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TRS Stand 20472 pair #381712190
details
property
value
status
complete
benchmark
lse.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n051.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.8898859024 seconds
cpu usage
4.714391465
max memory
2.67616256E8
stage attributes
key
value
output-size
15828
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof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) AND (5) QDP (6) UsableRulesProof [EQUIVALENT, 0 ms] (7) QDP (8) QDPSizeChangeProof [EQUIVALENT, 0 ms] (9) YES (10) QDP (11) UsableRulesProof [EQUIVALENT, 0 ms] (12) QDP (13) QDPSizeChangeProof [EQUIVALENT, 0 ms] (14) YES (15) QDP (16) QDPSizeChangeProof [EQUIVALENT, 2 ms] (17) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: Term_sub(Case(m, xi, n), s) -> Frozen(m, Sum_sub(xi, s), n, s) Frozen(m, Sum_constant(Left), n, s) -> Term_sub(m, s) Frozen(m, Sum_constant(Right), n, s) -> Term_sub(n, s) Frozen(m, Sum_term_var(xi), n, s) -> Case(Term_sub(m, s), xi, Term_sub(n, s)) Term_sub(Term_app(m, n), s) -> Term_app(Term_sub(m, s), Term_sub(n, s)) Term_sub(Term_pair(m, n), s) -> Term_pair(Term_sub(m, s), Term_sub(n, s)) Term_sub(Term_inl(m), s) -> Term_inl(Term_sub(m, s)) Term_sub(Term_inr(m), s) -> Term_inr(Term_sub(m, s)) Term_sub(Term_var(x), Id) -> Term_var(x) Term_sub(Term_var(x), Cons_usual(y, m, s)) -> m Term_sub(Term_var(x), Cons_usual(y, m, s)) -> Term_sub(Term_var(x), s) Term_sub(Term_var(x), Cons_sum(xi, k, s)) -> Term_sub(Term_var(x), s) Term_sub(Term_sub(m, s), t) -> Term_sub(m, Concat(s, t)) Sum_sub(xi, Id) -> Sum_term_var(xi) Sum_sub(xi, Cons_sum(psi, k, s)) -> Sum_constant(k) Sum_sub(xi, Cons_sum(psi, k, s)) -> Sum_sub(xi, s) Sum_sub(xi, Cons_usual(y, m, s)) -> Sum_sub(xi, s) Concat(Concat(s, t), u) -> Concat(s, Concat(t, u)) Concat(Cons_usual(x, m, s), t) -> Cons_usual(x, Term_sub(m, t), Concat(s, t)) Concat(Cons_sum(xi, k, s), t) -> Cons_sum(xi, k, Concat(s, t)) Concat(Id, s) -> s 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: TERM_SUB(Case(m, xi, n), s) -> FROZEN(m, Sum_sub(xi, s), n, s) TERM_SUB(Case(m, xi, n), s) -> SUM_SUB(xi, s) FROZEN(m, Sum_constant(Left), n, s) -> TERM_SUB(m, s) FROZEN(m, Sum_constant(Right), n, s) -> TERM_SUB(n, s) FROZEN(m, Sum_term_var(xi), n, s) -> TERM_SUB(m, s) FROZEN(m, Sum_term_var(xi), n, s) -> TERM_SUB(n, s) TERM_SUB(Term_app(m, n), s) -> TERM_SUB(m, s) TERM_SUB(Term_app(m, n), s) -> TERM_SUB(n, s) TERM_SUB(Term_pair(m, n), s) -> TERM_SUB(m, s) TERM_SUB(Term_pair(m, n), s) -> TERM_SUB(n, s) TERM_SUB(Term_inl(m), s) -> TERM_SUB(m, s) TERM_SUB(Term_inr(m), s) -> TERM_SUB(m, s) TERM_SUB(Term_var(x), Cons_usual(y, m, s)) -> TERM_SUB(Term_var(x), s) TERM_SUB(Term_var(x), Cons_sum(xi, k, s)) -> TERM_SUB(Term_var(x), s) TERM_SUB(Term_sub(m, s), t) -> TERM_SUB(m, Concat(s, t)) TERM_SUB(Term_sub(m, s), t) -> CONCAT(s, t) SUM_SUB(xi, Cons_sum(psi, k, s)) -> SUM_SUB(xi, s) SUM_SUB(xi, Cons_usual(y, m, s)) -> SUM_SUB(xi, s) CONCAT(Concat(s, t), u) -> CONCAT(s, Concat(t, u)) CONCAT(Concat(s, t), u) -> CONCAT(t, u) CONCAT(Cons_usual(x, m, s), t) -> TERM_SUB(m, t) CONCAT(Cons_usual(x, m, s), t) -> CONCAT(s, t) CONCAT(Cons_sum(xi, k, s), t) -> CONCAT(s, t) The TRS R consists of the following rules:
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