details

property	value
status	complete
benchmark	hydra.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n032.star.cs.uiowa.edu
space	Mixed_TRS

run statistics

property	value
solver	AProVE21
configuration	standard
runtime (wallclock)	10.8382670879 seconds
cpu usage	5.421262716
max memory	4.68529152E8

stage attributes

key	value
output-size	2657
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) QDPSizeChangeProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(cons(nil, y)) -> y f(cons(f(cons(nil, y)), z)) -> copy(n, y, z) copy(0, y, z) -> f(z) copy(s(x), y, z) -> copy(x, y, cons(f(y), z)) 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: F(cons(f(cons(nil, y)), z)) -> COPY(n, y, z) COPY(0, y, z) -> F(z) COPY(s(x), y, z) -> COPY(x, y, cons(f(y), z)) COPY(s(x), y, z) -> F(y) The TRS R consists of the following rules: f(cons(nil, y)) -> y f(cons(f(cons(nil, y)), z)) -> copy(n, y, z) copy(0, y, z) -> f(z) copy(s(x), y, z) -> copy(x, y, cons(f(y), z)) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 3 less nodes. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: COPY(s(x), y, z) -> COPY(x, y, cons(f(y), z)) The TRS R consists of the following rules: f(cons(nil, y)) -> y f(cons(f(cons(nil, y)), z)) -> copy(n, y, z) copy(0, y, z) -> f(z) copy(s(x), y, z) -> copy(x, y, cons(f(y), z)) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) QDPSizeChangeProof (EQUIVALENT) By using the subterm criterion [SUBTERM_CRITERION] together with the size-change analysis [AAECC05] we have proven that there are no infinite chains for this DP problem. From the DPs we obtained the following set of size-change graphs: *COPY(s(x), y, z) -> COPY(x, y, cons(f(y), z)) The graph contains the following edges 1 > 1, 2 >= 2 ---------------------------------------- (6) YES popout

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