) DependencyPairsProof [EQUIVALENT] || (2) QDP || (3) DependencyGraphProof [EQUIVALENT] || (4) AND || (5) QDP || (6) UsableRulesProof [EQUIVALENT] || (7) QDP || (8) QDPSizeChangeProof [EQUIVALENT] || (9) YES || (10) QDP || (11) QDPOrderProof [EQUIVALENT] || (12) QDP || (13) QDPSizeChangeProof [EQUIVALENT] || (14) YES || || || ---------------------------------------- || || (0) || Obligation: || Q restricted rewrite system: || The TRS R consists of the following rules: || || !factimes(%X, !facplus(%Y, %Z)) -> !facplus(!factimes(%X, %Y), !factimes(%X, %Z)) || !factimes(!facplus(%X, %Y), %Z) -> !facplus(!factimes(%Z, %X), !factimes(%Z, %Y)) || !factimes(!factimes(%X, %Y), %Z) -> !factimes(%X, !factimes(%Y, %Z)) || !facplus(!facplus(%X, %Y), %Z) -> !facplus(%X, !facplus(%Y, %Z)) || ~PAIR(%X, %Y) -> %X || ~PAIR(%X, %Y) -> %Y || || Q is empty. || || ---------------------------------------- || || (1) DependencyPairsProof (EQUIVALENT) || Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. || ---------------------------------------- || || (2) || Obligation: || Q DP problem: || The TRS P consists of the following rules: || || !FACTIMES(%X, !facplus(%Y, %Z)) -> !FACPLUS(!factimes(%X, %Y), !factimes(%X, %Z)) || !FACTIMES(%X, !facplus(%Y, %Z)) -> !FACTIMES(%X, %Y) || !FACTIMES(%X, !facplus(%Y, %Z)) -> !FACTIMES(%X, %Z)
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