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TRS Standard pair #516964705
details
property
value
status
complete
benchmark
ma96.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n007.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.66318583488 seconds
cpu usage
7.326892578
max memory
5.25869056E8
stage attributes
key
value
output-size
18996
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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, 41 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, 5 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(false, false) -> false and(true, false) -> false and(false, true) -> false and(true, true) -> true eq(nil, nil) -> true eq(cons(T, L), nil) -> false eq(nil, cons(T, L)) -> false eq(cons(T, L), cons(Tp, Lp)) -> and(eq(T, Tp), eq(L, Lp)) eq(var(L), var(Lp)) -> eq(L, Lp) 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(Tp, Sp)) -> and(eq(T, Tp), eq(S, Sp)) eq(apply(T, S), lambda(X, Tp)) -> false eq(lambda(X, T), var(L)) -> false eq(lambda(X, T), apply(Tp, Sp)) -> false eq(lambda(X, T), lambda(Xp, Tp)) -> and(eq(T, Tp), eq(X, Xp)) if(true, var(K), var(L)) -> var(K) if(false, var(K), var(L)) -> var(L) ren(var(L), var(K), var(Lp)) -> if(eq(L, Lp), var(K), var(Lp)) 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(false, false) -> false and(true, false) -> false and(false, true) -> false and(true, true) -> true eq(nil, nil) -> true eq(cons(T, L), nil) -> false eq(nil, cons(T, L)) -> false eq(cons(T, L), cons(Tp, Lp)) -> and(eq(T, Tp), eq(L, Lp)) eq(var(L), var(Lp)) -> eq(L, Lp) 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(Tp, Sp)) -> and(eq(T, Tp), eq(S, Sp)) eq(apply(T, S), lambda(X, Tp)) -> false eq(lambda(X, T), var(L)) -> false eq(lambda(X, T), apply(Tp, Sp)) -> false eq(lambda(X, T), lambda(Xp, Tp)) -> and(eq(T, Tp), eq(X, Xp)) if(true, var(K), var(L)) -> var(K) if(false, var(K), var(L)) -> var(L) ren(var(L), var(K), var(Lp)) -> if(eq(L, Lp), var(K), var(Lp)) 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)))
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