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TRS Standard pair #516967775
details
property
value
status
complete
benchmark
#4.35.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n009.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.76469802856 seconds
cpu usage
7.819188743
max memory
5.53095168E8
stage attributes
key
value
output-size
18277
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 19 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QReductionProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) QDP (15) QDPOrderProof [EQUIVALENT, 35 ms] (16) QDP (17) PisEmptyProof [EQUIVALENT, 0 ms] (18) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: and(true, y) -> y and(false, y) -> false eq(nil, nil) -> true eq(cons(t, l), nil) -> false eq(nil, cons(t, l)) -> false eq(cons(t, l), cons(t', l')) -> and(eq(t, t'), eq(l, l')) eq(var(l), var(l')) -> eq(l, l') eq(var(l), apply(t, s)) -> false eq(var(l), lambda(x, t)) -> false eq(apply(t, s), var(l)) -> false eq(apply(t, s), apply(t', s')) -> and(eq(t, t'), eq(s, s')) eq(apply(t, s), lambda(x, t)) -> false eq(lambda(x, t), var(l)) -> false eq(lambda(x, t), apply(t, s)) -> false eq(lambda(x, t), lambda(x', t')) -> and(eq(x, x'), eq(t, t')) if(true, var(k), var(l')) -> var(k) if(false, var(k), var(l')) -> var(l') ren(var(l), var(k), var(l')) -> if(eq(l, l'), var(k), var(l')) ren(x, y, apply(t, s)) -> apply(ren(x, y, t), ren(x, y, s)) ren(x, y, lambda(z, t)) -> lambda(var(cons(x, cons(y, cons(lambda(z, t), nil)))), ren(x, y, ren(z, var(cons(x, cons(y, cons(lambda(z, t), nil)))), t))) Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: and(true, y) -> y and(false, y) -> false eq(nil, nil) -> true eq(cons(t, l), nil) -> false eq(nil, cons(t, l)) -> false eq(cons(t, l), cons(t', l')) -> and(eq(t, t'), eq(l, l')) eq(var(l), var(l')) -> eq(l, l') eq(var(l), apply(t, s)) -> false eq(var(l), lambda(x, t)) -> false eq(apply(t, s), var(l)) -> false eq(apply(t, s), apply(t', s')) -> and(eq(t, t'), eq(s, s')) eq(apply(t, s), lambda(x, t)) -> false eq(lambda(x, t), var(l)) -> false eq(lambda(x, t), apply(t, s)) -> false eq(lambda(x, t), lambda(x', t')) -> and(eq(x, x'), eq(t, t')) if(true, var(k), var(l')) -> var(k) if(false, var(k), var(l')) -> var(l') ren(var(l), var(k), var(l')) -> if(eq(l, l'), var(k), var(l')) ren(x, y, apply(t, s)) -> apply(ren(x, y, t), ren(x, y, s)) ren(x, y, lambda(z, t)) -> lambda(var(cons(x, cons(y, cons(lambda(z, t), nil)))), ren(x, y, ren(z, var(cons(x, cons(y, cons(lambda(z, t), nil)))), t))) The set Q consists of the following terms: and(true, x0) and(false, x0)
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