details

property	value
status	complete
benchmark	#3.10.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n075.star.cs.uiowa.edu
space	AG01

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.406445026398 seconds
cpu usage	0.399870487
max memory	1.5740928E7

stage attributes

key	value
output-size	18290
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o add : [o * o] --> o app : [o * o] --> o eq : [o * o] --> o false : [] --> o if!6220min : [o * o] --> o if!6220minsort : [o * o * o] --> o if!6220rm : [o * o * o] --> o le : [o * o] --> o min : [o] --> o minsort : [o * o] --> o nil : [] --> o rm : [o * o] --> o s : [o] --> o true : [] --> o eq(0, 0) => true eq(0, s(X)) => false eq(s(X), 0) => false eq(s(X), s(Y)) => eq(X, Y) le(0, X) => true le(s(X), 0) => false le(s(X), s(Y)) => le(X, Y) app(nil, X) => X app(add(X, Y), Z) => add(X, app(Y, Z)) min(add(X, nil)) => X min(add(X, add(Y, Z))) => if!6220min(le(X, Y), add(X, add(Y, Z))) if!6220min(true, add(X, add(Y, Z))) => min(add(X, Z)) if!6220min(false, add(X, add(Y, Z))) => min(add(Y, Z)) rm(X, nil) => nil rm(X, add(Y, Z)) => if!6220rm(eq(X, Y), X, add(Y, Z)) if!6220rm(true, X, add(Y, Z)) => rm(X, Z) if!6220rm(false, X, add(Y, Z)) => add(Y, rm(X, Z)) minsort(nil, nil) => nil minsort(add(X, Y), Z) => if!6220minsort(eq(X, min(add(X, Y))), add(X, Y), Z) if!6220minsort(true, add(X, Y), Z) => add(X, minsort(app(rm(X, Y), Z), nil)) if!6220minsort(false, add(X, Y), Z) => minsort(Y, add(X, Z)) As the system is orthogonal, it is terminating if it is innermost terminating by [Gra95]. Then, by [FuhGieParSchSwi11], it suffices to prove (innermost) termination of the typed system, with sort annotations chosen to respect the rules, as follows: 0 : [] --> di add : [di * di] --> di app : [di * di] --> di eq : [di * di] --> wg false : [] --> wg if!6220min : [wg * di] --> di if!6220minsort : [wg * di * di] --> di if!6220rm : [wg * di * di] --> di le : [di * di] --> wg min : [di] --> di minsort : [di * di] --> di nil : [] --> di rm : [di * di] --> di s : [di] --> di true : [] --> wg We use the dependency pair framework as described in [Kop12, Ch. 6/7], with static dependency pairs (see [KusIsoSakBla09] and the adaptation for AFSMs in [Kop12, Ch. 7.8]). We thus obtain the following dependency pair problem (P_0, R_0, minimal, formative): Dependency Pairs P_0: 0] eq#(s(X), s(Y)) =#> eq#(X, Y) 1] le#(s(X), s(Y)) =#> le#(X, Y) 2] app#(add(X, Y), Z) =#> app#(Y, Z) 3] min#(add(X, add(Y, Z))) =#> if!6220min#(le(X, Y), add(X, add(Y, Z))) 4] min#(add(X, add(Y, Z))) =#> le#(X, Y) 5] if!6220min#(true, add(X, add(Y, Z))) =#> min#(add(X, Z)) 6] if!6220min#(false, add(X, add(Y, Z))) =#> min#(add(Y, Z)) 7] rm#(X, add(Y, Z)) =#> if!6220rm#(eq(X, Y), X, add(Y, Z)) 8] rm#(X, add(Y, Z)) =#> eq#(X, Y) 9] if!6220rm#(true, X, add(Y, Z)) =#> rm#(X, Z) 10] if!6220rm#(false, X, add(Y, Z)) =#> rm#(X, Z) 11] minsort#(add(X, Y), Z) =#> if!6220minsort#(eq(X, min(add(X, Y))), add(X, Y), Z) 12] minsort#(add(X, Y), Z) =#> eq#(X, min(add(X, Y))) 13] minsort#(add(X, Y), Z) =#> min#(add(X, Y)) 14] if!6220minsort#(true, add(X, Y), Z) =#> minsort#(app(rm(X, Y), Z), nil) 15] if!6220minsort#(true, add(X, Y), Z) =#> app#(rm(X, Y), Z) 16] if!6220minsort#(true, add(X, Y), Z) =#> rm#(X, Y) 17] if!6220minsort#(false, add(X, Y), Z) =#> minsort#(Y, add(X, Z)) Rules R_0: eq(0, 0) => true eq(0, s(X)) => false eq(s(X), 0) => false eq(s(X), s(Y)) => eq(X, Y) le(0, X) => true le(s(X), 0) => false popout

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